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Concepts: number sense and patterns

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 I don't think that I would show more than 1 video a day but these are great for number sense, patterns  and asking the question, "What do you notice?" 

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Focus: fostering flexible thinking and representations

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Focus: fostering flexible thinking and representations

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Concepts: operations, composing, decomposing

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Concepts: measurement,  geometry, data analysis

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Mathematical Content and Competencies:

• demonstration of number sense, what numbers mean

• flexibility and fluency with numbers

• composition and decomposition of numbers

• parts-whole relationships

• place value concepts

• operational skills and concepts

• equivalent expressions

• representing quantity

• use of models

• apply mental math strategies

• communicate mathematical ideas

• connect mathematical concepts to each other and to the world

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Concepts: content-specific vocabulary

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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You can print the vocabulary cards from Pearson.

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Kagan specializes in staff development and educational resources for teachers. Visit our online store, magazine and message board – the leading authority on cooperative learning, classroom discipline and multiple intelligences.

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Kagan specializes in staff development and educational resources for teachers. Visit our online store, magazine and message board - the leading authority on cooperative learning, classroom discipline and multiple intelligences.

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

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

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

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

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

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Introducing Esti-Mysteries! Each image invites students to wonder what number is represented by the image. As you click through the each Esti-Mystery, clues will appear that will allow the students to use math concepts to narrow the set of possibilities to a small set of numbers. In the end, the students will need to call upon their estimation skills to solve the mystery and find the missing number.

NOTE: In addition, to these original Esti-Mysteries, you may also want to visit the brand new post 51 Esti-Mysteries.

Here is an example:

Download the Esti-Mysteries, try them in your class, and let me know about your experience.

Update: Here are 4 Printable Esti-Mystery Charts you may enjoy using with Esti-Mysteries.

Update: Here is the Full Set of Esti-Mystery Clues (without images) to allow you to browse through the Esti-Mystery Concepts.

As always, you can find me on Twitter @stevewyborney

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.
Esti-Mystery #1 The First Mystery Esti-Mystery #2

Esti-Mystery #3

Esti-Mystery #4 ***This is the one where the numbers on the dice are first used as a clue.
Esti-Mystery #5

Esti-Mystery #6
***The most challenging one yet!

Esti-Mystery #7 "The Dice Jam"

Esti-Mystery #8 "Bright Beads"Esti-Mystery #9 "Cupside Down"Esti-Mysteries #10 "Yellow Yarn"
Esti-Mystery: The Smaller Numbers Request
Esti-Mystery: "Sinker?" (from The Smaller Numbers Series)Other Posts and Resources Which May Be of Interest
***This one that may lead to the greatest debate and surprise at the end.

Tiled Area Questions
The Smaller Number Series

This next Esti-Mysteries was requested for a kindergarten class. Enjoy!

***This is a great one to use with kindergarten students.

51 Esti-Mysteries - 51 (fifty-one!) brand new Esti-Mysteries which I've already started posting .

Splat! (50 downloadable, animated lessons)

The Fraction Splat! Series (with 20 more downloadable lessons)

Splat! for Google Slides (This is the one you want if you don't have PowerPoint but do have Google Slides.)

Cube Conversations (80 downloadable, animated lessons)

Thank you for visiting my blog!

All my best,

Steve

P.S. Please feel free to post your reflections in the comments below.

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Esti-Mysteries: Estimation Meets Math Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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Introducing Esti-Mysteries! Each image invites students to wonder what number is represented by the image. As you click through the each Esti-Mystery, clues

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Same But Different Math from Looney Math

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Same But Different Math from Looney Math

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Share diagram, chart, tables or story problem without all of the information or the question, etc. and ask students: What do you notice? Ask students to create more than one possible questions.

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lead4ward makes a difference in the lives of students by helping educators focus their work, creating structures that give teachers and students a sense of hope and confidence, and supporting leaders with systems they can trust.

