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Welcome! Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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L'idée de ce site a pris naissance grâce à une conversation avec Tracy Zager et Chris Hunter. De plus, d'autres personnes en dehors de la conversation initiale ont inspiré, d'une façon ou d'une autre, ce site.
The idea for this site was born out of a conversation with Tracy Zager and Chris Hunter. Furthermore, other people, in one way or another, have inspired the creation of this site. ​

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Custom Number Talk Images Créer vos propres images! Voici une ressource de Berkeley Everett . Offert en format PowerPoint ou Google Slides, vous n'avez qu'à modifier les diapositives afin de...

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Cube Conversations is a set of 80 (eighty!) animated lessons designed to promote visually rich math discourse. I've designed these lessons to invite many voices and vantage points into classroom conversations.

Much like Splat!, you control the animation with a few simple clicks - and each click presents an opportunity for students to see and discuss an image in new ways.

Of course, there is also a sense of mystery, much like what your students felt in Splat! The end of each slide includes The Reveal, when the answer is shown.

I hope your classroom will be filled with rich math talk, inspiring insights from your students, and moments of celebration as you guide your class through Cube Conversations!

Watch the video, download the lessons, and allow your students to amaze your with their visual math thinking.
***UPDATE: You can now download the 80 printable Cube Conversations pages here.
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.
Level 1: "Single Layer Structures, Part A" Grades: K-3 Cube Conversations Set 1 Cube Conversations Set 2 Cube Conversations Set 3 Cube Conversations Set 4 Cube Conversations Set 5 Cube Conversations Set 6 Cube Conversations Set 7 Cube Conversations Set 8 Cube Conversations Set 9 Cube Conversations Set 10 Grades: K-3 Cube Conversations Set 11 Cube Conversations Set 12 Cube Conversations Set 13 Cube Conversations Set 14 Cube Conversations Set 15 Cube Conversations Set 16 Cube Conversations Set 17 Cube Conversations Set 18 Cube Conversations Set 19 Cube Conversations Set 20 Level 3: "Twice as Thick" Grades: 2-6 Cube Conversations Set 21 Cube Conversations Set 22 Cube Conversations Set 23 Cube Conversations Set 24 Cube Conversations Set 25 Cube Conversations Set 26 Cube Conversations Set 27 Cube Conversations Set 28 Cube Conversations Set 29 Cube Conversations Set 30 Level 4: "Texture Time" Grades: 2-6 Cube Conversations Set 31 Cube Conversations Set 32 Cube Conversations Set 33 Cube Conversations Set 34 Cube Conversations Set 35 Cube Conversations Set 36 Cube Conversations Set 37 Cube Conversations Set 38 Cube Conversations Set 39 Cube Conversations Set 40 Level 5: "Challenging Structures" Grades: 3 - 8 Cube Conversations Set 41 Cube Conversations Set 42 Cube Conversations Set 43 Cube Conversations Set 44 Cube Conversations Set 45 Cube Conversations Set 46 Cube Conversations Set 47 Cube Conversations Set 48 Cube Conversations Set 49 Cube Conversations Set 50 Level 6: "Increasing Complexity" Grades: 3 - 8 Cube Conversations Set 51 Cube Conversations Set 52 Cube Conversations Set 53 Cube Conversations Set 54 Cube Conversations Set 55 Cube Conversations Set 56 Cube Conversations Set 57 Cube Conversations Set 58 Cube Conversations Set 59 Cube Conversations Set 60 Level 7: "Insightful Complexity" Grades: 5 - 12 Cube Conversations Set 61 Cube Conversations Set 62 Cube Conversations Set 63 Cube Conversations Set 64 Cube Conversations Set 65 Cube Conversations Set 66 Cube Conversations Set 67 Cube Conversations Set 68 Cube Conversations Set 69 Cube Conversations Set 70 Level 8: "Giant Structures" Grades: 5 - 12 Cube Conversations Set 71 Cube Conversations Set 72 Cube Conversations Set 73 Cube Conversations Set 74 Cube Conversations Set 75 Cube Conversations Set 76 Cube Conversations Set 77 Cube Conversations Set 78 Cube Conversations Set 79 Cube Conversations Set 80 Other Posts and Resources Which May Be of Interest
Splat! (over 140,000 free lessons downloads in 2017!)

The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Tiled Area Questions Primary Tile Questions

3 Powerful Tile Strategies (and 40 new downloadable pages)
Thank you for taking time to view my blog! I'm learning as I go!

