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Numberless Word Problem G3

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Notice & Wonder Math Routine: Third Grade

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Teacher and students engage in a Notice and Wonder Math Routine. Using text without numbers, the class tries to make meaning of the content. Aligns with Common Core Standard Math.3.OA.A.3, Math.Practice.MP1.

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Every year I said the same thing to myself, 'I am going to start math centers this year', and then I never did. Every year I continued to use our county's curriculum, which has been 'Go Math' for awhile now. I would still use math centers in my room but it would normally be A math center during my literacy block. The more I researched math centers, the more I realized that I wasn't doing what was best for my students. I needed to give them more hands on experiences and less time in the actual math book. Last year I finally made that change. It was the best math decision I had ever made!

Students here are playing 'One More' together. They roll one die, add one, and cover that number. They each use their own color manipulative so at the end of the game, whoever has the most colors on the board, wins! (If you roll the die, add one, and there are no more of that number on the board, you skip a turn!)

Do I still use my math curriculum from the county? Yes, I still use Go Math; however, I am lucky enough to work for a school that allows me to use the math book as a resource instead of a must! I use the math book as a guide for the standards that I need to teach. I also still use my math book for some of our whole group instruction. What does my math block look like? Your math block really depends on how much time you have allotted and what your school/county requires; however, I include math videos, a whole group mini lesson, guided math groups, and small group (or independent) rotations.
1. Math Videos: I LOVE youtube for math videos! I can pretty much find any skill that I need online and my students seem to learn best with songs! I'll have a math video post coming soon so you can see some of my favorites!
2. Whole Group Mini Lesson: This is when I'll use my math book to drive my instruction. I like to use the vocabulary and terms found in the book to ensure that my students are familiar with the terms that they will hear repeated throughout the school years with Go Math. We sit on the carpet in a huge circle with our math books in front of us. We do a ton of 'math talk' and even practice some examples in the book.
3. Guided Math Groups (15-20 minutes per group): As my students are working in their math centers, I pull small groups up to my table to work on different skills. Think of this as the same as your guided reading--different groups will be working on different skills based on their needs. This allows me to differentiate the learning to meet the needs of that particular group. I may have a group working on number formation while another group is working on addition.
4. Small Group Rotations (15-20 minutes a rotation): I have 8 math centers ready to go each Monday. My students will only go to 2 centers a week, Monday-Thursday. On Friday they have 'choice' and are not assigned centers. I do not pull math groups on Fridays either (unless I have a student really struggling). Below you can see a ton of pictures to see what my centers look like. Click HERE for another post to see more, easy prep, math centers. A math center may also be on the computer, iPad, or even a center for students to just explore manipulatives.

Above you can see a child 'counting the room' which is the same as 'write the room'. Below you can see a 'spinner center' where students are spinning two spinners and comparing to practice greater than and less than.

In the two images below you can see children working on using manipulatives to count objects and graph them. When they are finished with their graph, they have to analyze their data.

In the two images below you can see students working on subtraction.

Below is an activity you can use as an 'add the room' activity or you can just leave it at a center. Students have to add both sides of their cards to create an addition sentence.

These centers repeat month after month, just adding on to the skill or becoming a little bit more challenging. This way not only do my students already know how to complete the center, but they are constantly working on all of their standards. We don't just learn a standard in September and then never hit on that standard again.

Above, you can see a child working on 'what number comes next' to help them to count forward from any given number. Below, you can see that we have started our 3D shape unit. This child is sorting shapes.

In this center students will spin the spinner and write the number. Then they will create a number bond. LOVE this!

Again, we are working on number bonds just in a different way. This time, students will roll 2 dice and record the numbers. Then they will solve.

At this pocket chart math center students are sorting their equations.

Here we are working on greater than/less than again (as seen earlier on in this post); however, we are working on the same skill in a different way, this time using dice.

What if I don't have time to meet with all of my groups/complete 4 rotations? I don't either, so don't worry!! I only meet with 2 groups a day and my students only go to 2 rotations a day (even though there are 8 rotations introduced and going on in my classroom). This means that I meet with my students twice a week Monday-Thursday. (Fridays we do math tubs, but I let my students choose where they want to go). So if I have 4 math groups, I meet with group A and B on Monday, group C and D on Tuesday, and then back to A and B on Wednesday.
Try one of my math centers by clicking on the image below.

You can also see the entire BUNDLE below.

What are people saying about this math center bundle?
"This goes along exactly with the skills I teach month by month. It saves me so much work by not having to create it myself."
"This product was a HUGE time savor for math intervention groups and math centers. My K students loved them!"
"Every Kindergarten teacher needs this bundle! Thank you"
"This has made math centers in my room so much easier! Each month the centers are very similar and the students know what is expected. Love the I can cards. Thank you!!"
"One of my favorite purchases! This bundle is wonderful- thanks!!"
"This is such a wonderful product at a reasonable price! I love that it matches perfectly with the scope and sequence of my math series. I also like how I can pull centers from previous months for those who struggle or pull one from months we haven't gotten to yet for those who are more advanced. It's nice to have everything I need in one place!"
"In the past I have made many of my own math stations (what I call centers for math) to correspond with what I am teaching. This year I have no aide for the first time in twenty years of kindergarten. When I saw your packet, I dubbed you my "aide" (hahaha!!) and knew that I had to have this math bundle to help keep me sane this year. Thank you so much!! PS - I LOVE your products!! :)" SaveSave

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Math Centers in Kindergarten (Kindergarten Smiles)

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Every year I said the same thing to myself, 'I am going to start math centers this year', and then I never did. Every year I continued to use our county's curriculum, which has been 'Go Math' for awhile now.

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I used math rotations for years. After my first couple months of apprehensive experimentation, it became the most anticipated time of our day. Each year I managed rotations a little differently, based on the needs and personality of the class, but the general format remained in tact. This management system is so simple, I cannot wait to share it with you! Let's make math rotations a favorite time of day!

Before I share the secret with you, let me back up a few steps...

There's truly no "right" way to manage math rotations. I like to share what works for me, but I am one person! You are the expert of your classroom! Math rotations are, and should be, tailored to a teacher's specific class needs. However, sometimes I have seen teachers so bogged down in rotation "strategy", that their system rivals that of a football playbook. We've all been here, right?

Simplify

We can simplify the management of math rotations with 2 little things: The first is consistency. If you observe any teacher in the school, chances are if math rotations are going well, students have a consistent routine.

Choosing a rotation management system and sticking to it is key. Remember, it may take a couple days weeks to get comfortable. When I introduce rotations with teachers during workshops, the first few seconds of each rotation is a little confusing and there are questions. This is normal. After we have a couple of rotations under our belts, we are transitioning like a confident Beyonce with the wind blowing our hair. Once your routine is established, the content becomes the focus.

Adjusting the time increment of your rotations, number of rounds, and which choices students have, creates the backbone of your system. I was determined to make this easy, so I created an editable management system for math rotations! Simply drag and drop your choices into the group circles, choose your time increment, and number of rounds. Then click play! Students that struggle with transitions, those that need a visual cue, or have time management difficulty, can all benefit from this system! Personally, all three describe me, the teacher, some days! I need it as much as the students do!

Find the editable guided math rotation board HERE. It includes a wall version too if tech stuff isn't your friend.

Watch how easy it is to set up in the video below! (This video shows the guided reading version, but the rotations are set up the same way!)

Routine

To recap, step one, consistency of format. Whether or not you use my rotation system or a different one, is not important. Find a system that fits your personality and teaching style!

Let's talk about time increments and number of rotations. When choosing the time spent at each rotation, you have to watch your class. Just because you would love your rotations to last 15 minutes, doesn't mean that it is right for this class here in front of you this year. Base the time off of the natural stamina of the students. If day after day, students are restless after 15 minutes of independence, then it is time to tighten your pacing. Cut down your minutes to see increased urgency and better quality of work. Generally speaking the younger the students, the shorter the rotations. This generality depends on a lot of factors so don't stress if you have long rotations and young students. Don't fix what isn't broken!

Choice of Rotations

(SING THIS with me) Let's talk about choice ba-by, let's talk about you-and-me. Let's talk about all the good things and the bad things that may be... Let's Talk A-B-O-U-T CHOICE!

Step two is choice and materials. I thought I was a wonderful guided math teacher when my class consisted of 18 well-behaving mild-mannered students. I had choices galore and games from one side of the room to the other. When visitors came to our room, I was happy to have them. Then, the next school year, I had 24 students with a mixture of personalities that ranged from restless to rabid. I used the same choices and system as I had the year before, and my math rotation time was a scene from The Exorcism. My happy guided math world was rocked. (Don't cry, this story has a happy ending)

It was this particular class that made me go back to the books and do more research. (While eating and drinking terrible things #stress-eater) It was either change it or give it up. I knew how amazing it could be so I was determined to come up with a solution to the madness.

Math STACK

Rather than having groups all over the room simultaneously in math games, it was time to designate different types of activities for these groups to do. This was going to help reduce the amount of noise and chaos going on in our room. I came up with 5 activities for my students to do. I came up with an ACRONYM for these choices because that's what teachers do. The acronym STACK was a way for me to vary the types of resources I was using. This brought the noise and chaos to a minimum, and allowed me to help develop more well-rounded math experiences for my students.

Whether you need 3, 4, or 5 rotations, you can reduce the amount of noise and chaos by choosing activities from different modalities of learning. Here's a visual example of the different choices I may choose for a math block.

I am going to skip the small group table rotation for this post. You can check out a post all about small group HERE.

Technology Rotation
In a recent post, I shared games for each math strand that can be played on any device. Although there are some fantastic sites to reinforce learning through technology, I wanted some tried and true games that directly correlated to the standards I was teaching in my guided math lessons. I created 5 games for each math strand for the year! To check out the post on these games, you can read HERE. Below you can see two games on place value.

Application

The application station is a way for teacher to get in a grade or an independent practice activity during a rotation. Typically, you'll find some independent practice happening here. For this rotation, I created skills practice pages for each math strand.

If you are looking for math skills printables, I have individual sets of 20 skills practice pages for each math strand or a bundle for the year!

Below, this student is completing a daily math page that spiral reviews skills every day for the year. These can be found HERE.

Create

The create station is a math journal station! Each student's journal is a window into their thinking and skills! Math journals do not have to be repetitive or lack-luster! I love to vary the activities for students in their journals. Students from kindergarten up, can benefit from a math journal. I have many blog posts on math journals, and many math journal resources K-3 too!

Links to grade level journal bundles below (also sold in single volumes)
Kindergarten
Kinesthetic

The kinesthetic rotation is a hands-on math center! This is what most teachers typically think of when you say math center. It's a way for students to use concrete objects and interact with materials to further understand math concepts. Below, I have pictures of some of my math centers in action from teacher friends in our facebook group!

I have developed math centers for grades K-3! Find links below to the bundles for the year if this is something you need. (also in monthly sets)
Kindergarten
So there you have it! The rotations secret is out! You can start math rotations any time of the school year! Break up your routine and try something new or just tweak what you already have going on! I always hope to share a little something that can make your school life a bit easier. I hope some of my favorite practices can help!

Lost and Forgotten

Some of the most valuable math minutes happen and the start and close of the math block. I want to be sure to share some helpful resources to kick off and end your daily math sessions!

Math Warm-Up

A number chat is a great way to kick off your math block! The goal of a number chat is to prompt students to share strategies and mathematical thinking. Rather than focusing on answers, students focus on conceptualizing.

Project and ponder or print the half-sheet booklets!

My undle of math chats for the year covers every math strand for a discount!

Exit Tickets

These exit tickets act as a quick check, or a math reflection to wrap-up your learning! Like the number chats, you can project them or create a quick little half sheet for short assessments of learning. There are 20 exit tickets for each math strand.

Here's a new video I added this week to help explain the number chats and exit tickets a little better!

If you already have the guided math series, the supplements series will give you more printable practice to reinforce the concepts!

Have a terrific week! Try out a new technique or resource and let me know how it goes in the comments below or in our facebook group!

The post Math Rotations a Favorite Time of Day appeared first on Tunstall's Teaching Tidbits.

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Math Rotations a Favorite Time of Day (Tunstall's Teaching Tidbits)

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I used math rotations for years. After my first couple months of apprehensive experimentation, it became the most anticipated time of our day. Each year I managed rotations a little differently, based on the needs and personality of the class, but the general format remained in tact.

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Correlates to 5 E's in STEMscopes

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We have been working on Accountable Talk in our class, nicknamed "Team Talk" with students. You can read more about the visual cues we've been using HERE.

Math is a particularly important subject to use good discussion strategies, since there are often so many ways to solve a problem, and really understanding the concepts comes from being able to articulate them to others. We call this "Math Talk" and I like to break it down into three different pieces: Explain, Evaluate, and Extend.

Explain

This is a familiar step in which students walk through the work they did to arrive at the solution. They will explain their steps and the conversation they were having about the problem in their mind so we can all get on the same page as to how they solved the problem. Listing the steps is an important part of this first section; this helps us as we get to any error analysis or alternative solutions in future steps.

Evaluate

In this part, other students can now chime in and either agree or disagree with the solver. In order to do either, they need to be able to back up their thinking with their own work and strategies, similar to the "Explain" step above. This forces students to look carefully and try to see where the student presenting did things differently. My favorite part of these conversations is not just correcting an error they may have caught, but it's in finding multiple ways to arrive at the same answer. It's a great opportunity for the students to be the teacher as they share their thinking about a problem.

Extend

This final step is sometimes interwoven into the "Evaluate" step, but it has its own place outside of strategy-sharing. Similar to reading, I like students to make connections in their math work to other problems, strategies, or Math Talks to reinforce strategies and concepts throughout our entire year. I also like for them to ask questions of each other about the how's and why's of strategies. Sometimes this can seem pretty far-out, but allowing for this section to take place can also allow for follow-up around areas of misunderstanding or lingering confusion. I will also use this opportunity to model different strategies that may or may not work out, so that kids can see and hear me think aloud through various possibilities.

I hope this anchor chart around Math Talks can help your own class hold more in-depth conversations around problem solving and strategies. For more Accountable Talk stems and how I use them in class, be sure to see my Team Talk Pack on TpT HERE or read more HERE.

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Math Talk {Anchor Chart} (3rd Grade Thoughts)

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We have been working on Accountable Talk in our class, nicknamed "Team Talk" with students. You can read more about the visual cues we've been using HERE. Math is a particularly important subject to use good discussion strategies, since there are often so many ways to solve a problem, and really understanding the concepts comes from being able to articulate them to others.

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Using Guided Math to Strengthen Students' Math Learning, Grades 3-6

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A NEW Video Training Program offered by Bureau of Education & Research Guided math is a practical, small group approach that provides primary children with the instruction and coaching they need to develop foundational math skills and concepts.

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Math Engagement

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EL Students

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Math.Practice.MP1

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

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Math.2.NBT.B.5

Common core State Standards

Math: Math

2: Grade 2

NBT: Number & Operations in Base Ten

B: Use place value understanding and properties of operations to add and subtract

5:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. What tools does Ms. LaCour use to support her ELL students?

2. What are the benefits of having students lead the number talk?

3. How do number talks encourage students to try new math strategies?

School Details

Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621

Data Provided By:

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Engaging in Productive Struggle: Number Talks

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Students in Monique LaCour's second grade class explore subtraction strategies through student-led number talks. Class begins with a review of number talk roles and sentence frames. Then, students break off into small groups for the number talk, where they share and try new strategies to solve a subtraction problem.