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Custom Number Talks - 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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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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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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

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Steve Wyborney is on a learning mission to spread math joy to classrooms everywhere! On this blog you'll find math resources for teachers and for kids of all ages.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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K-5 HCPS Mathematics NUMBER SENSE ROUTINES

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K-5 HCPS Mathematics NUMBER SENSE ROUTINES

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NUMBER SENSE ROUTINES: DESIGNED TO BE USED AS CLASS STARTERS TO ENGAGE YOUR STUDENTS, FOSTER MATHEMATICAL DISCOURSE, AND CREATE CLASSROOM COMMUNITY. CLICK HERE TO LEARN ABOUT THE DIFFERENT TYPES OF ROUTINES.

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JAM Math Warm-Up Framework PD Aug 18/19, 2021

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JAM Math Warm-Up Framework PD Aug 18/19, 2021

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lead4ward makes a difference in the lives of students by helping educators focus their work, creating structures that give teachers and students a sense of hope and confidence, and supporting leaders with systems they can trust.

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Solve the Mystery Number at MathPlayground.com! Use your math skills to find the correct number.

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Mathematics is all about patterns. Some describe mathematics as the science of patterns, and the ability to understand patterns is described as a key concept in 's algebra standard.

I didn't like math growing up. Now, it fascinates me almost to the point of obsession, and I attribute that to two things: (1) I now understand the math behind the procedures I was taught, and (2) I see the patterns that were never pointed out to me before.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally recommend.

Since I love patterns, it should be no surprise that I am a big fan of hundred charts. The classic +1, -1, +10, and -10 pattern of a hundred chart is fundamental to a conceptual understanding of place value. So you can imagine my delight a couple of weeks ago when I saw that the remediation program my district uses had a hundred chart lesson for my 2nd graders. A lesson. As in one. That might have been fine, but I quickly found out that my struggling second graders did not see any of the patterns in the hundred chart that I hold so near and dear.

Enter Hundred Chart Bootcamp! We have spent two weeks exploring the hundred chart inside and out. Some of the students picked up the patterns right away, but others just couldn't see them. It was fascinating to me. Here are some things I tried.

Humpty Dumpty Hundred Charts

This activity involves students putting together the pieces of a cut up hundreds chart, like a puzzle, to make the complete chart. This is a great formative assessment! Watch as the students put it together. Do they know that the smaller numbers are at the top of the puzzle and the larger ones at the bottom? Do they look for the multiples of ten for the right-hand side of the puzzle? How easy or difficult is this task for them? You can read more and download your own free Humpty Dumpty charts from this blog post.

Missing Numbers on a Pocket Hundred Chart

A pocket hundred chart is a must-have tool. You can use it to isolate the numbers in a given row or column, which makes the patterns easier for students to see. They now actually sell the pocket charts that extend to 120, so students can see that the patterns go on past 100.

Hundred Chart Masks

This activity came from the book It Makes Sense: Using the Hundreds Chart to Build Number Sense, by Melissa Conklin and Stephanie Sheffield. These masks are groups of squares, which contain question marks, that are cut from a hundred chart. Students lay them over the hundred chart and try to determine the numbers that are covered. Because the rest of the numbers on the chart are visible, students can be successful with this activity, even if they are not yet sure of the hundred chart patterns. I created a recording sheet for the students to record their numbers, so they could then see the groups of numbers away from the rest of the hundred chart. I think that helps them to recognize the patterns more easily. You can download the recording sheet a little further down in this post.

Hundred Chart Puzzles

Once students understand the patterns on the hundred chart, they are able to work puzzles such as the ones shown. This set, from my To 100 and Beyond: Hundred Charts to 1000 unit, takes the patterns all the way up to 1000. I have the cards laminated, and students use wipe-off markers to complete them. I still have some students that do not 100% own the patterns, so I created a card they can use as a reminder.

Click to download the patterns card (shown above) and the recording sheets for the mask activity. Enjoy!

Update: be sure to check out for an easy hundred chart assessment.

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Conquering the Hundred Chart - Math Coach's Corner

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Mathematics is all about patterns. Some describe mathematics as the science of patterns, and the ability to understand patterns is described as a key concept in 's algebra standard. I didn't like math growing up.

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Curious Thoughts of Elizamath Brandenbook

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Read my original post (which includes a video) about the Number Chart Routine here! Here is the link to all of these electronic routines: Number Chart Routines Folder. Here is a link to the Fraction Number Charts: Fraction Number Chart Routines Folder. Directions to use this Routine Click the present button .

