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*Early Number & Counting
*Addition & Subtraction
*Progression of Division
*Progression of Multiplication
*Fractions:The Meaning, Equivalence, & Comparison

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The progression videos are a series of videos that show how math concepts build and grow through the grade levels. Here is a post that gives a "behind the scenes" of what it takes to make the videos.

Click on the image below to watch the progression video and download the resources.

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Build quizzes to use with a device to help build fluency. Go paperless!

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Free teacher online library. You can add your class for them to access a huge variety of books. There is a read aloud option for students who need listening support.

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Instantly access over 40,000 of the best books & videos for kids on Epic

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Barbara Webster: Final Integrated ELD Day 2019

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Lesson Plan Template

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Barbara Webster: Integrated ELD w/Math Session 2

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Build your students' deductive thinking skills, spatial reasoning, spatial vocabulary and teamwork skills with these 72, ready-to-use, logic activities. You'll find problems, answers and reproducible, line-up cards for 12 popular themes: barnyard...

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Build your students' deductive thinking skills, spatial reasoning, spatial vocabulary and teamwork skills with these 72, ready-to-use, logic activities. You'll find problems, answers and reproducible, line-up cards for 12 popular themes: barnyard...

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Jo Bohler's You Cubed

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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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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Most kids find it challenging to explain how they solve math problems and to put what they know about math into words. These ten simple classroom routines can help make math talk a regular part of your day:

1) Start your math block with a strategizing session instead of a traditional warm-up problem.

Rather than having students solve a math problem on their own, have them jot down notes about how they would solve the problem, then pair up with a neighbor to discuss and compare their strategies. When you're ready to bring the whole class together for a discussion, have a few pairs of students share how they'd solve, and invite students to test out their strategies.

2) Occasionally ask students to discuss strategies without actually solving the problem.

Present the math problem and ask students to explain (either orally or in writing) what operation they think they should use (and why), what steps they would take to solve the problem, or which tools could be helpful in solving. This shows students that there's more to math than just finding the right answer: understanding HOW to solve and why a strategy works (or doesn't work) is important, too.

3) Discuss math practices instead of just how a student arrived at an answer.

This can be tricky, so I created over 100 question stems for math practices to help you begin those conversations, as well as a reflection prompt that helps students think holistically about how they used all 8 math practices during a given activity. The prompts go beyond asking students to explain how they arrived at an answer: they require students to reflect on strong math practices and how those practices helped them approach the problem in a systematic, logical way. The prompts also help students reflect on their plan for solving, what happened when they noticed their plan was or wasn't working, how math tools assisted them, patterns they noticed, strategies they used for checking their work, and how they could prove their answer is correct. Click the images below to download a free preview.

4) Bring creativity into problem solving.

Many kids who dislike math are frustrated that there's only one right (and often elusive) answer to a problem, and they don't realize the tremendous amount of freedom and creativity that they have in choosing a problem-solving strategy. When a student explains how s/he arrived at an answer, ask the class, "Does anyone have a different way of solving?" Your enthusiasm for trying out different strategies will lead to students' increased engagement and risk-taking-kids love to hear their teacher say, "Wow, I never thought to solve it that way! Good thinking!"

5) Have kids use math journals to reflect on their strategies and assess their own learning.

Math journals are one of the most powerful tools for having students put their knowledge into words and to shift kids' focus from computation to problem solving and real-life application. Asking students to write about problem solving strategies on a daily or weekly basis gives you so much insight into their understandings and misconceptions. On the Math Journals page, you can learn more about how to easily manage and assess math journals and download free grade level-specific math journal prompts.

6) Have a go-to set of leading questions.

Some of my favorites are: What did you notice when solving this problem? What strategy did you use to get that answer? How do you know your answer is right? Are there any other ways we could solve this problem? These are questions that I ask so often that students can't help but pick up on them and integrate them into their own conversations about math.

7) Push student thinking with good questioning techniques.

If you're not sure where to begin, check out the discussion starters I created to help you facilitate conversations with and between students during problem solving. The PDF has over 150 questions organized into the following categories:

Preparing to solve problems

Stimulating students' thinking

Active listening

Choosing strategies

Analyzing strategies

Responding when students get stuck

Assisting students in talking to one another

Building on student responses in group conversations

Responding supportively to incorrect/incomplete answers

Pushing student thinking on incorrect/incomplete answers

Selecting and analyzing answers

Summing up/reflecting on math work

When using the question stems and prompts during math problem solving activities, you can use just one or two questions and have students delve deeply into them through written reflections or oral discussions. Or, you might use many of the questions in a single lesson as you facilitate a discussion. Click here to download the item preview which includes 5 pages of tips for having math conversations about problem solving.

8) Use math partner games.

I like to have students explore math concepts through game play for 5-15 minutes every single day. It's a great way to break up instruction during long math blocks or kick off shorter math blocks and prepare kids for the day's lesson. I pair them up with a partner of similar ability and have them play an open-ended game that allows them to construct their own knowledge about whichever math skill we're currently learning about. They have to discuss strategies with their partner throughout the game, and typically I give students a discussion prompt to use at the end, as well. And because all the students are playing games at the same time, I'm free to walk around the room and listen to/guide their conversations about math. Visit the Math Game Routines page to learn more about how I create, organize, and introduce the games to students.

9) Have students create videos or screencasts explaining their strategies.

Writing about strategies can be a long, tedious process for some kids, but using a free app like Show Me (or another program/app that lets kids record their voices and the screen) is fun, easy, and quick. Students simply solve the problem by writing on the iPad with their finger and narrate what they're doing. Have students watch each other's videos and compare/contrast their approaches, or give parents the link and encourage them to talk with their students about the strategies they saw their child model.

10) Have students create posters (digital or otherwise) that demonstrate all the different ways a problem can be solved, and refer to them often.

These can be large bulletin board displays that are added to throughout the year, or something that students create individually and keep in their math notebooks or journals. As you introduce a skill (such as 2 digit addition, multiplication, or dividing with remainders), have students start a chart or poster that lists the first strategy you teach, and then add more strategies as they're taught (or even better, discovered by the kids themselves.)
What routines or activities do you use to help students discuss and write about math strategies? Please share your ideas in the comments!
My Favorite Math Management Resources on Pinterest

Follow Angela Watson's Teaching Ideas's board Math Classroom Management on Pinterest.

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10 classroom routines that get kids talking (and writing) about math strategies

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Most kids find it challenging to explain how they solve math problems and to put what they know about math into words. These ten simple classroom routines can help make math talk a regular part of your day: 1) Start your math block with a strategizing session instead of a traditional warm-up problem.

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Written by Holly (Teach Starter)
Posted Wednesday August 10, 2016

Using visual brain teasers in the classroom encourages critical thinking in your students, plus, kids love them! We have searched the internet for some simple, yet effective visual brain teasers that will encourage logical thinking and develop problem solving skills. Teachers may get some enjoyment out of trying to work out some of these brain teasers too...

Put one up towards the end of class as a fast finisher activity. The discussions you have around how the students worked out the brain teasers are crucial.

1. What comes next?

A brain teaser for pattern recognition. Can your students work out which patterned block goes in the fourth spot?

2. How many blocks in this tower?

A brain teaser to test students' spatial visualisation and their ability to study 3D features. Can your students work out how many blocks are in this 3D tower?

3. Can you work out the net?

This brain teaser is great to test spatial visualisation. Students have to mentally put together the 3D cube to work out the correct net.

4. How many triangles?

In this visual brain teaser, students need to work out how many triangles there are in the image.

5. How many squares?

Similar to the visual brain teaser above, however, students need to work out how many squares they can see.

6. Move one glass only...

In this visual brain teaser students can see three glasses on the left that are full, and three on the right that are empty. They can only move one glass to make a row of alternately full and empty glasses. Which one do they move?

7. Make 10

This is a great problem solving brain teaser. Students need to remove six matches to make 10. Which ones do they move?

8. Top view

In this non-verbal brain teaser, students must work out which is the top view. You may like to time them to see who can work out this one the quickest...

9. What parking spot?

This visual brain teaser was on a Hong Kong first grade student admissions test. A great brain teaser to encourage children to think laterally. Can you work it out? Apparently children around the age of 6 are much more likely to solve this problem over older students and even adults.

10. What is our weight?

A great mathematical problem solving activity for students to work out the weight of all three animals in the fourth image.

Finished?

Finished these ten visual brain teasers with your class? No worries - check out some of our brain teaser resources:

Answers

1. Opposite squares are exchanged in this problem, so the answer is C.

2. There are 9 block.

3. B and C can be immediately rejected visually. D will create the mirror image of the given cube. So the correct answer is A.

4. There are 44 triangles.

5. There are 40 squares.

6. Pour the second glass from the left into the empty class second from the right.

7. You can make the word 'ten' by removing the bottom matchstick and two side matchsticks from the first letter. The far right matchstick on the second letter and the top and bottom matchstick on the third letter.

8. The answer is C.

9. Turn the picture upside down. You will then see the following number sequence: 86 ? 88, 89, 90, 91. So the answer is 87.

