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from Math Geek Mama Blog

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from Math Geek Mama Blog

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Day 3 Sir Cumference and All the King's Tens

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Day 3 Sir Cumference and All the King's Tens

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Activities to accompany the book

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from Math Geek Mama Blog

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Free printables

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Math Geek Mama - Fun and FREE Math Teaching Resources

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Math Geek Mama is a math education blog dedicated to helping teachers and parents teach math in a way that is engaging and fun! Free lessons and printable games are shared every week!

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Place Value Centers

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Fluency Centers

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Thinking Blocks Junior | MathPlayground.com

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Play Thinking Blocks Junior at Math Playground - Model and solve word problems with addition and subtraction.

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2nd Grade Place Value Task

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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3-Acts Lessons | Questioning My Metacognition

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3-Acts Lessons | Questioning My Metacognition

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Check out Dan's Blog or watch Math Class Needs a Makeover

Kindergarten Recording Sheet
Want more of the good stuff? 3-Act Recording Sheet
Dan Meyer's (6-12) Robert Kaplinsky' (K-12) Mike Wiernicki (K-8)

Andrew Stadel (6-12) Dane Ehlert (6-12) Kyle Pearce (3-12)

Jon Orr (6-12) Catherine Castillo(K-5) Kendra Lomax (K-3)

Kristen Acosta (K-5)

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Check out Dan's Blog or watch Math Class Needs a Makeover Kindergarten Recording Sheet Want more of the good stuff?

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Idea from First Grader at Last blog

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So sorry I haven't been around this old blog in awhile. I am TWO weeks away from my due date...and I just can't wait to meet my baby boy! All things baby have been on the brain. I promise to be a better blogger, but for now, please keep in touch with me through Instagram, Facebook, and Pinterest! {Even though I haven't been the best blogger the past couple of months, I can tell you that I've been an AMAZING "pinner"! #justsaying #truth}

On to the hundred chart puzzles!

If you follow me on Instagram, you have already seen this idea in my pictures, and I promised a few friends that I'd share my hundred chart with them! This isn't really a new and fancy idea--but my students have LOVED it this year!

Here's how to make your own hundred chart puzzles in 3 quick and easy little steps:

1. Go to Michael's or Hobby Lobby and grab yourself a giant pack of rainbow card stock. {The more colors, the better!} Is it just me, or do y'all just love buying colorful paper? So fun.

2. Print out the 100 chart I have posted below onto a variety of colors of your bright card stock, and laminate. {Click the picture below to download.}

3. Cut the 100 charts into pieces--making sure to cut each one differently to make it challenging! Add the cut "puzzle" pieces to a baggie, with a color label matching the puzzle inside the bag.

This activity has been a favorite for my early finishers. I also use them as a choice during math stations, and they were also a great addition to our 100th day activities!

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So sorry I haven't been around this old blog in awhile. I am TWO weeks away from my due date...and I just can't wait to meet my baby boy! All things baby have been on the brain. I promise to be a better blogger, but for now, please keep in touch with me through Instagram, Facebook, and Pinterest!

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Math Coach / Fact Fluency for Addition and Subtraction

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Math Coach / Fact Fluency for Addition and Subtraction

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Math Coach / Fact Fluency for Addition and Subtraction

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Day 3: Adding and Subtracting on the Hundreds Chart

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Day 3: Adding and Subtracting on the Hundreds Chart

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SCOE Teacher Support, Modesto, California. 425 likes. Stanislaus County Office of Education's Instructional Support Services provides professional development and assistance for teachers.

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Chrissy's blog

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*For Part 1 of this summer school blog series, go here!

Norm 2: We give every task a try.
In May, I attended YouCubed's Teaching Mindset Mathematics workshop at Stanford with some colleagues with the plan to implement their summer school curriculum for our summer school program. Having a curriculum with a focus on developing positive attitudes towards math, collaboration and openness felt like a nice fit for a four-week program that wasn't focused on credit recovery. The tasks we did at the workshop gave us a chance to get messy with math, put our heads together with thoughtful group members, and made us giddy imagining how the students we'd be teaching would fall in love with math done "this way". How naive of us! As you can imagine, not every task landed exactly how we had imagined. It turns out, it's not enough to open tasks.