All my best,

Steve

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Cube Conversations - Steve Wyborney's Blog: I'm on a Learning Mission.

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Cube Conversations is a set of 80 (eighty!) animated lessons designed to promote visually rich math discourse. I've designed these lessons to invite many

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A garden snail's average speed is about ​0.029 mi/h. The North American X-15's top speed is about 4,520 mi/h. How much time would it take for each to travel across the United States, a...

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From "What do you notice? What do you wonder?" (the essence of doing mathematics) to "How many/much?" (where students choose what to count and how to count it), images are a playful space to abstract the world around us, consider other people's perspectives, and build community.

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

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There’s a saying that a picture is worth 1000 words. I have never really tested that theory, however a picture in math class can generate plenty of discussion. (see my post on watermelons).

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Steve Wyborney's Blog: I'm on a Learning Mission.

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170 New Esti-Mysteries - Steve Wyborney’s Blog: I’m on a Learning Mission.

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This school year, I’ll be creating and posting 170 brand new Esti-Mysteries. I’ll be posting a new one nearly every day for the rest of the school year –

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Slow Reveal Graph is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways.

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Graphs to use in Core Maths lessons

This site includes screenshots of graphs that are likely to require some interpretation!
They might be complicated, unhelpful or just plain bizarre. There will be a few articles about how they might be used, but mostly it will be Graphs and Charts.
See here for a suggestion of how to use these resources, or scroll down for the graphs.

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Graphs to use in Core Maths lessons This site includes screenshots of graphs that are likely to require some interpretation! They might be complicated, unhelpful or just plain bizarre. There will be a few articles about how they might be used, but mostly it will be Graphs and Charts.

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Fun fact: The number 163 is prime, which we can prove simply by showing that it is not divisible by 2, 3, 5, 7, or 11. (Of those prime factors, the only one that's a little tricky to check is 7, but I can see that since 140 + 21 = 161 is a multiple of 7, the number 163 is not.). By the way ... why don't I have to check prime factors greater than 11? Howie Hua gives a nice little video explanation.

First, indulge me while I give a little plug for my own playful math project, a series of free math songs on my YouTube channel called Tunes that Count. We just released a new song about powers of 2 called The Power of Powers. Check it out!

Now, check out the great things I found below. Some are perfect little nuggets for use in classrooms or homeschooling. I also found some great math-art project ideas. Enjoy!
INTERNATIONAL DAY OF MATHEMATICS
March 14 was Pi Day, of course, but according to UNESCO it is also the International Day of Mathematics. One of the activities that was organized was a mathematics cartoon contest. Children and adults from all over the world entered, and you can see some of the selected cartoons in this gallery. Since the cartoons have no words -- only visuals and mathematical symbols -- the gallery is a testament mathematics as a universal form of communication. Below is one of my favorite of the cartoons, submitted by two students from Colombia.
FRENCH WEEK OF MATHEMATICS
Speaking of playful math....The French Ministry of Education sponsors a "week of mathematics" each year with a different theme in which it encourages people to create and share playful mathematics activities. This year, the "week" of mathematics ran from March 6 to March 15 and had the theme "Mathématiques à la carte." The contribution shown below is a clever game of vector dominoes by Jeux 2 Maths. For more details and for more games see their website. (Many of the games are so visual that you don't need to read French to understand them.) If you want to see more ideas, search for the hashtag #SDM2023 on Twitter.
HAPPY PALINDROME DAY!
NCTM reminded us with a tweet that March 20, 2023 was a palindrome day! Naturally that raises questions. I wonder how special that is? Do we get only one per year? Do we get one every year?

PLAYFUL CLASSROOM MATH Math for Love
A recent post from Math for Love helps teachers out with resources to plan a Family Math Night at their school. In general, I love games and puzzles where the rules are simple but the math is not. This blog post offers a nice sample of such games and puzzles. The image below shows one puzzle type (The Broken Calculator), which I think would be perfect for 4th or 5th grade. In fact, I loved the idea so much I created my own version for a 5th grade decimal unit. (For example, how would you make 0.364 without the decimal point and without a 3, 6 or 4? Tricky!)

Denise Gaskin's Let's Play Math

Denise has been sharing free games and activities from her collection of playful books. One of her books is called "Thinking Thursday: A new math journaling prompt every week!" From this book Denise recently shared the prompt, "Pick a topic you have learned in math. Write two correct statements and one false statement. Trade with a friend. Can you find each other's fibs?"