10. Maths calculations will give the weight of the dog as 17 kg. Therefore the weight of the cat and rabbit are 10 kg, so the answer is 27 kg.

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10 Visual Brain Teasers Kids will Love! - Teach Starter Blog

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Written by Holly (Teach Starter) Posted Wednesday August 10, 2016 Using visual brain teasers in the classroom encourages critical thinking in your students, plus, kids love them! We have searched the internet for some simple, yet effective visual brain teasers that will encourage logical thinking and develop problem solving skills.

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Are you ready to Play Math? Printable math games are just what you need to bring hours of fun and excitement to math learning. Lots of printable math games and resources all in one place so kids can get a kick out of learning math.

: Learning Decimals - Pairing Classroom Math Activity - This is a great math class activity that will keep students engaged. After each player gets a card, they are to begin searching for the person holding the card that when added to their card will make 10.....

: Fun two player math activity that helps youngsters learn to recognize shapes as they identify circles, squares, rectangles, and triangles.

Fishin' For Addition: Grade Levels 1 - 2. Kids will have fun practicing Addition facts through 9 + 9. Number of players: 2 to 4. Be the first player to cover five fish in a row.

Tic Tac Toe Addition: Kids enjoy playing this addition version of tic tac toe. Practice addition facts the fun way with a game (Tic Tac Toe) that most every child is already knows and enjoys!

Figure This: This printable activity is fun and is great for helping youngsters to recognize and name geometric shapes and solids. Players flip over any two cards and match a name card with a shape card. See who can match the most cards and win the game! Good for grades K-2.

2 and 3 Digit Multiplication: Monkeying Around with Multiplication is a third grade math game that will help your 3rd grader work on multiplying big numbers while having fun.

Long Division: Ready for some long division? Students will like this "Driving Into Division" as they race around the game board practicing division with 2,3 and 4 digit numbers.

Multiplying and Diviving Fractions: Fraction Flip is a fun printable game to help students practice multiplying and dividing fractions. And then there's Fraction Feud, where students will have fun learning and practicing comparing fractions.

Fraction Feud: Fun game that helps kids practice comparing fractions.

Name That Number: Students try to identify a sum or difference that names a given target number. Good for Middle and or High school. Pre-Algebra.

You can also play the of online version Name That Number. If you want to play more math games online, check out our online math games page.

One thing that's so great about these printable math activities, is that you can print them off and take them wherever you go. Take them on the family trip or where ever.

More Printable Fraction Games
Go to Elementary Math Games page
Go to Middle School Math Activities page
Return from Printable Math Games to Learn With Math Games Home

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Printable Math Games Students, Teachers, and Parents Love.

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Are you ready to Play Math? Printable math games are just what you need to bring hours of fun and excitement to math learning. Lots of printable math games and resources all in one place so kids can get a kick out of learning math.

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I saw a presentation by one of the authors at CMC conference. These are the sort of thing we need to be teaching and practicing.

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Teach the Math Practices to all students, students with learning disabilities and English language learners. Instructional Routines are the key to mathematical reasoning for all students.

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Erikson Institute Early Math Collaborative

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Teachers in four schools recently experimented with a "problem stem" protocol for helping their children understand the math going on in the word problems they face in class. This was part of our Big Shoulders project, which has been working with Chicago-area schools for the last five years.

Using a problem stem means discussing a problem without knowing what the question is. It is often part of what is called Three Reads, which involves reading the situation/problem three times, each time with a particular focus.

The first time, the goal is to comprehend the text (context). So it does not involve numbers or the question itself. The teacher may ask how they would describe the situation in their own words? What do they think is the context of the story?

The second time, the goal is to comprehend the mathematical structure of the problem. This introduces the numbers but does not pose any questions. At this point children may make a class list of possible questions, or perhaps make observations about the quantities.

The third time, the goal is to list all the possible mathematical questions. At this point the questions are laid out and students can discuss different ways of thinking as well as perhaps create diagrams to analyze the questions that are posed.

Many of the teachers read Beyond Answers by Mike Flynn as well as used the 3-act lesson resources posted by Graham Fletcher on his website gfletchy.com.

Two teachers at St. Thomas the Apostle tried the Three Reads strategy in their first grade classrooms using a math story and a series of engaging photographs they created. They read the situation three times, after each time stopping to discuss with students or allowing a turn-and-talk amongst themselves. Their particular story involved elves because it was leading up to the holidays, but that could be substituted for a thousand different thematic characters or objects.
Read 1: "There were some elves at St. Thomas the Apostle. There were some elves at Maggie Daley Park and there were some elves at the zoo."
Read 2: "There were 15 elves in Chicago. 4 elves were at St. Thomas the Apostle. 7 elves were at Maggie Daley Park and the rest of the elves were at the zoo."
Read 3: "There were 15 elves in Chicago. 4 elves were at St. Thomas the Apostle. 7 were elves at Maggie Daley Park and the rest of the elves were at the zoo. How many elves were at the zoo?"

Another teacher that is part of the project at St. Terese used the 3-Act problem Counting Squares to explore pattern and numbers. After being shown a picture of the pile, the kindergarten class discussed the situation and what questions may be posed about it. Students then used different approaches to solving the problem: How many tiles are in the pile. After working on solutions, the class came back together to discuss how making a pattern helped them answer the question to how many tiles were in the pile. An extension to the problem was if there was one more row added to the bottom, how many tiles would be in that row and what color would they be.
More Resources on the 3-Reads Protocol:

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Exploring the 3-Reads Math Protocol for Word Problems - Erikson Institute Early Math Collaborative

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Teachers in four schools recently experimented with a "problem stem" protocol for helping their children understand the math going on in the word problems they face in class. This was part of our Big Shoulders project, which has been working with Chicago-area schools for the last five years.

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The math department is producing videos to help you implement the SFUSD Core Curriculum and the Common Core State Standards for Mathematics. To watch a video fullscreen, use the "Pop-out" button on...

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The 3-Read Protocol

The Three Read Protocol is one way to do a close read of a complex math word problem or task. This strategy includes reading a math scenario three times with a different goal each time. The first read is to understand the context. The second read is to understand the mathematics. The third read is to elicit inquiry questions based on the scenario.

Why would I use this strategy?

The Three Read Protocol is designed to engage students in sense-making of language-rich math problems or tasks. It deepens student understanding by surfacing linguistic as well as mathematical clues. It focuses attention on the importance of understanding problems rather than rapidly trying to solve them. It allows for the use of authentic, instead of overly simplified, text. This strategy also allows for natural differentiation within a class of diverse learners.

When do I use this strategy?

This strategy can be used for math tasks that include complex language structures or language that lends itself to a variety of interpretations. While this is a particularly useful strategy for English Language Learners, all students can benefit from the deeper understanding of word problem structures and open-ended questioning.

How do I use this strategy?

The Three Read Protocol uses the " problem stem " of a word problem. This is essentially the word problem without the question at the end. The purpose of presenting the problem stem alone is to have students focus on the contextual and mathematical information before dealing with any question that is involved. This gives students the freedom to create their own questions for a given scenario, which is an excellent skill to develop both in math and in reading in general. It is important that the teacher choose the problem carefully and anticipate potential linguistic and mathematical roadblocks the students may encounter.

1. First Read: Teacher reads the problem stem orally.

The teacher may have visuals to accompany the oral read of the problem stem. Students listen to the story with the goal of turning to a partner and sharing what they remember of it. Memorizing it is not necessary. Students may act out the problem if that helps them grasp the context.

Key Question: What is this situation about?

After the Turn-and-Talk, the teacher asks students to volunteer information they remember from the story. Teachers and students ask clarifying questions about the vocabulary as needed.

2. Second Read: Class does choral read or partner read of the problem stem.

The teacher projects the problem stem so the whole class can see it. The teacher leads the class either in a choral read of the problem or has partners read the problem orally to each other. Choral read is preferable because it allows all students to participate without excessive pressure, but a partner read can work fine if that is a better fit to the classroom culture or age of students. The teacher explains that math stories usually have information about quantities (numbers) and the units that are being counted.

Key Question: What are the quantities in the situation?

An example is 25 cats, where "25" is the quantity and "cat" is the unit. Sometimes the quantities are implied. For example, "some cats" implies a quantity but we do not know what it is. There can also be implied units. An example is "I have one at home." The implied unit in this case depends on the context of the story. Bottom line : The discussion of quantities and units can be important for focusing student attention, but how deeply the teacher delves into the explicit and implicit information depends on the math and language objectives.

3. Third Read: Partner or choral read the problem stem orally one more time.

The teacher asks students to do one more read of the "story" and asks them to think, " What is missing to make this a good math problem? " Students volunteer their answers to that question. Responses will likely vary because many students assume there is a question without actually reading one. Without correcting student responses, the teacher probes until the class decides that a question is missing. The teacher asks, " Is there only one question that we can ask of this story? " Students responses may vary, but there are usually many different questions that can be asked of almost any scenario.

Key Question: What mathematical questions can we ask about the situation?

