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Counting Collections Videos for Preschool

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Counting Collections Videos for Preschool

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After children count their collections, teachers can ask them to represent their counting on paper (see C ounting Collections Overview for more information about counting and representing). For example, a preschool teacher might say "Can you show your collection on your paper? Can you draw it?"

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Erikson Institute Early Math Collaborative

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Book

Our new book extends professional knowledge for mathematics teaching to educators who work with the very youngest learners. How do babies and toddlers understand the precursors of math?

Learn more

The Erikson Institute Early Math Collaborative is transforming the understanding, teaching and learning of early mathematics from the ground up.

Online Learning

Professional development modules

Our self-guided modules provide materials, strategies, and expert guidance for working with adult learners to explore foundational mathematics. Whether you are working with childcare providers, in-service teachers, or pre-service teachers, modules give you what you need to support professional learning in your local context.

Start a module

Children love to count. Counting helps them make sense of the world and to find out how many of something. With time and practice, children develop an understanding of the "rules" or principles of counting.

From an early age, children notice and appreciate patterns in the world around them. Patterns and sequences of different kinds begin to pop up all over the place, especially in the books that children love.

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...

In May of 2023, a diverse group of six kindergarten teachers from across the United States were selected from a national pool of talented and committed kindergarten teachers to participate in the RJEM Teaching Fellowship....

From a racial justice centered perspective, books can be powerful tools to engage children in mathematics learning. The worlds, stories, adventures, characters, and possibilities that are made available through books - explicitly math focused and...

RJEM at Work highlights the everyday efforts of caregivers, community organizations, teachers, researchers, and educational institutions to promote racial justice in the mathematical experiences of children. For the RJEM Local Planning Committee, there are multiple...

Get more when you join. More resources and more ways to connect. Save your favorites so that more is at your fingertips.

Best of all, it's free. Sign-up today.

Early math is big.

Learn why we are so passionate about giving every child a strong foundation in math.

Funding for this initiative is generously provided by:

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Early Math Collaborative at Erikson Institute

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The Early Math Collaborative works to improve math instruction for young children in three ways: professional development, research, dissemination.

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Subitizing: Dot Cards and Ten Frame Cards

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Subitizing: Dot Cards and Ten Frame Cards

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Subitizing: "Find It" Bingo Game Option 1

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Subitizing: "Find It" Bingo Game Option 1

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Subitizing: "Find It" Bingo Game Option 2

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Subitizing: "Find It" Bingo Game Option 2

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From: KYMath
Created by: Amanda Miller

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Roll the dice and have students find the ten-frame card that has the same amount, if they roll a 11 or 12 they roll again.

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Students roll two dice and build that amount with counters on their ten frames mat. Use one die for five frame mat.

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The teacher shows a domino for a count of 5-10 seconds, depending on the ability level of the students, then covers it. Students look at the domino as it is shown, then build the domino from memory. The teacher circulates around the room as students work, to observe student performance. After some time, the teacher asks students to describe the domino they saw and how they remembered the patterns to build. Finally, the teacher shows the domino again so that students are able to self-correct.

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How many dots do you see?
How many empty boxes?
How many all together?

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How many dots do you see?
How many more to make ten?

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NCTM Five Frame Digital Interactive Tool

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NCTM Five Frame Digital Interactive Tool

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Modes

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

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

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

Add: Drag items to complete addition problems.

Play All: Randomize which of the four games above is played.

Options

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

How to Use

The Done button should be clicked when you believe that you have correctly completed a frame. The number buttons at the bottom of the screen can be used to enter an answer, or the computer keyboard can be used.

The Next button advances to the next problem.

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The four games that can be played with this applet help to develop counting and addition skills.

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

Modes

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

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

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

Add: Drag items to complete addition problems.

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

Options

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

How to Use

The Next button advances to the next problem.

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

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

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The four games that can be played with this applet help to develop counting and addition skills.

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Number Rack facilitates the natural development of children’s number sense. Rows of moveable, colored beads encourage learners to think in groups of fives and tens, helping them to explore and discover a variety of addition and subtraction strategies.

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Display or flash a rekenrek card.
Student creates same bead pattern on their rekenrek.
Ask student, "How many beads all together?" "How do you know?"

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Choose a target number with your students.
Create the target number on your rekenrek without your students seeing how you created it. Students do the same.
Ask students, "Can you guess what I did?"

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Slide an amount of beads over on the rekenrek.
Ask student, "How many more to ___?"
Student slides the amount over to make your target number.

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"Got Rekenreks?" video by Graham Fletcher

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"Got Rekenreks?" video by Graham Fletcher

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Rekenrek Activities for Small Group Instruction

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Rekenrek Activities for Small Group Instruction

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The rekenrek, or arithmetic rack, was designed by Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, to support the natural development of number sense in children. Smaller versions consist of two rows of 10 beads. Larger versions with ten rows of ten beads are also available. Each row is made of five red beads and five white beads. This allows students to make mental images of numbers. Using 5 and 10 as anchors for counting, adding and subtracting is obviously more efficient than one-by-one counting. This tool provides learners with the visual models they need to discover number relationships and develop a variety of addition and subtraction strategies, including doubles plus or minus one, making tens, and compensation, thereby leading to automaticity of basic facts.