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EL Students

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

Educational research -- not to mention experience and common sense -- tells us that students learn best and make better sense of what they're learning when they can make connections with previous learning or with different areas of learning...
Carol Goodrow, a first grade teacher and an avid runner, knows about the value of making connections. She has connected her curriculum by integrating running into almost every subject area -- and her students are reaping the benefits.

Mrs. Goodrow's first graders at Parker Memorial School in Tolland, Connecticut, took off running in September. By May, Goodrow told Education World, all the students could run a mile, had completed a mile fun run, and loved to write about running. According to Goodrow, many of the students started writing in their journals after running practice. Even those who had been reluctant writers loved the running practices so much they wanted to write about them.

"Also," Goodrow added, "they couldn't have any Gatorade until they wrote in their journals."

But, as Goodrow told Education World, the benefits weren't limited to physical fitness and writing. She saw improvement in math skills as well. For example, during year-end benchmark testing, the class completed sections on numeration more quickly, yet scored as well or better, than past classes.

In addition, Goodrow reported that many students demonstrated a better understanding of fractions. "My fraction committee, a group of the most capable math students, computed the class's [running] mileage on their own, working with 1/2's, 1/4's and 3/4's. They represented the fractions by models, but they could also compute them in their heads."

One of the class's favorite activities, however, was their ongoing "Trek Across America." In this project, Goodrow, her class, their families, and runner Don Allison set off on a virtual race from Boston to San Diego. Each time the participants ran, they kept track of their distances in personal mileage logs. As they progressed along the trek's 3,252 miles, the students traced the route, exploring 14 key cities.

Reports of the trek, as well as many other class activities, can be found on the class's Web site, Kids Running.com. According to Goodrow, this site is built so that kids can be authors, columnists, and more. There are sections where teachers can use running-related data, such as the voting booth data bank, to build math lessons. "It's also a site," she said, "where kids can practice reading stories written by other kids. And of course it encourages fitness and healthy attitudes."

Education World asked Goodrow if she had any suggestions to offer other teachers on how they can make learning more relevant. "Choose something you love," she said, "and integrate it into your curriculum."

But first, you might want to choose some of the activities below and use them to integrate Math across your curriculum.

MATH AND YOUR CURRICULUM

Math and Literature

Another good source for ideas on integrating math is Carol Hurst's Math and Children's Literature site. Though geared toward students in Pre-K through Grade 2, many of the activities here can be adapted for use with older students. For example, the article Time and Time Travel Fantasies, reprinted from Teaching K-8 Magazine, recommends setting up a classroom clock display and allowing students to take the clocks apart (and, hopefully, put them back together again) as they learn to tell time. The site includes a list of books with time-related themes, which you can use to accompany and/or inspire the activities.

Extension: You might extend the activities with older elementary students by setting up a clock repair shop, rather than a display, and having students prepare estimates and invoices for needed repairs. Students might also prepare written reports about the ways in which people have told time throughout history. One interesting site about gnomonics, the art of telling time using the sun's shadow, can be found at Cannon-Mania. Scroll down and click Sundial to learn about the sun dial cannon.

Math and History

At Mathematicians Commemorated on the Eiffel Tower, students in grades 3-12 will discover the names of French scientists and mathematicians that were placed on plaques in the Tower more than 100 years ago. Encourage students to visit The Official Site of The Eiffel Tower to learn more about this historic French landmark.

Extension: Following the tour, have each student return to the Mathematicians Commemorated on the Eiffel Tower site to read the biography of one of the mathematicians whose name is on the tower. Create a chart listing the name and major accomplishment of each mathematician. You might also encourage students to add to the chart the names of other mathematicians, some of whom might be found at Biographies of Woman Mathematicians.

Math and Science

After your middle- and high school students have toured the Eiffel Tower (see "History and Math" above) and perhaps helped build the Tower of the 3rd millenium, they may be ready to participate in Hands-On Bridge Building. This project, in which students use spaghetti, glue, and their knowledge of science and math to construct a weight-bearing bridge, begins with a lesson on scientific and mathematical vocabulary. Then, students create designs, reduce them to scale, prepare cost analyses, and build and test their bridges. The site includes quizzes, worksheets, and bonus and extension activities.

Math and Geography

At The Stowaway Adventure, "stowaways" in grades 6-12 can plot latitude and longitude to locate the route of the ship they're hiding on. They use that information, along with their math knowledge, to determine the ship's speed, distance traveled, and projected destination. Those stowaways who enjoy their voyage can move on to the second leg of their voyage, where they use what they have learned to determine future destinations and view satellite images to predict weather and ocean conditions.

Extension: When students return from their sea voyage, ask them to plan a trip on land or in the air. Students should use a map to set their starting point and destination, decide on an appropriate mode of transportation, and determine a reasonable speed. Then have them calculate the distance they'll travel and the time the trip will take. You might also encourage students to identify some landmarks along the way and to write postcards about the places they "visit."

Math and Health

At Fat Counting, students in grades 1-6 study and discuss the food pyramid. Then they compare the foods on the pyramid to the foods they eat, keep a fat-counting diary, calculate the number of calories from fat they eat in a week, find their daily average of fat, and compare their fat intake with that of other students. The lesson is less self-sufficient than many others, but the site does provide links to all the necessary information and resources.

Math and Art

At Greeting Card Geometry Math, a unit you can use to teach geometry to students in grades 2-5, students learn to identify and create congruent, similar, and equivalent shapes and then they use those shapes to make a holiday greeting card. The lessons are simple, yet effective, and include creative extension activities.

Extension: As a follow-up, you might encourage older students to use geometric shapes, and any medium, to create a poster showing the relationship between math and art. Then invite them to visit the National Museum of American Art or another online museum or art gallery, and identify examples of math in the art they find.

Math and Music

The Music section of Online Math Applications is one of the best sites available for introducing students to music and its relationship to math. The rhythm page explains how different musical notes represent the rhythm, or time, of a piece of music, while pages on tone and tune provide a thorough discussion of pitch, frequency, and amplitude. The site explains the mathematical relationship of adjacent notes on a keyboard and the theory that ratio is essential to harmony. Here, students can rediscover the discoveries of Pythagoras and listen to the music of Mozart. The clearly written, easy-to-read information makes this is a site that's appropriate for students of all ages.

Extension: After students have explored the site, taken some of the quizzes, or submitted quizzes of their own, give them an opportunity to listen to a variety of musical styles. Discuss the rhythm, tone, and tune of each selection, then ask students to compose a tune of their own. You might also encourage older students to research the lives of some classical musicians to discover how many were also mathematicians. Students of all ages will enjoy making, and experimenting with, a monochord.

Fun and Games

Finally, invite students to explore the activities at Fermi Questions. These problems, which encourage multiple approaches to problem solving and emphasize process over product, involve water balloons and jelly beans. Does it sound like fun? Does it sound like math? Check out this site and see what you think. But save it for the end of a very warm day!

ADDITIONAL RESOURCES

Article by Linda Starr
Education WorldÂ®
Copyright Â© 1999 Education World

Updated 04/26/2010

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You're Not in Math Class Anymore: Integrating Math Across th... | Education World

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

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Mistakes grow synapses

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Orton 3-Act-Lesson

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It's my hope that there are other elementary teachers out there that might find this analysis useful if they want to use this compelling and fun lesson by Graham Fletcher in their classrooms to engage their students in exploring addition strategies with regrouping ( 2.NBT.5, 2.NBT.6, 2.NBT.9). This engaging lesson is very open in the middle. Students have a wide variety of addition strategies they can use including concrete models (base-10 blocks, place value discs, etc) and abstract strategies (arrow method, decomposing, bar method, etc).

Please feel free to plagiarize and make it your own as you see fit. I'd love to hear from you if you use it so we can get better together. (Special thanks to Graham Fletcher for providing such an amazing 3-Act Lesson!)

Before reading further, it may be useful to watch the lesson resources on Graham's website. Go ahead and check them out the Bright Idea resources. I'll wait.

And...welcome back! Let's dive in.

Some quick background:

I conducted a lesson inquiry using Bright Idea with a team of 2nd grade teachers. Both lessons were unique experiences with their own twists and turns and choices. The lesson pathway below shows the main flow of the learning experience and took about 60 minutes. Further analysis and takeaways can be found at the end of this post, but I've tried to embed a lot of our thinking within the flow of the lesson.

This lesson was taught to 2 classrooms of 2nd grade students. Students had learned several abstract addition methods to build on their use of concrete manipulatives. We used this lesson as a way to formatively assess student conceptual understanding of addition and also their ability to persevere, communicate reasoning, and use appropriate tools strategically. We provided each table group with ample concrete manipulatives of a variety of types (straws and bundles, base-10 blocks, place value disks, etc). We were curious to see how many used the manipulatives versus how many went straight to an abstract procedure. What was their level of fluency and comfort with different abstract methods? What were their preferences telling us about how they were making meaning of place value and addition?

Our objectives (as teachers):

We wanted all students hooked, engaged, motivated, positive, energetic....and to persevere in solving a problem.

Specifically, we were curious about: What strategies will students use to make sense of a problem and solve it? What will my students do when I'm not explicitly telling them what to do?

Bigger questions we were wondering about: How do my students talk about math? How do I navigate openness in a lesson in a way that is structured enough to promote student learning for all?

Learning objectives (for students):

You will use strategies to solve an addition problem and communicate your reasoning with each other.

The objective was posted clearly on the board and referenced throughout the lesson at transition points.

Into (Act 1):
Hello everyone. Today, we're going to start today by watching a short video. We're really curious what you notice and wonder about it be we're interested in how you talk about your (mathematical) thinking with each other.
We played the short Act 1 video showing Graham filling up a container with Skittles. After the video, we did a little pair/share before launching in to a Notice-Wonder exploration.

The Notice-Wonder strategy is a very effective discussion strategy to get all students talking (because everyone can describe something they saw and ask an interesting question regardless of their math ability). It also lowers the floor into a math task because it's a low-risk strategy that allows student discourse to describe the problem rather than having us (the teacher) "give" them the problem.
What did you notice?
We kept this short. A quick Pair/Share and then some whole class discussion. Once students all agreed that "somebody filled up a container with Skittles" and "the Skittles are different colors" we moved forward on. As you can guess, second graders notice some crazy other stuff too! To help move the conversation forward we focused on "useful" math noticings by paraphrasing the the noticing, asking how many other students noticed the same thing, and then scribing it on the board. We did not scribe the "un-useful" noticings.
I'm really curious. What did you wonder? What questions do you have?
Again, many students wondered about interesting, but un-useful things. For example, some students wondered if you could power a lightbulb with Skittles or if it was a glass bulb or a plastic bulb. We would nudge them back toward the noticings we had scribed. Eventually the key question comes out:
How many Skittles are there?
We scribed this key question on the board and asked students to write it on their graphic organizer. Then we watched the Act 1 video again and asked them to make a prediction (estimate) about how many Skittles there might be.

We gave them a moment to discuss in groups, make an estimate, and write it on their graphic organizer. Teacher walked around and scanned student work for estimates to get a feel for their values. Then we asked them to share their estimates and we recorded a range of them on the board (usually about 30 to 80 in most classes).
Wow. That's a wide range of estimates. We have estimates less than 30 and all the way up to 80 or 100. If you wanted to make your estimate about the number of Skittles more accurate, what information would you like to know?
"How many of each color are there?"

We displayed the Act 2 image that answers this question. We allowed them some discussion time to make sure they all understood what the image was saying.

Through (Act 2):

Students got to work, and it looked like this (except the students had faces):

This problem sets up an open opportunity to conceptually and/or procedurally explore how to add 19 + 15 + 19 + 17 + 21 and find the sum of 91. We let students dive in for about 10-15 minutes. During this time we monitored the room and gathered as much data as we could. How are they making meaning of the problem? What approaches are they using?

We provided some more intervention for really struggling students. The teachers had posted the different strategies they had used for addition, and we often asked students to reference that for possible starting points.

Then 15 minutes turned in to 20-25 minutes. Students who arrived at 91 quickly were asked to convince themselves (and us) that they were correct by using a different addition strategy. Students who used a strategy but made a small error were asked to share their work with each other and try to resolve the conflict.

One of the interesting struggles that students faced was keeping their work organized. There are a lot of "ones" in this problem to organize and regroup for students who are using concrete manipulatives. Students who chose abstract procedural methods didn't face this organizational issue.

Here's a snapshot of some work we saw from students at all levels.

We saw students building the problem and finding the correct answer.

We saw students building the problem and finding the incorrect answer. In these cases, we had students with similar strategies (like these two) try to convince each other who was right.

This student drew 91 Skittles. While arriving at the right answer, we noticed that he had yet to develop strategies to make his calculations more efficient.

Students drew other models with varying degrees of success. Notice he drew 90 and said 89. We asked him to check his calculations to see which answer he thought was better. He did not end up arriving at 91.

Other students used place value disks. Check out this video below. She and her partner communicate about building numbers and adding them. She uses regrouping strategies with the manipulatives. She uses her fingers for single digit addition. She makes and remakes changes and calculations. She catches several mistakes. She struggles with some organization. And then there's the tragic (mathematically speaking) ending. I invite you to watch. I couldn't quite follow everything. What do you notice? What do you wonder? After watching the ending, what would you say to this student?

Did you catch her mistake at the end? She's off by 1 somewhere along the line, but let's let that go. What interests me is that she catches her own mistake as she counts 73. Then she builds 17 more and starts to add, but she uses the 10 of the 17 to regroup her existing 3 ones with the 7 ones from the 17 instead of grabbing another 10 from her pile. She does not catch that 73 plus 17 should not be 80.

There's so much to this video. What did you see? What would say to her and her partner?

All the examples above involve students using concrete or visual models. In general, these students made mistakes more frequently than students who used more abstract procedures. In other words, there was a fluency gap in both classes. We discussed this fluency gap in our reflections and how to address it moving forward.

How do you handle fluency gaps in your classrooms?

As for procedures, we saw students using the arrow method:

We saw students decomposing numbers in to 1s and 10s and adding strategically from there. Notice that this student makes a number bond with 9 and 1 to make a 10.

This student wrote about his decomposition.

Sam used a formal algorithm and backed up her work with a drawing.

Some students used a variety of strategies as they wrote down their thinking.

Richard was an interesting case. After revealing the image in Act 2, he eyeballed the list for about 20 seconds and then said "91." I asked him to explain how he got there. And he gave me a rambling explanation. Afterward, I asked him to write down the order of his calculations. Here's what he wrote.

He strategically added 19 and 21. Then added the other 10s and then has a fuzzy moment with notation as he writes "=14" before adding 7. (Sloppy and imprecise, but not a dealbreaker.) Many students strategically made a 10 out of the 9 and 1 in 19 and 21, but Richard was the only one that leapt right to 40.

Beyond (Act 3):

When productive struggle had been maximized, we selected a few student work samples to share with the class and to connect to their learning strategies. We tried to focus more on the abstract strategies.

What strategy did this student use? Can you describe the steps this student took? Pair/Share first and then a whole class discussion.

This lesson provides so many pathways to the solution. It's also highly unlikely you'll have the time (and the students will have the mental fuel) to go through each solution method. Be choosy and strategic.