There's always a lot of buzz about the nature of the tasks we put in front of students, with a tendency towards (suggesting) that ...

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For Part 1 of this summer school blog series, go here! Norm 2: We give every task a try. In May, I attended YouCubed's Teaching Mindset Mathematics workshop at Stanford with some colleagues with the plan to implement their summer school curriculum for our summer school program.

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My students had been struggling with how to solve addition and subtraction word problems for what seemed like forever. They could underline the question and they could find the numbers. Most of the time, my students just added the two numbers together without making sense of the problem. Ugh.
Can you relate?

I am a big proponent of NOT teaching keyword lists. It just doesn't work consistently across all problems. It's a shortcut that leads to breakdowns in mathematical thinking. I talk more in depth about why it doesn't work in The Problem with Using Keywords to Solve Word Problems.

You can read more about the Addition & Subtraction Word Problems Resource that I use in my classroom in this blog post.

Below are five math problem-solving strategies to use when teaching word problems using any resource.

So, how do I teach word problems? It's quite complex, but so much fun, once you get into it.

The main components of teaching addition and subtraction word problems include:

Teaching the Relationship of the Numbers - As a teacher, know the problem type and help students solve for the action in the problem

Differentiate the Numbers - Give students just the right numbers so that they can read the problem without getting bogged down with the computation

Use Academic Vocabulary - And be consistent in what you use.

Stop Searching for the "Answer" - it's not about the answer; it's about the process

Differentiate between the Models and the Strategies - one has to do with the relationship of the numbers and the other has to do with how students "solve" or compute the problem.

Teach the Relationship of the Numbers in the Word Problems

I teach word problems by removing the numbers. Sounds strange right? Removing the distraction of the numbers helps students focus on the situation of the problem and understand the action or relationship of the numbers. It also keeps students from solving the problem before we talk about the relationship of the numbers.

When I teach word problems, I give students problems with blank spaces and no numbers. We first talk about the action in the problem. We identify whether something is being added to or taken from something else. That becomes our equation. We identify what we have to solve and set up the equation with blank spaces and a square for the unknown number
___ + ___ = unknown
Do you want a free sample of the word problems I use in my classroom? Click here or the image below. FREE Sample of Word Problems by Problem Type

Differentiate the numbers in the Word Problems

Only after we have discussed the problem do I give students numbers. I differentiate numbers based on student need. At the beginning of the year, we all do the same numbers, so that I can make sure students understand the process. After students are familiar with the process, I start to give different students different numbers, based on their level of mathematical thinking. I also change numbers throughout the year, from one-digit to two-digit numbers. The beauty of the blank spaces is that I can put any numbers I want into the problem, to practice the strategies we have been working on in class.

At some point, we do create a list of words, but not a keyword list. We create a list of actions or verbs and determine whether those actions are joining or separating something. How many can you think of? Here are a few ideas:

Join: put, got, picked up, bought, made
Separate: ate, lost, put down, dropped, used

Don't be afraid to use academic vocabulary

I teach my students to identify the start of the problem, the change in the problem and the result of the problem. I teach them to look for the unknown. These are all words we use when solving problems and we learn the structure of a word problem through the vocabulary and relationship of the numbers.

In fact, using the same vocabulary across problem types helps students see the relationship of the numbers at a deeper level.

Take these examples, can you identify the start, change and result in each problem?

Hint: Look at the code used for the problem type in the lower right corner.

For compare problems, we use the terms, larger, smaller, more and less. Try out these problems and see if you can identify the components of the word problems.

Stop searching for "the answer"

This is the most difficulty misconception to break. Students are not solving a word problem to find "the answer". Although the answer helps me, the teacher, understand whether or not the student understood the relationship of the numbers, I want students to be able to explain their process and understand the depth of word problems.

Okay, they're first and second graders. I know. However, my students can still explain, after instruction, that they started with one number. The problem resulted in other another number. Students then know that they are searching for the change between those two numbers. It's all about the relationship.

Differentiate between the models and the strategies

A couple years ago, I came across this article about the need to help students develop adequate models to understand the relationship of the numbers within the problem. A light bulb went off in my head. I needed to make a distinction between the models students use to understand the relationship of the numbers in the problem and the strategies to solve the computation in the problem. Those two things work in tandem but are very different.