Possible Rekenrek Activities

Possible Math Journal Tasks:

There were 8 children on a bunk bed. Some were on the top bunk and some were on the bottom bunk. How many children were on the top bunk? How many children were on the bottom bunk? Show as many different solutions as you can. Number Stories: Have children use individual arithmetic racks as a tool to solve various types of addition and subtraction number stories. This may be used as a journal or oral activity, with the focus on children explaining their strategy for solving the problem. Be sure to include open-ended problems that have more than one solution that children can model on the arithmetic rack, such as the following:

There were 12 passengers on a double-decker bus. Some passengers were on the top deck and some were on the bottom deck. How many passengers were on the top deck? How many passengers were on the bottom deck? Show as many different solutions as you can.

The above two work samples were completed by a Kindergarten student who represented her work very clearly on the unlined pages in her Math Journal using pictures, numbers and words. To begin with some Kindergarten students may find it difficult to represent their work on paper. Having recording paper available for children who choose to use it is one way to scaffold early attempts at drawing.

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The rekenrek, or arithmetic rack, was designed by Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, to support the natural development of number sense in children. Smaller versions consist of two rows of 10 beads. Larger versions with ten rows of ten beads are also available.

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Using the Rekenrek as a Visual Model for Strategic Reasoning

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Using the Rekenrek as a Visual Model for Strategic Reasoning

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By The Math Learning Center

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The Progression of Early Number & Counting

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The Progression of Early Number & Counting

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The Progression of Early Number & Counting

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Numberblocks - Learn to Count | Maths for Kids | Learning Blocks

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Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

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

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https://youtu.be/WoI_I7RQ1-A

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A Game that Teaches More, Less, Same Using Dice

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Looking for fun ways to practice subitizing with your students? Try using games!

I love playing games - both with my family and in my classroom! Games are engaging, but they also help build math skills: number sense, subitizing, problem solving, critical thinking, and so much more. So I sneak learning games into my math instruction whenever I can. Math games can do so much to boost subitizing and number sense skills in kindergarten and preschool. That's why I'm going to share 4 awesome subitizing games you can use at school or at home with young learners.

But first, what is subitizing?

Subitizing is the rapid recognition of groups of items, without counting. When you roll a die, you don't have to count how many dots there are - you just know that dot arrangement is 4. That's subitizing (technically, perceptual subitizing.)

How does this help with math?

Subitizing is more efficient than counting each item - it saves time in math tasks. Students who can subitize have a better understanding of the numbers and what they represent; they recognize the numeral 4, have a concept of its quanitity, and can use that concept to help the order and compare small quantities/numbers. Additionally, subitizing is the foundation for future mathematical skills:

counting on/back from a given number

combining sets of larger numbers

decomposing larger sets of items

applying these strategies to addition and subtraction

These more advanced skills typically require conceptual subitizing, which means taking a larger number of items and mentally breaking them into smaller groups. For instance, when you see this group of 6 dots, you might see it as 3 and 3 or 5 and 1. The ability to "see" small sets within a large set makes addition and subtraction more efficient and rapid.

Now think about your students. We've all seen the little dears who still need to count every dot on the die when they roll 3 - even after months of practice. These children have not learned to subitizing small quantities, which will impact all the math skills listed above. Subitizing is foundational to much of math.

How can I help my students subitize?

This is where subitizing games and fun number sense activities come in. The most helpful thing for subitizing is anything that has children quickly look at a set and identify the quantity without counting. Here are some ways to do that:

Flash Dot Pattern Cards: Use cards that have groups of dots on them. (This can be as simple as a paper plate with dot stickers or dots drawn with markers). Quickly show the dot card (for literally a second), then lay it down. Students name the number of dots they think they saw. Then show it again and check. (This can be done with a group of students or with individuals.) As a variation, you can rapidly hold up fingers on your hand, then hide them.

First focus on quantities of 1-4 (for perceptual subitizing). As students become successful with those, move on to larger sets (for conceptual subitizing). Have students talk about how they "saw" small groups within the larger set.

War Games: Make cards with dot patterns. Each student flips over a card and quickly names the number shown (ideally, without counting). You could even have them show it, hide it, then say the number and check. The child with the greatest quantity keeps both cards (playing like the traditional war game.) As a variation for numbers 1-6, you could have each student roll a die and the child with the larger quantity takes a chip/counter to keep track of points.

As students become more confident in subitizing, you can add in other images, such as ten-frames or tally marks, to continue developing skills. Save yourself time and download this free Ten-Frame War game from my store.
This Ten-Frame War game is free at my TPT store.
I also have a more complex subitizing war game with dot patterns, finger patterns, ten-frames and tally marks for purchase in my store.

Memory/Concentration: Make dot cards with dot patterns and numerals, or two different dot patterns for each number. Lay the cards out in an array. Students turn over two cards and quickly name the number/quantity shown. If they match, they keep the cards, if not, turn them back upside down in the array.

Find the Card with ___: Students lay out several dot pattern cards on the table in front of them. The teacher says a number and students quickly find a card that represents that number.

These cards come from the Domino War game, but can be used flexibly for many subtilizing activities.