We played Graham's Act 3 video. For the most part, students were leaning in and eager to know what's going to happen next.In one class, there was an outright cheer, the type you'd expect in a sports bar as the local football team makes a big score! It was awesome, and I wish I had recorded it.

We concluded by asking students to think about the addition method that they liked most. And then had them reflect on a method that they liked but wanted to practice more so they could get better at it. These types of reflection questions are helpful for students to connect the work of others to their own thinking.

And then we gave out a differentiated exit ticket.

You can find our 3-Act template and our exit ticket here.

Reflections, Takeaways, Analysis:

At the end of the day, we reflected on our objectives and student learning. We noticed that this 3-Act Math lesson allowed for students to talk to one another about math because:

The task was appropriately challenging. It was in the sweet spot of accessible and challenging for almost all students.

Students had a choice and a voice in the whole learning process from start to finish.

The numberless introduction (Act 1 video) was low-floor so all students were on board right from the start.

We used Pair-Share and other conversation structures to increase student talk time. It also gave students time to think, work, and ponder.

The task creates a motivating sense of earned accomplishment as they start adding numbers and getting closer to a solution.

Other professional learning included:

There's no need to tell students what they can tell us or tell each other.

Problems like these help students abandon "learned helplessness" as a way to "survive" math class.

Productive struggle takes time...but it's worth it.

How can we step away from our textbook? It is too much like a "workbook." How can we open up other math concepts for students to explore?

What we are wondering about how to do better:

Being more clear around expectations for notice/wonder.

Refine sentence/question frames that further student thinking without restricting student thinking. What might those be?

What's the best balance between students expressing their thinking in "2nd grader language" and "academic language"?

How can we involve more movement in the classroom? Are there ways to make the carpet a useful space? Should we do Act 1 and Act 3 on the carpet? And Act 2 at their desks?

What could we have done differently to make student discourse more successful/productive?

An invitation:

As always, feedback and comments are welcome. What inspired you? What opportunities did we miss?

Help us get better together.

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A Bright Idea for 2nd Grade Addition Strategies - undercover calculus

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It's my hope that there are other elementary teachers out there that might find this analysis useful if they want to use this compelling and fun lesson by Graham Fletcher in their classrooms to engage their students in exploring addition strategies with regrouping ( 2.NBT.5, 2.NBT.6, 2.NBT.9).

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Teachers' Channel from Chase

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Modeling with mathematics is the practice of making sense of the world through a mathematical perspective. Take a moment to look around and get curious: How do you use mathematics to make decisions in your everyday life? Maybe you're deciding what to make for dinner. Does the recipe have enough servings to feed everyone or will you need to modify it, perhaps by doubling or halving the amount of each ingredient? When should you start making dinner if you'd like to eat at 6?

These questions can be viewed from a mathematical perspective. There is something to count, measure, or quantify and the answers to these questions have real and interesting implications for our lives.

Children also need opportunities to identify mathematical problems in their world, determine what information will help them solve a problem, develop mathematical models of situations, and revise their models to more closely predict real world phenomena. This is the work of modeling with mathematics, a mathematical practice identified by the Common Core State Standards as central to the work of K-12 mathematics.

Three-Act Tasks

A Three-Act Task is a lesson structure designed specifically to engage children in modeling with mathematics. The activity was created by Dan Meyer, a former high school math teacher and blogger. Teachers around the country are trying these tasks with students and sharing what they've learned. Here are just a few bloggers to check out: Graham Fletcher, Andrew Stadel, Mike Wiernicki, and Brian Bushart.

In Three-Act Tasks, students are shown an image or video that depicts an interesting situation. Examples of elementary tasks might include an image of two sisters standing side-by-side, one taller than the other, or a video of candy being poured into a jar. A good task will suggest some mathematical features or relationships that children may wonder about. After viewing the image or video, students are engaged in asking mathematical questions, identifying important information that is needed to answer those questions, constructing mathematical models of the situation, and comparing their models to the real world.

The first two videos in this series take us inside two primary classrooms where children are working on Three-Act Tasks and modeling with mathematics. As you watch Three-Act Tasks: Modeling Addition and Three-Act Tasks: Modeling Subtraction, consider:

What rich mathematical ideas do the children apply to these contextual situations?

How are Three-Act Tasks similar or different from other problem solving activities?

Two Strategies that Support Student and Teacher Learning

In Teacher Collaboration... While Teaching, we explore the ways teachers collaborate in the classroom to learn together, adapt lessons in the moment, and grow their instructional practice. The teachers use two strategies -- Teacher Time Out and Huddling -- to discuss instructional decisions together while lessons play out. These strategies are enacted by pairs of teachers working together, but can also be used by small groups of teachers who are learning about new instructional strategies or who are working together to improve their practice.

Finally, in the video Building Emotional Literacy, we get a glimpse into one small strategy that Sarah, Kristin, and their colleagues use to support students to develop emotional literacy skills and ready their bodies for learning. They link their work to a program called RULER, which involves a set of coordinated components to support students' socio-emotional learning.

Give these strategies a try and let us know in the comments below what you and your students learn.

For more on Modeling with Mathematics, visit these great resources:
Three-Act Tasks
Dan Meyer: Three-Act Tasks (grades 6-12)
Graham Fletcher: Three-Act Tasks (grades K-7)
Mike Wiernicki: Three-Act Tasks (grades 2-8)
Andrew Stadel: Three-Act Tasks (elementary-high school)
Other Resources
An entertaining 60 minute presentation by Dan Meyer: Fake-World Math: When Mathematical Modeling Goes Wrong and How to Get It Right

A brief blog post by John Pelesko with suggestions for elementary mathematical modeling: "How did the chicken cross the road?"

Have some fun with mathematical modeling! This website by Dan Meyer has interesting images and videos that you can ask mathematical questions about.
This work was made possible through support by the National Science Foundation. Elham Kazemi is a professor of mathematics education at the University of Washington. She loves to design professional learning opportunities for teachers, coaches, and principals to learn together about children's mathematical thinking. Kendra Lomax is a teacher educator at the University of Washington. She collaborates with local teachers to learn about children's mathematical thinking and designs job-embedded professional learning opportunities through projects like Teacher Education by Design. Curiosity about children's mathematical ideas is at the heart of her work.

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Modeling with mathematics is the practice of making sense of the world through a mathematical perspective. Take a moment to look around and get curious: How do you use mathematics to make decisions in your everyday life? Maybe you're deciding what to make for dinner.

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Duval County Public Schools Professional Development

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Duval County Public Schools Professional Development Station Rotations

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DCPS Math Centers, Duval County Public Schools Professional Development

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DCPS Math Centers, Duval County Public Schools Professional Development

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Session 2 Book Club

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Session 2

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I recently was fortunate to watch the great math educator Constance Kamii leading professional development with teachers, many of them new. Dr. Kamii is the author of many articles and books about math education for young children. She studied for 15 years under Jean Piaget, and currently teaches teachers at the University of Alabama.

Her focus is teaching math to young children, and her constructivist approach runs counter to most mainstream math instruction found in US schools today. Her research with real children in real classrooms is impeccable and widely cited, her video casework is undeniable, and she's read and studied worldwide - especially in Japan and Brazil.

The big idea of this post - questioning assumptions
Dr. Kamii makes me question everything I think I know about math and how children learn. What I do know is that the way that most children are taught math here in the US is successful for far too few people. But people seem to feel that it's the only way. Here in the US, it's perfectly acceptable to say, "I'm not good at math" and acknowledge that fractions mystify most college freshmen. Yet still we cling to our beliefs that somehow, if we just keep reciting times tables, handing out more worksheets, and doing "math minutes", eventually, the kids will get it.

It seems obvious to me that we have to question assumptions about teaching and learning math - especially in the face of overwhelming evidence that something is very very wrong.

What follows is my understanding of what Dr. Kamii shared with these teachers about teaching math to young children. These are not direct quotes, and I hope I got the gist of what she meant while discussing a complex subject.

Starting off - memory, perception, and representation
Dr. Kamii started with some basic thoughts about memory, perception, and representation.

In young children, memory is a reconstruction of their understanding. It's not a storage/retrieval mechanism. So for math, kids at a lower level of number concept will have a hard time remembering "facts".

Perception is a personal construction of what's out there, so it will change as a child grows.

Representation when talking about how children learn math is not the same as using the word "represent" as in a metaphor. The mind represents things - it's a verb. The nature of representation is not fully understood, but if you work with children, and listen and watch them, you can see when these understandings happen. Teachers have to carefully watch how children represent their understanding of the world, and with math in particular, and be careful not to try to simply impose an outside representation on a child.

You can't force them. If a child has no number sense, and you introduce numbers, there is no perception in the mind to connect it to. You can try to make them memorize it and practice it, but that just delays what needs to happen and confuses children.

By telling a child how to solve problems and memorize facts, we are trying to shortcut a developmental process that just can't be shortcut - and in the end, will actually delay progress and make it less likely that they will develop the deeper understanding they will need for lifelong mathematical ability.

Too much emphasis on symbols and equations
Kamii feels that in most traditional classrooms there is too much emphasis on writing equations. She teaches that there should be very limited exposure to equations in early grades.

Introducing symbols too early creates confusion where children feel the way to solve a problem is to choose the right symbol. Children may come to kindergarten able to answer questions like "If you have two apples and I take away one, how many do you have?" - but after a few months will respond, "Do I plus or minus?"

Many teachers try to "help" children with word problems by providing them with decoding strategies. For example, they tell children to look for certain words that signal the operation they are supposed to use to solve the problem - if you see the word "more" you add, if you see the word "per" you divide. This unfortunately encourages children to not really try to understand the problem, and often adds to a child's uncertainty of "what to do." Instead of thinking, they guess.

Throughout the day, the teachers are asking questions, about how do you know what to do, how do you see these signs in children. Stephanie, who runs the school, says - it takes years to get from the place where you say, "this might be right" to the place where you say, "I know how to teach like this." She assures them that everyone will be working together all year long to make sense of this.

Subtraction is not backwards addition
Dr. Kamii moves on to addition and subtraction. First, she talks about how most math education moves through these stages - add, subtract, multiply, divide. However, she says, this is not a natural progression. Subtraction is not a natural follow on to addition - multiplication is. But not as in "memorize the times tables" kind of multiplication. The kind of natural multiplication that students will do as they become more confident with addition. Things like creating groups, counting by fives, etc.

Example: Even as adults, people don't normally express things in terms of subtraction. When you go somewhere, you say you are getting closer to your goal, you don't say you are getting further away from your starting point.

If you are not successful in addition, you can't move on to subtraction. Conversely, if kids know addition very well, they will move easily to subtraction. Dr. Kamii says, "I wouldn't bother teaching subtraction in first grade."

Other points she makes:

Don't teach kids to count backwards to subtract. Too hard to keep track of the first count. (10-3 = 10, 9, 8...is the answer 8?). Similarly, number lines can be very confusing.

Manipulatives should not be used, it's an abstraction of an abstraction. Let students draw their own representations of a problem.

One of the worst things to teach is to "count on" (which means that teachers encourage students to add by saying the first number, and "counting" out the second number.) The problem is that it's a trick and not natural for kids. For example, if you watch kids play games where they move a game piece by counting, they always try to count the square they are on as part of their move.

When it's time to move to bigger numbers, the issue of "borrowing" comes up. If kids are introduced to this concept too early, they believe that borrowing creates a number that is bigger than original number. But some kids will be able to do the borrowing trick without understanding what the place value means. It looks like they are catching on, but they are just mimicking the trick. You have to constantly test their understanding by talking to them about real problems that use numbers.

So what do you do instead?
Her methods are to use a constant supply of word problems and games, not worksheets. She plays some games with the teachers and shows them several articles and books she has written about games and puzzles. She shows them assessment strategies that seem like games to students but reveal various types of mathematical sense in children.
Games that assess number sense
Word problems are crucial, she says. But let children solve them their own way, without imposing symbols or pre-canned strategies. They should work both together and in groups, and the class can discuss the solutions together. Children should be allowed to talk through their solutions to the group and will often come to see their own errors in ways that are much better learning experiences than just being told "you're wrong". (More about this later.)

The teacher's job should be to move the group discussion along and try not to impose their own understandings and ways to solve problems on any student. It's very important for every child to feel that there are multiple ways to solve a problem (not necessarily multiple solutions) and they are free to express their own solution. That way, if they have a logical flaw in their thinking, they will often hear it as they try to explain it to the class.

The teachers chime in
Some of the teachers are now bringing up their experiences from previous years. That it's hard to get the parents to understand this teaching methodology. The teachers say that parents teach algorithms and tricks to kids, and when this happens, it shows up right away that the kids are less willing to tackle problems because they feel they don't know the right trick. A teacher tells a story about having to help kids when they have been messed up by memorizing algorithms. They lose the confidence to invent good solutions when they encounter new problems.

A teacher asks - why is subtraction is more difficult? Dr. Kamii responds - It's human nature. First we construct the positive aspect of action (this is a basic concept from Piaget). The negative aspect follows only after you've done the positive aspect. You don't look at a picture and say, "oh, that's not green" or you don't say, "hand me the thing that's not a fork."

Another example is sorting - ask kids to sort things into two groups. Then ask them to name the groups. 4 year olds will just list everything in each group. Then comes a time when they can label some things, like "these are flowers and these are fruit." It's very rare that a child will create groups like "flowers" and "not flowers". The negative is a much later, secondary phase.

A teacher asks - How do you introduce subtraction? Dr. Kamii responds - A great way to encourage subtraction is to play games where kids can roll dice and use the numbers either added or subtracted. Early second grade is a good time to introduce these games. Some children will stick to only addition until they see that subtraction is better, then they will subtract. Let them come to that conclusion.

One game is called Sneaky Snake - played by two students. There are two pictures of snakes with the numbers 1 - 12 on them. You roll two dice and you can cover up a number on your snake, either the sum or the difference of the dice. The one who covers up all the numbers first wins.

Word problems that include subtraction are fine. Let them draw, cross the drawings out, but don't introduce the subtraction symbol.

Teacher - how do you know what kinds of problems to give them? You have to play games with kids and watch them. This is authentic assessment. Watch and see if they are just counting everything or trying new things. Listen to them. This is the primary role of the teacher - to understand the mathematical ability each child has by paying close attention as they solve problems. You have to have a good supply of games and puzzles that challenge children at different levels. It takes time to develop.

Video of a first grade problem-of-the-day session
After this we all watch a video of a first grade class working on a problem of the day. The problem is: if you have 62 cents, and the school store is selling erasers for 5 cents each, how many erasers can you buy? In the video, each child works out their own solution on a blank piece of paper, while the teacher circulates and listens to solutions. She never says anyone is right or wrong, just encourages them to explain their solution. One puts 62 marks and circles twelve groups. Another makes boxes that represent 5 and explains their answer. Another writes down 5, 10, 15... and counts those numbers, but when she gets to 62 she counts that as well - so comes up with 13. One draws nickels and counts them.

After a while the teacher in the video starts a class discussion and asks for all the answers - she writes about five different answers volunteered by the class on the board and asks for explanations. After a short time, there is only one girl left who is still sure the answer is 13, while the rest of the class has settled on 12. She maintains her answer for a while while other students explain that you can't count the last two cents because it won't buy a whole eraser. They use several different arguments and work hard to explain to her what she did wrong, and she defends herself until she changes her mind. Suddenly, she says made a mistake by counting the last two cents. During this, the teacher never says anyone is wrong (or right for that matter).