Here's an example of a more targeted prompt: "Tell me two truths and a lie about the median of a set of 5 numbers." If you try it yourself, as I did below, you'll see it's not so easy to write these kinds of statements. Open-ended tasks like this are great for differentiation within a classroom because students will each challenge themselves at an appropriate level.

A. The median of 5 numbers is always a number in the set.

B. The median of 5 numbers is always greater than the smallest number in. the set.

C. The median of 5 numbers does not change if you add 10 to the largest number.

Reflections and Tangents: Thoughts on Math, Education, and Technology

The Reflections and Tangents blog has done a series of posts using what they call the "Same and Different inquiry routine." The idea is that you present students with two similar mathematical situations, and (as the name suggests) ask students to brainstorm how the situations are the same and how they are different. The March 3 blog post gives an example from calculus, but you could really adapt the structure of the activity to any grade level at all. For a middle school classroom, you might ask, for example, what is the same and what is different about 3 different sequences.
@Mathgarden
This recent tweet by Sunil Singh sort of blew my mind. He shows a textbook illustration that extends Pascal's triangle upwards to include Row - 1, Row -2, and Row -3. Why didn't I think of this before? Extending the triangle would make a wonderful, playful activity for middle schoolers. For older students, it broadens the application of the binomial theorem to include negative exponents.
PLAYFUL MATH PROJECTS, PUZZLES, AND GAMES FOR MATH CIRCLES Playful Bookbinding and Paperworks
This blog is by an artist (Paula Beardell Krieg) who explores mathematics visually. In a recent post she turns a circle theorem about inscribed right triangles into an art project. Notice the visual impact of this drawing: In spite of the complexity and asymmetry of the drawing, many of the lines Paula created intersect in what appears to be the center of the circle. The drawing invites you to wonder why!
Julia Robinson Mathematics Festival activities blog
The Julia Robinson Math Festival is always a good source of playful activities. Their new blog for activities that are not quite ready for prime time is a great find. The most recent post on Modular Origami with Sonobe Units is a rich activity that could keep a math circle busy and engaged for a few sessions. The origami squares become building blocks to create polyhedra, which can then be explored geometrically (exploring structures) and algebraically (exploring numerical patterns).

Early Family Math

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A math blog by Sian Zelbo for elementary and middle school. Emphasizes problem solving and mathematical reasoning.

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This picture is taken from the Problem Pictures CD-ROM of photographs with activities for mathematics teaching.

Park railings

The horizontal bar in the photograph has holes spaced 10 cm apart for the hoops to pass through. One hoop is 30 cm wide.

How many hoops would you need to make a railing that is 250 cm long?

Can you find a rule that gives the length of railing for any given number of hoops?

C34

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4.NBT.6 5.NBT.7 5.OA.1 6.EE.1 6.EE.2c 6.EE.3 6.NS.4 8.EE.1 8.EE.1a Adrianne Burns Bryan Anderson DOK 2: Compétence / Concept DOK 3: Réflexion Stratégique Howie Hua Jonathan Newman Julie Wright Michael Fenton N-RN.2 Owen Kaplinsky Phillip Haislip-Hansberry Robert Kaplinsky Zack Miller

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Take out the numbers to make word problems make sense Learn More Try one tomorrow Primary (K-2) Older Students Explore ready-made problems Problem Banks More Problems This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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Airtable is a low-code platform for building collaborative apps. Customize your workflow, collaborate, and achieve ambitious outcomes. Get started for free.

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… efforts to intensify attention to the traditional mathematics curriculum do not necessarily lead to increased competency with quantitative data and numbers. While perhaps surprising to many in the public, this conclusion follows from a simple recognition that is, unlike mathematics, numeracy does not so much lead upwards in an ascending pursuit of abstraction as it moves outward toward an ever richer engagement with life’s diverse contexts and situations.

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The Math Viking: Elementary Math Exploration

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Math Enrichment K-6 Ideas, Resources & NCTM Best Practices

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Reasoning based math enrichment ideas and resources for elementary students, teachers and parents. Warm up routines, rich tasks & independent activities.

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Analyzing Picture Books-An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more counting books.Review How to Use Picture Books for some general tips for how to plan to read books with children.

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Previous DLLs: Assessing Geometry and Spatial Relations

Next Describe, Draw, Describe

Recommended Shape and Spatial Relations Picture Books

Supporting Engagement with Shape and Spatial Relations Books

Preparing to Read

You can use Analyzing Picture Books—An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more shape and spatial relations books. Review How to Use Picture Books for some general tips for how to plan to read books with children.