A few final tips:

With all of these activities, keep in mind that the purpose is to rapidly identify the quantity, not to count the dots. As students play some of these games with partners, you will want to emphasize that they should say a number first, then count to check.

Once students become familiar with some of these subitizing activities, you can use them as sponge (or filler) activities in your day. They are also a great addition to a soft start to your school day. My students LOVE playing math games, and don't even realize they are learning as they play!

Finally, remember that perceptual subitizing (small sets) occurs before conceptual subitizing (combining/decomposing larger sets). So stick with sets with 1-4 dots (or finger patterns, ten-frames, etc.) until your students are able to rapidly recognize these sets. Then move on to numbers to 10 and beyond.

A solid understanding of number sense in kindergarten will support mental math in older grades. Have fun helping your students develop stronger number sense!

Pin it to remember these games later!

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How to Use Games to Build Subitizing Skills - Primary Delight

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Looking for fun ways to practice subitizing with your students? Try using games! I love playing games - both with my family and in my classroom! Games are engaging, but they also help build math skills: number sense, subitizing, problem solving, critical thinking, and so much more.

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Geometric Subitizing: Grade 5 Mathematics

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

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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DISCLAIMER: GregTangMath.com is owned and operated by Creative Smarts Inc which is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.

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DISCLAIMER: GregTangMath.com is owned and operated by Creative Smarts Inc which is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.

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Counting Collections with a Partner - Recording Sheet

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Counting Collections with a Partner - Recording Sheet

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Counting Collections: Third Grade - a common core classroom friendly exercise

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this video also available on the teaching channel website
teachingchannel.org

thanks for watching.  Comments welcome!

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Share your videos with friends, family, and the world

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123s! Numbers & Counting - Read Alouds for Early Learning

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These children's books are perfect for Pre-K and Kindergartners learning numbers, how to count and starting early math!

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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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Early Numeracy - SAME BUT DIFFERENT MATH

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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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Number lines are a reliable method teachers have been using for ages to teach number sense, arithmetic, and all sorts of other math skills. This collection of number line activities works with littles and not-so littles, as they learn the concepts they need to be successful at math. Pick a few to try today!

1. Use sticky notes to line up numbers.

Write numbers on sticky notes and ask kids to place them in order on the number line. This simple idea is perfect for little ones first learning to sequence numbers. But number line activities are useful for older students too; try this same exercise with fractions, decimals, or negative numbers. ( We love sticky notes in the classroom!)

Learn more: Busy Toddler

2. Build a life-size number line.

A life-size number line in your classroom allows you to do all sorts of active math games and practice. Kids will get even more out of number line activities when they become the numbers! (Pro tip: Carpet spots are fantastic for this project.)

Learn more: School Is a Happy Place

3. Line up your shoes.

Here's one of those number line activities just made for your life-size line! Have the class count and line up their shoes, or workbooks, or crayons. The possibilities are endless.

Learn more: Days With Grey

4. Paint a dotted number line.

Kids use cotton swabs and paint to represent the value of each number on a line, helping them visualize what each number means. They can see how numbers grow in size from left to right.

Learn more: A Pinch of Kinder

5. Go vertical for number line activities.

Most number lines used in the classroom are horizontal, but vertical lines can help give kids better number sense. Since we associate "up" with "greater," a vertical number line makes that concept easier to grasp.

Learn more: Mr. Elementary Math

6. Match dominoes to the numbers.

Kids count the dots on dominoes, or add the two numbers they see to get the sum, and place them by the corresponding number on the line. You could do this with subtraction, too.

Learn more: Busy Toddler

7. Build a number line with LEGO bricks.

Playing with LEGO bricks is learning? Who knew! We love this idea for practicing counting on using a LEGO minifig and dice.

Learn more: Gluesticks & Giggles/Instagram

8. Hop and drop along the line.

Here's a number line activity that's sure to get kids giggling. Challenge them to carry a ball along the line and drop it on a specific number-without using their hands! They can hold it between their knees, under their neck, or any way they choose. Their antics will make you laugh, but they'll be learning all the while.

Learn more: Teach Me Mommy

9. Turn a zipper bag into a number line slider.

Well, how ingenious is this idea? Write a number line across the top of a zipper bag with a slider. Then insert a math fact to practice and slide along to find the answer. So fun!

10. Plant a number line garden.

Turn cupcake wrappers and craft sticks into numbered flowers, and "plant" them in a cardboard tube number line. (A pool noodle would also be fun for a number line garden.)

Learn more: 123Homeschool4Me

11. Use clothespins for number line activities.

Pick up a bag of clothespins at the dollar store ( you know you're shopping there for teacher supplies anyway) and write numbers on them with a Sharpie. Then create individual number line manipulatives from paint stirrer sticks. Simple and cheap!

Learn more: Fantastic Fun and Learning

12. Craft a number line bookmark.

Hit the link below for the free printable and print these bookmarks out on card stock. ( Laminate if you like.) Then punch holes at the top and bottom, slide a bead onto a pipe cleaner, and attach it as shown. Kids now have a handy bookmark to help them with number line activities.