Models are the visual ways problems are represented. Strategies are the ways a student solves a problem, putting together and taking apart the numbers.

The most important thing about models is to move away from them. I know that sounds odd. You spend so long teaching students how to use models and then you don't want them to use a model. Well, actually, you want students to move toward efficiency. Younger students will act out problems, draw out problems with representations, and draw out problems with circles or lines. Move students toward efficiency. As the numbers get larger, the model needs to represent the relationship of the numbers

This is a prime example of moving from an inverted-v model to a bar model.

Here is a student moving from drawing circles to using an inverted-v.

Students should be solidly using one model before transitioning to another. They may even use two at the same time while they work out the similarities between the models.

Students should also be able to create their own models. You'll see how I sometimes gave students copies of the model that they could glue into their notebook and sometimes students drew their own model. They need to be responsible for choosing what works best for them. Start your instruction with specific models and then allow students to choose one to use. Always move students toward more efficient models.

The same goes for strategies for computation. Teach the strategies first through the use of math fact practice, before applying it to word problems so that students understand the strategies and can quickly choose one to use. When teaching, focus on one or two strategies. Once students have some fluency in a few strategies, have them choose strategies that work for different problems.

Be purposeful in the numbers that you choose for your word problems. Different number sets will lend themselves to different strategies and different models. Use number sets that students have already practiced computationally. If you've taught make 10, use numbers that make 10. If you're working on addition without regrouping, use those number sets. The more connections you can make between the computation and the problem-solving the better.

The examples above are mainly for join and separate problems. It's no wonder our students have so much difficulty with compare problems since we don't teach them to the same degree as join and separate problems. Our students need even more practice with those types of problems because the relationship of the numbers is more abstract. I'm going to leave that for another blog post, though.

Do you want a FREE sample of the resource that I use to teach Addition & Subtraction Word Problems by Problem Type? Get the FREE Sample of Addition & Subtraction Word Problems by Problem Type by clicking the link or the image below.

The full resource is also available in my store for purchase.

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5 Tips - How to Teach Students to Solve Word Problems

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My students had been struggling with how to solve addition and subtraction word problems for what seemed like forever. They could underline the question and they could find the numbers. Most of the time, my students just added the two numbers together without making sense of the problem. Ugh.

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Cathy Kessel wrote an article with Liping Ma that discuss "unit fraction" vs "fractional unit" and has added a remark to the appendix about this.

Here is the new version.

Hi everybody, Cathy Kessel has compiled all the suggestions that people have made here and other places over the years to produce a final version of the progressions. Here is the compiled document of all the progressions.

And here are two documents outlining the major changes from previous versions.

Note that the University of Arizona has deleted the website that used to host the progressions. I am working to have that url redirect here.

Hi everybody, in order to deal with the spam problem I have deleted all users regarded by WordPress as spam users. These are defined as users who have never posted. Unfortunately this seems to have caught some legitimate users as well. Their content is still on the blog, with the author marked as anonymous.

Cathy Kessel is working on editing the progressions documents into final versions, incorporating comments from this blog and elsewhere and filling in gaps. Here is the fractions progression. We will be rolling out the others over the next few months. Comments welcome!

With the high school writing work in full swing, I've been remiss in posting here lately. I do have some ideas saved up! Meanwhile, Kate Nowak and I have a piece about instructional routines over at the IM blog.

I've been meaning to let you know about the Illustrative Mathematics blog, which launched a few weeks ago. It has blog posts by members of the IM community about our grades 6-8 curriculum and about teaching practice, including a whole series on the 5 practices framework of Smith and Stein. Also, we will be cross posting any IM related posts I write here over there as well. I hope you find our new blog useful!

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Counting on activity

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Sesame Street Heave Ho Song video

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Sesame Street: Elmo The Musical - "Heave Ho Addition Song"

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When Elmo imagines that he is a Sea Captain, he realizes he needs a crew for his ship. Enter eight chicken sailors. This season on Sesame Street, Elmo is starring in a brand new segment: Elmo The Musical! Each episode is a rollicking, music-filled math adventure, and Elmo wants you to come along.

