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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Picture books about math are the perfect cross-curricular tool to introduce your kids to complicated concepts and mathematical thinking. We chose some of our favorite authors and stories, both new and old, to add to your classroom library and inspire your students' mathematical minds.

Our picks for the best books about math are listed by grade level and math concept so you can easily find the right selection for your class.

1.by Mac Barnett and Jon Klassen

A sassy story about sneaky Triangle trying to play a trick on his friend Square that turns into a shape showdown. Kids will be mesmerized by this whimsically illustrated tale.

Math concepts: Shapes, relative size

Best for: Grades K-4

2. Place Value by David Adler and Edward Miller

Love the story about monkeys jumping on the bed? You'll adore this version that tells the story of the monkeys at Banana Cafe making one very large banana cupcake.

Math concept: Place value

Best for: Grades 1-5

Also by this author: Fraction Fun, Mystery Math: A First Book of Algebra, How Tall ,How Short, How Far Away, Shape Up!: Fun with Triangles and Other Polygons, Perimeter, Area and Volume: A Monster Book of Dimensions, Millions, Billions and Trillions: Understanding Big Numbers, and more.

Mr. and Mrs. Comfort are having a family reunion and need to arrange the tables so that everyone in the family can enjoy their fabulous spaghetti and meatballs. A witty tale by math guru Marilyn Burns.

Math concepts: Area and perimeter

Best for: PreK-Grade 3

Also by this author: The Greedy Triangle, Math for Smarty Pants, The $1.00 Word Riddle Book, This Book is About Time, and more.

Brave knights, a strong ruler, and a dilemma that needs to be solved using math. This book about math is great for introducing geometry concepts in a fun and accessible way.

Math concepts: radius, diameter, circumference

Best for: Grades 2-7

Also by this author: The Sir Cumference series has more than 10 books that explore math concepts from algebra and geometry to measurement and fractions.

Delightful illustrations and a dreamy young girl pondering the vastness of the universe make a very difficult concept approachable and interesting in this book about math.

Math concept: Limitless numbers and infinity

Best for: Grades K-5

Watch as this busy construction crew creates impressive structures by grouping bricks by twos, fives, and tens. Kids will love the catchy repetitive verse and charming illustrations.

Math concept: Counting in quantities

Best for: PreK-Grade 2

Ethan wakes up one morning with a strange cat on his head and the only way it will agree to get it off is if Ethan agrees to play a game of probability with it. This kooky book about math will entertain your students as it teaches a difficult concept.

Math concept: Probability

Best for: Grades 2-5

Also by this author: Fractions in Disguise: A Math Adventure

Kids will love this fun story with delightful cartoon illustrations that teach the importance of zero as a placeholder in our number system. Without Zero the Hero, we wouldn't be able to count beyond the number nine!

Math concept: Concept of zero

Best for: Grades 1-5

A beautifully illustrated book about math that shows how flips, slides, and turns can create amazing symmetrical images.

Math concept: Geometry, symmetry

Best for: Grades 1-3

A playful book with silly characters and perfect rhyming that teaches not just the basics of telling time, but the tricky concept of relative time.

Math Concept: Time

Best for: Grades 1-4

Also by this author: Cleary has written a whole series of books called Math is CATegorical, including The Mission of Addition, The Action of Subtraction, A Dollar, a Penny, How Much and How Manym, A Fraction's Goal- Parts of a Whole, and more.

Mouse and her friends want to play a game of tug-of-war but have a hard time making the sides fair. This charming story teaches the concept of balance and equality.

Math concept: Equality

Best for: Kindergarten-Grade 3

Two more rhyming tales with colorful, busy illustrations that kids will love. In each of these books about math, a boy wakes up one day and finds that things are kookily out of order. Great as a read-aloud or for independent readers who will love hunting through the detailed pictures to find the odd or even items.

Math concepts: Odd and even

Best for: Kindergarten-Grade 3

Your students will love quirky Henry and his wild imagination as he uses his dog Frank as a unit of measure. Henry thinks about real life objects and how they can take up specific spaces. This story will get kids thinking creatively about numbers and many other math concepts.

Math concepts: Problem-solving, measurement, estimation, and calculatio n.

Best for: PreK-Grade 3

Colorful fish bob, glide, and swish through the ocean until POP, a shark appears! Kids not only love hearing and seeing this story, it will get them interested in learning and creating their own patterns.

Math concepts: Patterns and variations of pattern types

Best for: Kindergarten-Grade 2

16. A Remainder of One by Eleanor Pinczes and Bonnie MacKain

The 25th Beetle Army Corp is trying to solve the problem of how to divide their troops into equal groups for the parade march without leaving any stragglers. A fun, rhyming book about math that will get kids thinking about how numbers are put together and pulled apart.