Learn more: Highland Heritage Homeschool

13. Tell the story of the "naughty numbers."

If your students sometimes have trouble remembering which directions the written numerals should face (hello, backwards 3 that looks like capital E!), the story of the naughty numbers may help. Hit the link below to hear the tale and learn how it works.

Learn more: The First Grade Parade

14. Teach rounding with number lines.

Number line activities are handy for more advanced students, too. They're ideal for learning about the concept of rounding numbers. Use a clever anchor chart like this one to show kids how it works.

Learn more: Crafting Connections

15. Send messages in secret code.

Assign each number on the line a letter (mix them up to make it more challenging). Then, craft your message using arithmetic problems for students to solve. Kids figure out the answers, find the corresponding letters, and spell out your message (which hopefully does not self-destruct!).

Learn more: Creative Family Fun

16. Drive along to learn fractions.

Understanding equivalent fractions can be a challenge, but number line activities can help. In this one, drive a toy car along the lines and use equivalent fractions to prove your answer. See how it works at the link below.

Learn more: Beyond Traditional Math

17. Use a number line to understand improper fractions.

Improper fractions can be a bit tricky, but number line activities make them easier to understand. Get this free printable cut-and-paste activity at the link below.

Learn more: Math Tech Connections

18. Put decimals on the line.

Fractions and decimals go hand in hand, and both are easier with number lines. Get free printable worksheets at the link below and learn how to use number lines with decimals.

Learn more: Math Geek Mama
Number lines are terrific for estimation, too. Find 18 estimation activities for your classroom here. 10 frames are another incredibly useful math tool. Here are some fantastic and fun 10 Frame Activities you'll want to try next.

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18 Number Line Activities You'll Want to Try in Your Classroom

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Number lines are a reliable method teachers have been using for ages to teach number sense, arithmetic, and all sorts of other math skills. This collection of number line activities works with littles and not-so littles, as they learn the concepts they need to be successful at math.

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Build fluency in math facts with this fun bug-catching game! Featuring a hungry frog, this game encourages students to practice addition and subtraction within 10.

How do you play? You need to help the frog catch the bugs by moving him along the number line to where the bug is. Count forward or backward to see how many spaces are between the frog and the bug. Then, determine which equation displays the operation that will move the frog to the correct spot. If you answer correctly, the frog will enjoy a yummy meal. If you answer incorrectly, the bug will fly away and return to a different spot on the number line. Don't let the frog go hungry!

This game helps build number sense. Plus, young students build fluency with basic math facts related to addition and subtraction within 10. The number line also provides students with a concrete tool, reinforcing counting and cardinality.

The bug catcher math fluency game is perfect for indoor recess, as a math station, or for early finishers. Challenge your students to see how many bugs they can catch!

Visit classplayground.com for more information and printables related to number lines, addition, and subtraction.

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Bug Catcher Number Line Game | Toy Theater

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Boost your student's fluency in addition and subtraction within ten with this fun bug catcher game. Try it, it's free!

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Play a matching game with different representations of equivalent items.

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Play a matching game with different representations of equivalent items.

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As we said in the original post, our ideas for our blog are wide-ranging. We are excited to have a space that offers us the opportunity to answer common questions from the field. This Q&A is the first of that type of blog post. Have questions you'd like to see answered? Email us.
Question: How do Kindergarteners learn to write the numbers, and use them to represent quantities?

Answer: We are frequently asked about how Investigations supports young students in the development of numeral writing. One thing it's important to remember is that learning to write the numbers is intricately connected with students' developing understanding that a number -whether the spoken word "three", a group with 3 objects, or the written number "3"-describes a quantity. Consider this excerpt from the Teacher Note: Observing Kindergarteners as They Count:

"In Kindergarten, students come to understand that a quantity can be represented in a variety of ways. Many activities ask students to use numbers, pictures and/or words to show how many, or to count out a set when given a number, orally or in writing. Students need many opportunities to see how numbers are used to record, and in this context they practice correct numeral formation. Recording mathematical information such as the number of students in school today or objects in the Counting Jar provides such opportunities. Tools such as the calendar and number line provide a model of numerals in their natural order. While recognizing numerals and knowing how to write numerals are important skills in communicating math ideas, they are not directly related to counting and understanding quantity. Whereas young students who are learning how to write numerals frequently reverse certain ones, this is not a mathematical problem but often a matter of experience. Like letter formation, number formation and practice writing numerals should be part of handwriting instruction rather than mathematics." (KU2, p. 157)

In addition to providing many opportunities for students to see and use numbers as they solve problems and show their work, the curriculum encourages teachers to model number formation as they record:

Finally, the curriculum includes activities explicitly aimed at providing practice with writing the numbers across the year. Roll and Record is one such activity. In Unit 2, students roll a 1-6 dot cube and record the number, as a numeral, in the appropriate column. In Unit 4, the game shifts and involves rolling two dot cubes (1-6, 1-3), and recording the total.

In Unit 6, students roll two 0-5 dot cubes, and in Unit 8, students play variations of this game, now called Race to the Top, on gameboards that provide practice writing the numbers to 20.

(Note that, while these games provide explicit practice with writing the numbers, they are also engaging students in other, significant mathematical work (e.g. subitizing amounts to 6, connecting counting and combining, developing an understanding of the teen numbers as ten ones and some number of ones) at the same time.)