Let’s consider a specific example from Round Is a Tortilla by Roseanne Greenfield Thong, which is a book about shapes. These pages show, among other things, different objects that are triangular in form.

Text © 2013 by Roseanne Greenfield Thong. Illustrations © 2013 by John Parra

Look through the book from a child’s perspective. Think about what might help children understand the shapes on each page. Consider what children might find confusing; this will give you some clues about how you can help them develop their understanding. For example, on the right hand page above, there are tortilla chips shaped like triangles. However, they are oriented in different ways. Turning a triangle so its base (straight side) is not on the bottom may be confusing to children just learning what a triangle is. They may not see that the turned shape is still a triangle.

During Reading

Ask questions.

As appropriate, ask a variety of question types, both lower-level and higher-level.

Lower-level questions are relatively simple and concrete, addressing what children see directly on the page or remember from a previous page, as well as key words from the text that you think they might not understand. For example:

Recall: What shape did we see on the page before this one?

Label: What shape is this?

Describe: How many sides does this triangle have?

Higher-level questions are relatively complex and abstract, asking children to engage in deep thinking and go beyond the literal events on the page. For example:

Reason: If we added one more side to the triangle, would it still be a triangle?

Compare: Do a triangle and a square have the same number of sides?

Relate: Can you think of another food that is shaped like a triangle?

Explore children’s responses.

Elaborate on children’s responses and follow up with open-ended questions asking children to explain their reasoning. For example:

Teacher:  (points to the little girl) You said the little girl is holding a triangle. What shape is the chip this woman is holding? (points to triangle in woman’s hand, which is oriented differently)

Child: I don’t know. It looks different. This is a triangle (pointing to little girl’s triangle). But this is not a triangle – it’s sideways.

Teacher: Ahh, yes, they look different.  Is there something that is the same?

Child: (points to the sides of one triangle) One, two, three. (points to the sides of the other triangle) One, two, three!

Teacher: You counted the sides! What did you notice?

Child: They both have three sides.

Teacher: So, is it a triangle?

Child: I guess so.

Teacher: It is. Can you find some other triangles on the page?

Model complex thinking.

Children learn by listening to you, the adult, model productive ways of thinking about the story. For example:

Teacher: I can count the sides to help me figure out if this shape is a triangle. Let me see…one, two, three. It has 3 straight sides, so it’s a triangle. But this star shape has more sides than that. I count… one, two, three, four, five, six, seven, eight, nine, ten sides. So, it’s not a triangle.

More Examples for Shape and Spatial Relations Books

Shapes aren’t the only geometry topics that can be examined using storybooks. Spatial relations—or the relationships of objects to one another and objects to yourself— may also be explored through storybooks. The next example is from Albert is Not Scared by Eleanor May. In this story, Albert is a mouse who is too frightened to go on any of the rides at the amusement park. On this two-page spread, spatial words are used to describe the motion of the carousel ride.

Text copyright © 2013 by Eleanor May. Illustrations copyright © 2013 by Deborah Melmon

What Children Can Learn

Using Albert is Not Scared, a teacher can focus on a variety of spatial concepts that children need to understand. Children need to learn the following about spatial thinking.

Spatial words can describe the movement of objects.

How do the birds move on the carousel?  (Look for children to use spatial words like up and down.)

What direction is the carousel moving? (Look for children to use a spatial word like around.)

Spatial words can be used to describe locations of objects.

Where is Wanda standing? Is she standing close to the carousel or far away? (Look for children to describe Wanda’s location using words like on the left or farther away.)

Who is standing the farthest away, Wanda or the Albert the mouse?

Can you find the three blue birds? Which one is up the highest? Which one is the lowest?

Children use spatial reasoning in their everyday lives. They can make sense of the spatial concepts in this book by relating it to their own experiences going on rides at an amusement park or carnival.

Imagine yourself in the story acting out the movement of the rides. Can you spin around like the Mousey-Go-Round?

Can we make a train with our bodies and move forward like the Chew Chew Train? Now let’s move backward.

Questioning the Child

As you read books with spatial concepts, you should ask both lower-level and higher-level questions.

Lower-level Questions

Ask children to describe the scene to find out how many relevant spatial words they use spontaneously.

What’s happening on this page?

Ask children to describe the location and movement of objects and characters as you point them out.

How is the carousel moving? Does Albert like this kind of motion?