The big idea
Dr. Kamii explains - Kids should hang on to their beliefs, it creates autonomy. They shouldn't give in to pressure until convinced internally that there is a better solution (not that they are wrong). They should move from one solution they own to a better solution they believe in.

I can certainly see that in most math education, teachers and parents end up pressuring students to adopt a solution or methodology they don't really understand. Some kids will actually "get it", some kids will cave and learn the trick, some kids will resist to the very end. Of course some will be successful, but many, many children are left feeling that they are "bad" at math.

It's very difficult to let go of beliefs, even in the face of evidence that they are wrong. As a society, we believe that the way we were taught math is the "right" way, and the only way. Having to give memorization-based tests to children unfortunately reinforces this assumption.

But I hope that some of you out there are open to thinking about a different way to teach math, to question assumptions, to ask questions, and take a look at evidence that there are other ways that might be more successful in developing life-long math ability in children.

For more information
Recent article - Teachers Need More Knowledge of How Children Learn Mathematic s
Recent published research - Teaching arithmetic to low-performing, low-SES first graders

) (Young Children Reinvent Arithmetic: Implications of Piaget's Theory - Series of three books for first, second and third grade. The books take you from theory to practice in a real classroom. Each contains many games and ideas for teaching math in a constructivist way. ( Teachers College Press)

Other Kamii books and videos at Teachers College Press

Amazon - other books - some of Constance Kamii books and videos are available from Amazon.com (look at the used ones, you can get some of these for just a few dollars)

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Questioning assumptions with Constance Kamii

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I recently was fortunate to watch the great math educator Constance Kamii leading professional development with teachers, many of them new. Dr. Kamii is the author of many articles and books about math education for young children. She studied for 15 years under Jean Piaget, and currently teaches teachers at the University of Alabama.

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Session 2 Book Club

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Welcome! So glad you stopped by to join us for our new book study sponsored by the Elementary Math Maniac. Today we focus on chapters 1 & 2 of Number Talks by Sherry Parrish.

While we are participating in a book study, we also want to provide followers (who have not purchased the text) with additional resources to help them understand the essence of number talks and the impact they have in the classroom. These will be imbedded into chapter discussions, hopefully not to confuse, but to create further understanding beyond the text. Over the course of the coming weeks, our own experiences with number talks will also be shared. Please feel free to join in!
Chapter One: What is a Classroom Number Talk?
I appreciate how Sherry Parish begins chapter one, sharing her experiences visiting a second and third grade classroom and asking students to share their reasoning behind subtracting. Their reasoning was focused on using the standard algorithm, but the conceptual understanding behind its use was lacking. As the second grader stated, "That's just how you do it when the bottom number is bigger than the top."

This brought back memories of pretesting my fifth graders many years ago and discovering they were able to add fractions, change improper fractions to mixed numerals and vice-versa, etc.-with very few students understanding why they were performing the steps they were. They had memorized the steps taught the previous year, and three quarters of the class did not understand the meaning of a fraction or mixed numeral in the first place. Some teachers, when faced with this situation, would spend some time complaining and casting stones at the previous year's teacher, but I would like to think that most would immediately begin helping their students develop the conceptual understanding and why what they were doing worked and that there are other ways of thinking. Parrish provides support for this very thing-talk about it.

One of the things I like most about Sherry Parrish's presentation of number talks is that she shares a journey she has taken-one that has "challenged and refined my thinking about what it means to be mathematically powerful". I think anyone who delves into this text will challenge and refine their thinking as well-no matter where they are in their own journey.

It is also a journey she has not taken alone. She acknowledges many, including Ruth Parker, who began work with number talks many moons ago. Enjoy the following video of Ruth Parker's presentation, Do We Really Want them to Reason? at the Key Curriculum Ignite event at the 2012 CMC-North conference in Asilomar.

So, what is a number talk? Parrish defines a number talks as "a classroom conversations around purposefully crafted computation problems that are solved mentally."

In chapter one, Parrish goes on to describe a number talk in a third grade classroom and shares five key components of a number talk, yet seeing a number talk in action brings it all to life. Below you can watch three videos. The first is the introductory video clip shared on the DVD that accompanies Number Talks, by Sherry Parrish. The second is a third grade number talk video that comes directly from the DVD as well (both courtesy of MathSolutions). The third is a fourth grade number talk (courtesy of Math Perspectives). After watching the videos, an overview of chapter one will be shared.

You can also read a brief history of number talks on the Math Perspectives website where the above video was taken from.
Five key components of a number talk are shared in chapter one. I have pulled one quote from each component that best illustrates the component.

Classroom Environment and Community - "The culture of the classroom should be one of acceptance based on a common quest for learning and understanding."

Classroom Discussions - As you saw in the above videos, the teachers are recording students' thinking and giving them the opportunity to explain their own strategies and express their understanding of fellow students' strategies. Answers are shared and justified. In both videos you can also see the students' use of a thumb to indicate a solution. Students should also be encouraged to put up additional fingers as they come up with other strategies while they are waiting. This is a strategy that I do not currently use and plan to implement this week! Love this quote, "In number talks, wrong answers are used as opportunities to unearth misconceptions and for students to investigate their thinking and learn from their mistakes."

The Teacher's Role - "Since the heart of number talks is classroom conversation, it is appropriate for the teacher to move into the role of the facilitator." In the fourth grade video, you saw the multiple pathways shared for figuring out the perimeter of the square and halving the area of the rectangle. I liked how the teacher also presented a "situation" or context for the problem, yet she did not lead students in any way.

The Role of Mental Math - "When students approach problems without paper and pencil, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated." In this way, focus is not place on steps that are memorized. Students are forced to use their understanding of place value. Parrish also discusses the importance of writing problems horizontally to encourage the use of a number's value instead of focusing on digits when arranged in columns.

Purposeful Computation Problems - "The teacher's goals and purposes for the number talk should determine the numbers and operations that are chosen." One of the best parts of the text is the inclusion of number talks with a strategy focus. Readers are given a strategies table in the beginning of the text that outlines the strategy, appropriate grade levels, and page number where it can be found in the text. Do not use random problems.

Thought you might enjoy reading the following articles as well...

Here's another number talks resources: Inside Mathematics-Number Talks
Chapter 2: How Do I Prepare for Number Talks?
Great chapter! My first suggestion for preparing--BUY THE BOOK! It is well worth the investment, I promise! There's a lot in this chapter, so I have decided to break chapter 2 up into an additional post this coming Thursday to accompany our Makin' It Math mid-month linky. Below is a discussion of the beginning of the chapter...

Even though number talks are designed to be only 5 to 15 minutes long-Parrish presents four procedures and expectations that are essential to number talks.

Select a designated location that allows you to maintain close proximity to your students for informal conservations and interactions. This serves to build community and lends to informal assessment on your part.

Provide appropriate wait time to ensure the majority of the students have accessed the problem. Student engagement and participation are expected from all students. The quiet thumb signal is a great strategy for this. Please stop back in a future post when I share how I begin use of this with my students.

All answers are accepted, respected, and considered. Model this as a teacher! Show your acceptance of ideas, affirmation of thinking, and praise all efforts.

Encourage student communication throughout the number talk. THINK-PAIR-SHARE! It's been around ever since I can remember-use it! Student engagement is high and those who are reluctant to share have an opportunity to share outside of the whole group. I have seen this strategy build confidence in those reluctant to share as they DO begin to share in the whole group. "Having the opportunity to ponder other approaches strengthens our won mathematical foundation and understanding."

Please feel free to visit a previous post shared during our Guided Math in Action, by Dr. Nikki Newton, book study that relates to this procedure/expectation.

Woo-eee! Hope you are hooked and want to learn even more-or as the fifth grade teacher in the introductory video stated it perfectly, "walk through that door".

Please feel free to share anything you are thinking or wondering about in a comment!

Please stop back this coming Thursday for more of chapter 2 and some free made-its. AND thank you again to Tara, the Elementary Math Maniac, for hosting this book talk. Head over to check out her post! Below is a schedule for future chapters. Hope you will continue the exploration with us!

All the best-

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Number Talks Book Study - Chapters 1 & 2

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Welcome! So glad you stopped by to join us for our new book study sponsored by the Elementary Math Maniac . Today we focus on chapters 1 & 2 of Number Talks by Sherry Parrish.

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Chase Orton

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Eureka Based

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EUREKA MATH CENTERS/ACTIVITIES - YouTube

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Discussion and Supporting Materials

Thought starters

1. How does kindergarten teacher Ryan Berger use lights and a song to transition between centers?

2. Notice how Mr. Berger repeats instructions prior to the transition How is content addressed during transitions to make the most use of time?

School Details

Springfield Township Elementary School-Enfield
1118 Church Road
Oreland PA 19075

Data Provided By:

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Ryan Berger is in the middle of his first year as a new Kindergarten teacher. He asks Jim Knight to observe a lesson and share strategies to help him specifically with transitioning students between centers. Mr. Knight looks for classroom management strategies he can recommend to help Mr. Berger improve class structure.

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Analyzing math

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Show Day 4 of 4 Intermediate Group

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Math Circles for the 5th Grade Classroom

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Math Centers

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Math Center Organization for Guided Math Rotations

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4th Grade Differentiated Math Lesson Part

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4th grade math centers Jen Bersch Gifford

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RUSD Gifford Elementary 4th grade math centers Jennifer Bersch

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Math Workshops
Show Day 1 of 4 Intermediate

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Watch and see how with the help of a math menu board, I incorporate guided math in to my 6th grade math block.

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Great Resource for Parents

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Parents know that we need to read 20 minutes a day with our kids.

But teaching math to your kids doesn't have to be intimidating. It can be fun. Just as children say goodnight to the moon, they can say hello to numbers, shapes and measurement.

Talking Math with Your Kids provides ideas and products that get children and caregivers talking about math with creativity and joy.

Whether you're reading books on the couch, cooking dinner, running errands, or scheduling your day, opportunities for math talk abound.

This website collects research about, and examples of, math talk with children. Each post offers suggestions for adapting the examples for your own children, interests, and lives.

Enjoy and let me know how those conversations are going in your home. Use the contact form to ask questions, send feedback or to send along a conversation for highlighting on this site.
Thanks for reading. Read more about Christopher

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Parents know that we need to read 20 minutes a day with our kids. But teaching math to your kids doesn't have to be intimidating. It can be fun. Just as children say goodnight to the moon, they can say hello to numbers, shapes and measurement.

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For Math Center

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Debbie Diller ideas for math centers to reinforce vocabulary.

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Interactive Model Math Work Station

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Debbie Diller: Measuring Distance Whole-Group Lesson (from Moving into Math Workstations)

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Eureka Based Games

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I think the key is to have enough games so that the kids do not get bored at this station. It is important to also have a variety of math skills for them to practice. I try to supply games that fit in with our current math topic, although sometimes that is easier said than done. You can rotate the game each day you have math stations or rotate the game once a week. I personally rotate the game each day. I think it leads to less boredom, which leads to less off task behavior. At the beginning of the math stations I will announce which game is open for that day. Sometimes I may say, "Today you may play any addition/subtraction game or multiplication." I choose a math theme and they can have a choice within that theme. ex: Multiplication Monday

It is a good idea to have a posted list of every game that is available for kids to choose and which math category it goes under. Once a week I have Choice day. During this day students may choose what game they want to play.
Now as most teachers know, you cannot just let the kids start the math game station without setting rules, guidelines and practicing correct station behaviors. You also have to teach the kids how to play the games.
Starting up a math game station does not mean you have to go out and spent a lot of money on games. In fact there are a lot of math games you can create yourself using simple materials such as dice. Here are some links to some great math dice games. There is enough here to teach quite a few different games. This is something that I would teach at the beginning of the school year. They are quick, simple games to learn and play.

Check Out These Game Ideas

My math game station consists of mainly math board games. Over the last several years I have acquired quite a variety of different board games. I have been very fortunate to receive several grants to purchase math materials through DonorsChoose . I have also used classroom money and dipped into just a little bit into my own pocket to purchase games. One year, when I did dip into my own pocket, I invested in Frog Math. They have a variety of different levels and one box set comes with numerous math category game cards. Check it out... Also LakeShore Learning has a great variety of math games. Frog Math Game Set DonorsChoose uses LakeShore as one of their vendors, so I was able to get my math games through LakeShore . Of course students have their tried and true favorites...
LakeShore Learning

The Allowance Game: The kids can't get enough of this game!! Every year, it is a hands down class favorite. During choice day, students always choose this one. Of course I have two of these on hand. I was very fortunate to find one at a garage sale on summer! You can also find this for cheaper through LakeShore Learning.

I added this one this school year and it quickly became a favorite. Are you familiar with the original version of Sequence? If so, this is just like the original version, however it has addition and subtraction problems for the kids to solve. They put their chips down on the answer. I would also highly recommend getting the original sequence as a choice for math game station. Remember that math is also under the realm of logic, Sequence is great for building logic skills.

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I think the key is to have enough games so that the kids do not get bored at this station. It is important to also have a variety of math skills for them to practice. I try to supply games that fit in with our current math topic, although sometimes that is easier said than done.

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http://www.openmiddle.com/

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PDF

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Counting Games

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The basic foundation of math is understanding numbers and quantities. One of the best ways to develop these understandings, or number sense, is through handling objects and counting them.

We can listen to preschoolers recite numbers in order, but we want them to apply that to counting objects and understand that those numbers represent quantities of items. Games and activities encourage preschoolers to "play" with numbers and quantities and build math skills and number sense in natural ways. These ideas can help you build math and counting skills with preschoolers.

Counting Games and Activities

1. Dog Bone Counting Game (Pre-K Pages)

2. Farm Animal Counting Activity (Pre-K Pages)

3. Printable Counting Book (Pre-K Pages)

4. Homemade Counting Board Game (Pre-K Pages)

5. Mouse Counts Game (Pre-K Pages)

6. Fire Truck Counting Game (Pre-K Pages)

7. Penguin Counting Game (Pre-K Pages)

8. Ocean Theme Counting Activity (Pre-K Pages)

9. Nursery Rhyme Number Game (Pre-K Pages)

10. DIY Photo Counting Book (Teaching Mama)

11. Button Counting (Busy Toddler)

12. Football Counting Game (Sunny Day Family)

13. Snowman Hole Punch Counting (JDaniel4's Mom)

14. Ladybug Busy Bag (Preschool Inspirations)

15. Cookie Counting Game (Still Playing School)

16. Counting Snowballs (Fun-a-Day)

17. Race to Fill the Cup (Mom Inspired Life)

18. Count and Compare (Stir the Wonder)

19. Little Miss Muffet Path Game (Preschool Spot)

20. Tally Marks with Pencils (Munchkins and Moms)

Counting Games and Activities

21. DIY Counting Boxes (Parenting Chaos)

22. Play Dough Numbers and Counting (Little Pinch of Perfect)

23. Passing Car Count (Prekinders)

24. Ways to Teach Counting (Prekinders)

25. Ants on a Log Game (Teach Preschool)

26. The Math Box (Teach Preschool)

27. Counting and Addition Tray (Imagination Tree)

28. Simple Montessori Counting Activity (My Mundane and Miraculous Life)

29. Things to Count With (Pre-K and K Sharing)

30. How Many Blocks Long? (Brick by Brick)

31. Make Groups of Numbers (Teach Me Mommy)

32. Count and Smash Activity (Stir the Wonder)

33. Activities with Counting Blocks (Educators' Spin on It)

34. Where the Wild Things Are Game (Mom Inspired Life)

35. Listen and Spray Game (Fantastic Fun and Learning)

36. Race to Lose a Tooth Game (Toddler Approved)

37. Roll and Count (Buggy and Buddy)

38. Count Forward and Back Game (Fantastic Fun and Learning

39. Build a City Game (Learning 4 Kids)

40. Mystery Mitten Tactile Counting Game (Preschool Toolbox)

Also check out the free Winter Play Dough Counting Mats and our other thematic counting mats.