Being able to accurately write the numbers is one aspect of the Kindergarten curriculum. But it's important to remember that, "just as saying the alphabet does not indicate that a student can read, being able to say" or write 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 "does not necessarily indicate that students know what those counting words" and numerals mean. (KU2, Teacher Note: Counting is More Than 1, 2, 3, p. 156) What's critical in Kindergarten, and what the Investigations curriculum takes seriously, is that students can use numbers to communicate mathematical information and ideas.

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A Kindergarten Q&A: Numbers Represent Quantities - Investigations3

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As we said in the original post, our ideas for our blog are wide-ranging. We are excited to have a space that offers us the opportunity to answer common questions from the field. This Q&A is the first of that type of blog post. Have questions you'd like to see answered?

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High Leverage Assessments and CRA Assessments

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High Leverage Assessments and CRA Assessments

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Improve your math instruction with high-leverage assessments and classroom tools from ALN! Partner with us to enhance math learning for all students.

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Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young children need for later school success.

Learn more, get extras, and watch author interviews here!

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Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young childre

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SplashLearn's games on anchoring 5 and 10 can help kids overcome problems with speedy calculations of numbers between 5s and 10s. Makes calculations a fun activity through our specially designed interactive platform, where kids can enjoy solving math problems.

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Games for Kids on Addition up to 1000000 Online - SplashLearn

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SplashLearn's games on anchoring 5 and 10 can help kids overcome problems with speedy calculations of numbers between 5s and 10s. Makes calculations a fun activity through our specially designed interactive platform, where kids can enjoy solving math problems.

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Rekenrek Activities with Christina Tondeveold

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Rekenrek Activities with Christina Tondeveold

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A number string is a set of related math problems, crafted to support students to construct big ideas about mathematics and build their own strategies (Fosnot & Dolk, 2002). Typically, a teacher gathers her students near the board and presents the problems - one at a time - providing plenty of time for students to think. Students first solve the problems mentally, then share their strategies with the class while making sure they understand others' thinking. Meanwhile, the teacher is representing students' strategies on a model and facilitating conversation among students about the sense they are making within and between the problems. Strings are not a rigid recipe but a flexible classroom routine - used by teachers daily or weekly with both small groups and entire classes.

Here is a narrative of a first grade number string or a video of a fourth grade number string to get you started.

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A number string is a set of related math problems, crafted to support students to construct big ideas about mathematics and build their own strategies (Fosnot & Dolk, 2002). Typically, a teacher gathers her students near the board and presents the problems - one at a time - providing plenty of time for students to...

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Students place markers on the numbers 2-12. &nbsp Students toss two 6-sided dice, find the sum and remove a marker from that number, if there is still one. &nbsp The first player to remove all markers wins the game. &nbsp This game can be used as addition practice or as an introduction to the probability of the different outcomes of rolling two dice. &nbsp This game was developed by a Monmouth University student for the Probability Fair.

Download the Face Off! Game directions, center icons and gameboards for both the one-die and two-dice versions of the game.

Data Collection: &nbsp Post a frequency table and have students record the last number they needed to win the game. &nbsp After students have played several rounds, analyze the data to see if each number seems to have an equal chance of being the winning number.

In the M&M Probability Game, students place M&M markers on the numbers 2-12. Students may place one M&M marker on each number or place several on some numbers and leave other numbers blank. Next, students toss two 6-sided dice, find the sum, and remove an M&M marker from that number, if there is still one. The first player to remove all markers wins the game. The game, designed by Susie Siegel, a New Jersey teacher, includes PDF files for the directions,and a recording sheet.

In response to several requests, Terry Kawas has created M&M game pieces that may be printed, cut apart, and used with sentence strips, as pictured above. Some teachers opt to use round foam pieces, available at craft stores, as alternative game pieces.

M&M Probability Game Pieces

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Mathwire.com | Addition & Subtraction Games

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Students place markers on the numbers 2-12. &nbsp Students toss two 6-sided dice, find the sum and remove a marker from that number, if there is still one. &nbsp The first player to remove all markers wins the game.

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The Math Viking: Elementary Math Exploration

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Links » The Math Viking: Elementary Math Exploration

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The best games engage kids and allow for exploration as well as practice. Many tiles expand to show lots of games. Go ahead and EXPLORE! Notice that counting, composing and subitizing games are at the top left before number lines

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Need a way to get students more excited about building math skills? A deck of playing cards might just be the answer. These math card games work for little ones and older kids alike, and they're all free to learn and play. Draw a few to add to your winning math class hand today!

1. Match to make 11

Lay out three rows of three cards each, face up. Then check to see if you can find any two cards that add up to 11. If so, remove those cards and set them aside. Replace them with new cards from the deck. Continue until you run out of cards or can't make any more matches.

Learn more: Game Rules

2. Race to 100

Flip a card and add its value to your running total. First person to reach 100 without going over wins! (Remove face cards for younger players; use these values for older kids: Jack = 11, Queen = 12, King = 13, Ace = 0.)

Learn more: 123 Homeschool 4 Me

3. Play a game of 21

In Vegas, they call this one Blackjack, but it makes a great learning game for kids too (no need to place bets!). Not only do they practice their addition skills, but they'll also get a little practice at thinking logically and calculating the odds.