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Sesame Street Barnacle Subtraction video

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Sesame Street: "Barnacle Subtraction" Song | Elmo the Musical

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Sesame Street video

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Sesame Street: Abby and Cookie Monster Subtract (Eat) Cookies

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North Carolina

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K-2 Formative Instructional and Assessment Tasks - First Grade Tasks

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K-2 Formative Instructional and Assessment Tasks Home

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North Carolina

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K-2 Formative Instructional and Assessment Tasks - K Tasks

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K-2 Formative Instructional and Assessment Tasks Home

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North Carolina

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K-2 Formative Instructional and Assessment Tasks - Second Grade Tasks

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K-2 Formative Instructional and Assessment Tasks Home

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Day 1: Counting Collections Template in Spanish

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Day 1: Counting Collections Template in Spanish

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Thank you for visiting the home of Read Tennessee, a joint project designed to allow teachers, families and community members to work together for the benefit of young children throughout the state of Tennessee. We encourage you to explore our Reading and Math toolkits to take advantage of the information provided to help accelerate the learning of Tennessee's most important resource, our children.
Mission
ReadTennessee.org is a joint project designed to allow teachers, families and community members to work together for the benefit of young children throughout the state of Tennessee. The goal of readtennessee.org is to provide teachers with learning expectations and appropriate activities for their students, sample lesson plans, video clips, and articles that will help them plan lessons and assist them in teaching the more challenging lessons in greater depth. ReadTennessee.org provides families and community members with an online resource for information, guidance, and useful tips to help them understand what children might be learning and doing at different stages of their development, and activities they can do to promote these skills. This website also helps you understand what is happening in classrooms, and about how families, teachers, and community can be partners in education-in the classroom and at home. Our goal is to engage and inspire children to learn and achieve more.
Thank you
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Read Tennessee | Engage, Inspire, Educate, Achieve!

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Thank you for visiting the home of Read Tennessee, a joint project designed to allow teachers, families and community members to work together for the benefit of young children throughout the state of Tennessee.

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good ideas for teaching addition and subtraction, shared by teachers

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What are the Characteristics of a Good Math Journal Question?

Tasks that ask students to apply memorized procedures to routine problems require one kind of thinking. Non-routine, or open-ended tasks that ask students to engage with concepts and to make connections between ideas and representations require a very different kind of thinking. Although applying memorized procedures is important for developing fluency and should not be dismissed, engaging in thinking and reasoning at a higher level is necessary to develop problem solving skills. While routine, or closed tasks, may be used to assess students' comprehension of number facts, strategies for solving algorithms accurately, or knowledge of other math facts, open-ended tasks involve investigative responses that stimulate mathematical reasoning and foster the understanding that mathematics is a creative endeavor. Some open-ended tasks may have more than one correct answer but a maximum of correct answers while others may have an infinite number of correct responses. For example the task, There are 16 apples to be put into bowls. Each bowl must have the same number of apples. How many different ways can the apples be put into bowls?' has several correct answers while the task 'I solved a division number story and got a quotient of 7. What might the number story be?' provides almost endless possibilities of acceptable responses. Other non-routine tasks such as 'Would you rather eat 1/3 or 2/8 of a plate of broccoli? Use math to justify your reasoning.' have no one correct answer but instead focus on the student choosing an option and justifying their choice using math reasoning. The important thing to consider when selecting, or writing, a math journal task is whether you are providing opportunities for students to regularly engage in a variety of routine and non-routine tasks in order to develop both conceptual understanding and procedural fluency.

A good math journal question ....

builds in differentiation by allowing for multiple entry points and recording techniques, thereby allowing all students to work at their individual level of thinking,

provides the opportunity for students to learn by moving beyond what they already know when answering a question, and for the teacher to learn about each student from their attempt,

may have more than one solution or a variety of possible solution paths that range from simple to complex,

requires some degree of cognitive effort (more than just remembering a fact or reproducing a skill),

provides opportunities for students to represent their mathematical ideas using models and written language,

provides opportunities for students to justify their reasoning and evaluate the reasoning of others,

has clear, concise directions.

Can Tasks be Revisited During the Year?

Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On the first occasion the student may be focused on 'how to do' the task. Subsequent visits provide an opportunity for students to communicate their mathematical thinking and reasoning more clearly. Making slight variations to a task (e.g. changing the numbers, context, or materials used) will help to maintain interest while students further develop skills and concepts. Some teachers like to introduce tasks whole class and then place tasks in centers for children to revisit at other times throughout the year. Other teachers choose one journal task and repeat it, with slight variations, several times throughout the year as a record of the development of math skills and understandings for student portfolios.

The methods that children use for representing their thinking will change over the course of a year. Repeating a task provides a record of this growth for teachers, parents and students. For example, in Kindergarten an open ended addition task (see work samples below) may be explored early in the year before children begin to write number sentences. Early in the year most kindergarten students will record their thinking in relation to this problem pictorially and may only record one or two solutions to the problem. As the year progresses symbolic representations will gradually begin to appear and representations will become more detailed. The work sample below on the left shows a kindergarten students' attempt to record her thinking early in the school year in response to the task ' Vanessa had 5 cupcakes. Some were chocolate. Some were vanilla. How many were chocolate? How many were vanilla?' Three months later this student completed a similar task, ' Cameron had 6 buttons. Some were green. Some were purple. How many were green? How many were purple?' On this occasion the child's written representation (below right) is more detailed and clearly demonstrates her developing understanding of addition. Although she repeats some number sentences, her drawings show all possible combinations of the six buttons.

How often should I use Math Journals in my class?

Some teachers use several tasks a week as a warm up to the math lesson. Other teachers set aside one period per week for journals, select a task that correlates with the current unit of study and allow more time for students to share their thinking with one another. Tasks may also be used for assessment purposes, or as homework. The important thing is to ensure that students are being given regular opportunities throughout the year to represent their mathematical thinking in ways which makes sense to them.

What type of book should my students use as a Math Journal?

Our experiences in numerous K-5 classrooms have shown that a notebook with blank pages produces the best results. Although these are not always as readily available as ruled notebooks (and are often more expensive) they have a distinct advantage in that students are not restricted by lines and have the space to choose whether to use pictures, numbers, words or a combination of these to record their thinking. Click on the links below to visit our gallery pages to see examples of the types of written responses made by Kindergarten - 5th Grade students when encouraged to make their own decisions about how to record their thinking.

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What are the Characteristics of a Good Math Journal Question? Tasks that ask students to apply memorized procedures to routine problems require one kind of thinking. Non-routine, or open-ended tasks that ask students to engage with concepts and to make connections between ideas and representations require a very different kind of thinking.

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Ten Friends | Peg + Cat | Mathematics, Preschool | Video | PBS LearningMedia

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Ten Friends | Peg + Cat | Mathematics, Preschool | Video | PBS LearningMedia

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Use this video to help children count numbers between 1 and 9 to make 10. Ten friends sing about sticking together. Utiliza este vídeo para ayudar a niños a contar números entre 1 y 9 para hacer 10. Diez amigos cantan sobre quedarse juntos.

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good ideas for teaching addition and subtraction, shared by teachers

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Math Teaching Resources for K-5 Classrooms

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Math Teaching Resources for K-5 Classrooms

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K-5 Math Teaching Resources is a leading New York City based math consultancy firm. Our mission is to transform the teaching and learning of mathematics, improving outcomes for all students in elementary and middle school. Click on a tab below for information on our research-based professional development and customizable consulting services. Our results-driven elementary and middle school consultants are committed to working side-by-side with administrators, coaches and teachers to build exceptional quality math instruction and curriculum for schools and school districts, transforming students' math education and achievement.

On this website you will find mathematics to support standards-aligned math instruction. Use the grade level tabs at the top of this page to download sample resources for each grade level from Kindergarten through 5th Grade or visit our EBook Store to purchase a complete set.

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Research based resources and professional learning opportunities to transform math teaching and learning communities.

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Expand That Number!: Composing and Decomposing Numbers Using Standard and Expanded Form

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Expand That Number!: Composing and Decomposing Numbers Using Standard and Expanded Form

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Expand That Number!: Composing and Decomposing Numbers Using Standard and Expanded Form

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Day 3: Place Value, CRA Style - Math Coach's Corner

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Day 3: Place Value, CRA Style - Math Coach's Corner

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What is CRA you ask? It stands for concrete, representational, and abstract, and it's a research based instructional sequence that results in deeper understanding of mathematics concepts.