Follow myCounting Pinterest Board for more great ideas!

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Counting Games and Activities for Preschoolers - Pre-K Pages

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The basic foundation of math is understanding numbers and quantities. One of the best ways to develop these understandings, or number sense, is through handling objects and counting them.

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Chase Orton TK-5

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It's my hope that there are other 5th and 6th grade teachers out there that might find this analysis useful if they want to use this lesson in their classrooms to engage their students in exploring decimal division ( 5.NBT.6, 5.NBT.7, and 6.NS.3). Please feel free to plagiarize and make it your own as you see fit. I'd love to hear from you if you use it so we can get better together. (Special thanks to Graham Fletcher for providing such an array of amazing 3-Act Lessons!)

Before reading further, it may be useful to watch the lesson resources on Graham's website. Go ahead and check them out here. I'll wait.

And...welcome back! Let's dive in.

Some quick background:

I've conducted lesson inquiries using Tomato-Tomato with two teams of 5th grade teachers at two different schools. In total, I've taught, co-taught, or observed this lesson five times. Every lesson was a unique experience with it's own twists and turns and choices. The lesson pathway below shows the main flow of the learning experience and took about 60 minutes. Further analysis and takeaways can found at the end of this post, but I've tried to embed a lot of our thinking within the flow of the lesson.

This lesson was taught to 5th grade students that had not yet explored decimal division operations. I think Tomato-Tomato is a more valuable learning experience for students this way because they are encouraged to use a wide variety of sense making strategies. It also creates the headache (the need) for the aspirin (the long division algorithm with decimals). (Find out more about Dan Meyer's headache/aspirin metaphor.)

Our objectives (as teachers):

Students will be motivated and inspired to ask questions, engage in discourse, and persevere in solving a task.

Students will show what skills they have using models or symbolic operations to solve a problem.

Teacher will foster mathematical inquiry for groups using questions and discussing problem solving strategies. Teacher will use differentiated versions of the problem if necessary for struggling students.

Teacher will monitor student learning, look for anticipated students responses, select and sequence student work to share in discussion, and make connections between their models and symbolic notation.

Specifically, we wanted to see what sense making strategies they choose. Would they draw models? Which models? Would they do repeated addition or subtraction? Trial and error with multiplication? How many would attempt the long-division algorithm?

We were also asking these questions as observers: Are students enjoying math? What mood structures their interactions with each other? Where are they emotionally? What's their level of initiative? How do they self-advocate? Are they going to be able to do this without my direct guidance?

Learning objectives (for students):

I will show how I can use math strategies to solve a problem.

I will collaborate and actively listen to my classmates.

Some quick notes here... We wanted to keep the language very simple. We also felt strongly about using the general phrase "math strategies" instead of talking specifically about the four operations or drawing models. We certainly didn't want to use the word division. We wanted to keep the process as open as possible for a variety of pathways to the solution so that all students could play.

We added the second objective because if we wanted to see students collaborating in sharing strategies and engaging in discourse, we needed to make that explicit with our students.

These objectives were posted clearly on the board and referenced throughout the lesson at transition points.

Into:

After explaining the learning objectives to the students, we launched by getting students to think about ketchup containers.
Today we're gonna talk about ketchup. Yup. Ketchup. You know that ketchup comes in different sizes. At McDs, it comes in those little packets you can't open easily. At your house, it probably comes in bigger bottles. At Costco it comes in giant tubs.
At this point, kids are nodding in agreement.
We're going to watch a short video. I'm really curious about what you see in this video and what you notice and wonder.
We played the short Act 1 video showing both bottles of ketchup. After the video, we did a little pair/share before launching in to a Notice-Wonder exploration.

The Notice-Wonder strategy is a very effective discussion strategy to get all students talking (because everyone can describe something they saw and ask an interesting question regardless of their math ability). It also lowers the floor into a math task because it's a low-risk strategy that allows student discourse to describe the problem rather than having us (the teacher) "give" them the problem.

We paused the movie about 2 seconds before the end of the video so that the image remained on the screen.
Tell me all the things you notice.
We did not scribe these statements. We did often ask: How many of you also said the same thing? Who can say it in a different way?

We used these questions when students shared "noticings" that were about the sizes of the bottles because we wanted to make sure that this concept was clear to all students. These questions allowed for more student participation and provided opportunities to practice listening to each other.
Now, I want you to ask some questions about this video. What questions can you ask? What do you wonder?
In some lessons, we didn't need to ask the wondering question because we were able to paraphrase the things they noticed in way that led to the following key question:
How many of the little bottles ketchup make up the big bottle of ketchup?
We scribed this question clearly on the board below the objectives. We had them describe different ways to ask the same question because we really wanted to make sure that ALL students understood this question conceptually. How many little bottles could the big bottle fill up? How many little bottles go in to the big bottle? How many times bigger is the bigger bottle? How many times smaller is the smaller bottle?

We also unpacked what we meant by "filling" bottles. There is a gap of air in each bottle. In other words, we were talking about the volume of the ketchup in the bottle, not the volume of the bottle itself.

With our key question on the board, we continued: Huh. I'm curious what you think. Can you make estimate? Students make an estimate. Then there's a pair-share moment. We had them write their estimate on their paper to hold them accountable.
Who would like to share an estimate? Did anyone get fewer? Greater?
We scribed these estimates on the board, loosely ordering them from least to greatest. In some classes, we attached names to estimates.
You have made some interesting estimates. As you know, estimates are just educated guesses. If you wanted to make your estimate more accurate, what more information would you like to have about the ketchup bottles? (And why is that information helpful to you?)
This phrasing really sets up the pivot between Act 1 and Act 2 of the lesson. It hinges their question to a reasonable numeric answer. It also makes it explicit that math is a device that can allow us to make our reasonable estimates more accurate. And that sometimes, math only leads to more reasonable estimate, not an exact answer. (This lesson and Array-Bow do a particularly job of showing how math can be used to model situations that yield reasonable, but not exact answers.)

For these reasons, I often use this language at this transition point in many 3-Act math lessons.

In every lesson experience, students realized that they needed to know how much ketchup is in each bottle and asked for that information. (In some lessons, students wanted to know the size each bottle. We usually let that question stay even though it is slightly inaccurate. In some cases, we pushed back a bit more and asked students to clarify that we were talking the volume of the ketchup, not the volume of the bottle. And while we're at it, we're technically talking about the mass of the ketchup and not about volume at all...but...) In one lesson, we had to nudge them there with some effective paraphrasing of student responses.

Through (part 1):

Because we wanted to focus on decimal sense making strategies (and also because the numbers are smaller and therefore more accessible to all learners), we did not use Graham's Act 2 image. Instead we wrote the sizes (14 oz and 2.25 oz) on a frozen image at the end of the movie. We did not write the weight in grams.
I'm curious to see how you approach this problem and how you make sense of it. Let's do some math and see who got the closest estimate!
This is that scary moment in the lesson. Will they take off? Will there be launch failure? Have we baited the hook with a juicy enough worm?

In our preparation for this lesson, we talked a lot about this moment and what our choices were as a teacher. If we wanted students to persevere and make sense of the problem, we knew we needed to back off as instructors and resist the temptation to intervene with direct instruction. Prior to the lesson, a few teachers identified a handful students that might need a quick check-in/pep talk/accommodation right from the start, but for the most part, we had made a commitment that for at least the first 5-10 minutes, we would just float and observe and intervene only with questions and encouragement.

After 5-10 minutes, the teacher would step back and see which students were not succeeding/engaged and determine if it was because of a lack of clarity, a lack of skill, or a lack of confidence/desire. In most classes, there were usually 2-5 students that needed this boost.

Some quick notes here:

Encourage students to come up to the board. Because then this happens:

"What if the small bottle was 2 oz? What would your answer be?" was a question we phrased to struggling students who needed a lower floor.

A lot of students immediately multiplied 14 x 2.25. In some classes, the reasoning error was so prevalent that we called a quick timeout and addressed it as a whole group. We compared the product (31.5) to their estimates. This helped them to see that their answer didn't make reasonable numeric sense. I also started to draw a diagram of several 2.25 oz bottles on the board to show them that the product could be the total ounces in fourteen 2.25 oz bottles. This image helped to show that multiplying 14 x 2.25 didn't make conceptual sense for this problem.

We made an intentional effort to praise students explicitly for sharing their thinking and reasoning with each other. We wanted the focus to be off of just answer getting because we wanted to see of lot of this:

Since we also wanted to focus on multiple strategies, we encouraged students to show their thinking in as many ways as they could.

Through (part 2):

The numerical answer to the question is 6 and 2/9 or 6.222.... Most students quickly surmise that the answer is in between 6 and 7. Much of the amazing joy of this lesson is watching how students grapple with and make sense of the amount of the remainder. It was a big part of our discussion at the end of Act 2.

I want to unpack some student work samples because I think they are important to sequence from most conceptual (visual diagrams) to most abstract (long-division algorithm). We anticipated many of these approaches and made note of which work samples we wanted to select for discussion at the end of Act 2.

Students made pictures. We encouraged these students to put numbers to their bottles. They quickly realized they needed more bottles; 6.75 wasn't enough.

Students made a tape diagram. We liked this example because it linked to the diagrams like the one above. It also helps students see that 6 bottles (13.50 ounces) is too few and that 7 bottles (15.75 ounces) is too many.

The tape diagram also sets up nicely with student work samples that showed repeated addition and multiplication.

We hoped to see students using repeated subtraction from 14, but only a few students did that. We tried to leverage this work as much as possible because it creates the conceptual need for division as an appropriate strategy here.

Many students set up the problem for the long division algorithm, but quickly realized that they didn't know how to handle the decimal in the divisor and abandoned their plan. This created the headache for the aspirin (decimal division) that they were going to learn in the next chapter. We stressed this very explicitly with students to help them be aware that they've recognized a need for what they were going to learn about tomorrow.

Some students who were confident with the long division algorithm persevered onward. This student was even able to explain why he needed to multiply both dividend and divisor by 100. None of us knew when he learned this and how he came to know it.

This student persevered through some of the algorithm, but interestingly enough, she struggled to explain what the two-tenths meant in the context of the problem. In other words, she knew that 14 ÷ 2.25 was close to 6.2, but couldn't think in parts of bottles and her work served as an interesting display of procedural fluency without conceptual understanding.

After about 20 minutes, many students were starting to run thin on productive struggle. Most had figured out that it was between 6 and 7 bottles and could show why in several ways, but we found lot of hidden value in going deeper by asking students:
Do you think the answer is closer to 6 or 7? How do you know?
For many students, setting up a number line like this was helpful and offered an opportunity to bring in this model to the mathematical process.

While this problem is set up beautifully for double number lines and some 6th grade proportional reasoning skills, we went with a simple number line like this. Like many students, this student realize that he "was 0.50 ounces short" and "that isn't very much" so that the answer had to be closer to six bottles because "0.50 is way less than half of 2.25." Several say the answer is closer to 6 because 14 is closer to 13.50 and 15.75. A few strive to get more exact with a variety of reasoning strategy. The conversation around this topic was vibrant.

With this number line in place, a lot of students were able to grapple with the remainder issue in their own way.

A quick aside: a colleague witnessed one student think hard about this problem. He wrote the number 6 down before he changed it to 6.5 after another of moment of thought. Then he thought longer and wrote in 6.25. He listened to others, but never wrote anything down or showed calculations. We asked him to share his thinking, and he willingly attempted to explain, but really struggled to articulate why he knew the answer had to be less than 6.5. "Because that's how the numbers are" was his ultimate answer. It was an interesting occurrence where conceptual reasoning and number sense skills can precede that ability to communicate reasoning.

Beyond:

When the ceiling of productive struggle had been reached for most students, we selected examples of the student work we wanted to share and sequenced them similar to as they are presented above. At certain points, we had students share their work to the class. We made a point to start with conceptual solutions first (visual models), then solutions using addition/subtraction notation, then solutions using multiplication/division, and then discussed strategies for figuring out the "closer to 6 or 7?" question.

After we had shared our thinking, we concluded that as a group we were sure that our answer was between 6 and 7 and that is was closer to 6 and might be close to 6.2 or 6.25. We then compared that to class estimates from earlier. We talked about the value of mathematics because everyone was able to use numerical reasoning to move their original estimate closer to the real value.
Want to see the answer?
We are about 45-50 minutes from the beginning of the lesson, and kids are still jazzed at this point and all are leaning in. Before playing the video we explain that they'll watch colored water instead of ketchup because ketchup is gooey and it's hard to get it all out.

We then watched Act 3. After the 5th bottle, we pause the video and students groan with unfulfilled anticipation. But it's a teachable moment. We now have more information. How do we feel about our math answer? It's a good chance to keep the answer (6.2) contextual.

We then play the video through and pause with the final reveal on the screen. The video provides a tremendous opportunity to reflect. For starters, it shifts the answer key away from the teacher. It sits there as an objective fact and exists as raw evidence of the answer. It also allows all students to see that they had math skills that allowed them to improve the accuracy of their original estimate. Lastly, it creates the intellectual need to learn some more skills about dividing with decimals.

We concluded Act 3 with these reflection questions. Students were asked to pick one and write a response on an exit ticket or in their journals. After 5 minutes of writing, we asked for student volunteers to share what they wrote.

Reflections, Takeaways, Analysis:

This activity is naturally open and differentiated, it appeals to all learners regardless of mathematical skill.

Likewise, it allows for a variety of learning styles to shine and diversifies our idea of what math talent looks like.

It's a great launch in to decimal division.

It is fertile ground for student discourse, discussion, and perseverance.

Estimation and Notice/Wonder are powerful instructional tools.

Sharing student work to frame discussion creates a more authentic context for direct instruction about mathematical structures, strategies, and reasoning.

We should have listed the student strategies on the board. This would have strengthened their learning experience.

If we want to celebrate mistakes, we should encourage students to stop erasing their work.

What are some upcoming concepts in our curriculum that we can open up with this 3-Act math lesson structure?

These types of lessons can be a rewarding, whole class collaborative assessment. How close can we get as a class? Let's see what we can do!

As always, feedback and comments are welcome. What inspired you? What opportunities did we miss?

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Decimal Division Strategies and Sense Making for 5th Grade - undercover calculus

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It's my hope that there are other 5th and 6th grade teachers out there that might find this analysis useful if they want to use this lesson in their classrooms to engage their students in exploring decimal division ( 5.NBT.6, 5.NBT.7, and 6.NS.3). Please feel free to plagiarize and make it your own as you see fit.

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Start at Minute: 31.16 Stop at  36.29
Start at Minute: 37:40 Stop at 40:36

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Sherry Parrish: Number Talks: Building Numerical Reasoning

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Centers

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math groups planning sheet. I simply added an area for the whole group lesson for the day. I have once again updated this form. Now I only do whole group on Fridays as a general rule. However, please note that I do not ONLY use guided math groups ALL the time.