Math concept: Grouping, division

Best for: Preschool-Grade 3
What picture books have you used in your math lessons? Come and share in our WeAreTeachers HELPLINE group on Facebook. Plus, Why It's Important to Honor All Math Strategies.

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16 Picture Books About Math to Inspire Curious Kids - We Are Teachers

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Picture books about math are the perfect cross-curricular tool to introduce your kids to complicated concepts and mathematical thinking. We chose some of our favorite authors and stories, both new and old, to add to your classroom library and inspire your students' mathematical minds.

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Erikson Institute Early Math Collaborative

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One sure fire way to warm up children's attitude towards mathematics is to build math activities and lessons out of the books they all love to listen to and read.

Children explore the Big Ideas about foundational mathematical concepts as they interact with math in everyday life. When reading and listening to books, mathematical situations come to life in new and fanciful ways. And, we're not just talking about books that are explicitly mathematical, since math is often central to the problem and resolution of our favorite stories. So many questions that drive children, such as "Is it fair?", "Who is bigger/faster/stronger?", "What will happen next?" are shared by the characters they read about.

But, don't forget to take the math out of the book! Play with the stories. Act them out and innovate. Ask the what-if questions. Create your own version. This is where mathematical thinking gets creative.

We have collected many lists and activity ideas related to some of the best children's books we know of, all infused with math concepts. We've outlined links below, organized under the early math topics of our website. Use books to bring math to life today!

Where's the Math? Books, Games, and Routines to Spark Children's Thinking

Make math learning both meaningful and fun by building on children's natural curiosity to help them grow into confident problem solvers and investigators of math concepts.
Learn more ›

Big Ideas of Early Mathematics:

What Teachers of Young Children Need to Know

The Big Ideas that convey the core concepts of mathematics are at the heart of this book that gives early childhood educators the skills they need to organize for mathematics teaching and learning during the early years.
Order a copy

Online MS in Early Childhood Ed - STEM Focus

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Elevate your practice and strengthen your knowledge of teaching and learning in the disciplines of science, technology, engineering, and mathematics (STEM), with an emphasis on children in preschool through third grade.
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Best Childrens Books for Early Math Learning | Early Math Collaborative

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One sure fire way to warm up children's attitude towards mathematics is to build math activities and lessons out of the books they all love to listen to and read. Children explore the Big Ideas about foundational mathematical concepts as they interact with math in everyday life.

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6th Grade Literature List

Related Links

See advice from Everyday Mathematics teachers on working with parents, using technology in the classroom, pacing, and more.

The UChicago STEM Education offers strategic planning services for schools that want to strengthen their Pre-K-6 mathematics programs.

McGraw-Hill Education's website features supplemental materials, games, assessment and planning tools, technical support, and more.

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6th Grade Literature List - Everyday Mathematics

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See advice from Everyday Mathematics teachers on working with parents, using technology in the classroom, pacing, and more. The UChicago STEM Education offers strategic planning services for schools that want to strengthen their Pre-K-6 mathematics programs. McGraw-Hill Education's website features supplemental materials, games, assessment and planning tools, technical support, and more.

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Marilyn’s current thinking about math education and her ongoing classroom experiences and learning.

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Operation Models with Algorithms - Ferradas.docx

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Staying organized is the #1 way I have found to save time! Finding the right systems can take time, but once you have it, say hello to all of the hours you didn't know you had! Below is the math area of my classroom. Today, I'm going to break down 10 of my favorite math center organization tips that really work!

One way that I have really cut down on my math center prep is by organizing my manipulatives in a way that my students can access them independently. I find that having all of the items they at their fingertips helps them build responsibility while saving me hours of prep time every week. You can find these math bin labels [HERE] or newly as part of my CLASSROOM LABEL BUNDLE [HERE]!

As you can see, they are clearly labeled with pictures, and are on a low shelf that they can easily reach. In some cases, I have organization built in to each bin. For example, each bin of unified cubes is pre-sorted into two different colors. This means that students can just take a bin to their table and already have that part taken care of (and no additional colors to distract them!) We use these to help visually represent composing and decomposing numbers, so two colors are essential!

I also have my dice organized within each bin. I love organizing dice in this way, because I no longer have dice flying off tables! I used baby food containers, because I'm at a point in my life where I have an excess of these in my house! You can just as easily use small serving tupperware (which you will see below.) When I taught younger grades, I also hot-glued a piece of felt to the bottom of each container to mute the sound!