The teacher asks partners to determine at least two questions that can be asked using the problem stem. Students share their questions. The teacher writes a couple of the questions and clarifies language as appropriate. After each question, the teacher asks the class, " Can this question be answered with the information from this story? " and the class discusses why or why not.

4. Students work in collaborative groups on the problem.

Students work in groups to solve a question based on the problem stem. The teacher may assign a specific question for all groups to answer, or groups may choose a question from the list asked by the class. If groups are asked to choose their own questions, it is important that the teacher circulate and clarify expectations for the work. This can be an opportunity to differentiate the math work because the range of possible questions to a problem stem is broad.

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Download the description of the 3-Read Protocol from our Math Teaching Toolkit

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The 3-Read Protocol in Kindergarten and First Grade

See the 3-Read Protocol General description for more information on this strategy.

Many teachers of Kindergarten and First Grade have adapted the 3-Read Protocol for use in their classrooms. Here are some suggested modifications:

1. First Read: Teacher reads the problem stem (story) orally.
Use visuals and / or a rebus to accompany the oral read of the problem stem. Students listen to the story with the goal of turning to a partner and sharing what they remember of it. Memorizing it is not necessary.

Key Question: What is this story about?

After the Turn-and-Talk, the teacher asks students to share information they remember from the story. Students may share details that are not from the story, as they try to relate the story to their own context. Teachers and students ask clarifying questions about the vocabulary as needed.

2. Second Read: Teacher reads the problem stem (story) orally. May be omitted if students already talked about the numbers in the story.
Use visuals and / or a rebus to accompany the oral read of the problem stem. Students listen to the story with the goal of turning to a partner and sharing what they remember of it. Memorizing it is not necessary.

Key Question: What are the numbers (or quantities or amounts in the story?

As students share numbers, teacher helps them state the units by asking: 25 of what?

3. Third Read: Combined teacher and choral read with images.
The teacher reads the story out loud, asking students to help read the words with images. In this example, students would read "7 apples" and "3 oranges."

Key Question: What do you wonder about this story??

The teacher records all questions that students generate. Students may still be learning what questions are and how to use question words.
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4. Students work on a question of their or the teacher's choosing.

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The 3-Read Protocol in Kindergarten and First Grade See the 3-Read Protocol General description for more information on this strategy. Many teachers of Kindergarten and First Grade have adapted the 3-Read Protocol for use in their classrooms. Here are some suggested modifications: 1. First Read: Teacher reads the problem stem (story) orally.

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Structured Language Practice Routine Flip Book

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Structured Language Practice Routine Flip Book

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Use the visuals to prompt students on how to share the ideas

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I will add to my math focus wall with a vocabulary chart using either pictoral input chart or process grids.

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I will ask students to create a Learner Profile to help me meet their learning needs.

I will also create vocabulary anchor charts using student input and use sentence frames to provide the language support for ELLs.

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Two for Two strategy with my students needing more time with me
Math: Using more of a variety of math sentence frames and designing more questions and prompts for different proficiency levels.

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I’m inspired to set high expectations for ALL my students by encouraging them and helping them believe they can be successful, and reaffirm them that I do believe they can achieve goals.

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I want to create learner profiles using google classroom, google forms.
I also plan to post sentence frames for math talk and work on teaching the skills to use math talk more successfully.

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Teaching Tools | Resources for Teachers from Scholastic

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A novel about students searching for Pi. I haven't read it yet, but it sounds great.

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Great Fraction Art Project!!

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ed emberley's picture pie (ed emberley drawing books)

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Ed Emberley's Picture Pie (Ed Emberley Drawing Books)

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Ed Emberley's Picture Pie (Ed Emberley Drawing Books) [Ed Emberley] on Amazon.com. *FREE* shipping on qualifying offers. This book shows how a circle, divided like a pie, can be used to make pictures of all kinds. Using just 4 simple shapes

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One of my favorites, great to introduce large numbers and place value.

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Mr. Sandoval: Use a variety of sentence frames for math.

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Mr. Sandoval: Use a variety of sentence frames for math.

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Teachers Pay Teachers

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Number Talk * Number Sense * Mental Math **Graphic Organizer

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This graphic organizer is PERFECT for developing NUMBER SENSE and MENTAL MATH STRATEGIES! It was created to be displayed as my class did our daily number talks. This is how I begin my math lesson. After a few days, the kids caught on and now complete it without me!

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Short videos on growth mindset
https://ideas.classdojo.com/

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Mrs. B Contreras: I am going to try the 2 min. by 10 days with struggling students.

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Mrs. B Contreras: I am going to try the 2 min. by 10 days with struggling students.

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Math Sentence frames and math word bank.

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Establish a joy factor
Use sentence frames
Design questions and prompts for different proficiency levels

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I am going to build a stronger relationship with struggling students by having daily conversations.

Utilize partner talk

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Two by Ten Strategy with my challenge kiddos
Math: Use Sentence Frames/Vocabulary Bank

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Mr. Sandoval: daily confer with two students for 2 minutes. 

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Mr. Sandoval: daily confer with two students for 2 minutes. 

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I'm willing to confer one on one with students to show how much I care about their learning.
I will incorporate more partner talk with students during math.

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Brain Based Learning | Brain Based Experts

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Reflect for a moment on one of your favorite teachers and think about why he/she was your favorite.  Was it the teacher’s:  Fun and engaging environment?  Kindness to you and others?  Belief in you and your achievement?  Calm nature? Care about your personal life?  Care that you learned every single day?  Or a combination of these items?  All of these items are important in building a positive learning culture.

High student achievement needs a positive learning culture.  Positive learning cultures encompass strong relationships built on trust and care among the teachers and students.  Positive relationships among teachers and students are a vital piece in a high-poverty school since poverty can stunt the growth of healthy relationships.  There are so many daily stressors all around these students and their families which can result in less positive communication, support, and time together.  Dr. Eric Jensen, author of Teaching With Poverty in Mind (2009), said, “Not getting the opportunity to form solid attachments initiates a stream of long-term physiological, psychological, and sociological consequences for children…no curriculum, instruction or assessment, however high-quality, will succeed in a hostile social climate.”

The Research about the Power of Teacher-Student Relationships

All kinds of relationships contribute to a positive learning culture:  student to student, caregivers/parents to their children, school staff to school staff, and teachers to students.  This article will focus on teacher relationships with their students, which by the way, will most likely improve the student to student relationships too.  John Hattie, author of Visible Learning: A Synthesis of over 800 Meta-Analyses Relating to Achievement, found that the teacher-student relationship had a .72 effect size on student achievement (FYI – an effect size of .4 and above is highly significant for student achievement).  The research showed that the following teacher skills developed stronger relationships:  listening skills, empathy, mutual respect, caring and positive regard for the students.

Most students who do not wish to come to school or who dislike school is primarily because they dislike the teacher.  Cornelius-White’s research/claim (collected in Hattie’s work) was stated this way: “To improve teacher-student relationships and reap their benefits, teachers should learn to facilitate students’ development, see their perspective, and communicate it back to them so that they have valuable feedback to self-assess, feel safe, and learn to understand others and the content with the same interest and concern.”   There is even research to support the decrease of drop-out rates when there were positive bonds with teachers and students (Lee & Burkam, 2003).

Poor or weak student- teacher relationships can cause any of the following negative effects:  chronic elevated cortisol levels (stress hormone)(which can shrink or kill brain cells and hurt memory skills);  lower-level thinking rather than higher-level thinking; impaired social decisions;  and decrease in desire to learn (Sapolsky, 2005).

When we put forth effort to strengthen and build our relationships with students, there are benefits toward the teachers and the students such as the release of oxytocin.  Oxytocin, a hormone that also acts as a neurotransmitter in the brain, is directly linked to bonding and increasing trust.  Research says it’s the face to face interactions (not texting or Facebook) with humans and “tribal-like” connections around people that release oxytocin.  Hugging, shaking hands, and positive eye contact can actually release oxytocin quickly and the effects can linger for some time afterward.  Snuggling and playing with a pet can produce oxytocin as well (Reason to have a Class Pet that is furry and nice).  Oxytocin has so many benefits like:  staving off many psychological and physiological problems, breaking social barriers, inducing feelings of optimism, increasing self-esteem, overcoming fears, reducing pain, increasing generosity and building trust (Kosfeld, Heinriches, Zak, Fischbacher, and Fehr, 2005).

Last but not least we have two types of systems in our body:  closed-loop and open-loop.  The closed loop system such as the circulatory system is self-regulating and does not affect or impact other’s systems.  On the other hand, the open-loop system can best describe our limbic system or emotional centers of our brain and bodies and can be affected by external sources, like other people.  Research in intensive care units shows one person can actually lower a person’s blood pressure.  Scientists found that one person can transmit signals that can change hormone levels, sleep rhythms, immune systems, and even oxytocin levels of another person.  (Lewis, Amini, Lannon, 2000).  Bottom line, the open-loop system research shows how powerful one person can change another person’s physiology and emotions.

As you can see from these numerous research examples, we affect each other quite a bit – for the positive and the negative.  Read on to find out seven actions that you can take in your classrooms to make a difference in creating a positive learning culture with strong relationships built on trust and care.