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Success in Math Class

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Everyone's favorite math guru shares the top 10 ways you can enhance your students' math learning, test scores, and skills

Several years ago, Michael, one of my third graders, wrote this in his journal: "I never used to look forward to math. All we did was add and subtract. Now I like it more. We work together in class, and we still learn math but in a better way." In a sense, Michael described the challenge we face as math teachers-to help students become flexible thinkers who are comfortable with all the content areas of mathematics and able to apply their learning to problem-solving situations. I have to admit-my early teaching resembled the math class Michael described, but over time I have found more engaging and effective approaches. Here are the ten "big ideas" I now embrace for helping children learn, understand, and enjoy math class.

1. Success comes from understanding. Set the following expectation for your students: Do only what makes sense to you. Too often, students see math as a collection of steps and tricks that they must learn. And this misconception leads to common recurring errors-when subtracting, students will subtract the smaller from the larger rather than regrouping; or when dividing, they'll omit a zero and wind up with an answer that is ten times too small. In these instances, students arrive at answers that make no sense, and they rarely know why.

Help students understand that they should always try to make sense of what they do in math. Always encourage them to explain the purpose for what they're doing, the logic of their procedures, and the reasonableness of their solutions.

2. Have students explain their reasoning. It's insufficient and shortsighted to rely on quick, right answers as indications of students' mathematical power. During math lessons, probe children's thinking when they respond. Ask: Why do you think that? Why does that make sense? Convince us. Prove it. Does anyone have a different way to think about the problem? Does anyone have another explanation?

When children are asked to explain their thinking, they are forced to organize their ideas. They have the opportunity to develop and extend their understanding. Teachers are accustomed to asking students to explain their thinking when their responses are incorrect. It's important, however, to ask children to explain their reasoning at all times.

3. Math class is a time for talk. Communication is essential for learning. Having students work quietly-and by themselves-limits their learning opportunities. Interaction helps children clarify their ideas, get feedback for their thinking, and hear other points of view. Students can learn from one another as well as from their teachers.

Make student talk a regular part of your lessons. Partner talk-sometimes called "turn and talk" or "think-pair-share"-encourages students to voice their ideas. Giving them a minute or so to talk with a neighbor also helps students get ready to contribute to a discussion. It's especially beneficial to students who are generally hesitant to share in front of the whole class.

4. Make writing a part of math learning. Communication in math class should include writing as well as talking. In his book Writing to Learn (Harper, 1993), William Zinsser states: "Writing is how we think our way into a subject and make it our own." When children write in math class, they have to revisit their thinking and reflect on their ideas. And student writing gives teachers a way to assess how their students are thinking and what they understand.

Writing in math class best extends from children's talking. When partner talk, small-group interaction, or a whole-class discussion precedes a writing assignment, students have a chance to formulate their ideas before they're expected to write. Vary writing assignments. At the end of a lesson, students can write in their math journals or logs about what they learned and what questions they have. Or ask them to write about a particular math idea-"what I know about multiplication so far," or "what happens to the sums and products when adding even and odd numbers." When solving a problem, encourage students to record how they reasoned. Writing prompts on the board can help students get started writing. For example: Today I learned ..., I am still not sure about ..., I think the answer is ..., I think this because....

5. Present math activities in contexts. Real-world contexts can give students access to otherwise abstract mathematical ideas. Contexts stimulate student interest and provides a purpose for learning. When connected to situations, mathematics comes alive. Contexts can draw on real-world examples. For example, ask students to figure out what you might have bought and how much it cost if, after paying for it, you received $0.35 change. Or ask children to figure out how much money each of four children would get if they shared $5.00 equally. Or ask a group of children to estimate and then figure out how many raisins each of them would get if they shared a snack-size box.

Contexts can also be created from imaginary situations, and children's books are ideal starting points for classroom math lessons. After reading Eric Carle's Rooster's Off to See the World (Simon & Schuster, 1991), for example, ask children if they can figure out how many animals went traveling. Or ask children to follow the calculations in Judith Viorst's Alexander, Who Used to Be Rich Last Sunday (Simon & Schuster, 1978), and figure out how Alexander spent his money. For a ready-to-use, literature-linked math lesson, see "A Step-by-Step Lesson with Marilyn Burns," above.

6. Support learning with manipulatives. Manipulative materials help make abstract mathematical ideas concrete. They give children the chance to grab onto mathematics ideas, turn them around, and view them in different ways. Manipulative materials can serve in several ways-to introduce concepts, to pose problems, and to use as tools to figure out solutions. It's important that manipulatives are not relegated to the early grades but are also available to older students.

For teachers just getting started using manipulatives, classroom staples should include at least 400 color tiles (1" square tiles in four colors), three to six sets of pattern blocks (six different shapes which typically include green triangles, yellow hexagons, blue and tan parallelograms, orange squares, and red trapezoids), 500-1000 interlocking cubes (usually in 10 colors, about 3/4"), and a supply of measuring tools.

7. Let your students push the curriculum. Avoid having the curriculum push the children. Choose depth over breadth and avoid having your math program be a mile wide and an inch deep. As David Hawkins said in The Having of Wonderful Ideas, by Eleanor Duckworth (Teachers College Press, 1996), "You don't want to cover a subject; you want to uncover it." There are many pressures on teachers, and the school year passes very quickly. But students' understanding is key and doesn't always happen according to a set schedule. Stay with topics that interest children, explore them more deeply, and take the time for side investigations that can extend lessons in different directions.

8. The best activities meet the needs of all students. Keep an eye out for instructional activities that are accessible to students with different levels of interest and experience. A wonderful quality of good children's books is that they delight adults as well. Of course, adults appreciate books for different reasons than children do, but enjoyment and learning can occur simultaneously at all levels. The same holds true for math. Look for activities that allow for students to seek their own level and that also lend themselves to extensions.

For example, challenge children to find the sum of three consecutive numbers, such as 4 + 5 + 6. Ask them to do at least five different problems and see if they can discover how the sum relates to the addends. (The sum is always the middle number tripled.) Allowing the children to select their own numbers to add is a way for students to choose problems that are appropriate for them. Even those students who don't discover the relationship will benefit from the addition practice. Invite more able students to write about why they think the sum is always three times the middle number, or to investigate the sums of four consecutive numbers.

9. Confusion is part of the process. Remember that confusion and partial understanding are natural to the learning process. Don't expect all children to learn everything at the same time, and don't expect all children to get the same message from every lesson. Although we want all students to be successful, it's hard to reach every student with every lesson. Learning should be viewed as a long-range goal, not as a lesson objective. It's important that children do not feel deficient, hopeless, or excluded from learning mathematics. The classroom culture should reinforce the belief that errors are opportunities for learning and should support children taking risks without fear of failure or embarrassment.

10. Encourage different ways of thinking. There's no one way to think about any mathematical problem. After children respond to a question (and, of course, have explained their thinking!), ask: Does anyone have a different idea? Keep asking until all children who volunteer have offered their ideas. By encouraging participation, you'll not only learn more about individual children's thinking, but you'll also send the message that there's more than one way to look at any problem or situation. That's when the potential for delight occurs.

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Marilyn Burns: 10 Big Math Ideas | Scholastic

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Everyone's favorite math guru shares the top 10 ways you can enhance your students' math learning, test scores, and skills Several years ago, Michael, one of my third graders, wrote this in his journal: "I never used to look forward to math. All we did was add and subtract.

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YouCubed

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This clip is an example of a number talk from a third grade classroom as described in the book Number Talks: Helping Children Build Mental Math Computation Strategies by Sherry Parrish.

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TK-5

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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In this blog post we will uncover best practices for the teacher table or small group time during guided math! You'll read what the research suggests as well as teacher to teacher tips on what makes the biggest impact during those precious minutes at the teacher table! Meet me at the teacher table!

Active Learning

When you begin your planning for guided math small groups, it is essential to think about active learning at the same time. What will my students be doing at the small group table? Flip the responsibility of doing the math from teacher to student. Take a look at your standard and look for active learning potential. To do this, pay attention to the verbs in the standard.

Rather than the old days of the teacher standing in the front of the class "doing the math" and having students record the answers in their workbooks, students now learn by doing. Every student is an active participant and responsible for the learning. Look at the learning standard for your lesson. What are the verbs? Use that to guide what students will be doing in the lesson. Is it create? Build? Understand? Explain? Whatever your verb, that is your guide to making it active. Next, layer it with the level of depth and complexity that matches each group's learning needs.

In the lesson below, students take turns telling addition stories which their peers then acted out with dinosaurs before writing the math equation and answer.

This activity based approach is about learning by doing. Students engage in activities to explore and learn mathematical concepts and skills. Using manipulatives or other resources students construct meaning and understanding. During the activity, students communicate and share their understanding using concrete and pictorial representations. The role of the teacher is that of a facilitator who guides students through the concrete, pictorial, and abstract levels of understanding by providing appropriate feedback.

Concrete and Pictorial Learning

We all need exensive practice to gain mastery in just about anything. When students have consistent time learning new math concepts through concrete objects, pictorial representations, and abstract math, they progress through stages of learning with the greatest potential for soaking up the understanding.

While it is important for students to ultimately work soley from the abstract, this is not the superior mode across all mathematical situations. When students attack a new problem, if they are unable to switch to a different modes of understanding, this limits their problem-solving abilities. Familiarity with other modes allows students to "fall back" on a different understanding in order to solve the problem. There is no way for a student to "fall back" if there is no history of meaningful learning in other modes of understanding.

We've all had the conversation at recess or lunch with the exasperated teacher friend that is frustrated that her students don't "get it". What seems so clear to the teacher may not be clear at all to students. This is likely due to the level and modes of the student's understanding. The more we can expose students to concrete and pictorial understanding, the more we nuture their ability to make connections in order to problem solve.

Talk About It

As students develop their understanding of what mathematics is and what it is useful for, they are more likely to insert themselves in the role of the mathematician. They can see themselves being part of a mathematical community.

In order to completely understand the language we know, we have to use it, and hear other people using the same language. So from a practical perspective, students need to talk in order to develop their use of language (mathematical or otherwise). Rather than teacher talking and students giving a one word response, students need to have parallel discussions with peers. Below students are not just making math card matches, but must then explain why this is a match in their own words.

We remember what we think about. When students construct ideas and communicate them to each other, they have to purposely think about these ideas, which means that they are building memories.

Finally, students talking to each other also provides their teachers with more information about the ways they are thinking which makes it easier for teacher to plan activities that respond to the ways students are actually thinking. When students talk to each other, their teacher can gather formative assessment information about not only what they understand but how they understand it. In the picture below students are discussing shoe fractions and justifying and agreeing on their findings. Each child has contributed one shoe to the table. 2 out of 4 shoes are sandals.

This picture below encompasses so much about why we meet with our students in a small group! Teacher can clearly see how students attack a problem. Which strategies are being used? How comfortable are students? How accurate are their strategies? Is there another way? Was a connection made? All of this mathematical goodness is happening in front of us daily. These students are working in the abstract in a timed situation which brings their mental strategies to the forefront.

Plan for Success

Nothing motivates me more than a full teacher bag of prepped materials for my classroom. Nothing...ahem.... Okay, okay, maybe Taco Tuesday but other than that...NOTHING. Knowing students' needs and having materials ready to teach is the pathway to a successful day of teaching. The day flies by because we are so excited to engage students in new understanding during our day! But then, the days keep coming one after another, there's meetings, parents, and oh yeah...our own families and all of their needs. It's a lot. Sometimes manageable and other times not. We feel like we are drowning so comprimise slips in and we find ourselves scrambing to have quality materials for our students. I.have.been.there. Not for a day, not even for just a week. I have lived in that space. It's frustrating. Out of that frustration grew a list. That list grew into a guided math series that I wrote containing whole group and small group lessons. Not just the lessons, but the materials I needed for that lesson.

Ducks in a Pond -Introductory lesson with kindergarten for addition to ten.

Every Standard Every Day

Let's talk about prep. Small group requires materials. Materials require prep. Prep takes time.

The way I have always looked at this issue is that investing my time in prepping materials that make my life easier in the long run is worth the time investment. The first year of prep is an uphill climb with laminators running hot with overuse. Year two is euphoric with beautifully prepped materials awaiting use. Sometimes I just sit and stare at them with happiness.

The area that you are able to save time is in your future lesson planning. It's done! It's written, prepped, and ready! The investment of time upfront pays in spades.

Materials

I have guided math materials for K-3 grade. You can check them out in my TpT store. These links will send you to the category page for your grade level. You will need to scroll just a little past the top of my store to find the guided math materials.
Kindergarten First Grade Second Grade Third Grade
No matter which materials you use, I hope the information in this post helps get you excited to say, "Meet me at the teacher table!"

New Product!

There's a new timer in the STACK family! I have shared the management aspect of having guided math groups on the blog before. Using a management system is crucial in keeping students organized, on task, and accountable. As I have spent time with different schools the last two years, I have worked with so many different teachers to find a rotation plan that meets their needs. Each class is unique. The amount of time a teacher needs with her groups is different for a few reasons. Number of students, length of math block, resources available for students. One fact remains the same, the management system makes the rotations run smoothly!

To address this need, I wanted an updated managementsystem that would address all the different times and choices that teachers love with their guided math groups. This is a powerpoint that you project on your whiteboard or smartboard when it is time to get into guided math stations.

Introducing....

Rounds and Choices

You do not need to know technology to use this! Everything is programed and ready for you to hit play! The timers countdown. Then they ring a bell while the timer flashes "Time's up!" The next rotation begins and the time automatically counts down again! There is a clean-up slide set to one minute at the very end. You just need to decide the time, number of rounds, and choices for rotations. Every combination of choices has been created and put into folders for you!

Wall Chart

If you enjoy a wall or pocket chart rotation system and are ready to switch things up, these icons are set to go! I also love to use them to label materials for those stations in the classroom. If you like the clean white version, just print as is! If you want it to match your classroom color scheme, choose your favorite colored paper for the group and rounds!

Rotation Choices

If you are unsure on which rotation choices you would use or want, I have a graphic to help! Choosing from different learning modalites in your rotations creates a more well-rounded mathematician. Plus there's the added bonus of some of these choices being very calm and quiet.

Questions?

Leave a comment or question if you have further thoughts on small group that I wasn't able to touch on in this post! I would love to hear from you!

The post Meet Me At The Teacher Table! appeared first on Tunstall's Teaching Tidbits.

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Meet Me At The Teacher Table! (Tunstall's Teaching Tidbits)

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In this blog post we will uncover best practices for the teacher table or small group time during guided math! You'll read what the research suggests as well as teacher to teacher tips on what makes the biggest impact during those precious minutes at the teacher table! Meet me at the teacher table!

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Image shows reading but scroll down to math centers

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We started our living things project by researching something living together. Yesterday we talked about Text to World Connections and asked ourselves "What do we know about the ant world?"

We wrote down what we thought we knew about ants and added it to our chart. We then read a few sections of a Non fiction ant book and listened for our ideas. If we heard our facts mentioned...we moved them to "confirmed. "If we didnt, they stayed under "What I think I know" If we thought something and then realized it wasnt correct, we move it to "misconceptions."

I love this idea for kids as it allows them to move their ideas around on sticky notes and organize their information.