I don't know about you, but I am OBSESSED with dice! I have more than I probably should, but my students love them too! After years of outgrowing my storage systems, I have finally found a system that works for me. I give you, the Dice Box!

You can use any storage toolbox from Lowes, Home Depot, or the Container Store. Now if my centers require dice beyond the standard 1-6 doled dice, my students can get them independently, eliminating one more thing I have to prep! After some requests, I have posted the labels over at my TpT Store. Find them [ HERE]

Second only to dice, I have a serious weakness for Target's Dollar Spot Erasers. I needed a way to let my students access and choose their erasers independently, so another organization system was born.I use the small square toolboxes (similar to the Dice Organizer). I do this because I have them sorted by season. For example, the Fall/Halloween erasers are in one box, while the Winter/Holiday erasers are in another. This means that I can switch them out throughout the year to keep them new and exciting for students.

I have hot-glued one eraser to the front of each drawer so students can visually see them at a glance! The only problem with this system is that I have to keep buying more storage because I just can't say no to Target!I used to cringe at how much time we lost while students got the correct amount of counters/chips they need for a game or center. To solve this problem, I decided I'd just have them pre-sorted! I used small Dollar Store containers, and filled them with counters and chips. For the translucent chips, I include two different colors so that they can be used for partner games.

Another organization hack are my Kaboom storage containers. If you don't know about Kaboom! you need to read about my favorite center [ HERE!] Popsicle sticks are really hard to store, because they're an awkward shape. I used to have them in open cups, but that made them hard to pack up at the end of the year.

Now, I just use empty Crystal Light powder containers. I don't personally drink it, but my family is very good about supporting their teacher niece/daughter/cousin/sister. I just place a piece of construction inside to cover the bottom half of the container, and it's all ready to go! Instant center!

For years I struggled with finding a way to organize the piles of coins in my classroom. A tray was great, but not stackable. Cash registers were fun, but only good for one table at a time. Sorting them for individual centers made me want to rip my hair out! What a time suck! Finally, I figured out something that really works!

These individual student banks have been a life saver! They're quick to pull out for centers, students can independently sort and put them away when they're done, and they're small and stackable (and when you have minimal space, that's a MUST!) You can grab these individual student bank labels for FREE [ HERE!]

My Math Word Wall is another organizational tool that I use year after year. I only laminate them once, and they're good to go FOREVER! They keep our vocabulary organized, and when I need visuals for a lesson, they're right there ready to go! My students refer to this focus wall Every.Single.Day. I put magnetic tape on the back of each card, so my kids can take them down to use at their tables, and put them back up when they're done.

These Math Word Walls are available K-5, and include Australian & Canadian coins and spellings! You can find them [ HERE!]

In addition to meeting with me in my guided math groups, students also go to two activities, two games, math journals, as well as independent work in their math journals. The games and activities don't necessarily change every week, since they only go to each center once.

Their group bins are color specific, so the work board coordinates with the bins. This has really helped my students navigate their center rotations independently, which means... MORE TIME FOR YOU TO WORK WITH KIDS, which is really the most important part!

I hope this has helped give you a few new ideas for organizing your classroom. While it takes some serious effort up front, the rewards are absolutely worth it!

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10 Math Center Organization Tips to Save You Hours of Prep Work! - Teaching with Jillian Starr

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Staying organized is the #1 way I have found to save time! Finding the right systems can take time, but once you have it, say hello to all of the hours you didn't know you had! Below is the math area of my classroom. Today, I'm going to break down 10 of my favorite math [...]

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This post contains affiliate links for your convenience. View disclosure policy HERE.

Math manipulatives are small objects that help with teaching math. They are useful tools for teachers and students. They provide a hands-on way in which to explore and learn. When children are using these materials in physical ways, they are learning differently than they are when they are simply listening or watching a lesson. This tactile learning builds a deeper, personal understanding of math concepts.

Math manipulatives make math FUN! Children of all ages enjoy using these concrete tools to make sense of the problems they are given. They especially help our younger learners who are learning new math concepts for the first time. A relationship is built when shown visually how to solve problems and given opportunities to "try" something using math manipulatives. With repeated practice and "play" with manipulatives, math fluency develops.

As a teacher with many years experience incorporating math manipulatives into my lessons, I appreciate how useful they are in helping me teach different math concepts. Many items can be used in multiple ways. I enjoy watching children have "lightbulb" moments when they finally understand a concept thanks to the tools they are using. I am ecstatic when children are exploring with a tub of manipulatives and they discover something new, a pattern, or way of use.