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Focus: analyzing mathematical relationships and algebraic reasoning

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Focus: analyzing mathematical relationships and algebraic reasoning

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Concepts: relationships representations

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Denise Gaskins' Let's Play Math

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Math concepts: odd numbers, even numbers, greater-than/less-than, rounding off, addition, subtraction, multiplication, division, fractions, negative numbers, prime numbers, square numbers, problem solving, mental math
Number of players: two or more
Equipment: pencil (or pen) and paper for every player

Set Up

Each player needs pencil and paper of his own. One person plays the role of the function machine, and he must make up a rule for calculating with whatever numbers the other players will give him. In math, a function is any rule that turns one number into another*, such as:

Double the number, and then add seven.

The function machine should write his function rule on a piece of paper and slip it in his pocket.

All the other players make themselves a chart to keep track of the game.

*[In reality, the definition of a function is a bit more complicated than that, but it suffices for this game.]

How to Play

Play proceeds to the left around the table.

Each player in turn says any number he wishes, and all players write that number in their Input columns. The function machine calculates with that number, mentally or on scratch paper, and says only the answer to his calculation.

If that input number is too difficult for the player to work with, he should say, "That's too hard," and ask for a different number. Occasionally, players will give an input number that does not make sense with the chosen rule, in which case the machine answers, "That does not compute."

Whatever answer the machine gives, all other players write it in their Output columns.

After receiving an answer, the player whose turn it is may make a guess at what calculation the machine is doing. Other players may not guess at the function rule until their own turns.

Endgame

The first player to guess the rule of the function machine wins that round. If you have time to play a full game, where every player has a chance to be the machine, then the winner of the game is the player who gave the most output numbers before the others guessed his function rule.

Variations

My math club students have always enjoyed this game, especially when it is their turn to be the function machine with the secret rule. But some freeze mentally at the task of creating their function rule, while other students make up rules that are so complex they are nearly impossible to guess. You may want to make a list of suggested function rules in advance, writing the rules on index cards and letting each player draw a rule from your deck.

Here are some function ideas to get you started:

Add 15 to the number.

Subtract 4 from the number.

Pick your favorite number. Whatever the input, the output is always your number.

Multiply the number by 8.

Cut the number in half.

Cut the number in half, and then add one.

Double the number, and then subtract three.

Add the next larger number, so an input of 3 gives an output of 3 + 4 = 7.

Multiply by the next larger number, so an input of 5 gives an output of
5 × 6 = 30.

Triple the next larger number.

Subtract the number from 25.

If the input number is even, say that number. If the input is odd, or if it's not a whole number, then say the next larger even number.

Square the number, and then add one.

Say the largest multiple of 3 that is less than the number.

Round off to the nearest hundred.

Double the odd numbers, but cut the even numbers in half.

All odd numbers are 17, but all even numbers are 12.

Say the ones digit of the number.

Add the digits in the number together.

If the number is prime, say the number. If the number is not prime, say 1. Remember that one, zero, and all negative numbers are not prime.

Say the tenths digit of the number (the first digit after the decimal place). The student may need a calculator to rapidly convert fractions to decimal numbers.

Comments

This is a great game to play in the car on family trips, since there are no little game pieces and the paper does not need to be passes around. Even the driver can join in the fun.

Beware that some function rules can be described in more than one way. For example, the rule:

Double the number, and then add two.

...could also be written as:

Double the next higher number.

It helps to have a referee who knows algebra to judge the guesses. "Double the number, and then add two" is written as , while "double the next higher number" is , and anyone who knows algebra can easily see these are the same. The player who tries to guess the rule does not have to put it in the exact words the function machine used, as long as the statements are equivalent.

Edited to Add

You can play an interactive online version of the game here:

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Math concepts: odd numbers, even numbers, greater-than/less-than, rounding off, addition, subtraction, multiplication, division, fractions, negative numbers, prime numbers, square numbers, problem solving, mental math Number of players: two or more Equipment: pencil (or pen) and paper for every player Set Up Each player needs pencil and paper of his own.