"What I think I know" "Confirmed" "Misconceptions" "New Information" "Wonderings"

I run my math the same as I run my Daily 5 literacy in the Morning. Here are the kids choices:

I would love to have Math Technology, but I don't have a Smartboard or anything yet :(

Here are a few of the activities my kids are choosing from right now:

Math with Someone: Double It!

( students need a deck of cards Ace-10 and 10 game pieces each. You turn over a card and read the math talk card . EX: you turn over a 3, you say " the double of 3 is 6." Then you look for a 6 on the game board and cover it. The first person to get rid of all ten counters is the winner. )

Math by Myself: Backwards Number Sort

Math by Myself: Alligator Greater than Less Than (there is a recording page for this)

Math by Myself: 1 More 1 Less

Math Writing: Question of the Day

Math by Myself: Number Puzzles

Math Work: Replicating Patterns

Math Writing: Number of the Day

Note: I am on Maternity Leave right now and will not be sending out any free items. Thanks for understanding.

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Thinking about Non Fiction and Math Daily 5

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We started our living things project by researching something living together. Yesterday we talked about Text to World Connections and asked ourselves "What do we know about the ant world?" We wrote down what we thought we knew about ants and added it to our chart.

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TK-

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

Educational research -- not to mention experience and common sense -- tells us that students learn best and make better sense of what they're learning when they can make connections with previous learning or with different areas of learning...
Carol Goodrow, a first grade teacher and an avid runner, knows about the value of making connections. She has connected her curriculum by integrating running into almost every subject area -- and her students are reaping the benefits.

Mrs. Goodrow's first graders at Parker Memorial School in Tolland, Connecticut, took off running in September. By May, Goodrow told Education World, all the students could run a mile, had completed a mile fun run, and loved to write about running. According to Goodrow, many of the students started writing in their journals after running practice. Even those who had been reluctant writers loved the running practices so much they wanted to write about them.

"Also," Goodrow added, "they couldn't have any Gatorade until they wrote in their journals."

But, as Goodrow told Education World, the benefits weren't limited to physical fitness and writing. She saw improvement in math skills as well. For example, during year-end benchmark testing, the class completed sections on numeration more quickly, yet scored as well or better, than past classes.

In addition, Goodrow reported that many students demonstrated a better understanding of fractions. "My fraction committee, a group of the most capable math students, computed the class's [running] mileage on their own, working with 1/2's, 1/4's and 3/4's. They represented the fractions by models, but they could also compute them in their heads."

One of the class's favorite activities, however, was their ongoing "Trek Across America." In this project, Goodrow, her class, their families, and runner Don Allison set off on a virtual race from Boston to San Diego. Each time the participants ran, they kept track of their distances in personal mileage logs. As they progressed along the trek's 3,252 miles, the students traced the route, exploring 14 key cities.

Reports of the trek, as well as many other class activities, can be found on the class's Web site, Kids Running.com. According to Goodrow, this site is built so that kids can be authors, columnists, and more. There are sections where teachers can use running-related data, such as the voting booth data bank, to build math lessons. "It's also a site," she said, "where kids can practice reading stories written by other kids. And of course it encourages fitness and healthy attitudes."

Education World asked Goodrow if she had any suggestions to offer other teachers on how they can make learning more relevant. "Choose something you love," she said, "and integrate it into your curriculum."

But first, you might want to choose some of the activities below and use them to integrate Math across your curriculum.

MATH AND YOUR CURRICULUM

Math and Literature

Another good source for ideas on integrating math is Carol Hurst's Math and Children's Literature site. Though geared toward students in Pre-K through Grade 2, many of the activities here can be adapted for use with older students. For example, the article Time and Time Travel Fantasies, reprinted from Teaching K-8 Magazine, recommends setting up a classroom clock display and allowing students to take the clocks apart (and, hopefully, put them back together again) as they learn to tell time. The site includes a list of books with time-related themes, which you can use to accompany and/or inspire the activities.

Extension: You might extend the activities with older elementary students by setting up a clock repair shop, rather than a display, and having students prepare estimates and invoices for needed repairs. Students might also prepare written reports about the ways in which people have told time throughout history. One interesting site about gnomonics, the art of telling time using the sun's shadow, can be found at Cannon-Mania. Scroll down and click Sundial to learn about the sun dial cannon.

Math and History

At Mathematicians Commemorated on the Eiffel Tower, students in grades 3-12 will discover the names of French scientists and mathematicians that were placed on plaques in the Tower more than 100 years ago. Encourage students to visit The Official Site of The Eiffel Tower to learn more about this historic French landmark.

Extension: Following the tour, have each student return to the Mathematicians Commemorated on the Eiffel Tower site to read the biography of one of the mathematicians whose name is on the tower. Create a chart listing the name and major accomplishment of each mathematician. You might also encourage students to add to the chart the names of other mathematicians, some of whom might be found at Biographies of Woman Mathematicians.

Math and Science

After your middle- and high school students have toured the Eiffel Tower (see "History and Math" above) and perhaps helped build the Tower of the 3rd millenium, they may be ready to participate in Hands-On Bridge Building. This project, in which students use spaghetti, glue, and their knowledge of science and math to construct a weight-bearing bridge, begins with a lesson on scientific and mathematical vocabulary. Then, students create designs, reduce them to scale, prepare cost analyses, and build and test their bridges. The site includes quizzes, worksheets, and bonus and extension activities.

Math and Geography

At The Stowaway Adventure, "stowaways" in grades 6-12 can plot latitude and longitude to locate the route of the ship they're hiding on. They use that information, along with their math knowledge, to determine the ship's speed, distance traveled, and projected destination. Those stowaways who enjoy their voyage can move on to the second leg of their voyage, where they use what they have learned to determine future destinations and view satellite images to predict weather and ocean conditions.

Extension: When students return from their sea voyage, ask them to plan a trip on land or in the air. Students should use a map to set their starting point and destination, decide on an appropriate mode of transportation, and determine a reasonable speed. Then have them calculate the distance they'll travel and the time the trip will take. You might also encourage students to identify some landmarks along the way and to write postcards about the places they "visit."

Math and Health

At Fat Counting, students in grades 1-6 study and discuss the food pyramid. Then they compare the foods on the pyramid to the foods they eat, keep a fat-counting diary, calculate the number of calories from fat they eat in a week, find their daily average of fat, and compare their fat intake with that of other students. The lesson is less self-sufficient than many others, but the site does provide links to all the necessary information and resources.

Math and Art

At Greeting Card Geometry Math, a unit you can use to teach geometry to students in grades 2-5, students learn to identify and create congruent, similar, and equivalent shapes and then they use those shapes to make a holiday greeting card. The lessons are simple, yet effective, and include creative extension activities.

Extension: As a follow-up, you might encourage older students to use geometric shapes, and any medium, to create a poster showing the relationship between math and art. Then invite them to visit the National Museum of American Art or another online museum or art gallery, and identify examples of math in the art they find.

Math and Music

The Music section of Online Math Applications is one of the best sites available for introducing students to music and its relationship to math. The rhythm page explains how different musical notes represent the rhythm, or time, of a piece of music, while pages on tone and tune provide a thorough discussion of pitch, frequency, and amplitude. The site explains the mathematical relationship of adjacent notes on a keyboard and the theory that ratio is essential to harmony. Here, students can rediscover the discoveries of Pythagoras and listen to the music of Mozart. The clearly written, easy-to-read information makes this is a site that's appropriate for students of all ages.

Extension: After students have explored the site, taken some of the quizzes, or submitted quizzes of their own, give them an opportunity to listen to a variety of musical styles. Discuss the rhythm, tone, and tune of each selection, then ask students to compose a tune of their own. You might also encourage older students to research the lives of some classical musicians to discover how many were also mathematicians. Students of all ages will enjoy making, and experimenting with, a monochord.

Fun and Games

Finally, invite students to explore the activities at Fermi Questions. These problems, which encourage multiple approaches to problem solving and emphasize process over product, involve water balloons and jelly beans. Does it sound like fun? Does it sound like math? Check out this site and see what you think. But save it for the end of a very warm day!

ADDITIONAL RESOURCES

Article by Linda Starr
Education WorldÂ®
Copyright Â© 1999 Education World

Updated 04/26/2010

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You're Not in Math Class Anymore: Integrating Math Across th... | Education World

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

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Fun!

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This post might contain affiliate links (it might not, your guess is as good as mine). Let's just assume any links below are affiliates though, okay?

There was a point in which none of my children could read and my husband and I could pass notes to each other to keep secrets. Then Baloo learned how to read and he and I would exchange written secrets. Now, all three boys are reading (nearly, at least) and we cannot use that tactic. However, code breaking? Totally coming into play. At this point, Baloo is the only one who knows enough multiplication to solve this code breaker! So we can use the multiplication code breaker to exchange notes!

Update: There is now an addition version of the Code Breaker!
And a Space Version too!

This is day 2 of the Winter Printable Bonanza! (not the official name, just trying things out!). Cassie and I both have some wonderful printables coming in the next few days. To stay up to date on all printables, the newsletter is the place to be:

How to Set Up the Multiplication Code Breaker

Cut out the snowflake and inner circle. Poke a small hole in the middle of both.

Push the fastener through the small hole and bends sides of fastener on bottom of code breaker.

Spin the inner circle to match the multiplication problems!

How to Use the Winter Multiplication Code Breaker

I included 4 jokes or riddles with the code breaker. The answer to all of them is hidden in code on the back! If your child can solve these, ask them to write their own riddle or joke and include the code on the back. Then try to see if you can solve the question!

Send secret notes back and forth! There is not much as exciting as sending and receiving secret notes! You can use a direct code form the breaker or make it a bit more difficult! Use your imagination!

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Snowflake Code Breaker with Multiplication - Royal Baloo

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There was a point in which none of my children could read and my husband and I could pass notes to each other to keep secrets. Then Baloo learned how to read and he and I would exchange written secrets. Now, all three boys are reading (nearly, at least) and we cannot use that tactic.

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Laney Sammons Site

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This week I am participating in a blog hop with a group of amazing educational bloggers, and we are sharing professional resources that have changed our teaching. There are so many great books to choose from, and you will read about many of my favorites along the blog hop. After reading my post, simply click on the link at the bottom of the page to follow the trail to the next stop. Oh! And did I mention that we are each giving away a copy of our book? So be sure to visit each stop and enter the giveaway!

Guided Math Conferences, by Laney Sammons

In 2009, Laney Sammons' book Guided Math was published and, quite honestly, it changed the way we think about teaching math. In this groundbreaking book, Sammons outlined a framework for teaching math that was based on tried-and-true literacy instructional practices. I think the group impacted the most has been primary teachers (K-2), who often felt very confident teaching reading, but usually less so teaching math. By connecting a process they were familiar with, Guided Reading, to math instruction, she empowered teachers in a whole new way. As a math instructional coach working with K-2 teachers, I felt I was speaking their language when discussing Guided Math. I saw their confidence grow, right along with the achievement and confidence of their young mathematicians. It was, therefore, an absolute thrill to meet Laney at the NCTM Annual Meeting & Exposition in New Orleans this past April. In addition to being an inspirational author, she is also a genuinely warm person.

Since publishing Guided Math, Laney has continued to write and publish additional books to support the Guided Math framework. In January of this year, she released Guided Math Conferences, and that is the book I am writing about today. My current focus for personal professional development and research is the use of accountable talk in math instruction. So when I saw that Laney had a new book on conferring, I snapped it up! It did not disappoint.

Let me first say that even if you do not teach using the Guided Math or workshop approach, there is still much to be learned from this book. Throughout the book, Sammons addresses the fact that not all teachers use the Guided Math structure and provides suggestions for implementing math conferences regardless of your instructional setting.

Buried deep in the book, I found this gem of a quote that sums up the value of conferring with students: "When teachers confer with students, student thinking becomes more visible-to teachers and to the students themselves."

In Guided Math Conferences, Sammons provides a compelling, research-based argument for making math conferences a priority in your classroom, citing the emphasis on increased rigor and critical thinking skills, the focus on the CCSSM Standards for Mathematical Practice, the value of formative assessment, and the importance of student learning goals, among other things. As with all of her books, though, she addresses the practical aspects of implementation, with chapters that tackle the most common reasons why conferring does not take place (time and managing the other students during conferencing) and provide step-by-step instructions for managing conferences, including helpful forms for recording conference notes.

You may be thinking, "I do small-group instruction. Why do I need conferencing, too?" Sammons covers that early on in the book, comparing and contrasting the math conference with a math interview and small-group instruction. Later in the book, she also describes the connection between conferring and small-group instruction and explains that the conferring process compliments small-group instruction by providing insight into the needs of students and data for grouping.

When you're ready to get started, she outlines the structure of a guided math conference and explains the different types of conferences. That's right! Conferences are not one-size-fits-all. Snapshots from a variety of grade levels provide glimpses into the different types of conferences.

Like all of my other Laney Sammons books, this one will soon be dog-eared and worn. It is a book you will continue to use and reuse as your refine your teaching practices.

And now for the best news! Laney has graciously agreed to provide a signed copy of her book to the winner of my giveaway! My sincerest thanks to Laney and Shell Education for their support. Please be sure you fulfill the requirements for each entry-I will check the validity of entries before awarding the prize.
a Rafflecopter giveaway
Ready for the next great book? Head on over to Beyond Traditional Math!

You might also like these posts:

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Math Books That Will Change Your Teaching Blog Hop - Math Coach's Corner

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This week I am participating in a blog hop with a group of amazing educational bloggers, and we are sharing professional resources that have changed our teaching. There are so many great books to choose from, and you will read about many of my favorites along the blog hop.

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Hi everyone! It's Kim again from Elementary Antics! Today I'm going to be sharing a fun math game I liked to use in my classroom to quickly practice multiplication facts everyday. Shortly after I started teaching 3rd grade my coworker told me about this and we call it Donut Math.

It's so simple! All you do is make several poster board "donuts." Then, number around them 0-12 (or whatever facts you want your kids to know and practice) in random order. You can laminate them if you want for durability. Just use a magnet to attach the donut to your whiteboard. Tell students they have 60 seconds (or whatever time limit you want to put) to solve all the problems around the donut. Put any number (1-12 for facts) in the middle and students start solving! Students can time themselves individually or compete with each other.

I would do donut math every morning on my whiteboard. I usually had about 4 or 5 set up. Each group would send up one member, I'd put a number in the middle and they'd solve in the time limit. Afterwards, we'd check them and they would earn group points for their correct answers. The kids loved it! I love this game too because you can make it work for any facts- you're doing 1's, 2's & 5's facts in class, then just put those numbers in the middle. Easy peasy. You could even use this as an interactive center- just put a stop watch with it. The kids can time themselves and try to beat their times, race each other, or set up their own contests.

I really hope this is something you can use in your class! Check out my TpT store for more math resources. Happy Thanksgiving!

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donut math: a fun way to practice multiplication facts

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Donut Math: A Fun Way to Practice Multiplication Facts (All About 3rd Grade)

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Hi everyone! It's Kim again from Elementary Antics! Today I'm going to be sharing a fun math game I liked to use in my classroom to quickly practice multiplication facts everyday. Shortly after I started teaching 3rd grade my coworker told me about this and we call it Donut Math.