Seven Power Actions to Build Positive Relationships with your Students

1. Ask students to help you create the rules and expectations of the classroom so behaviors are managed proactively versus reactively. Students who lack positive, social attachments can show this need through acting out, acting anxious, seeking attention, creating power struggles, and other negative behaviors.  When students help you create these pieces, there is more buy-in.  I actually took the students through a process called the Six Thinking Hats which is a series of 6 different types of relevant questions that formulated the rules for our classroom (email LeAnn at lnickelsen@comcast.net if you want this lesson).  We came up with a beautiful list of rules that were posted and signed by every student.  I saw more ownership, and I could use the line:  “You helped create these rules,” when students were losing the “ownership” of these classroom rules.

2. Set your expectations high for ALL students. High expectations and specific constructive feedback about assignments, efforts, attitudes, strategies, thinking, and skills portray that one cares.  In fact, one study (Coe, 2002) found that teacher expectations had an effect size of 1.03 on student achievement.  The 1968 famous research, Pygmalion Effect or self-fulfilling prophecy, showed that teacher expectations influence student performance.  In that research, the teachers communicated to students that they each had “unusual potential for academic growth.”

3. Establish a joy-factor in the classroom. There is a wonderful feeling when you walk into a classroom that is filled with joyful teachers and students.  Time flies for one.  Secondly, students are actively engaged in relevant, meaningful assignments in small groups. Thirdly, you rarely see the teacher or students sitting for long periods of time.  Finally, they smile much!  They are actually enjoying the learning.  Kids want to return to these kinds of environments where the relationships are flourishing and positive.  Dr. Eric Jensen, author of Engaging Students with Poverty in Mind,  says  that every classroom needs to establish a “We are Family” mindset.  Families take on each other’s problems, help give ideas to solve some of the problems, hold each other accountable for goals that need to be completed, and encourage kindness among the members to keep the peace.  John Hattie’s research shows that group cohesion and peer influences have a strong .53 effect size on student achievement (Hattie, 2009).  Social bonding and trusting one another can decrease the negative side effects of chronic stress by priming the brain to release oxytocin, a neuropeptide that suppresses the cortisol stress hormone. (Kosfeld, Heinriches, Zak, Fischbacher, & Fehr, 2005; Leuner, Caponiti, & Gould, 2012).
I love being in classrooms where students and teachers are laughing and learning at the same time.  Laughter is hard to fake and is highly contagious – it involves highly complex neural systems that are largely involuntary.  Research shows that laughter is the most direct communication possible between people (brain to brain; chemical to chemical).  Could we say, the amount of laughter, smiles, and joy we see in a classroom could be a way to measure the relationships in that classroom?  People who relish each other’s company laugh easily and often.  The relationships where there is little trust often have the least amount of laughter among them.

4. Build trust among the students. Trust is the foundation of all strong relationships.  Trust is a big concept and when you break it down, you will find the following components:  being present, doing what you say you will do, being aware of others, keeping information confidential, not talking badly about anybody (if you do, you might be looked upon as possibly talking about that student behind his/her back), being open and real, listening without judging, showing empathy, and honoring the person and friendship process.  Trust takes time and is built with almost every big and small interaction with others.

5. Care about each student. Differentiate by pulling a small group of students in order to respond to daily data.  A data-driven classroom shows that the teacher cares about each student attaining the learning goal.  When teachers confer with students one-on-one during guided reading, writing workshop, guided math, or after tests, it conveys that the teachers care about growing that one student with specific needs.  What if every teacher set a goal to confer with 2 students for 2 minutes every day?  That 4 minute investment will shock each teacher.  Can you imagine the growth that could occur in that classroom because of the specific feedback that was given to those 2 students about where they are with the standards and how they can better get to those standards?  It’s the teacher listening, sharing the data with the students, and giving feedback on how to achieve the goals.
I was once told by one of my students after reteaching him a math concept in a small group of about 5 students:  “Mrs. Nickelsen, you are a much better teacher with a small group of students.”  I was not quite sure how to respond, except I chose to take it as a compliment.  He was right!  I think ALL teachers are better with smaller groups of students when targeted instruction occurs because errors were studied, analyzed and the next steps were determined to help students understand the learning goal.  That action shows care, concern and let’s-close-gaps attitude.

6. Ask students to create a Learner Profile that will explain how they learn best, their interests, feelings and attitudes about the content areas. This Learning Profile is a file folder designed by each student that is full of surveys, interest inventories, attitudes about subjects, preferences for learning styles, multiple intelligences assessments, and other content that explains who that student is socially, emotionally, physically and academically.  In the book, Deeper Learning (2008) by Eric Jensen and LeAnn Nickelsen, there are several pages dedicated to how to create this file folder for each student.  This book has samples of reproducibles that you can use, website suggestions so students can do the inventories on-line, and examples.  We can use this information to help us meet their learning needs better but to also form stronger relationships.For example, the research called 2 x 10 (Two-by-Ten) shows that by listening to your most challenging students talk about their personal lives or about whatever that student wants to talk about for just 2 minutes every day, 10 days in a row (obviously you can skip weekends), then you can get to know that student well enough to make a huge difference in his/her behavior.  Raymond Wlodkowski found an 85-percent improvement in that one student’s behavior. In addition, he found that the behavior of all the other students in the classroom improved.  By the way, don’t take Raymond’s word on this – try it out soon with one of your most challenging students.  Remember, there is a reason for every misbehavior (even in adults).  Use the information from the Learning Profile to help you ask questions about that student’s personal life.

7. Put on a growth mindset (see LeAnn Nickelsen’s article) and assume the best in all students.  Author of the book, Conscious Classroom Management, Rick Smith, said that we should glue to our brains the “invisible contract” when kids walk into our classrooms every day:
“Whenever students walk into the classroom, assume they hold an invisible contract in their hands, which states, ‘Please teach me appropriate behavior in a safe and structured environment.’ The teacher also has a contract, which states, ‘I will do my best to teach you appropriate behavior in a safe and structured environment.’”

Rick further explains in his article (2008), “The bottom line is that when students test us, they want us to pass the test. They are on our side rooting for us to come through with safety and structure. When students act out, they are really saying, ‘We don’t have the impulse control that you have. We are acting out so that you will provide us with safety and structure—be soft yet firm—so that we can learn the behavior we need to learn to be happy and successful.’”

When you assume the best in your students, they lose their labels such as:  Nancy is the angry girl; Raoul just checks out all the time; Shane is the class clown; and Latoya is the aggravator. We see them a unique individual that has certain needs at certain times, and they are each worth our time to get to know and understand.  This mindset will help us own the thought that when students act out, they are really telling us they need and want a positive connection. When this mindset is in place, the “discipline moments” are seen as opportunities for teaching an essential piece that students want to learn.

Conclusion

Bottom line:  Your relationships with each student in your classrooms make a dramatic impact on their ability to learn well.  When students engage in positive teacher-student relationships, they:  adjust to school more easily, want to attend school, view school as a positive experience, exhibit fewer behavior difficulties, display more positive social skills, and demonstrate higher academic achievement (Buyse, Verschueren, Verachtert, and Van Damme, 2009).

My favorite saying that was printed in beautiful ink, framed and placed on my desk as a daily reminder of my power to build or break apart the relationships in my classroom is how I want to conclude this article.  It’s a powerful statement that I hope you don’t forget, but our moods influence how effectively people work – upbeat moods boost cooperation, fairness and achievement.

I have come to a frightening conclusion.  I am the decisive element in my classroom.  It is my personal approach that creates the climate.  It is my daily mood that makes the weather.  As a teacher, I possess tremendous power to make my student’s life miserable or joyous.  I can be a tool of torture or an instrument of inspiration.  I can humiliate or hurt, humor or heal.  In all situations, it is my response that decides whether a crisis will be escalated or de-escalated, and my student humanized or de-humanized.

Adapted from Haim Ginott

Resources:

Buyse, E., Verschueren, K., Verachtert, P., and Van Damme, J. (2009).  Predicting school adjustment in early elementary school:  Impact of teacher-child relationship quality and relational classroom climate.  Elementary School Journal, 110(2), 119-141.

Coe, R. (2002, September 12-14).  It’s the effect size, stupid:  What effect size is and why it is important.  Paper presented at the annual Conference of the British Educational Research Association. University of Exeter, England.

Cornelius-White, J. (2007).  Learner-centered teacher-student relationships are effective:  a meta-analysis.  Review of Educational Research, 77(1), 113-143.

Hattie, John. (2009).  Visible Learning:  A Synthesis of Over 800 Meta-Analyses Relating to Achievement.  New York, NY:  Routledge Taylor & Francis Group.

Jensen, Eric. (2013).  Engaging Students with Poverty in Mind.  Alexandria, VA:  ASCD.

Jensen, Eric. (2009).  Teaching with Poverty in Mind.  Alexandria, VA:  ASCD.

Jensen, Eric and Nickelsen, LeAnn. (2008).  Deeper Learning:  7 Powerful Strategies for In-Depth and Longer-Lasting Learning.  Thousand Oaks, CA:  Corwin Press.