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present a number line that may be used with computation, typically an empty number line.

Students mark only the numbers that are needed for their calculations.

Students are then asked to record their computational strategies on the number line and explain their thinking.

Ex. 15 + 8 102 - 14 302 - 296

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High-Yield Routines for Grades K-8, released by the National Council of Teachers of Mathematics (NCTM), is a book that presents diverse mathematical routines recommended for use at a variety of grade levels and with a variety of mathematical content. The book also includes ideas for infusing mathematics into the non-mathematical routines that take time away from instruction.

Each chapter begins with classroom vignettes to provide a glimpse of how the routine might look as it is implemented at a variety of grade levels. A description of the routine and implementation strategies follow, and the authors provide examples of student work from various grade levels for each of the routines, including examples of ways to assess student thinking by using the routines, and suggestions for adapting them. The book includes connections to the Standards for Mathematical Practice in the Common Core State Standards and focuses on creating opportunities for differentiated instruction.

Watch Today's Number in Action on The Teaching Channel:

Visualizing Number Combinations:

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High-Yield Routines for Grades K-8, released by the National Council of Teachers of Mathematics (NCTM), is a book that presents diverse mathematical routines recommended for use at a variety of grade levels and with a variety of mathematical content. The book also includes ideas for infusing mathematics into the non-mathematical routines that take time away from instruction.

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The Routine: A number line that is strategically marked with values is presented to students. Students are asked to locate a value on the number line or determine the value of a marked location on the number line. Students explain or show their thinking (how they know that is the location of the value or that it is the value of the marked position). Students can explain themselves in words or by annotating the number line.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Area using fractions, can be Monday or Tuesday. Watch the video!

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

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3 Powerful Tile Strategies will equip you to provide number sense opportunities to your students that involve composing and decomposing either whole numbers or fractions. This is a very flexible resource that can be used in any grade, K-12.

This post follows up the wildly popular Tiled Area Questions and Primary Tile Questions posts with even more strategies - and with 4 0 brand new downloadable pages!

By using some or all of the 3 Powerful Tile Strategies your students will have strong ongoing opportunities to develop number sense in bright, colorful, and insightful ways.

Download pages 1-10 here.

Download pages 11-20 here.

Download pages 21-20 here.

Download pages 31-40 here.

Here is a glimpse into how Molly Rawding and the amazing fourth grade team at her school are including tiled area questions in a 3-week challenge! You can follow Molly on Twitter @MollyR54321
Update: If you have not yet read Chase Orton's blog post, entitled "Using tile problems to introduce fractions and create intellectual need," you should stop and read it now! The way Chase uses story, images, student examples, and instructional tactics vividly brings readers directly into a powerful experience. His post also allows you to see how he keeps pressing himself and those around him to reach for deeper levels of learning. You can find Chase on Twitter @mathgeek76 and find his blog here.
Update: Here is a pic from Jon Orr (@MrOrr_Geek) who tweeted "I'm seeing extensions into @SteveWyborney 's Tiled Area problems into algebra..." Nice extension, Jon!

You may also be interested in:

This post includes 50 (fifty!) animated number sense lessons for K-12 teachers.

The original Tiled Area Questions, which includes a wide a variety of downloadables

Primary Tile Questions, which focuses on number sense with whole numbers, and includes many more downloadables.

The runaway post, The Animated Multiplication Table

The more recent, highly popular The Maze Hundreds Chart

If you are interested in being notified as soon as new resources are posted, please take a moment to subscribe.

Thank you for visiting my blog!

Steve

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3 Powerful Tile Strategies (and 40 new downloadable pages) - Steve Wyborney's Blog: I'm on a Learning Mission.

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3 Powerful Tile Strategies will equip you to provide number sense opportunities to your students that involve composing and decomposing either whole numbers or fractions. This is a very flexible resource that can be used in any grade, K-12. This post follows up the wildly popular Tiled Area Questions and Primary Tile Questions posts with even...