Learn more: Planning With Kids

4. Try pyramid solitaire alone or in teams

Some versions of solitaire are really just sneaky math card games, and pyramid is one of them. Try to find cards that add up to 10 as you clear your pyramid row by row. Learn how to play at the link below.

Learn more: Multiplication.com

5. Flip and add 1 or subtract 1

There are a few versions of this basic addition and subtraction game. We like this one: Remove the face cards from the deck. Flip a card. If it's red, add 1 and say the amount out loud. If it's black, subtract 1. If you get it right, you get to keep the card.

Learn more: Plus 1 Minus 1/Creative Family Fun

6. Go fish for pairs that make 10

Your students probably already know how to play Go Fish, but in this version, they're fishing for pairs that add up to 10. Have them ask: "I have a 2. Do you have an 8 to make 10?" Change aces to 1 for this game and leave face cards out entirely.

Learn more: Go Fish/The First Grade Roundup

7. Calculate the gain or loss

Each player starts with 15 points. Player one flips a card (remove face cards or assign them point values first). If the card is black, they add it to their total. If it's red, they subtract it. Highest point total when all the cards are gone wins! Get a free printable worksheet to use with this game at the link.

Learn more: Teacherspayteachers.com

8. Practice counting on with cards

Remove the face cards for this one, and grab a die. Players flip a card and roll the die. Starting with the number on the card, they "count on" using the number on the die. For instance, if the player flips a 7 and rolls a 4, they would say, "7 ... 8, 9, 10, 11." If they get it correct, they keep the card.

Learn more: Creative Family Fun

9. Card turnover and multiply (or add)

This one is so simple! Have students pair up. One person flips two cards from the deck. The first student to multiply (or add, depending on what you want to practice) them correctly and call out the answer wins and takes both cards. Play continues until all the cards are gone, and the winner is the one with the most cards.

Learn more: Turnover/Top Notch Teaching

10. Try for a total of 10

Play this math card game alone or as a team. Lay out 20 cards on the table (leave out face cards or change them to equal 0, while aces equal 1). Kids remove sets of cards that add up to 10, ultimately trying to remove all the cards from the table. It's harder than you think!

Learn more: Total of 10/The First Grade Roundup

11. Practice number sequencing with Builder's Paradise

Simple math card games can help kids learn how to put numbers in order. To play Builder's Paradise, discard the face cards and lay out the four sevens in a deck side by side. In each round, players work to add the next higher or lower number in each suit, trying to be the first to get rid of all their cards. Get the full how-to at the link below.

Learn more: Builder's Paradise/Math Geek Mama

12. Add decimals to "make a buck"

Draw, swap, and discard to make a hand that equals $1. Learn what face cards equal and get all the rules at the link.

Learn more: Make a Buck/Math Geek Mama

13. Declare a fraction war

War is one of the original math card games, but this version adds a fraction aspect. Students deal two cards-a numerator and denominator-then determine whose fraction is the largest. The winner keeps all four cards, and play continues until the cards are gone. ( Click here for more fun and free fraction games.)

Learn more: Math File Folder Games

14. Learn numbers with card bingo

Remove the face cards and have each student lay out a 4 x 4 playing "board" of cards. The remaining cards (or another deck) are placed face down, and a caller flips over a card. Any player who has that number on their board turns the card face down. Play continues until one player has a row flipped over horizontally, vertically, or diagonally and calls "Bingo!"

Learn more: Card Bingo/Top Notch Teaching

15. Play a game of "I Spy"

Lay out cards on the table, then take turns giving clues. "I spy two cards that add up to 12." Differentiate for younger kids with options like, "I spy a card that's less than 4," or for older ones: "I spy two cards that are factors of 12."

Learn more: Susan Jones Teaching

16. Use order of operations to get to 24

Math card games aren't just for little kids-even adults will find this one a bit tricky. Each player is dealt four cards, then uses the order-of-operations rules to try to make a number as close to 24 as possible. Simple but challenging!

Learn more: Learn With Math Games

17. Take a gamble with triple-digit dare

Each player gets three cards and privately determines the highest three-digit number they can make (you can use decimals or not, depending on age). Then, each player has a turn to stick with the cards they have, swap with one from the deck, or steal one of the other player's. All players then lay down their best number to see who wins. See more at the link below.

Learn more: Math Coach's Corner

18. Deal and round to tens to win

Each player deals two cards and lays them on the board. Then, round to the nearest 10 to find the winner of that hand.

Learn more: Adventures in Third Grade

19. Find a way to make 10

One of the terrific things about math card games is that many of them can be customized for various concepts and skill levels. The original goal of this game was to look at the cards you're dealt to find ones that add up to 10, but it can be changed to 15, 20, or any number you choose. You can also add to the difficulty by allowing addition and subtraction (for example, you could use 8 + 4 = 12 and 12 - 2 = 10). Get the rules and free printable mats at the link below.

Learn more: Mama.Papa.Bubba

20. Use Close Call to practice two-digit addition or subtraction

The best math card games are simple at heart. To play Close Call, each player deals themselves four cards, then determines how to arrange them so they make two two-digit numbers that add up as close as possible to 100 without going over. For a subtraction version, work to get as close to zero as possible. Learn how to play at the link.