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Buddy Games
Using Manipulatives
Independent Reading/Work
Learning About Numbers
Doing Math

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So sorry to everyone who has e-mailed and asked about BUILD Math Stations! I have had such a busy and exciting first 6 weeks of school! Here is an entire post dedicated to everything I know about BUILD Math Stations. Please feel free to leave me a message asking any questions. Thanks for your interest!

BUILD is not a curriculum, it is a management piece for Math Stations. Each letter stands for something different and you choose activities/assignments for students to complete. The BEST thing about BUILD is that you can tweak it to fit your teaching and your classroom.

This is where I put games that my kiddos have practice practice practiced multiple times. They know the expectations: whisper voice, play the right way, play the whole time. My school uses Investigations as our math curriculum, so this goes perfectly b/c the basis of the curriculum is them playing games to master math skills.

This is where I put manipulatives for exploration. For the first few weeks of school I have had pattern blocks and workmats. You could also put play money, Judy Clocks, unifix cubes.

The title on this one pretty much explains it. My kiddos read math books during this time- and amazingly they really like it. Seemingly way more than Read to Self during Literacy stations. This is where you could also have them working on something pencil and paper if you need them to.

For this one I have hundreds chart games, matching, number scrolls, student made books about numbers.

This is where I put a game when we first learn it. After they have played it on their own a good amount of times and I have made sure that the majority of the class knows how to play- then I move it to Buddy Games.

Let me preface this by saying that I am NOT an expert on how you should run your math centers. I can simply tell you what I've done and what works for me! :) Like I said earlier, the best thing about BUILD is that it is easily modified for your classroom.

My students go to 2 BUILD rotations a day.
So, in a five day week, they go to each bucket twice. I use a spreadsheet and the students check in with me before we do each rotation to tell me what they want to do. Sometime I have to override it, but they don't seem to mind too much.I usually see a small group during each rotation. Normally it is the same small group(s) each day, so that means that most weeks, certain kiddos only do each letter once in a week. That doesn't bother me because they are with me for roughly an hour and 15 minutes a week in a small math group getting individualized attention.Example time frame on a typical day in my classroom:
12:30-12:45 Calendar
12:45-1:00 Whole Group Lesson (usually from Investigations)
1:00-1:15 BUILD Rotation #1 (I pull 3-4 students who need reinforcement on a common topic)
1:15-1:25 Whole Group Meeting (discuss procedures, talk about a strategy, share out, etc.)
1:25-1:40 BUILD Rotation #2 (I pull 3-4 students who need reinforcement on a common topic)
1:40-2:00 Whole Group Lesson (similar to earlier)It's important for kiddos to get up and DO something. They can't handle whole group instruction for that long. I choose not to do my entire Investigations lesson all in one stretch. (Also, if you use Investigations: for Math Workshop my students do BUILD). I don't know any 6 year old who can sit and listen to me talk for an hour... and I wouldn't want to sit and talk for an hour for that matter! :)

I do not own nor claim to own the BUILD concept. I did not create BUILD. I am simply producing management tools and ideas to use for ANY kind of guided math.

Check out some resources for math centers in my store.

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BUILDing the Math Workshop with BUILD Math Stations

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So sorry to everyone who has e-mailed and asked about BUILD Math Stations! I have had such a busy and exciting first 6 weeks of school! Here is an entire post dedicated to everything I know about BUILD Math Stations. Please feel free to leave me a message asking any questions.

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Pacing, Perspective, Preparation

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Guided Math

Whether you are just thinking about getting it started, or in the full throes of guided math, finding support is essential! Throughout this school year, I have enjoyed all of the pictures and feedback that I have received through social media and email regarding the guided math lessons. It's exciting to see the lessons unfolding in your classrooms! Your personal interpretation of the content is my absolute favorite! I just returned from a conference yesterday where I spoke with teachers about the joys and obstacles of implementing and teaching guided math. I thought it was a great time to bring light to some of those thoughts through a guided math check in!

Guided Math The Three P's

I believe that there are three teaching practices that contribute to the success of implementation. I would love to offer three strategies that helped me immensely as I navigated through the research and implementation of guided math. It's exciting to know that a myriad of classroom difficulties can be transformed by focusing attention on the three P's.

Pacing

The first, and perhaps most impactful, is pacing. Through my 18 years in the classroom I grew and developed as a teacher. No matter the age or range of a teacher's experience, there are some practices that can transform teaching. One area that I think determines success is the ability to pace correctly. I have experienced it first hand.

Terrific lesson, terrific teacher, terrible pacing. Crash and burn.

I do believe even our worst lesson experiences still add value to our student's lives. It's not a total loss, but it can leave us feeling frustrated.

Time Frame

First, we need to consider our time frame. Make a list of the essential components you plan to cover in your time frame. Then, jot down the minutes roughly needed to get through those components. Cry and erase all those minutes down to half. (am I right?)

If we are looking at the typical curriculum, there is truly no way to cover it all in a subject period. We have to filter all of the information and resources down to the best for our students with the time that we have. Is it a frustration? Absolutely! But let's focus on making the best of it. We know that we want to provide lessons that meet all students' needs to give them the best possible understanding of math concepts. When planning for time, be realistic but always have high expectations. Once you have this plan, you'll have that end goal in mind which creates the structure for your pacing.

Range of Abilities

Next, let's talk about the range of abilities in our classrooms. During a standard lesson, roughly a third of the students already know it, a third will get it, and a third need to hear it numerous times in order to "know it". It can be heart-breaking to realize that a student isn't "getting it" and have to keep moving on in our lesson. If we don't move but continue to reteach, we end up losing the students that don't want to hear it over and over when they already had it to begin with. Rather than teaching a full standard lesson, we can use a mini-lesson to better utilize our time and energy.

I used to think a mini-lesson meant that I needed to teach the exact same information in a shorter amount of time. Talking really fast wasn't exactly my best strategy. Mini-lessons allow students to share thinking, make connections, and become involved with the new learning. Students capable of going deeper will begin forging those connections on their own. Those on level will have their interest peaked. Students below level will be introduced to the concept without becoming overwhelmed and lost.

Remember that keeping a good pace is way of being respectful of every students' needs. We don't need to carry that teacher guilt. We will spend the time saved meeting those struggling students in small group which will reduce anxiety for them and allow them to absorb much more information than they would have in a long drawn out lesson.

Engagement

Pacing and student engagement go hand in hand. One thing that will disrupt your perfectly laid pacing plan is student behavior. When I say 'disrupt', I mean as a teacher we are constantly scanning the room for mayhem. If I have a set length of time that I want to have for my rotations, but my students always get restless two minutes before the timer, then I need to adjust the pace. Allow the natural stamina of your class help determine the length of your guided math rotations. If you want 15 minute rotations, but your students begin to deteriorate in quality of work around the 12 minute mark, then create a shorter rotation. This eliminates that time that would likely be wasted on redirection each day.

Perspective

One of the most powerful things we can do as teachers is to put ourselves in our students' shoes. I was a very eager student, ready to please, and give 100% in school, yet I had a lot of anxiety and difficulty when it was time for math. As I reflect on that experience, I believe it was because my exposure to math concepts was limited to procedural understanding. Conceptual understanding was not taught so I had never been exposed to the relationship of numbers. The way I knew math was that you follow steps to find an answer. done. When I didn't know the steps I simply didn't solve. I didn't ever consider that there was a series of math relationships happening in that math problem. For me, there was a complete disconnect from a math problem to any real life application.

Three days before my first teaching job, large boxes were delivered to my classroom. When I opened them I found tub after tub of math manipulatives. I was really excited about using them in my math teaching but had no idea how to do so. The timing of that delivery made it so that I began my teaching career exploring conceptual math. As I dove into the research and experimented with my student, I found joy in explaining the connections and the WHY and HOW behind the math! It was that missing piece for me and I was able to make it whole for my students.

Having the experience that I did growing up, helped me to stop and think about how my students were processing the different concepts. How I can make a math concept meaningful and dare I say it?...FUN!

Preparation

Preparation is HUGE in the success of any teaching lesson. Because guided math explores a range of learning modalities through a variety of daily activities, preparation is essential. We all have limited time in the day. It can be hard to stay on top of the mountain of teacher responsibilities. Finding and filtering through the right lessons each day is a daunting task. I have a teacher friendly resource that I hope makes teaching math the BEST part of the day for both teacher and students! It sure did for me!

Guided Math Lessons

Over the last year and a half I have created guided math whole group mini-lessons and small group lessons for grades kindergarten through third grade. These lessons are standards based. Inside you will find math warm-ups, math mini-lessons, small groups and all the materials to go along with the lessons.

Kindergarten

First Grade
guided math for first grade
Second Grade
guided math units for second grade
Third Grade
guided math units for third grade
Along with the whole group and small group lessons, we also want to provide our students with the type of activities that excited them and engage them to practice and apply the skills being taught. These resources are offered apart from the guided math lessons and do not overlap.

Math Centers

Guided Math wouldn't be complete with out hands-on math centers! Students LOVE to practice through play! I have monthly math center packets as well or these bundled sets for the year.

Kindergarten Centers for the Year

First Grade Centers for the Year

Second Grade Centers for the Year

Math Journals

Kindergarten Journals for the Year

First Grade Journals for the Year

Second Grade Journals for the Year

Third Grade Journals for the Year

Click HERE To be taken to even more posts on guided math!

The post Guided Math: The Three P's appeared first on Tunstall's Teaching Tidbits.

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Guided Math: The Three P's (Tunstall's Teaching Tidbits)

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Whether you are just thinking about getting it started, or in the full throes of guided math, finding support is essential! Throughout this school year, I have enjoyed all of the pictures and feedback that I have received through social media and email regarding the guided math lessons.

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Discussion and Supporting Materials

Thought starters

1. How does Ms. McPhillips decide what hints to use?

2. What are the effects of using hint cards?

3. How does Ms. McPhillips use hint cards to scaffold understanding?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

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Middle school math teacher Audra McPhillips explains how she uses hint cards to support her students and encourage independence. Audra explains how she writes probing questions on the hint cards to help scaffold her students' understanding. Audra shares how she has noticed her students benefiting from the extra support of the hint cards.

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Splash some fantastic

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Jo Boaler

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From Stanford Online's "How To Learn Math for Teachers and Parents": Number Talks

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First Grade

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This number talk focuses on developing computational fluency with 8 using ten frames. Notice that the teachers welcomes all solutions, and re-voices student thinking to ensure that all students understand.

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Guided Math

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I created my own version of math Rotations a few years ago when I just couldn't meet the needs of all of my students doing whole group instruction. I found that my high kids were bored and not listening, my middle of the road kids were mostly listening (I mean, I was teaching to them!!), and my low kids were staring off in space. Not good. That's when I did some research and decided to do Differentiated Math Rotations. Here is a quick overview of what I do. I am NOT claiming to be an expert at all!! This is just works for me (and my kiddos' state test scores)
I will also add that I DO NOT do rotations EVERY SINGLE DAY! I still find it incredibly valuable to have students participating in Math Talks, completing Performance Events, playing Games, and figuring out difficult problems with students who are not on their level. Their conversations are so important This blog post describes the majority of my time.

So.. how does it work you ask? I pre-assess my students at the beginning of each unit. Make it easy on yourself and just give them a five question multiple choice sheet that covers the topics of the unit. That way you can QUICKLY assess their strengths and weaknesses. I have to use our district Common Assessments, but it accomplishes the same thing.

Next, I group them according to the results. I use the Cardinal Directions as groups because it is a Compass Rose, shaped like a cross. There is not really a top or bottom because all four sides are important to find your way.

All 5 correct: West (advanced)

0-1 correct: North (low)

I usually play around a little bit with the East and South groups to even out the number of kiddos. I also assign each student a partner who is in their group to play at the game station.

Now remember, these groups are flexible. I am constantly monitoring my students to see if they need to change groups. I will usually get a few kids who can move up to West (advanced) and some kiddos who move up from North. I have had a student or two who has moved down to North for a few lessons. You are meeting your kids where they are. I also DON'T do stations EVERY Day. I do it MOST days!!

Notice that North group begins with the Teacher. This is so your low group is the first group of the day and they go directly to their desk to practice after meeting with you.

West group on the other hand, meets with you last. The first thing that they do is practice. These kiddos can usually start an inquiry based activity alone and then meet with you later to discuss it. Or you can have them practice something from yesterday's lesson.

Since the groups are flexible, I use a sticky note to record the group members' names. I also use pencil so that I can erase. Your groups will not always be even. You may have to have two low groups for example.

I hot glue the other labels to a white board. I write the materials needed and assignments students will complete at each station.

Once I have all my little honey buns in groups, I teach them about the rotations they will be making each day. Each rotation is "supposed" to last for 10 mins . I have been "flexible" with my timing for each group, depending on their understanding of the lesson. There are four rotations: Teacher, Desk, Game, Fast Facts. While I don't do a whole group lesson at the beginning, we do come back for share time to talk about our new learning.

T his is when the kiddos come to me at the carpet or small group table for the actual lesson that is presented on their level.

Your middle groups are easy to plan. You just use your Math Program. North and West are more tricky. You have to plan specifically for them.

I do A LOT of hands-on activities with my North group. While I am teaching a modified version of the curriculum, I am still expecting to get them to be successful on the grade level assessment. This takes flexible planning on your part. I KNOW my end goal and how I need to get them there, but I have no idea if this group will "get" the lesson or if I will need to reteach in a different way. I am prepared either way.

West group needs a challenge. These are most likely your gifted learners. They do NOT need MORE work. They have already proven to you that they have met the grade level expectation. These kiddos can work on performance events and projects. You will still be teaching them, but something more advanced.

Where do I get my resources?

At practice kiddos work on the practice assignment at their desks after the lesson. This is usually a worksheet that students work on to continue the learning they just had. (West group starts here first since they are the advanced group. They get an assignment before the lesson.)

I have a game for each skill. I usually keep the same game for one week so that I only have to explain it once. Some games are differentiated and some games are not. We may play a game from the current unit or we may play a game from a previous unit to review skills.

I play around with a couple of different activities for Fast Facts and what you do will depend on the availability of technology in your building. If you have tech, keep reading, if not, scroll down.

For those with tech I HIGHLY, HIGHLY recommend Prodigy! It is AMAZING! My kids beg me to play it and they even go home, call each other, and play online! This is a computer program that allows you to choose the standards, assign quizzes , and it grades it for you. The kids love it because it lets them create a wizar d avatar and they go around a magical world battling and earning coins and pets! It's free unless parents want to pay for their kiddos to be able to "win" more things. Some have purchased it but most have not.

I have also had students use www.xtramath.org for math facts. I highly recommend this site. We use it for homework now instead.

Before Prodigy I would have recommended www.frontrowed.com This site is AMAZING! It gives pretests for all CCSS standards and builds a program for each student !

If you do not have technology, We create these Fact Folders. We create them at the beginning of the year and use them for Fast Finishers. Watch this ten second video. You can pause if you need to!

I really hope this helps give you some ideas for Math Rotations! If you want the already created board, check it out by clicking the pic below!

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Math Group Rotations Made Easy- Why I'll Never Teach Whole Group Math

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I created my own version of math Rotations a few years ago when I just couldn't meet the needs of all of my students doing whole group instruction. I found that my high kids were bored and not listening, my middle of the road kids were mostly listening (I mean, I was teaching to them!!), and my low kids were staring off in space.

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Kindergarten

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Elementary math is so complicated these days, right? Not for students like David, a Nevada first-grader thriving in Connie Hall's classroom.