Ask children to recall what happened on previous pages in the story:

Do you remember the Dare Devil Drop? What direction did it move? How about the Pi-Rat Ship? What direction did that ride move?

Has Albert gone on any rides yet?

If the children struggle to use precise spatial words, model how to describe locations and movements with spatial language:

Teacher: Where are Wanda and Albert standing?

Child: They’re standing there.

Teacher: Wanda is standing close to the carousel, while Albert is standing farther away from the carousel.

Higher-level Questions

Ask children to relate the story to their lives and use their bodies or hands to mimic the movement of the objects and characters in the story.

Can you think of something else that goes up and down like the birds on the carousel? Can you show me up and down with your hand?

Can you make your hands go around just like the carousel ride?

Ask children to compare the movements of the objects:

(After children have demonstrated the circular motion of the carousel ride) Do the birds and the cats on the ride move in the same direction? How are they different?

Ask children to interpret the character’s motivations and feelings:

Do you think Albert really doesn’t like the Mousey-Go-Round because he doesn't like rides that go around? Why else might he be scared of the ride?

You can respond to children’s answers to any of these questions by asking:

How do you know?

Why?

Can you explain what you said?

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You can use Analyzing Picture Books-An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more shape and spatial relations books.Review How to Use Picture Books for some general tips for how to plan to read books with children.

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Previous Addition and Subtraction Assessment Videos

Next Supporting Counting to Problem Solving

Recommended Addition and Subtraction Picture Books

Supporting Engagement with Addition and Subtraction Books

Preparing to Read

You can use Analyzing Picture Books—An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more addition and subtraction books. Review How to Use Picture Books for some general tips for how to plan to read books with children.

Consider a specific example. These pages are from Rooster’s Off to See the World by Eric Carle, a book about a rooster who meets many friends on his journey. On this two-page spread, one rooster, two cats, and three frogs are joined by four turtles.

© 1972 by Eric Carle Corp.

Try to look through the book from a child’s perspective. For example, o n the page above, we see symbols—schematic pictures—in the squares drawn on the upper right side of the page. These symbols represent the rooster, cats, frogs, and turtles that have embarked on the journey so far. The symbols are shown, from top to bottom, in order of the appearance and number of animals. However, young children often have difficulty with interpreting symbols and therefore may not understand how they connect with the animals they’ve met in the story. If asked to count the total number of animals, they may not realize that they can use these symbols to help them add the one rooster, two cats, three frogs, and four turtles. Instead, they may, for example, count eight turtles on the page (four large illustrations and four schematic symbols).

During Reading

Ask questions.

As appropriate, ask a variety of question types, both lower-level and higher-level.

Lower-level questions are relatively simple and concrete, addressing what children see directly on the page as well as key words from the text that you think they might not understand. For example:

Recall: What animals has the rooster met so far? What did the rooster ask the animals?

Label: What is this animal called?

Describe: How many turtles do you see? How were the turtles crawling down the road?

Higher-level questions are relatively complex and abstract, asking children to engage in deep thinking and go beyond the literal events on the page. For example:

Predict: What do you think will happen next in the story?

Infer: Why do you think the turtles agreed to join the other animals to see the world?

Make judgments: Do you think it was a good idea or a bad idea for all the animals to join rooster on his adventure?

Explore children's responses.

Elaborate on children’s responses and ask follow-up questions. For example:

Teacher: What is this animal called?

Child: A turtle.

Teacher: That’s right, a turtle. Its shell protects the turtle. Can you think of another animal that has a shell or protects itself some other way?

Follow up with open-ended questions asking children to explain their reasoning. For example:

Teacher: So far the rooster met two cats, three frogs, and four turtles. What do you think will happen next in the story?

Child: I think they’ll meet five more animals!

Teacher: Why do you think they’ll meet five more animals? What animal might they meet next?

Model complex thinking.

One way children learn is by listening to you, the adult, model productive ways of thinking about the story. For example:

Teacher: I notice that the rooster always asks the other animals to join him on his adventure to see the world. That makes me think the rooster is friendly and likes the company of his animal friends. What do you think?

More Examples for Addition and Subtraction Books

Below are suggestions for how you can use picture books that lend themselves to addition and subtraction as part of classroom instruction. While reading and discussing a storybook about addition and/or subtraction, children can learn and demonstrate their understanding of many different kinds of number concepts. Here are some examples.