Kosfeld, M., Heinriches, M., Zak, P., Fischbacher, U., & Fehr, E. (2005).  Oxytocin increases trust in humans. Nature, 435(2), 673-676.

Lee, V. & Burkam, D. (2003).  Dropping out of high school:  The role of school organization and structure.  American Educational Research Journal, 40(2), 353-393.

Leuner, B., Caponiti, J.M., & Gould, E. (2012).  Oxytocin stimulates adult neurogenesis even under conditions of stress and elevated glucocorticoids.  Hippocampus, 22(4), 861-868.

Levenson, Robert and Ruef, Anna.  (1997).  Empathic Accuracy.  New York:  Guilford Press.

Lewis, Thomas, Amini, F., and Lannon, R.. (2000). A General Theory of Love.  New York:  Random House.

Provine, Robert. (2000).  Laughter:  A Scientific Investigation.  New York:  Viking Press.

Sapolsky, R. (2005). Sick of Poverty. Scientific American, 293(6), 92-99.

Smith, Rick and Mary Lambert.  (September 2008).  The Positive Classroom.  Educational Leadership. Volume 66; Number 1; Pages 16-21

Wlodkowski, R. J. (1983). Motivational opportunities for successful teaching [Leader’s Guide]. Phoenix, AZ: Universal Dimensions.

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7 Powerful Actions You Can Take To Improve Relationships with Your Students - Brain Based Learning | Brain Based Experts

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Reflect for a moment on one of your favorite teachers and think about why he/she was your favorite. Was it the teacher’s: Fun and engaging environment? Kindness to you and others? Belief in you and your achievement? Calm nature? Care about your personal life? Care that you learned every single…

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Preschool teacher Jennifer Hawkins has her students perform an emotional check-in at the beginning of the day by having them identify their current emotions. Students put popsicle sticks with their names on them in jars labeled with different emotions. This helps students to identify their emotions and helps Jennifer know what her students are feeling.

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by Eric Carle

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children's / teenage fiction & true stories

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juvenile fiction / concepts / date & time

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juvenile fiction / concepts / size & shape

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juvenile fiction / social themes / manners & etiquette

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juvenile fiction/social themes - manners & etiquette

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eric carle; carle; grouchy ladybug; ladybugs; animals; manners; sharing; please; thank you; books about manners; books about manners for kids; books about animals for kids; books about sharing for kids; bugs; classic books; classic books for kids

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juvenile fiction / concepts / date & time

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juvenile fiction / concepts / size & shape

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juvenile fiction / social themes / manners & etiquette

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juvenile fiction/social themes - manners & etiquette

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children's / teenage fiction & true stories

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From Eric Carle, New York Times bestselling author of The Very Hungry Caterpillar and From Head to Toe, comes the classic story of one very grouchy ladybug. Eric Carle's bright artwork and signature style will charm both ardent fans and new readers alike. As children follow the Grouchy Ladybug on...

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Access Google Drive with a Google account (for personal use) or Google Workspace account (for business use).

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Multiplying
9s

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9 Times Tables Song For Kids | Multiply and Skip Count by 9

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Fractions Song For Kids | 2nd Grade - 3rd Grade

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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)

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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Count to 100

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Let's Get Fit | Count to 100 by 1's | 100 Days of School Song | Counting to 100 | Jack Hartmann

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One Two Buckle My Shoe
Magana Kinder

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LaPrelle Kindergarten "The Doorbell Rang"

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Monique LaCour explains how she uses sentence frames to support academic conversation in her math classroom. She shares how these frames are especially helpful for English Language Learners.

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In the 1970s, Albert Bandura, a psychologist at Stanford University, uncovered an interesting pattern in working-group dynamics. He observed (1977) that a group's confidence in its abilities seemed to be associated with greater success. In other words, the assurance a person places in his or her tea

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Discussion and Supporting Materials

Thought starters

1. Why is it important for students to talk it out before writing?

2. What supports are in place to help students write out their ideas?

3. Why is this an especially effective strategy for English Language Learners?

School Details

Banting Elementary School
2019 Butler Drive
Waukesha WI 53186

Data Provided By:

Teachers

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My Thinking Logs: A Literacy Practice for Math

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Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Why is it important for students to talk it out before writing?

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Math Read Alouds for introducing, or reviewing mathematical content in meaningful contexts, while simultaneously promoting high levels of student engagement.

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Are you searching for an easy way to "hook" your kids into your newest math lesson? Or maybe you want to make a math concept more relatable. One of the first things that pops into my mind when brainstorming new ways to introduce a new math topic is: "Which book should I read?"

Surprised? Of course, math is my favorite content area, BUT there are many positives to integrating reading and writing strategies into your math block.

There are so many cool math-themed books out there that focus on math topics like addition, geometry, fractions, and more!

But wait...I almost forgot the best part of using read-alouds to teach math. Extension activities! After students are familiar with the book, drop it in a math station with a follow-up activity. Can't think of any? Use the ones listed below as a starting point.

Here are some of my favorites math read-alouds listed by skill:
Book Title: The Crayon Counting Book
Best for: Kindergarten and 1st Grade

What I like most about this book is the use of crayons for counting. Young kids LOVE crayons and which makes this book even more relatable.

Extension Activity: This tip is only if you have a second book. I can't believe that I am about to say this but tear out the pages of the book (I'm sorry to all the media specialists) and laminate them. Then let students count the number of crayons on the page.

If you don't want to have any part of a book massacre, get a real box of crayons and a set of number cards. Let students pick a random card and then count out the same number of crayons.

Addition and Subtraction

Book Title: 12 Ways to Get to 11

Best for: Kindergarten - 2nd Grade

This book says yes to multiple representations in a big way. Use this to reinforce composing and decomposing numbers. I like to use magnets (shout out to Target) on a magnetic whiteboard to represent how the number eleven is broken apart in each one of the examples. This is a great opportunity for a math talk. For more advanced students, practice writing the equations that match.

Extension Activity: Give students manipulatives (snap cubes, color tiles, buttons, etc.) and let them try to decompose a given number as many ways as they can. They can draw their findings and more advanced students can write the matching equations.

Multiplication and Division

Book Title: One Hundred Hungry Ants

Best for: 2nd - 3rd Grade

Yet another book that helps show multiple ways to represent a number. And it's funny! In the book, the ants keep changing their marching formations which end up being different arrays.

Extension Activity: Change the number of ants and let students show all the different ways that the ants could have marched to the picnic area. Allow kids to create math models and write equations.

Book Title: The Great Divide

Best for: 3rd - 5th Grade

This fun book focuses on a larger team of racers that keeps getting split into 2 groups. There is also a little surprise ending that offers a great opportunity to teach about remainders.
Book Title: If You Were a Fraction
Extension Activity: Provide students with large numbers. Let students keep separating them into smaller groups. Choose numbers that have remainders and ones that do not have remainders. Then let them sort the numbers into two groups (Remainder and No Remainder).

Best for: 3rd - 5th Grade

I LOVE the way this book is intentional about the use of math vocabulary. I have found that many of our kids struggle with understanding what fractions represent and don't know how to express parts of a whole. This book presents different scenarios where students visualize themselves as "the fraction."

Extension Activity: Make this book come to life by having your kids act out the different scenarios that are presented on the pages and use the math vocabulary.

Book Title: Fraction Fun

Best for: 3rd - 5th Grade

This book is great to use but very information heavy, so I recommend breaking it up into parts or only using the sections that you need for your specific lesson. There are sections about parts of a whole, weight, money, and more.

Extension Activity: There is actually an activity that is described in the book that would be a great activity for math centers. It involves using a paper plate and dividing it into equal parts.

Book Title: The Shape of Things

Best for: Kindergarten - 1st Grade

Awesome book for teaching shapes and examples of shapes in real life. Each scenario starts off with a regular shape and then it becomes part of a larger picture. You can get real creative and ask some good questions when reading this one to your kids.

Extension Activity: This book serves as a great model for a class book. Have your kids recreate new scenarios with shapes and keep the same wording (Ex. A square is just a square until ......)

Book Title: The Greedy Triangle

Best for: 2nd - 3rd Grade

Fun story about an unsatisfied triangle (maybe having a mid-life crisis? LOL) that transforms into other shapes. Since his looks change, it can lend to a good discussion about shape families and characteristics.

Extension Activity: Let students use toothpicks to make shapes. They can change their Greedy Triangles into all of the shapes he transformed into in the book and record the different shape characteristics (sides, angles, etc.)

Book Title: The Coin Counting Book

Best for: Kindergarten - 2nd Grade

Clean and clear photos of coins with nice visual representations of adding coins that include coin names and amounts. These photos help reinforce using skip counting when adding money.

Extension Activity: There are two pages at the end of the book with photos of coins and missing amounts. Have students write equations that match the photos. For more practice have students use real coins or fake money and create their own coin scenarios.