During Lessons

I use math manipulatives for almost every math lesson I teach. When planning my lessons, I think of ways that the concepts can be taught using visuals, as well as orally or on a chart. I prep tools ahead of time so they are ready for our lessons. I vary the tools in order for students to get practice using different types. During our lessons, math manipulatives are used usually during or after the initial lesson is taught. I will explain a concept, give examples on a chart, practice orally, and demonstrate with math manipulatives. Students use those manipulatives to practice the concept or solve a problem.

Examples of Use

When teaching basic addition, I use magnetic counters that can be used on the whiteboard to illustrate a problem (i.e. 2+5=7). Students use two-sided counting chips to solve another similar problem at the carpet.

When teaching counting or identifying numbers to 100, I use a large 100's chart and a pointer. We take turns pointing to the numbers as we practice counting by 1's, 2's, 5's, and 10's. Students use small 100's charts to point and follow along as we count or they locate different numbers given orally.

When teaching geometric solids, I use large foam 3D shapes that I can hold and point out its features. Students use smaller similar shapes to find those same features, to locate similar objects in the scavenger hunt around the class, and use them to create structures.

When teaching measurement, I use many non-standard units, such as cubes, to illustrate how long, tall, wide something is. Students use the cubes to compare and measure with the cubes around the classroom (i.e. my arm is 20 cubes long).

During Independent & Group Work

Students use math manipulatives at their workspace to completed their work. We have math centers set up that incorporate manipulatives to use during their work. I also give students "free time" to grab a bin of math manipulatives to explore on their own or in small groups. This is where some of the most amazing findings happen. I occasionally put a problem on the board for students to complete with a math bin of their choosing. This encourages "real world" problem solving when they must think of the most applicable tool and try different ones out through trial and error.

Examples of Use

Before we start a lesson, students are given time to explore the tub of math manipulatives for that day. I limit my suggestions as to what they should do with them, as I want to encourage creativity and mathematical thinking.

During "free time" or math centers, I will put out a basket containing around 20, 50, or 100 small items depending and ask students to complete a task. The task could be "make groups and count to find out how many objects you have" or something that encourages thinking and problem solving.

I will put small tubs together with manipulatives and ask students to explore, create, or show me something with it. It could be a tub of pattern blocks and the instructions "use all of the blocks to create a picture" or a geoboard and the instructions "show me a picture using 8 elastic bands".

I have tubs, baskets, and containers full of math manipulatives in our math area, as well as on our math supply shelf. I use a different bin or tub to hold each type of manipulative. I suggest labeling each bin or container with a name and/or picture on it. I suggest taking photos of your students using each manipulative correctly and attaching that to the bin as an example to students.

Try to have a designated place for each type of manipulative. Have them in a place that is accessible and ready for use. Using a large storage area that holds bins for those types you use often is helpful. Teach students where they can find each type and show them how to use them and put them away properly. This will help with clean up and maintain organization.

There are many types of math manipulatives available to teachers. Many can be used in multiple ways. It's a good idea to have a variety of types available in your school or ready in your classroom to help with teaching the variety of math concepts. Below I have categorized them into must-have (those you will use often and for many things) and useful (those that you may not use everyday but are very helpful in teaching concepts. I have used all of the manipulatives provided below and I recommend them for primary teachers (with Amazon Affiliate links).

Must-Have Manipulatives

Dice are a great tool to have on hand for math games and activities. There are many types available today, such as these dice in many colors. There are also different sized dice available, such as these large foam dice. Jumbo dice are great for rolling during a class game or for "flashing" to kids to have them call out the number shown. I suggest putting pairs of dice into small clear containers that students can quickly grab and shake while playing games. My favorite type of dice for teaching addition and playing games are the dice in dice.
Playing Cards
Playing cards make useful math tools because they have numbers on them. They can be used to teach addition and subtraction through games like addition "war" and subtraction "war". Playing cards, like these, come in traditional decks that you can find at most stores or dollar stores. Buying them in bulk playing card sets and having a deck for each student is helpful. Teachers would benefit from a set of jumbo playing cards to use for lessons and demonstrations as they provide a large visual for kids.

Unifix cubes are the colored cubes that connect in one way and snap cubes are colored cubes that can connect in different ways. Both can be used in many ways to teach many math concepts, such as patterning, place value, and measurement. Snap cubes are one of the most used math manipulatives. They visually demonstrate many number concepts, such as counting, grouping, adding, and taking away. Children love snapping the cubes together to make number "trains".