What Children Can Learn

Using the book shown above, Rooster’s Off to See the World , a teacher can focus on a variety of number concepts. For example, you can ask children to solve oral word problems involving adding or subtracting one, which builds on the child’s understanding of the counting numbers. For example,

Rooster is joined by two cats. If one more cat joins them, how many cats will there be?

There are four turtles. If one turtle leaves, how many will be left?

Oral word problems or situations with totals less than or equal to 10. For example:

Rooster is joined by his friends, the two cats. How many animals are there now?

There are ten animals. If the four turtles leave, how many animals will be left?

Problems that involve putting together and taking apart small quantities. For example:

I see four turtles. These two turtles and these two make four.

Young children may benefit from using their fingers to help them add and subtract. When calculating how many animals there are when rooster is joined by the two cats, they can hold up one finger for the rooster and two for the cats, then count up all the fingers to find the sum of three. Young children also benefit from acting out addition and subtraction scenarios or using physical materials, such as counters or bears, to help them when they are learning how to add and subtract.

Questioning the Child

Copyright © 2000 by Pat Hutchins

Regardless of the content, teachers should ask both concrete and abstract questions as appropriate. The picture book, Ten Red Apples by Pat Hutchins, is another book that can be used to teach operations.

Lower-level Questions

Ask children to describe the scene to find out how many relevant words they use spontaneously.

What’s happening on this page?

Ask children to name the number of objects in the illustration.

How many apples are on the tree?

Can you count the number of animals?

Ask children to locate and count the seven apples.

I see seven apples. Can you point to the seven apples?

If the children struggle to correctly count the apples, you can provide guidance by counting along with them.

Let’s try again. Count with me as I point to each apple: one, two, three, four, five, six, seven. There are seven apples!

Higher-level Questions

Ask children to make a prediction about what will happen if you subtract.

Oh no, Goat just ate one apple! There were seven apples. How many are left?

If Farmer loses another apple, how many will be left then?

Ask children to make a prediction about what will happen if you add.

Farmer has seven apples. What if he found another tree with two apples? How many apples would Farmer have altogether?

Ask children to put together or take apart the number of apples.

Farmer has seven apples. How many are on the bottom row? How many are on the top row?

Four and three make seven. Can you think of another way to make seven?

Ask children to make an inference about numbers.

Goat has an apple. If each of his animal friends wants an apple too, how many more apples will Goat need?

You can respond to children’s answers to any of these questions by asking:

How did you know?

Why did you say that?

Why did you predict that?

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Using Picture Books: Addition and Subtraction | DREME TE

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Previous Pattern and Algebra Assessment Videos

Next What Do You Notice?

Supporting Engagement with Patterns Books

Preparing to Read

You can use Analyzing Picture Books—An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more patterns books. Review How to Use Picture Books for some general tips for how to plan to read books with children.

Let’s consider a specific example. Here is a two-page spread from Mr. Noisy’s Book of Patterns by Rozanne L. Williams. On these pages, Mr. Noisy’s footsteps make a sound pattern as he walks.

© 2013 Creative Teaching Press Inc.

Look through the book from a child’s perspective. Think about what might help children understand the math on the page or what they might find confusing. The repeating pattern is demonstrated for children in the text, by means of a sound pattern: “Click Click Clack, Click Click Clack.” But some children may not understand that sounds can be the basis for a pattern. They may think patterns have to be visual.  Other children may easily understand sound patterns—after all they know many songs—but may not see that the visual events on these pages can make a pattern too.

During Reading

Ask questions.

As appropriate, ask a variety of question types, both lower-level and higher-level.

Lower-level questions are relatively simple and concrete, addressing what children see directly on the page or remember from a previous page, as well as key words from the text that you think they might not understand. For example:

Recall: What pattern did we see on the last page?

Notice: What pattern are the trees making? How would you describe the pattern?

Describe: What is Mr. Noisy doing on this page?

Higher-level questions are relatively complex and abstract, asking children to engage in thinking and go beyond the literal events on the page. For example:

Predict: “Click Click Clack, Click Click Clack” is the pattern Mr. Noisy’s shoes make. If Mr. Noisy kept walking, what sound would he make?

Generalize: Mr. Noisy’s shoe pattern is “Click Click Clack, Click Click Clack.”  Can you make the same pattern with these shapes—the triangles and circles?”

Compare: Is the “Click Click Clack” pattern of Mr. Noisy’s shoes the same as the pattern that the trees are making?

Explore children’s responses.

Elaborate on children’s responses and ask follow-up questions. For example:

Child: The trees make a pattern, too.