Book Title: Alexander Who Used to Be Rich Last Sunday

Best for: 2nd - 3rd Grade
Book Title: Piece=Part=Portion
A teacher's favorite. Alexander starts off rich, and you can guess the rest from the title. (I understand Alexander. I have been there before too.) This is a good story for teaching different subtraction strategies like counting up, expanded form, bar model, and more.

Extension Activity: Have students work in partner pairs. Let them create their own real-world money problems using the names of classmates. Then let their partner solve it.
Book Title: Telling Time
Best for: 4th- 5th Grade

What I like best about this book are the real-life photos (i.e. a traffic light, and soda cans) that show real-world examples of fractions, decimals and percents.

Extension Activity: This is a great opportunity for your students to brainstorm other real life representations of fractions, decimals and percents. Give them a camera and let them hunt for some in the classroom. You may be surprised at what they find.
Book Title: Inch by Inch
Best for: Kindergarten - 3rd

This informational book is a nice overview of all things time. Seconds...Minutes...Hours...Days of the Week...Months...Years...Digital...Analog!

Extension Activity: Throughout the book, there are multiple questions for students to answers. As an extension, I would just put out some more problems with some clock manipulatives. Or have students use clock manipulatives to represent times that are written on sticky notes.

Measurement

Best for: Kindergarten and 1st Grade

A little inch worm talks his way out of certain death and measures his way to safety. Kids love this book, so why not use it to introduce measurement?
CLICK Here to Download the FREE List of the Books!
Extension Activity: This is such a popular book. It's an award-winner, after all. Use colorful inchworm rulers or make your own and let students measure things around the room. Don't forget to have them record their findings.

Book Title: Measuring Penny

Best for: Kindergarten - 5th Grade

Like Fraction Fun, this book is jam-packed with information making it a great book to use when introducing new topics. Again, I would recommend only reading the pages that you need.

And we are at the end. I hope you enjoyed reading about my Top Read Alouds for Teaching Math. Be sure to download my list of top math read-alouds because there are some additional books that I didn't mention in this post.

Greg

** If you are interested in any of these books I included an Amazon Affiliate link to each one. FYI, if you purchase something through an Amazon link, I get a small commission at NO extra cost to you. This helps me keep the site going so that I can share more and more math tips and ideas with my Math Fam!

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14 Math Read Alouds and Extension Ideas for Elementary Kids - Mr Elementary Math

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Searching for ways to get kids interested in a new math topic? Check out my Top Math Read Alouds for elementary kids. Plus try these simple math activities.

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Bring multiplication concepts to life with these multiplication read alouds and follow up problem solving activities.

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Books shelved as math-read-alouds: One Grain Of Rice: A Mathematical Folktale by Demi, Zero the Hero by Joan Holub, Working with Fractions by David A. Ad...

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Reading and Understanding Written Problems

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Reading and Understanding Written Problems

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Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation. Many ELLs may have difficulty reading and understanding the written content in a word problem. If a student is learning English as a second language, he might not yet know key terminology needed to solve the equation. In other words, ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered (Bernardo, 2005). For this reason it is recommended that students learn key terminology prior to attempting to solve mathematical word problems.

Key Benefits

Once English language learners know the key terminology used in mathematical word problems, it will be easier to learn how to write numerical equations. It is important for teachers to provide ELLs with opportunities to learn and practice key vocabulary words.

While key words are very important, they are only part of the process. Understanding the language in word problems is critical for all students. They need to know the meaning of words. But because words are often used differently and problems are set up differently, there are some cautionary messages. Here is an example of problem that uses "fewer than" to set up a subtraction equation.

Maria has 24 marbles which is 8 fewer than Paolo has. How many marbles does Paolo have? If we were to only focus on using key words, "fewer than" is a signal to pick out the numbers and subtract. The student may immediately make the conclusion that the answer is 16, but that is not what the problem is asking, and the child would be wrong. (The correct answer, by the way, is 32).

What research has found is that if we ask students to only rely on knowing that certain key words signal specific operations, we can actually lead them away from trying to understand the problems. They will tend to look only for those words and whatever numbers are in the problem, even if they are not relevant to the answer. This will not help them be mathematically proficient later, even when they are proficient with English.

Although the finding on key words was done with regular students, the consequences for ELL students of relying on them is the same. They would not be able to solve the problem above. However, if teachers follow the suggested process of reading a problem several times (at lower as well as upper grades) and discussing what it means, students will understand. Another good tool is to teach them to draw or model the problems. To illustrate the problem above, you could state: "Here's Maria's 24." Then, draw 24 units, figures, shapes, etc. to represent 24. "Here's Paolo's; he has more because Maria has fewer than he does". Draw 24 units, figures, shapes, etc. to represent 24 and add 8 more. "So Paolo's has to come to more than 24. How many more? 8. So what is Paolo's total?"

The difference is between knowing the meaning of the words "fewer than" and using "fewer than" as a key to an operation. We want students to know the meaning of the words, but also to see them in the context of the whole problem.

Suggested Activities

Lower Grades

Practice problem solving daily by simply asking more questions. For example:

How many students brought their homework today?

How many more children brought their homework yesterday?

We had 8 markers on the board, but now we only have 3. How many did we take away?

How many animals are there in this magazine? How many are mammals? How many are birds? (introduction to fractions and percentages)

Continue to use key terminology daily and put it in context (e.g., less than, more than, difference, times, each, etc.). Show students how easy it might be to misunderstand the problem.

Upper Grades

Read word problems slowly and carefully several times so that all students comprehend.

If possible, break up the problem into smaller segments.

Allow students to act out the word problems to better comprehend what they are being asked to solve.

Provide manipulatives to help students visualize the problem.

Take field or walking trips to figure out distances, speed, area covered, etc.

Ask students to do surveys, interviews, hands-on research in real-world situations to figure out percentages, differences, and higher-order math skills.

Allow students to make drawings or diagrams to help them understand problems.

For more ideas that can be used to support math instruction in the ELL classroom, take a look at Math Instruction for English Language Learners and this related resource section.
Everything ESL: Challenges for ELLs in Content Area Learning
This article provides an overview of the challenges ELLs face in their content-area classes, such as math, science, and social studies. Understanding these challenges will help both ELL and content-area teachers adapt instruction for ELL students.
National Center for Research on the Educational Achievement and Teaching of English Language Learners
The National Center for Research on the Educational Achievement and Teaching of English Language Learners (CREATE) is a research program designed to improve educational outcomes for ELLs by using a combination of strategies focused on readers in Grades 4-8 and teacher professional development. The CREATE Web site includes webcast seminars hosted by CREATE researchers, and listings of CREATE conferences and presentations around the country.
TeacherVision: Word Problem Resources for Teachers
TeacherVision offers lessons, printables, and quizzes to support math word problem instruction for grades K-12.
Translating Word Problems
This is a great site for teachers in the elementary levels, as it provides a list of keywords you can teach your ELLs to look for as they read word problems. Also included are useful ideas and tricks to better prepare students to understand written math problems.

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Reading and Understanding Written Math Problems

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Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation. Many ELLs may have difficulty reading and understanding the written content in a word problem.

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My dad gave me one dollar bill
'Cause I'm his smartest son,
And I swapped it for two shiny quarters
'Cause two is more than one!

- Excerpt from "Smart," by Shel Silverstein

As a student, I struggled with math. I didn't understand why it came so naturally to some students, but not to me. Looking back, however, I realize that I had an advantage that I wasn't even aware of - I understood the language in which the problems were written, even if I didn't understand how to solve them! Although it is easy to assume that many English language learners (ELLs) will excel in math because math is a "universal language" and students may have had prior educational experience that included mathematical instruction, that assumption can lead educators astray.

As I spoke with teachers and did research for this article, it became very clear that making sure that students understand math vocabulary and have ample opportunities to use it are very important. Solving word problems, following instructions, understanding and using mathematical vocabulary correctly - all of these skills require a language proficiency that sometimes exceeds our expectations. We tend to think of mathematics as a subject that does not require a strong command of language. In reality, however, mathematical reasoning and problem solving are closely linked to language and rely upon a firm understanding of basic math vocabulary (Dale & Cuevas, 1992; Jarret, 1999).

For many educators, the challenge of bringing language and math instruction together is a relatively new one. ELL teachers who hadn't taught content areas previously are now being asked to lead or support instruction in the math classroom, and many math teachers who don't see themselves as language instructors are now responsible for providing effective math instruction to ELLs.

High school math teacher Hillary Hansen learned just how big a role language plays in math instruction when she taught her first Basic Math course for ELLs last year. She wanted so much to provide the students with the good foundation they needed, but she felt unable to reach the students or engage them in her lessons, and by the end of the year she was exhausted and frustrated.

That summer she had an opportunity to join a district Sheltered Instruction Observation Protocol (SIOP) cohort to receive professional development and support to meet the needs of ELLs in content classes. She learned about the importance of language acquisition, building background knowledge, increasing student language production, and explicitly teaching academic language. She began this school year with a new set of tools and a deeper understanding of the instructional scaffolding ELLs need in order to learn the content while also learning English. I am happy to report that while Hillary still feels challenged and is working very hard, this year has been much more successful for her and her students.