Concrete learning is hands on. It's using manipulatives to make meaning of a new concept.

Representational is showing that same concept using pictures.

Abstract is representing a concept using symbols.

Now that I've set the stage, let's talk about place value. I talked with both 2nd and 3rd grade teachers today, and both grade levels are starting the year with place value. In 2nd grade, they will use groupable manipulatives, linking cubes, to model numbers with tens and ones (a review from 1st grade). Van de Walle recommends groupable manipulatives prior to using traditional base-10 blocks, because they can physically be joined together and broken apart. Traditional base-10 blocks are actually a little more abstract because, for example, you can't break the tens rod apart into ones-you have to trade it for ones. 2nd grade will then transition from the linking cubes to base-10 blocks as they extend their learning to hundreds.

In 3rd grade, my good math buddy Jeremy wanted a place value mat that the kids could use to work with base-10 blocks (concrete) and that also had representations of each place value (representational), so I whipped up this PV mat for him. Note that it prints on 11 x 17 so the columns fit the base-10 blocks. Of course, you can scale it down to print it on letter-sized paper, but the columns won't fit the manipulatives. I love how he wanted the ten-frame for the ones! Great bridge to prior learning. Click to grab yours and read on for suggested uses and another freebie.

And to complete the picture, let's slide the two ones into the ten-frame. Hmmm, I wonder what would happen if we added 8 tens ... 🙂

So this is a great whole group mini-lesson, now let's move the place value mat into a workstation for a little game of Race to 100. I wonder if I could beat Jeremy... 🙂

Click to grab a copy of the I Can card instructions.

You might also like these posts:

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Place Value, CRA Style - Math Coach's Corner

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What is CRA you ask? It stands for concrete, representational, and abstract, and it's a research based instructional sequence that results in deeper understanding of mathematics concepts. Concrete learning is hands on. It's using manipulatives to make meaning of a new concept. Representational is showing that same concept using pictures.

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multiplication vertical with and without trading

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fractions to decimals to percentages conversions

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decimals to percentages to fractions conversions

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percentages to decimals to fractions conversions

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Maths Charts || Math Posters || Free, printable || by Jenny Eather

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Over 250 free printable maths reference charts for interactive whiteboards, classroom displays, math walls, student handouts, homework help, concept introduction and consolidation and other math reference needs. © Jenny Eather 2012. Mathematical areas covered include Numbers, Operations on Numbers, Fractions, Decimals, Percent and Percentages, Ratios and Rates, Beginning Algebra, Data and Statistics, Probability, Geometry, Measurement, Time and Money.

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Make Math Fun For Students: 2nd Grade Math Lesson

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Make Math Fun For Students: 2nd Grade Math Lesson

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Math.2.NBT.A.1a

Common core State Standards

Math: Math

2: Grade 2

NBT: Number & Operations in Base Ten

A: Understand place value

1a:
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens -- called a "hundred.\"

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Download Common Core State Standards (PDF 1.2 MB)

|

Math.2.NBT.A.4

Common core State Standards

Math: Math

2: Grade 2

NBT: Number & Operations in Base Ten

A: Understand place value

4:
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Download Common Core State Standards (PDF 1.2 MB)

|

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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Thought starters

How does the repetition in a game allow for practice without redundancy?

Notice the different ways in which game requires students to compare quantities using place value. In what ways does the partner and whole group work help to scaffold learning?

School Details

Jerabek Elementary School
10050 Avenida Magnifica
San Diego CA 92131

Data Provided By:

Teachers

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Second grade teacher, Lisa Balongna, uses games to motivate student learning and provide practice as students learn about place value. She calls the first game "The Trash Can Game" in which she asks students to work in pairs to make the largest possible three-digit number from four numbers rolled on a die.

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Using Ten Frames and Dot Cards
Enlarged dot cards can be used during mental math sessions to prompt mental images of numbers and different mental strategies for manipulating these numbers. Activities with enlarged ten frames enable children to automatically think of numbers less than ten in terms of their relationship to ten, and to build a sound knowledge of the basic addition and subtraction facts for ten, which are an integral part of mental calculation. Listed below are a few examples of the many ways that these materials can be used during mental math sessions and/or in math centers to build number sense:

Flash a dot or ten frame card briefly and have students write the number on a whiteboard. Using dry erase boards rather than having students say the number, ensures that all children attempt to respond and allows the teacher to assess class progress. When the response is oral, not all student responses are audible. Encourage students to share the different strategies used to find the total number of dots for cards, "How did you see it?" This can be varied by asking students to write the number and draw the pattern they saw, or by having them build the number flashed on their own blank frame.