Another must-have manipulative are the two-color (red and yellow) counters. They have many uses and help little learners learn to count, make patterns, add, and subtract. They are an essential tool for teaching addition that I use frequently. Students use them for independent practice and help in solving addition and subtraction problems. I keep sets of 20 these colored counters in small containers students to use when needed. This set of ten frames with magnetic counters would be great for many number concepts.
Number Lines
Pattern blocks are small shaped blocks that can be used in multiple ways. They make great learning tools because they are consistent in shape and color. They work for teaching sorting, patterning, fractions, geometry, and more. They promote creativity and encourage students to create unique designs. I keep pattern blocks in a few large tubs for students to grab and explore with during math centers. Sets like the one below are available that include activity cards for students to complete.

Place value blocks are very helpful in teaching counting, number concepts, double-digit addition and subtraction. Place value concepts are more difficult to grasp and using these concrete manipulatives helps build understanding. I suggest have a large bin of of place value blocks similar to those below with enough for each student to represent the numbers you are learning. The magnetic set would be helpful for whole class demonstrations on a whiteboard. If you are teaching PreK or Kindergarten, consider introducing place value during calendar time with this counting pocket chart and straws.

Useful Manipulatives

Dominoes are a fun math manipulative to have available for games and other activities, such as matching numbers together. There are endless options for use, but my favorite for little learners is to use them to practice addition and subtraction. Give students a small pile of dominoes and have them record a number sentence and solve by counting. You can find dominoes at most dollar stores, but I love these colored dominoes for the classroom.

Magnetic numbers are great to have in a math center for children to play with. Children love to stick magnets on anything! They are helpful during lessons when counting, ordering, and number identification is taught. You can find plastic ones, foam ones, and wooden ones and they are available at most dollar stores and teacher supply stores. I like these foam magnetic numbers because they make less noise when they are played with or fall on the ground. These jumbo magnetic numbers would be helpful for teachers during lessons.

Shape counters are fun to use in a math center for little learners. Encourage them to sort the shapes by color, size, type, and create different patterns with them. They are also great for teaching beginning addition and subtraction (i.e. I have five bears and I take one bear away). Shape counters come in many fun shapes, such as bear counters, animal counters, bug counters, and transportation counters.

Large Teaching Clock & Mini Clocks
Geoboards
Geoboards are great for building shapes and learning about different geometry concepts. They make a great math center for children to explore. You could give children pictures to copy or specific tasks to complete with a geoboard. Teaching proper care and safety with the elastic bands is important. Check out this set of small plastic geoboards.

Play Money & Cash Register
Teaching financial literacy at an early age is important. Encouraging children to shop at a class made store and exchange items for money. Use a cash register like this and kid wallets like this to hold the pretend money. Play money games where coins and bills are used. Teach lessons and have children practice sorting coins, ordering coins by size and quantity, and creating different quantities. This deluxe coins & bills set includes tons of play money for all your activities.

Bucket balances are helpful tools in comparing different objects and volumes of liquid. In primary grades, we often use them to observe and estimate which of two objects is the heaviest. I like this balance scale because items can be easily put in and taken out by children during their exploration.

Mini Whiteboards & Markers

Mini whiteboards are amazing items that I use daily. I store a class set of boards, markers, and erasers in a basket at the carpet with our other math items. They make those quick moments when you want students to record their findings or solve a problem easy. We use ours daily during our number of the day activities (read HERE). Check out this class pack of whiteboards to go along with my go-to dry erase markers that last the longest ( these Expo markers).

While teacher supply stores have great quality math manipulatives, they are often expensive. If you can get your school to fund your classroom supply, then go this route. Lakeshore Learning has endless types and varieties of manipulatives and wonderful games that would fulfill your needs.

I suggest buying the majority of your items when they go on sale or when you can purchase them at affordable prices through Amazon. Each type of manipulative listed above is linked to Amazon to help you create your classroom wishlist. You can sign up for Amazon Prime and get all of your materials quickly, no matter what the weight of your package. Awesome! Make sure to enter the Math Manipulatives Every Classroom Should Have GIVEAWAY below.

There are many places to purchase math manipulatives. Get creative and have fun searching for materials in your home or find them for cheap at the dollar store. Read about free and affordable math manipulatives from Stir the Wonder.

Teachers Pay Teachers is another wonderful option for finding math resources, games, centers, and printable manipulatives for your classroom.

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Math Manipulatives Every Classroom Should Have

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This post contains affiliate links for your convenience. View disclosure policy HERE. Math manipulatives are small objects that help with teaching math. They are useful tools for teachers and students. They provide a hands-on way in which to explore and learn.

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Math is all around us. We can see it in nature and in our homes. We use math skills every day, even if we don't realize it. And you can help your students see math in all of its forms with fun and engaging math manipulatives.