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Share your videos with friends, family, and the world

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https://vimeo.com/394336847 Copy and Paste the link. Them click on Berkeley Everett's name. Scroll down to see Same/Different videos

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Same Different Adding Ones and Adding Tens

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Students write a story problem and equation that goes with the diagram

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One of my very favorite time filler activities to do with my class is " Mystery Numbers ". I tell my kids that I am thinking of a number. I give them four clues and they have to guess the number I am thinking about.

I have a new product that is all about " Mystery Numbers ".

It includes:

12 full size mystery number sheets
6 1/2 page {perfect for centers} mystery number cards
1 recording sheet
10 black and white mystery number sheets

I use the mystery number cards on my document camera.

We also enjoy doing them whole group on the "mat area" during our morning meeting.

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One of my very favorite time filler activities to do with my class is " Mystery Numbers ". I tell my kids that I am thinking of a number. I give them four clues and they have to guess the number I am thinking about.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Mix it up Monday: which doesn’t belong and why? Go to the corner of the answer your feel doesn’t belong. Discuss it, then go back to your table and share what you heard.

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How are they the same? How are they different?
Display to images of students work on the same question side by side.
If they are both correct, talk about how they solve it differently and got the same answer.
If one is incorrect ask them where the mistake was made.

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Great conversation starters

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Recognize at-a-glance numbers by using dot cards.

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Math Vocabulary Cards by The Math Learning Center

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Math Vocabulary Cards by The Math Learning Center

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Math Vocabulary Cards by The Math Learning Center

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Math Vocabulary Cards helps students deepen their conceptual understanding of key terms in mathematics.

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Braining Camp to 500 -  hund chart activities

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Braining Camp to 500 -  hund chart activities

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4 templated linked below. You need to already be logged on to braining camp for them to open for you.
Noticing Patterns 1-120  https://connect.brainingcamp.com/s/UE2WYJKY

Noticing Patterns 101 - 220  https://connect.brainingcamp.com/s/9XDCBN73

201 - 320 noticing Patterns and hidden numbers  https://connect.brainingcamp.com/s/XUJNBMZM

501-600 hidden number (clear chart)  https://connect.brainingcamp.com/s/MJGCA84P

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Please launch Brainingcamp from your district portal.

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Pick and choose the ones you want to do.

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10 Math Games That'll Boost Your Brain Power By 80%

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Share your videos with friends, family, and the world

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Teacher Education by Design

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Number strings by the Recovering Traditionalist

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Number strings by the Recovering Traditionalist

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Number Strings are a series of related problems that lead kids to a particular strategy or a particular model.

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That leads me to when should you use which one? So to me, this is based on how I've been using the two. You may disagree with me, so let me know in the comments, but to me, I like to use Number Talks when I'm working with a group of students who already have strategies. If I put a problem and you get the "deer-in-the-headlights" look, then the Number Talk may not be the best thing because they don't have different strategies and they are all solving it the same way. That makes it hard to do a talk about the different ways kids are solving it.

So in a Number Talk, you have to have a group of kids who have some strategies and then you can talk about the different strategies and how they are alike and how they are different. That's one of the powerful parts of a Number Talk, is that you're not just showing all of the different ways that kids solved it because that can be overwhelming for a lot of kids. To do a number talk correctly, you also need to make connections. If Johnny did it one way and Jose did it another way, we've got to talk about how those ways are still alike and how they are different. What did Johnny do that's different than what Jose did and but yet still connected.

For our struggling kids, sometimes a Number Talk can be very overwhelming because they see six different ways that people solved the problem and they don't get any of them. So you've got to spend some time in Number Talks to be able to make connections between the different ways that kids are solving them.

In a Number String, I like to use them to help develop strategies. If I'm working with kids who don't have strategies already, a string of problems is super powerful to help build those strategies. So let's take a look at this example.

This can definitely be different depending on the grade level that you work. However, in this example, I could start with the string off to the left if my kids don't have a strategy or strategies for that bottom problem. So I might start out just showing 9 + 7 and talking about how they solved that problem. Then I would show 29 + 17 and see if they're using the same type of strategy. They may have a different strategy for that problem but I want to make the connection of how they solved 9 + 7 connects to how they can solve 29 + 17. Then how that connects to how you can solve 498 + 267. Finally, I get to the problem which is what I actually want my kids to develop at this grade level. When I'm adding decimals, can I use those same strategies? You bet!