Flash: One More
Once students are familiar with the basic patterns, and know them automatically, flash a 10 frame or dot card and ask them to name the number that is one more than the number flashed.
Variation: ask students to give the number that is two more/one less/double/ten more than the number flashed

I Wish I Had 10
Flash a dot card or ten frame showing 9 or less and say, "I wish I had 10". Students respond with the part that is needed to make ten. The game can focus on a single whole, or the "wish I had" number can change each time.
Variation: teacher flashes card and students write the complement of ten on individual whiteboards with dry erase markers.

I Wish I Had 12
As above but students respond with how many more are needed to make twelve. Students should be confident in facts of 10 before this is attempted. For example to go from 8 to 12, they should realize they need 2 more to get to 10, then 2 more to 12. 2 and 2 is 4.
Variation: students draw an empty number line on their whiteboards to show the two jumps used to get to the target number.

1 more/1 less/10 more/10 less
The following four prompts are written on the board:
one more
one less
ten more
ten less
The teacher flashes a dot or 10 frame card as the 'starting number'. The first student selects one prompt. For example, if the teacher flashes a card showing '5' the first student might say, "one more than 5 is 6", the second student might say, "ten more than 6 is 16", and the third student might say, "one less than 16 is 15". Continue until all students have had a turn.

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COVID-19 Update: We hope that you are finding ways to keep you and your loved ones safe and healthy. We are being inundated with emails from districts, schools, teachers and parents who are looking for offline activities due to the fact that many families do not have the number of electronic devices needed for multiple children to do online learning while parents work from home.

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A Brief Ode to Blank Paper - The Stenhouse Blog

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A Brief Ode to Blank Paper - The Stenhouse Blog

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Prescriptive worksheets can often cheat children out of real thinking and understanding. Read how Tracy Zager encourages her own children to explore and communicate their mathematical thinking through writing-on simple blank paper. And then hop over to her blog to read how she continually makes math a natural, fun, and important part of her family's conversation. A Brief Ode to Blank Paper
Maya (7) brought home a folder full of completed math worksheets yesterday, which put me in a funk. First, there was the bugs problem.

I couldn't decide which part of this problem bothered me most. Was it the ridiculous premise? I mean, come on. Was it that the problem was, yet again, a multiple-choice question? Was it the stubborn insistence on drawing bugs with the wrong number of legs? Was it that students have no room to work, but the publisher took plenty of room for cutesie drawings? Harumph.

As awful as the bugs problem was, the page that really upset me was this one:

Sigh. A few issues:

The strategies are named wrong, and made to look more complicated than they are.

There are better and other ways to solve this problem.

Students are left with 2″ to do math on this entire page, which is barely enough room to do the standard algorithm. There's no chance they'll try out one of the other strategies with no space to work.

Once again, we're turning useful, general computation strategies into prescriptive algorithms. Breaking the numbers up by place value and adding the partial sums becomes: Step 1) Add hundreds...

I'm not the first math teacher to notice that prescriptive worksheets are a problem. Kamii, the CGI group, and others have all written about it. Yesterday, though, I was upset as a parent because Maya has stellar, flexible mental math skills, and her instinct to think is being undermined by this curriculum. I asked her why she'd opted for the standard algorithm on all the problems, and she said, "Those other strategies are too confusing." I covered up her solution to 597 + 122 and asked her to solve it mentally.

"Well, I'd give 3 to the 597 to make it 600. Then 600 + 122 is 722. I'd take the 3 back, so it's 719."

I did the same thing for 209 + 376:

"200 + 300 is 500. 500 + 70 is 570. 9 + 6 is 15. 570 + 15 is 585."

I pointed to the top of the page and said, "You just used this strategy. You broke the numbers up into place value parts, and then added each part together, starting with the biggest part."

Her jaw dropped.