As a result of more effective instruction, her students:

understand the content better and are working together to find creative ways to learn

discuss math more and know how to use the instructional supports their teacher has in place

are comfortable with math and asking questions to get the help they need.

Hillary feels that she is providing them with the foundation they need not only to understand the mathematical concepts, but also to successfully interact within a math classroom in order to continue learning more advanced concepts.

Following are some strategies that Hillary and some of the other teachers I spoke with found helpful this year, and that they recommend as best practices when teaching math to ELLs.

The importance of teaching academic vocabulary

Vocabulary instruction is essential to effective math instruction. Not only does it include teaching math-specific terms such as "percent" or "decimal," but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word.

The following example, used in a presentation by Dr. Judit Moschkovich of the University of California at Santa Cruz, underscores why vocabulary must be introduced within the context of the content (Moschkovich, 2008):

In this problem, the student is instructed to "find x." The student obviously knew the meaning of the word "find" because he/she "found" it on the page and circled it. The student even put a note on the page to help the teacher in locating the lost "x". The student understood the meaning of "find" in one context, but not in the appropriate mathematical context.

I recently helped a math teacher create a Sheltered Lesson, and I was surprised to find that there were some vocabulary words that I didn't understand. My lack of familiarity with the words hindered my ability to do the math problem and gave me a deeper empathy for ELLs who struggle in the same way with vocabulary and comprehending math assignments. Following is a list of tips for explicitly teaching mathematical academic vocabulary:

Demonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words such as "table" and "quarter," as well as how to use them correctly in a mathematical context.

Encourage students to offer bilingual support to each other. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language. (Check the hotlinks for a list of bilingual translations of math vocabulary in multiple languages).

Provide visual cues, graphic representations, gestures, realia, and pictures. Offer students the chance to work with objects and images in order to master vocabulary. If there aren't enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students. For example, Hillary created a Math Word Wall that has three parts: key vocabulary, "in your own words" definitions, and a variety of ways to portray a function. For example, multiplication is portrayed by the following symbols: x, *, and ( ).

Identify key phrases or new vocabulary to pre-teach. This strategy will help students decide which math function they should apply. Example: "more than" means "add." (See hotlinks for more references about math vocabulary.)

The importance of reading and understanding written math problems

Written word problems present a unique challenge to ELL students and teachers alike. In Reading and Understanding Written Math Problems, Brenda Krick-Morales writes, "Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation - ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered" (Bernardo, 2005).

Teacher Xiao-lin Yin-Croft has encountered this pattern in her classroom of bilingual Chinese students in San Francisco. She has developed a very creative way to use her students' background knowledge of math as a stepping stone for other language learning. She does this by accelerating math instruction at the beginning of the school year and then building on what students have learned in math in reading and other content areas. In Building Bridges for the Future, a Colorín Colorado "From the Heart" article, Xiao-lin explains her strategy:

First, we read math word problems; I demonstrate the logical thinking process while translating words into pictures and, finally, into number sentences. Soon, they start to explain their own thinking after reading complicated word problems that involve several steps. They correct each other, and argue about which number sentences they should use to arrive at the correct final results. As they sharpen their math skills, I capitalize on their enthusiasm to teach them how to extract the most important information from texts, and move them toward the oral and reading fluency they need to understand and discuss more challenging texts.

Even if you aren't accelerating math instruction, however, there are a number of ways to help students master word problems. Krick-Morales offers suggestions in the previously mentioned article, such as explicit instruction of key vocabulary, daily practice of problem solving, repeated readings of the word problem together as a class, and hands-on activities such as movement, experiments, or drawing to help students comprehend the problem. As students become more familiar with math vocabulary, they will be able to solve problems more easily.

The importance of building background knowledge

As the opening quote from the Shel Silverstein poem reminds us, background knowledge plays a critical role in math class! My colleague Hillary found that sometimes her students would get "lost" in a problem simply because they didn't understand the context. Following are some tips to help in building background knowledge of students.

Modify the linguistic complexity of language and rephrase math problems. Students will understand the problem better if it is stated in shorter sentences and in language they understand.

Guide students to cross out the unnecessary vocabulary in word problems. Doing so allows students to focus on the math function required. For example, one problem Hillary's students came across referred to a "school assembly." Even though the meaning of that phrase wasn't important in the solving of the math problem, students didn't know it wasn't important, and the lack of understanding contributed to their confusion.

Build knowledge from real world examples. Try to reinforce concepts with examples that students can picture and talk students through the situation. For example, if you need to paint a room, you need to know how much area will be covered so that you know how much paint to buy. Look for familiar ideas or props that can be used to engage students such as recipes, news stories about the economy, or discussion of personal spending habits.

Use manipulatives purposefully. This is important at all grade levels. Hillary has found math cubes to be very useful in having students represent the numbers in the problems and then manipulate the cubes to get the answer. She used the cubes and the terms "hot" and "cold" numbers when teaching with the concept of negative numbers. Students would use the red cubes as "hot" or positive numbers and the blue cubes as "cold" or negative numbers. As students laid out the number of hot cubes and cold cubes represented, they could easily see if the answer would be a positive or negative number by which color had the most cubes. A problem such as -2 + 1 = -1 would look like this:

The student then removed pairs of cubes - one red, one blue - until they could no longer remove any blocks. The remaining blocks represent the answer.

The importance of increasing student language production in the content area

As I've worked with content area teachers in my district to develop Sheltered Instruction lessons and activities to enhance ELL learning, I've told them, "If a student doesn't say it in your class, they're never going to say it." This is a bit dramatic, but it's true to some extent. When students learn new vocabulary, the opportunity to use it must be presented in class, because students are unlikely to try it out on their own - especially academic words like "parallelogram" or "function"!

Here are some tips to increase student-to-student interaction with academic language in the math classroom:

Have students translate symbols into words, and write the sentence out. Hillary used this strategy to check students' comprehension of problems before they solved them. For example, 3x + 4 = 16 would be written out, "Three times X plus four equals sixteen." This helps students process the operations involved in the question and gives them an opportunity to think through how to solve it. It also gives students a chance to familiarize themselves with important vocabulary words.

Create a "sentence frame" and post it on the board. Write the format of the sentence you would like students to use in discussion and then hold them accountable for using it. For example, "The answer is _______ degrees because it is a _________ triangle.

Have students share problem-solving strategies. This involves asking a simple question such as, "Did anyone else get the answer in a different way?" Then allow enough wait time so students can think through how their problem-solving process was similar or different to the one offered.

Allow students to discuss how they are thinking about math. This is a way of redirecting the lesson from teacher-to-student to student-to-student. For example a student might ask a question, "How do you know what kind of triangle it is?" Instead of the teacher answering and going to the board and pointing out the names and different triangles, the teacher can simply ask, "Does someone have an answer? Or "Would someone like to offer help to Mario?" Allow students to share how they think about the math concept and any tips they have for remembering the information.

Incorporate writing activities like math journals. This is an excellent way for students to process what they've learned and what questions they still have. The journal could start with simple prompts such as, "One thing I learned today..." "One thing I still don't understand..." "One way I can get the help I need..." "The answer to this problem is..." Writing out the answer to a problem is a very important skill to develop because many state math tests require a constructed response to questions.

Challenge students to create their own math problems. This can be a fun activity if students create a problem similar to the ones you have used in class and they exchange problems with a partner. By creating the problem and checking the answer they are reinforcing their own learning.

Using technology

Technology can also be a powerful tool in math instruction for ELLs. Here are some ideas ways you can play with technology in a math lesson:

Look for educational resources that accompany your school's technology tools and programs. There may be online or software programs available for teachers. For teachers who have an electronic whiteboard in the classroom, there are many resources available on links that can be easily accessed and brought into the classroom.

Look for interactive games that offer students a chance to practice their mathematical skills. Nintendo DS has an educational game called Brain Age, which is not language specific. The game provides excellent mathematical training for numbers and tracks results, showing student improvement over time.

Find out what's available online. Vital NY (Video Teaching and Learning for NYS Educators) on Teachers' Domain offers an online library of free media resources from the best in public television. Teachers' Domain resources include video and audio segments, Flash interactives, images, documents, lesson plans for teachers, and student-oriented activities. (Free registration required.)

If students are using a graphing calculator, ensure that they learn how to use it. Based on background and prior educational experience, students might not be familiar with how to use a calculator nor some of the more sophisticated models, such as the graphing calculator. Give students a chance to practice solving problems with their calculators once you have reviewed different functions. Texas Instruments offers numerous activities and product tutorials in their educational materials.

Even if it doesn't come easily at first, there are ways to get ELLs excited about math. By keeping their language skills and needs in mind when planning mathematical instruction (and by helping your colleagues do the same), you will be taking important steps in helping students master mathematical concepts and skills - and who knows? Your students may be the next generation of economists, rocket scientists, and math teachers just waiting for the tools they need!