Teacher: I think you’re right. Can you describe the pattern?

Child: Triangle-circle-circle-triangle-circle-circle-triangle-circle-circle.

Teacher: That IS a pattern. If you were drawing the next tree, what would it look like?

Child: Triangle!

Teacher: What about the tree after that?

Model complex thinking.

Children learn by listening to you, the adult, model productive ways of thinking about the story. For example:

Teacher: I notice that Mr. Noisy’s shoes sound like Click Click Clack, Click Click Clack. I wonder what sound they’ll make if Mr. Noisy keeps walking. Let me tap my feet to the pattern: Click Click Clack, Click Click Clack. I think they’ll keep making that pattern and sound like Click Click Clack if he keeps walking!  What do you think?

More Examples for Patterns Books

Young children can benefit from reading a story to help them examine different kinds of patterns. Pattern Fish by Trudy Harris shows several different kinds of patterns, including ABAB, AABAAB, and AABB and more.

This one is about how the sea horse is eating.

Text copyright © 2000 by Trudy Harris. Illustrations copyright © 2000 by Anne Canevari Green

What Children Can Learn

Using Pattern Fish, a teacher can focus on a variety of pattern ideas and concepts.

To understand patterns, children need to not only say patterns but also to extend them.

The sea horse’s eating is a pattern. “Chomp-chomp-munch-munch, Chomp-chomp-munch-munch, Chomp-chomp-munch…” What comes next? How do you know?

Children also benefit from being asked to compare patterns.

What pattern do you see on the sea horse?

Is the pattern “chomp-chomp-munch-munch” the same as the pattern of blue and yellow on the seahorse?

Questioning the Child

Regardless of the type of pattern being shown or described, you should ask both lower-level and higher-level questions.

Lower-level Questions

Ask children to describe the scene to find out how many relevant words they use spontaneously.

What’s do you see on this page?

Ask children to name objects as you point them out.

What is this? (while you point to the seahorse)

Ask children about the bubbles coming from the mouths of the fish.

How many bubbles do you see here?

Do the bubbles make a pattern?

Higher-level Questions

Ask children to compare:

Let’s name all the patterns we can find on this page. Are all the patterns the same?  If not, how are they different?

Ask children to reason:

We call this pattern an “AABB” pattern. Can you guess why?

Ask children to create their own AABB patterns. For example:

Can you use these shapes to make a pattern that’s the same as chomp-chomp-munch-munch?

You can respond to children’s answers to any of these questions by asking,

How do you know?

Why?

Can you explain what you said?

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You can use Analyzing Picture Books-An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more patterns books.Review How to Use Picture Books for some general tips for how to plan to read books with children.

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Previous Data Assessment Videos

Next I'm the Greatest: A Measurement Activity

Recommended Measurement Picture Books

Supporting Engagement with Measurement Books

Preparing to Read

You can use Analyzing Picture Books—An Overview with its downloadable Math Picture Book Analysis Guide to help you examine and select one or more measurement books. Review How to Use Picture Books for some general tips for how to plan to read books with children.

Consider a specific example. This two-page spread is from Just a Little Bit by Ann Tompert, a book about an elephant and a mouse who play together on a seesaw, with the help of their animal friends. On these pages, the animals pile up on the right side of the seesaw to try to balance the elephant’s weight.

© 1993 by Ann Tompert

Look through the book from a child’s perspective. On the pages above, the seesaw can be thought of as a scale, or a tool to measure weight. However, children may confuse balancing the weight of the animals with balancing the number of animals on either side of the scale. Here the number of animals on either side does not matter. We have one animal on the left side and nine animals on the right side, yet the scale is tilted towards the one animal. The child can work on understanding that the one animal is heavier than the other nine animals combined. It is the weight and not the number of animals that will eventually balance the seesaw.

During Reading

Ask questions.

As appropriate, ask a variety of question types, both lower-level and higher-level.

Lower-level questions are relatively simple and concrete, addressing what children see directly on the page as well as key words from the text that you think they might not understand. For example:

Recall: What animals have climbed on the seesaw so far?

Label: What is this animal called?

Describe: How many animals do you see? What are the animals doing on this page?

Higher-level questions are relatively complex and abstract, asking children to engage in deep thinking and go beyond the literal events on the page. For example:

Predict: Do you think the elephant will ever get off the ground? How?

Infer: Why do you think the seesaw hasn’t moved, even after all these animals climbed on the other end?

Summarize the story across multiple pages: Has anything changed from the beginning of the story to the end?