These hands-on objects and activities enhance your math lessons, giving students a concrete way to practice and play with math concepts. Sometimes it can be difficult for children to grasp the abstract concepts of adding, subtracting and multiplying numbers. But math manipulatives can help them actually see what the numbers are doing.

Common math manipulatives include blocks of all kinds, whiteboards, and interesting online materials. Even if you don't have access to these resources right now, you can easily find creative alternatives for your classroom, especially once you understand what math manipulatives are and how they're used.
This article will give you a strong grasp of what math manipulatives are, the key benefits of using them, and our top 10 favorite math manipulatives for the classroom.

What are math manipulatives?

Math manipulatives are objects, charts, and activities that engage learners while helping them develop their math skills.
They can assist in teaching lessons such as graphing, decimals, geometry, arithmetic, and more.

Using math manipulatives during a lesson brings hands-on learning to your classroom. And this can appeal to a multitude of different learners.

As you know, not every student learns in the same way. Math manipulatives allow students to work with math in the way that's best for them. By working independently with math manipulatives, a student is better able to work at their own pace and spend more time on concepts or problems that are particularly difficult for them.

Many math concepts are conceptual and hard for students to visualize on paper. By practicing math processes with math manipulatives, learners can see exactly how the process affects the numbers and how problems are solved.

There are many places to buy math manipulatives or manipulative kits, including online or in school supply stores. But you don't need to buy an expensive, specialized kit to bring manipulatives to your classroom. Especially for younger grades, any toy collection or set of blocks will work.

There are also many printable options available online. We're talking loads of variations and choices, some geared towards homeschooling families, math centers or traditional classrooms. The digital choices are endless.

With all these options, it can be overwhelming and difficult to know where to start. Here's our list of the ten most common and versatile math manipulatives to get you started.

10 Math manipulatives to implement in your classroom

1. Dominoes

Dominoes are much more than just a fun game. They're also one of the best foundational math manipulatives. Dominoes can be used to teach a variety of math skills - like addition, multiplication, division, and subtraction. And they're particularly helpful in younger grade levels.

They're easy for even the youngest students to grasp and move, and they can help math learning feel like a game.

Dominoes work well for both individual and small group problem-solving. They also allow you to take a quick trip around the room, gauging student understanding at a glance.

During your math manipulative time, encourage your students to create and solve their own math problems by arranging the dominoes in different ways. There are loads of math games you can play with dominoes. If you need some ideas, a quick Google search can pull up enough ideas for the entire school year.

2. Pattern blocks

Pattern blocks are a math manipulative perfect for geometry lessons. These blocks are made of either plastic or wood and come in a variety of shapes - like triangles, squares, rectangles, and trapezoids.

Your students can experiment with how these shapes fit together to make new shapes or images. These blocks often come with pattern cards. These can guide your student in how to make a picture, or encourage them to be creative and create their own pattern.

Pattern blocks are also great for basic math learning. Lessons in fractions, counting and patterns can all be enhanced with pattern blocks. With so many diverse applications, many educators feel these blocks are an important and necessary component of their teaching toolkit - especially in younger grade levels.

3. Online math games

Regardless of your classroom setup - traditional, virtual, homeschooling or hybrid - digital math manipulatives are a great option! They allow students to engage with math in a unique and fun way. And there's a huge variety of online math games online, targeting whichever math skills you're currently teaching.

Online math games can even support student learning over the summer months or during school breaks. The fun nature of online games keeps students excited and learning at home - because they don't feel like homework.

Looking for a math game for your class, try Prodigy Math!

A lot of my higher level students are really motivated by Prodigy, but the part that I like the best is when my students can work cooperatively. My lower level math students can play with my higher level ones and they both are engaged in their math work and having fun. It's a great supplementary tool to help keep math fun and engaging, and it works.

William Stenross

4th Grade Classroom Teacher

4. Cuisenaire rods

Cuisenaire rods are rectangular rods of various lengths. They're often made of wood, and each length corresponds to a different color. For example, all red rods are 10 units long, while all yellow rods are 5 units long.

These colorful manipulatives can help bring the otherwise boring number line to life. Students can visualize the distance between numbers, and see the relationship numbers have with each other. How many times does 5 go into 10? Grab the number rods and find out!

Cuisenaire rods are a math favorite, mostly due to their versatility. They can be used to teach everything from basic number sense to fractions and patterns. Whether you teach Pre-K or 8th grade, you can find a use for Cuisenaire rods.

5. Two color counters

Another popular manipulative in math classrooms is two-color counters. Color counters are simple plastic circles with one color on each side. You'll see them most often used to demonstrate fractions, basic addition, subtraction and counting skills.