If they haven't made those connections, I'm going to use a string to help bridge the gap between the things that they learned prior to what I'm wanting them to learn now. If I just throw up 3 and 99 hundredths plus 17 hundredths, and they don't have strategies already and they haven't made connections, then I'm probably going to get every kid solving it the same way or not knowing how to solve it.
So again, a Number String to me is a way to help develop strategies whereas a Number Talk is to talk about the different strategies kids have for that one problem, how they connect together, how they're alike, and how they are different.
I hope that that's helped you build your math mind, so you can go build the math minds of your students. If you would like to learn more about using Number Strings, I talk about them as Number Talks because most of you are familiar with Number Talks.

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Number Talks Versus Number Strings - The Recovering Traditionalist

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That leads me to when should you use which one? So to me, this is based on how I've been using the two. You may disagree with me, so let me know in the comments, but to me, I like to use Number Talks when I'm working with a group of students who already have strategies.

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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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Number Talks ~ Counting On Strategy within Sums to 20 (DIGITAL and Printable)

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These Number Talks are perfect to grab and use when you are teaching first grade students the computational strategy,Counting On to Add. All of these math talks lend themselves to counting up to solve addition problems within 20.

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Solvemoji - Emoji teaching resources - Emoji math puzzles, great as a primary math starter, download our pdf worksheets - great for home schooling

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Math Flips are flashcards with a problem on the front and a similar problem on the back (instead of a problem and an answer) to encourage relational thinking rather than answer-getting.

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Math Flips are flashcards with a problem on the front and a similar problem on the back (instead of a problem and an answer) to encourage relational thinking rather than answer-getting.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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If we only add 2 numbers, how many answers can we find?

What if we add 3 numbers, or 4 numbers?

What about any number of numbers?

What if we only subtract, or only multiply, or only divide?

What’s the longest number sequence you can find that hits the target number?

Can you hit the target number if you only use a single number, such as the number 4, in your equation?

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The teacher writes a "target" number on the board. The students try to write down as many different number sentences that have that the target number as the answer. Then students share their favorite answers. For younger students, drawing different pictures or arrangements of ways to see/understand that number is an ok alternative.

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Fill-the-Stairs-Ordering 2 digit numbers Game

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Fill-the-Stairs-Ordering 2 digit numbers Game

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Fill-the-Stairs-Ordering 2 digit numbers 2017

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Scroll Down to located expamples by g
rade level

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Teacher: Time for our morning Number Talk.
Everyone consider this question. (She writes 9 + 17 on the board).
(A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)
If you get more answers, show me by holding up more fingers. (She waits for 30 seconds. Several students are holding up multiple fingers, though many have just a thumb.
The teacher is noting to see if anyone hasn't solved the problem-this is a great opportunity for formative assessment.
Finally, she begins calling on students for their answers, starting with those who have only one solution.)

Teacher: Lucy?
Lucy: 26. (Teacher writes 26 on the board.)

Teacher: Charles?
Charles: 107 (Teacher writes 107 on the board.)

Teacher: Michelle?
Michelle: 25. (Teacher writes 25 on the board.)

Teacher: Any other answers? (No one has any.)
Who would like to explain how they got their answer? Tyrone?
(The teacher records what the students write as they explain.)

Tyrone: I know that 9 + 7 is 16, and then I added another 10 to get 26.
Sarah: 10 + 17 is 27, and 10 is 1 more than 9, so 9 + 17 must be 26.
Charles: 9 + 1 is 10, and then you put a 7 after, so it's 107.
Lucy: I counted one by one, but I just realized that I miscounted.
I agree with 26
(Teacher crosses out 25 and replaces it with 26.)
Sam: I respectfully disagree with Charles.
You can't add the 9 + 1 because the 1 stands for 10.
Charles: But that's how you add. I did it right.
(Teacher lets conversation continue until class consensus, or near-consensus, is reached.
Meanwhile, she's noting where students are in their understanding of place value and addition.)

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Teacher: Time for our morning Number Talk. Everyone consider this question. (She writes 9 + 17 on the board). (A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.