Explore children’s responses.

Expand on children’s thinking by elaborating on their responses and asking follow-up questions. For example:

Teacher: (reading from the text) He’ll never get off the ground, said someone in the crowd.

Child: I think the elephant will get off the ground!

Other children: Me too!/No it won’t!

Teacher: Some of you think the elephant will get off the ground. How do you think that will happen?

Child: With more animals.

Another child: More and more and more and it will go down.

Teacher: So you think more animals will make their side heavier? Let’s keep reading and find out.

Model complex thinking.

Children learn by listening to you, the adult, model productive ways of thinking about the story. For example:

Teacher: I notice that these animals are all squished on the right side of the seesaw, but the elephant is still on the ground! That makes me think the elephant must be heavier than all those animals. What do you think?

After Reading

After finishing the book, engage the children in a discussion about the story.

More Examples for Measurement Books

Below are suggestions for how you can use picture books that lend themselves to measurement as part of classroom instruction. In books of this type, the measurement content may be implicit or explicit in the story and the title may or may not make explicit mention of measurement. The next example comes from Ae-hae Yoon’s Who Eats First?, a book about animal friends who find a delicious peach but can’t decide who should take the first bite. Each animal makes an argument explaining why it should go first. On this two-page spread, the caterpillar is explaining why it should be first. Note that the content is mostly about measurement, and in fact uses the word measure in the text. But the title of the book does not explicitly state measurement as the theme. This is very different from a book like Anno’s Counting Book, or Eve Merriam’s 12 Ways to Get to 11 (about the decomposition of numbers).

© Yeowon Media Co., Ltd. U.S. and Canada edition © TANTAN PUBLISHING INC in 2015

What Children Can Learn

While reading and discussing a storybook like Who Eats First? children learn and demonstrate their understanding of many math concepts. Here are some examples of what children can learn about measurement and how you can ask questions. The questions below are suggestions only, not a script. You need to modify them in response to the individual child and the story and pictures.

How to measure many different attributes of objects. For example:

I see the animals lined up in size order from shortest to tallest. Besides height, how else can the animals measure themselves?

The giraffe is the tallest, but he’s not the heaviest. Which is the heaviest animal?

How to compare the sizes of different objects using a tool. For example:

Some animals are heavy and some animals are light. How can we find out which animal is the heaviest and which animal is the lightest?

Some animals are tall and some animals are short. What can we use to find out which animal is the tallest and which animal is the shortest?

How to put items in size order from shortest to tallest or biggest to smallest. For example:

If we lined up the animals from heaviest to lightest, who would be first in line? Who would be last?

Questioning the Child

Regardless of the content (attributes of objects, size comparison, size order, etc.) you should ask both lower-level and higher-level questions as appropriate.

Lower-Level Questions

Ask children to describe the scene and notice how many relevant words they use spontaneously.

What’s happening on this page?

Ask children to identify objects based on their size.

Can you find the tallest animal?

Which animal has the shortest ears?

Ask children to attend to two attributes simultaneously.

Do you see a short animal with a long snout?

Which animal has a long tail and small ears?

Higher-Level Questions

Ask children to predict the order of animals if you line them up in various ways.

Let’s say they lined up in order from the animal with the shortest tail to the animal with the longest tail. Which animal would be first in line? Which animal would be last?

Ask children to summarize what happened across multiple pages.

First, giraffe thought that the tallest animal should eat first. What happened after that?

Ask children to explain the character’s motivation.

Why are the animals each suggesting different ways of measuring themselves?

Why does the rhino think that the heaviest animal should get the first bite of the peach?

Ask children to consider how they would measure the animals.

How would you measure the height of a giraffe?

How would you find out the weight of the rhino?

After the Story

Young children benefit from many experiences measuring the attributes of objects they encounter in their everyday lives. After reading the story, you can have children choose different classroom objects, such as a wooden block, a pencil, and a toy from the play area to measure.

You can give children stuffed, plastic, or rubber animals to work with.  Children can choose an attribute to measure, such as weight, and make a prediction about which object is heaviest and which is lightest. Then children can practice using a scale to measure the different objects and discuss whether their predictions were correct. They could also put the objects in a line and order them based on the attribute.

# data[].attributes.attachment_link.description
Who Eats First?, a book about animal friends who find a delicious peach but can't decide who should take the first bite. Each animal makes an argument explaining why it should go first. On this two-page spread, the caterpillar is explaining why it should be first.