Two color counter's simplistic nature means they're most popular in lower grade levels. And even better, two-color counters are often magnetic, making them the perfect choice for whiteboard activities and math games. Use them to demonstrate lessons when you're front of class, or divide students into small groups so they can experiment and learn.

6. Fraction tiles & fraction circles

Fraction tiles and fraction circles are two different math manipulatives with a similar purpose.

Fractions can be particularly difficult for students to understand and work with. These manipulatives can help students deepen their conceptual understanding of fractions with two different math visuals - making them a perfect pair.

Fraction tiles are often flat, rectangular pieces of plastic or cardboard made of different colors and varying lengths. They usually have the corresponding fraction printed on them so kids can quickly look and compare. The varying lengths allow students to experiment with how fractions work together to create not just whole numbers, but also different fractions within the whole.

Fraction circles are very similar, but instead of rectangles, they use parts of a circle. This is the manipulative version of the pie or pizza example. Students can use differently sized pieces to understand how fractions can add up to 1.

Bonus - both of these math manipulatives are easy to DIY with paper print outs if you're on a time or budget restraint.

See how to make your own fraction tiles below!

7. Rekenreks counting frames

Rekenreks counting frames are often one of the first math manipulatives a student will use. In fact, many use similar bead counters before they ever come to school.

These simple arithmetic frames combine the concepts of the number line, individual counters, and base-ten models to create a useful learning tool. Students move the beads from one end to the other to practice counting or assist with basic addition and subtraction problems.

Younger students, like those in Pre-K and elementary school, benefit the most from Rekenrek counting frames. Once students have mastered counting and single-digit math problems, they're ready to move on to more diverse manipulatives.

8. Bear counters

Bear counters are another great option for younger students.

These fun and colorful plastic bears will keep your little learners excited to play with math. The bears are perfect for teaching the foundational math skills of counting and sorting. They can also be paired with a scale to teach measurement and weight.

If you don't have bear counters in your classroom, look for other small toys that can serve the same purpose. It's helpful for them to be similar in type, but that's not a necessity. Students can practice counting zoo animals, cotton balls, or erasers just the same.

9. Place value blocks or base ten blocks

Place value blocks, also called base-ten blocks, are used in classrooms from Pre-K all the way to 8th grade. These little plastic blocks connect to each other, making them a fun option for teaching a variety math concepts - like addition, subtraction, fractions, measurement, counting and more.

Most sets are colorful and can help students visualize different parts of an equation. They're perfect for exploring place value as well. Once students move up to solving double-digit problems, different colors can be used to represent the tens and even hundreds place.

Bonus tip: You can also use this place value chart as another in-class supplement!

10. Geoboards

Looking for something besides blocks for your geometry activities in class? Geoboards are the answer.

Geoboards are small wooden or plastic pegboards that use string or rubber bands to create a variety of shapes. They're a great hands-on activity for practicing shape recognition and names.

Geoboards can double as a fun brain break for young students. Pre-K and elementary students are often still working on the fine motor skills needed to draw shapes and write numbers. And manipulating the rubber bands or strings can be a welcome departure from the frustration of writing.

Like pattern blocks, you can have students use these in a structured way by making specific shapes. Or give them the freedom to create whichever shapes they'd like. You're sure to end up with some fantastic, mathematical art!

See how one teacher used a geoboard to explain basic shapes to her first grade students below!

Physical vs. virtual math manipulatives

Classrooms today don't look the same as they did twenty years ago, or even 3 years ago. The number of students in virtual or hybrid classrooms has increased dramatically. So, when you can't physically hand your students math manipulatives, what are your options?

There's actually quite a few! In the last few years, many free, online programs offering virtual math manipulatives have popped up. These may not be manipulatives in the traditional sense, but online games stretch the brain using a variety of learning models. They help students nail down complicated concepts in much the same way as the manipulatives mentioned above.

And it's not just virtual classrooms that can benefit from these tools. Homeschooling rates are on the rise. But many parents may not have the budget to purchase a large variety of math manipulatives. Online options provide a budget-friendly way to teach math at home or in the classroom.

It's easy to see how virtual manipulatives are beneficial for both students and teachers. Teachers now have a wide variety of effective teaching tools at their fingertips. And learners can gain a deeper understanding of math concepts on a platform they already enjoy. That means less frustration and more opportunity. Let's dive deep into a few more benefits of math manipulatives, whether virtual or physical.

3 Key benefits of using math manipulatives in the classroom

Increase interactive learning

In a classroom of 15-30 students, no two students are alike. They all learn in unique ways. And trying to make one lesson fit all those students is impossible.