Learn more: Close Call/Math Geek Mama

21. Let card color indicate negative or positive

In this game, red cards are negative integers, while black cards are positive. Students attempt to play pairs of cards that total 6 or -6. You can change the goal number as needed.

Learn more: Filling the Frame With Learning

22. Take a trip around the card spiral to practice math facts

You'll need a pair of dice for this math card game. Lay out cards randomly in a spiral formation as shown, and set a marker for each player on the center card. Player one rolls the dice then moves their piece that number of spaces shown. They then must multiply (or add or subtract, depending on preferences) the card number by the number on the dice. If they get the answer correct, they stay where they are. If not, they return to their original card. Play continues until one player reaches the end.

Learn more: My Baba

23. Flip to make a prime number

Flip two cards. If you can add, subtract, or multiply them to make a prime number (use one or all of these operations), you get to keep them.

Learn more: Flip for Prime/Games4Learning

24. Be the fastest in the race to pi

In this game, kids work to lay out the digits of pi in order. It's a simple draw-and-play game that will help familiarize students with this important number. You can write out the digits first or see who knows them from memory. Find out how to play at the link below.

Learn more: Race to Pi/Math Geek Mama

25. Pick three to make number sentences

Flip any three cards. If you can use them to form a valid equation (8 - 3 = 5), you keep the cards!

Learn more: Number Sentences/Games 4 Learning

26. Do some basic fast facts practice

Give your flash cards a rest and practice facts with math card games instead. Simply lay down two cards from the deck (remove the face cards first) and add, subtract, or multiply them. Kids can work on this alone, or you can make it a contest to see who can call out the correct answer first.

Learn more: Fast Facts/Top Notch Teaching

27. Challenge them to beat the teacher

Practice place value by drawing cards and trying to build the largest number possible. Kids play against the teacher to see who wins! Get the rules at the link below. ( Find more fun place value activities here.)

Learn more: The Teaching Love Fest/TpT

28. Read minds to figure out the correct numbers

Two students draw a card from the deck without looking and hold it up to their forehead facing out. A third student mentally multiplies the numbers and gives them the product. The students then must figure out what number each is holding. You can do this with addition and subtraction too. You'll find this game along with dozens of other math card games in the free printable book at the link below.

Learn more: Acing Math (PDF)

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All you need is a deck of cards to play these clever math card games. Kids will learn all sorts of important math skills and have fun too!

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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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How are number strings designed? Typically, people tend to describe number strings as having the following structure

Entry problem

Helper problems

Challenge problem (or clunker)

This post from Math Coach on Demand (which also has a bunch of addition and subtraction number strings) describes the structure like this:

Again, the concept of helper problems. But is there just one "formula" for a number string?

Many number strings have this helper problem structure, such as strings that develop jumps of ten (and multiples of ten) in addition and subtraction, like the number string above, as well as number strings that develop the use of the distributive property of multiplication such as:

Again, you can see the series of helper problems that scaffold increasingly difficult problems. But what about this string for early multiplication?

Here, the number string is designed with equivalent problem structure. The first four problems are all equivalent, allowing students to think through why doubling one factor and halving the other results in an equivalent product. Other number strings with equivalent problem structure are constant difference in subtraction strings, such as:

Here the first four problems are equivalent to illustrate how constant difference can make a seemingly difficult problem like 131 - 66 simpler to solve, by shifting the difference up the number line to 130 - 65.

There are also number strings that have a compare structure, such as this number string which asks students to consider whether to add on or remove in subtraction

This distinction matters when you are designing strings, and also when you are facilitating them. When you are facilitating the number string above with a compare structure, you want to make sure to draw out a discussion of which strategy works for which set of numbers, and why. Much like a compare discussion in Elham Kazemi and Allison Hintz's Intentional Talk, the structure of the mathematics leads to a particular structure for discussion. For a number string with an equivalency structure, you want students to be talking about the equivalency and proving that these problems are truly equivalent. For a number string with a helper problem structure, discussion can focus on which simpler problems helped you solve a more challenging problem. For all the problems, discussion can center around the patterns that they notice in the number string. But for different problem structures, those patterns are different.

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How are number strings designed? Typically, people tend to describe number strings as having the following structure Entry problem Helper problems Challenge problem (or clunker) This post from Math Coach on Demand (which also has a bunch of addition and subtraction number strings) describes the structure like this: Again, the concept of helper problems. But is...

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The Progression of Addition and Subtraction

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The Progression of Addition and Subtraction

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The Progression of Addition and Subtraction HD

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This simple 10-15 minute routine builds number sense across many grade levels and content areas. Use organized images below (under Examples) for inspiration as you plan your Choral Counting. Check out this book for detailed support.

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The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.

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How to Use Subitizing | 5 Different Ways - The Recovering Traditionalist

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Have you ever wondered how to use subitizing in your classroom? Subitizing is the ability to instantly recognize ‘how many’.

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Counting Collections Whole Group Instructions

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Counting Collections Whole Group Instructions

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Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young children need for later school success.

Learn more, get extras, and watch author interviews here!