And my mind clicked. She has made NO connection between the mental math strategies she uses with fluency and all this junk on the worksheets. The reason? She's never been given the chance to record her own thinking at school.

I think I've decided what one of my bigger problems with this curriculum is: they never use blank paper. They never write 209 + 376 at the top of a big piece of paper and let kids have at it. The kids never get a chance to wrestle with keeping track of their thinking or figure out organizational strategies. All math problems are either on worksheets or educational technology. The kids just don't write enough.

So now I know what to do with Maya at home. We're going to spend some time with blank paper, where she has to work out how to write down what she does in her head. She needs to make mistakes, lose track, not be able to follow her own thinking, and then ultimately figure out ways that make sense. She needs to be able to write down her thinking so that she and her mathematical community can follow it. I'm on it.

Two hours later, after dinner, Daphne (5) got us started. Our dining room chairs have decorative nailheads, and the kids are forever running their fingers over them and counting them. Daphne said, "Someday, I'm going to get out a math journal and count all these nailheads and write it down so I know how many there are." Before I knew it, she was off! Someday turned out to be right then. Both kids got in the game.

Daphne was incredibly excited to count AND write down her results. Check them out:

If you want to understand her notation, take a peek at the short videos:

The power of blank paper, baby.

Perhaps inspired by all of this discussion and my venting, Maya asked if she could get a piece of blank paper when she did her homework, which is truly a counter-cultural act with this curriculum. "Of course!" I nearly sang.

She created this number line and used it to solve the final problem.

When I asked her about it, I pointed out that she didn't just answer the question by saying, "The red one." She wrote about the problem more generally: "I used a number line and found that anything less than 350 would fit and 270 is less so red paint is less than 350!"

She said, "Well, when I wrote it myself I thought about it more."

Precisely my point.
This post first appeared on Tracy's blog.
Entry Filed under: math

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Prescriptive worksheets can often cheat children out of real thinking and understanding. Read how Tracy Zager encourages her own children to explore and communicate their mathematical thinking through writing-on simple blank paper. And then hop over to her blog to read how she continually makes math a natural, fun, and important part of her family's conversation.

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Open Middle - Challenging math problems worth solving

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Open Middle - Challenging math problems worth solving

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Open Middle - Challenging math problems worth solving

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Open Middle offers interactive math problems designed to foster critical thinking. Explore unique challenges that boost problem-solving skills and creativity.

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Boys & Girls-1st Grade Task

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Finding a Chair-1st Grade Task

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Pet Snake-1st Grade Task

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Operations & Algebraic Thinking | Open Middle

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Operations & Algebraic Thinking | Open Middle

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Operations & Algebraic Thinking | Open Middle

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Mr Elementary Math: Math Problem Solving 101

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Mr Elementary Math: Math Problem Solving 101

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Looking for a strategy to help students solve math word problems? Check out this post. Included you will find 2 FREE math problem solving templates and Steps to Problem Solving.

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Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2 (Volume I) (3rd Edition)

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NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase...

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Van de Walle

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Free Printable Hundreds Chart Activities for the Classroom

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Free Printable Hundreds Chart Activities for the Classroom

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A video tutorial is also available to demonstrate how to use this applet.

Modes

How Many: Identify how many items or empty squares there are.

Build: Drag a certain number of items to the frame.

Fill: Determine how many items are needed to fill the remaining squares.

Add: Drag items to complete addition problems.

Choosing Play All from the Games menu will randomize which of the four games is played.

Options

The items to be used can be chosen in the upper left corner: circles, bugs, stars, or apples.

How to Use

The Next button advances to the next problem.

The Done button should be clicked when a student believes that she has correctly completed a frame.

The number buttons at the bottom of the screen can be used to enter an answer, or the computer keyboard can be used.

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A video tutorial is also available to demonstrate how to use this applet. How Many: Identify how many items or empty squares there are. Build: Drag a certain number of items to the frame. Fill: Determine how many items are needed to fill the remaining squares.

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Play a matching game with different representations of equivalent items.

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Practice counting and subitizing by playing this game (also available on iOS and Android).

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Help the alien spaceship move cows into corrals by counting, adding, and subtracting. This activity helps children learn grouping, tally marks, and place value.

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SMP Tasks

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Overview

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

Standards

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.