Note: I'd like to thank my Minnesota colleagues, Hillary Hansen at Burnsville Senior High School and Kim Olson at Hidden Valley Elementary, as well as Xiao-lin Yin-Croft from San Francisco, for providing many of the helpful math teaching tips in this article. It is inspiring to know that there are talented, creative teachers who are always finding better ways to teach and are willing to share the knowledge.
Common Core Math and ELLs: Blog Posts
These posts from our Common Core blog highlight resources that can be used in Common Core math instruction for ELLs.
EngageNY: Common Core and Math
The EngageNY website provides materials focused on curricular examples, standards for mathematical practice, and other materials for professional development.
Discovery Education: Puzzlemaker
Puzzlemaker is a free puzzle generation tool for teachers, students and parents where users can create and print customized word search, criss-cross, math puzzles, and more using their own word lists.
Catherine Snow: Word Generation
Catherine Snow's new website provides information and resources for educators who would like to learn more about Word Generation and how it is implemented. Includes links to comprehensive academic word list that students need to master to comprehend academic content.
Dave's Math Tables: English/Spanish Dictionary
List of English math vocabulary words with the Spanish equivalent.
PBS Teachers: Math Lessons
PBS Teachers offers a database of multimedia math lessons and activities that can be searched by grade or topic.
SMART Notebook Lesson Activities
Browse lesson activities and materials for classrooms using SMART notebook software. Choose the country or region, and search by curriculum standards, subject and grade level.
Colorín Colorado Webcast: English Language Learners in Middle and High School
This webcast features Dr. Deborah Short and discusses effective instructional strategies for teaching English language learner students in middle and high school, such as the SIOP model.
Translating Word Problems
This is a great site for teachers in the elementary levels, as it provides a list of keywords you can teach your ELLs to look for as they read word problems. Also included are useful ideas and tricks to better prepare students to understand written math problems.

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Math Instruction for English Language Learners

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My dad gave me one dollar bill'Cause I'm his smartest son,And I swapped it for two shiny quarters'Cause two is more than one! - Excerpt from "Smart," by Shel Silverstein As a student, I struggled with math. I didn't understand why it came so naturally to some students, but not to me.

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Inspire ALL Students with Open, Creative Mindset Mathematics

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Universal Access Chapter Math Framework 

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Universal Access Chapter Math Framework 

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Macarena Count to 100 - Learning with Music - Macarena Count to 100

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Rhyme Desk--interactive writing tool for poets, songwriters, and creative writers 

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Rhyme Desk--interactive writing tool for poets, songwriters, and creative writers 

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The most extensive dictionary of perfect and near rhymes. Mobile friendly.

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Use math journals and interactive notebooks to help students learn and practice their skills. Increase the amount of time in these to help students "show your work." Here are some interactive and foldable ideas to make journaling and notebooking interactive to use for showing examples in different ways, illustrating a concept and defining math terms.

Give math practice to students that is meaningful and reflects their learning by using these tips on your Common Core curriculum. Have another way to show math work? Tell us by uploading your tip to the Teach Junkie community. We can't wait to see your lesson ideas.

When you use pieces that move, expand, fold, etc... you are creating a novel set of materials and adding function. Students will remember the way specific foldables work and use those to associate memories and content with, increasing the likelihood of applying what they've learned!

Swivel Book - Take this swivel book for example. It's a great way to illustrate a multi-step process. This teacher uses it to illustrate the order of operations, but oyu could easily adapt the idea to even how to solve word problems. When students create the steps they are engaged in breaking down the process of figuring out the math skill.

Pockets - Use paper to create built-in pockets right into a math journal. These are exceptional ways for older students to keep small materials at hand and keep it interesting. When they help create the pocket and what goes inside they take ownership over showing their work.

Be Choosy - Use Portions of Worksheets

You don't have to use every inch of a worksheet. When you find a great example, illustration or diagram - use it! Use difficult drawings or exact models when measuring from a worksheet, but don't define the way they use it by limiting their space to show their thinking with the rest of the worksheet.

Symmetry - Use this example of free symmetry worksheets. You could easily cut portions out and paste them into a journal. Students could fold and glue half of the shapes down, illustrating the lines of symmetry with folding. Then use the space surround their shape in their journal to write about why both sides are symmetrical. Most often, worksheets don't include a lot of room to write or explain in a way that makes sense to the individual student, so give them the freedom (and expectation) to do so in their journal around the worksheet pieces. {Free downlaod}

We all learned in our first education class that there is value in divergent thinking. So, get your students showing their thinking and work using a variety of ways in their journals.

Showing Examples in Different Ways - Here is a sample of how you could give the expectation to your students of illustrating a concept in 4 different ways. Create a master example or anchor chart and then let them use one page for each, or turn this into a foldable that will be memorable related to the concept you're teaching. Keep it glued in next to other examples or in-class examples that they've used to refer to and use as their own personal anchor charts. {Free download}

Funtcionality is key for math journals. The types of foldables you can include are endless. Don't just choose a foldable to make a foldable though... choose one that adds function and helps explicitly teach your concept.

"Types of" Foldables - This tri-fold foldable is a good example of how to use a foldable when trying to illustrate "types of." It allows you to display up to 6 sections of information and can become a go-to resource for students. These examples include teacher created pieces, but you can always release it to students during group work, paired activities or during small group work.

Thanks to these fantastic teachers for sharing their printable and cootie catcher lesson plan ideas. They are fabulous! Feel free to grab the "I'm a Featured Teach Junkie" blog button as your creations are definitely worth the shout out.

More Math Journal Ideas

More Math Activities

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How to Make Math Journals Interactive - Teach Junkie

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Use math journals and interactive notebooks to help students learn and practice their skills. Increase the amount of time in these to help students 'show your work.'

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Puzzle Pics Subtraction | Math Playground

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Play Puzzle Pics Subtraction at MathPlayground.com! Find the missing number and complete the mystery picture.

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Math.Practice.MP4

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP4: Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Download Common Core State Standards (PDF 1.2 MB)

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Math.1.OA.C.5

Common core State Standards

Math: Math

1: Grade 1

OA: Operations & Algebraic Thinking

C: Add and subtract within 20

5:
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Download Common Core State Standards (PDF 1.2 MB)

|

Math.1.OA.C.6

Common core State Standards

Thought starters

1. How does Ms. Gelormino create an environment where students are comfortable sharing their thinking?

2. How does Ms. Gelormino use questioning to encourage the use of academic language?

3. What strategies does Ms. Gelormino use to support her English Language Learners?

School Details

Think College Now School
2825 International Boulevard
Oakland CA 94601

Data Provided By:

Teachers

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Dot Talks: Building Fluency with Numbers

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Students in Julia Gelormino's first grade class engage in a dot talk in order to build fluency with numbers. Students look at a set of dots and share how many dots they see and how the see them. They share strategies for adding within twenty.

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5th: Making Sense of Fractions through Discourse 

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5th: Making Sense of Fractions through Discourse 

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Math.5.NF.B.6

Common core State Standards

Math: Math

5: Grade 5

NF: Numbers & Operations--Fractions

B: Apply and extend previous understandings of multiplication and division

6:
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. How does Ms. Carey intentionally group the students?

2. What scaffolds are in place throughout the lesson?

3. How does Ms. Carey formatively assess throughout the lesson?

School Details

Banting Elementary School
2019 Butler Drive
Waukesha WI 53186

Data Provided By:

Teachers

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Making Sense of Fractions Through Discourse

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Math.5.NF.B.6 Common core State Standards Math: Math 5: Grade 5 NF: Numbers & Operations--Fractions B: Apply and extend previous understandings of multiplication and division 6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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2016-2019 District Strategic Improvement Plan

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Hattie Ranking: 252 Influences And Effect Sizes Related To Student Achievement

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Hattie Ranking: 252 Influences And Effect Sizes Related To Student Achievement

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John Hattie developed a way of synthesizing various influences in different meta-analyses according to their effect size (Cohen's d). In his ground-breaking study "Visible Learning" he ranked 138 influences that are related to learning outcomes from very positive effects to very negative effects. Hattie found that the average effect size of all the interventions he studied was 0.40. Therefore he decided to judge the success of influences relative to this 'hinge point', in order to find an answer to the question "What works best in education?"
Originally, Hattie studied six areas that contribute to learning: the student, the home, the school, the curricula, the teacher, and teaching and learning approaches. (The updated list also includes the classroom.) But Hattie did not only provide a list of the relative effects of different influences on student achievement. He also tells the story underlying the data. He found that the key to making a difference was making teaching and learning visible. He further explained this story in his book " Visible learning for teachers ".

John Hattie updated his list of 138 effects to 150 effects in Visible Learning for Teachers (2011), and more recently to a list of 195 effects in The Applicability of Visible Learning to Higher Education (2015). His research is now based on nearly 1200 meta-analyses - up from the 800 when Visible Learning came out in 2009. According to Hattie the story underlying the data has hardly changed over time even though some effect sizes were updated and we have some new entries at the top, at the middle, and at the end of the list.

Below you can find an updated version of our first, second and third visualization of effect sizes related to student achievement.
Order VL for Teachers!

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Hattie effect size list - 256 Influences Related To Achievement

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Hattie's updated effect size list of 256 influences across all areas related to student achievement.