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Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young childre

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Two of the most interesting responses to questions came from these questions: w hat do you notice about the hundreds chart and does anybody have any questions about the hundreds chart?

They had been paying more attention to the 100's chart than I realized! They started to notice on their own that if they look down the hundreds chart a one repeats the two repeats a three repeats both horizontally and vertically and they started to ask why is that what does that even mean by discussing it and working with it you can really start to lay the foundation for place value and making sense of larger numbers.

I had been counting collections for years but didn't ever dive into the choral counting section of Choral Counting and Counting Collections. With their interest in the 100's chart that needed to change.

Want to watch or listen to this post instead of reading or skimming? Watch the video here!

What is choral counting?

Counting as a group is something we do daily in kindergarten, and when learning to count to 100 if your kids understand that the number system works in a pattern it becomes really quick and easy for them to keep their count going because it repeats and especially if they know their decades are counting by tens.

There are always some students who notice this pattern right away but some might need it to be a little more explicit and a little smaller because a hundred numbers can be overwhelming especially if your students are just learning to count and understand that those numerals have value.

One way that I really like to discuss the number system explicitly is by doing a number sense routine called a choral count and writing down the numbers we are counting. I highly recommend the Choral Counting and Counting Collections book by Megan L Franke, Elham Kazemi, Angela Chan Turrou.

In a choral count, you choose a range of numbers that you want the students to count highlighting a specific concept or idea you want your students to explore and think more deeply about. As you count together, you will be scribing the numbers you say in a specific formation. Then have your students take some think time to tell you what they notice and you will underline, circle, and write what they say. This helps the class notice new number patterns, practice tricky number sequences, and build classroom community by listening and understanding that other people's ideas have value.

Counting chorally without any recording helps students learn the number sequence in a low-pressure way because they can be part of the "choir." If they skip a number or get stuck, they can listen to other students until they begin to learn the number sequence on their own.

Planning Your Choral Count

When planning a choral count , either digitally or written out, you will want to decide what you want to call attention to, the direction of your written numbers, and the range of numbers you will count in one session. I use to plan my counts.

When planning a choral count, it's important to consider where your students are and what your goal is with a choral count. Some ideas for things to highlight with a choral count are:

Number Order

Skip counting

Crossing a decade

Areas of a count that your students may get mixed up or stuck (teen numbers)

Call attention to a specific number pattern

Counting beyond 100 (Difference between how numbers are written 2 and 3 digits)

Counting beyond 1000 (Difference between how numbers are written 3 and 4 digits)

Horizontal or Vertical, Start from the Top or Bottom?

Playing with how you are going to present the numbers when you count can greatly affect what your students notice about the numbers. I'll use counting from 1-20 as an example, with the goal of students noticing that 1 always comes first in teen numbers since a lot of students reverse the order of double-digit numbers when they are just learning.

If I start at the top going horizontally with 1 and go to 10 then start with 11 under the one so students can see that numbers in the one's place repeat.

If I go vertical, the attention might be pulled to the 1 in the tens place and always coming first in teen numbers.

If I start by writing the numbers at the bottom, some students might notice that the numbers are getting bigger as they go up which is a reflection of the value increasing.

A choral count can include as few or as many numbers as you want starting at any number, depending on the patterns that you want your students to see. If you start with a number other than one, you can prompt your students to think about what the next number will be before you begin counting out loud as a class.

Recording Student Thinking

Whether on chart paper, on a document camera, or digitally, it is important to record student noticings to support their thinking being understood by their classmates. I usually use a different color to underline or circle student ideas, and depending on the goal I might also write down their thinking under their counts. This helps students see the patterns their classmates are noticing and decide if they agree, disagree, or want to add to others' thinking. Seeing and hearing other ideas can also generate new ideas and promote the mobility of information and ideas around the room.

How to you teach Choral Counting? An Example of Choral Counting

Choral counting can be used anytime, as a warm-up, mini-lesson, or at the end of a lesson/ or math workshop time as a reflection. I usually use Choral Counting as a warm-up with the class or a warm-up in small groups.

I start by telling the students the range that we will count to, and to think about what number comes next before we count together, reminding the kids that is it a choral count so we should be counting at the same pace and it may be a little slower so I can keep up with writing the numbers as we count. "We are going to be starting our count at 5 and stopping at 22. Think about the number that comes after 5 and remember that we are a team so we should count together, not too fast because I won't be able to keep up with you while writing!"

Then I ask if they notice anything about the numbers we counted. You can have students turn and talk about what they notice before sharing out or just start sharing. After each student, I try to change the colors of the marker to underline or circle what they notice and bullet points their main ideas. The notes serve to consolidate our noticing as quickly reflect on what we have seen. You can also as the students to draw conclusions based on what patterns they see. For example, if a student notices that 1 repeats in 11 and 2 repeats in 22, where would the next repeated number be? Where will 25 be? Where will 30 be? If your students have a background in patterns, this will be helpful for them to predict where certain numbers will be. You can learn more about how to teach patterns, pattern centers, and unique pattern math centers in previous posts.

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Two of the most interesting responses to questions came from these questions: what do you notice about the hundreds chart and does anybody have any questions about the hundreds chart? They had been paying more attention to the 100's chart than I realized!