For students who are struggling with math, hands-on learning activities with manipulatives can be a huge help. Not everyone can make sense of math on paper alone. Hands-on activities give learners a deeper understanding of how numbers work. And this understanding will continue to help them as they progress through school.

Students need to have a full understanding of basic concepts. Math builds on itself, so have a strong foundation will only help them as they gain more knowledge and advanced skills.

Also, manipulatives keep math learning exciting. Students grow bored of always using the same learning method. There's little to love about lectures and equations on a whiteboard. Math manipulatives can help you diversify your teaching style. You'll reach more students by using more methods, and that means more engagement and more learning. Awesome!

Develop problem-solving skills

Math manipulatives help students develop more complex problem-solving skills. When a student fully understands a math concept, they're better able to apply that concept to real-world problems. We want to teach students how to apply math skills across all of life, not just to next week's test.

Also, math manipulatives allow for a variety of problem solving methods. Students often interpret and think about problems in different ways. And that means they'll approach the solution differently too. Math manipulatives give your students the freedom to explore multiple paths to a solution. And if it doesn't work, it's easier for them to see why.

Build confidence in each math lesson

All of this problem solving with math manipulatives can give your students a major confidence boost! Activities with math manipulatives allow students to take the reins of their learning process. And because many math manipulatives are self-correcting, they can work individually on their problems. When they reach the right answer, all on their own, they'll feel an amazing sense of pride and accomplishment.

When students are able to understand and apply mathematical concepts, they're filled with that I did it feeling. Mastering the steps of a complicated math process gives students the confidence and encouragement to keep moving forward.

Students can then translate this deeper conceptual understanding to tests, quizzes, and standardized tests. They won't need a last minute cram session to succeed. They can stress less knowing they have the knowledge to tackle a variety of math and life problems.

Whether physical or virtual, math manipulatives can create a ripple effect that helps students throughout their entire educational journey.

Develop your student's math skills in a fun and engaging way

Math manipulatives are fantastic tools for helping your students understand and engage in their math lessons. And there are so many math manipulatives to choose from - something to fit every lesson and each student's unique needs.

Even if you don't have physical math manipulatives at your disposal, you can easily find virtual and online options that are just as helpful.

And some of them come at no-cost to teachers and schools! 👇

A no-cost, virtual math manipulative that's fun!

When you're exploring virtual options for math manipulatives, be sure to check out Prodigy Math. Prodigy's online math game is a stress-free way to help students master standards-aligned math skills. It's safe, fun and engaging, keeping your students excited and ready for their next lesson.

And with a free teacher account you can:

Set up engaging math practice in just a few clicks

Easily find out any learning gaps your students may have

Track how your students are progressing through your local or national curriculum

Sign up for free

Math is all around us. We can see it in nature and in our homes. We use math skills every day, even if we don't realize it. And you can help your students see math in all of its forms with fun and engaging math manipulatives.

These hands-on objects and activities enhance your math lessons, giving students a concrete way to practice and play with math concepts. Sometimes it can be difficult for children to grasp the abstract concepts of adding, subtracting and multiplying numbers. But math manipulatives can help them actually see what the numbers are doing.

Common math manipulatives include blocks of all kinds, whiteboards, and interesting online materials. Even if you don't have access to these resources right now, you can easily find creative alternatives for your classroom, especially once you understand what math manipulatives are and how they're used.
This article will give you a strong grasp of what math manipulatives are, the key benefits of using them, and our top 10 favorite math manipulatives for the classroom.

What are math manipulatives?

Math manipulatives are objects, charts, and activities that engage learners while helping them develop their math skills.
They can assist in teaching lessons such as graphing, decimals, geometry, arithmetic, and more.

Using math manipulatives during a lesson brings hands-on learning to your classroom. And this can appeal to a multitude of different learners.

As you know, not every student learns in the same way. Math manipulatives allow students to work with math in the way that's best for them. By working independently with math manipulatives, a student is better able to work at their own pace and spend more time on concepts or problems that are particularly difficult for them.

Many math concepts are conceptual and hard for students to visualize on paper. By practicing math processes with math manipulatives, learners can see exactly how the process affects the numbers and how problems are solved.

There are many places to buy math manipulatives or manipulative kits, including online or in school supply stores. But you don't need to buy an expensive, specialized kit to bring manipulatives to your classroom. Especially for younger grades, any toy collection or set of blocks will work.

There are also many printable options available online. We're talking loads of variations and choices, some geared towards homeschooling families, math centers or traditional classrooms. The digital choices are endless.

With all these options, it can be overwhelming and difficult to know where to start. Here's our list of the ten most common and versatile math manipulatives to get you started.

10 Math manipulatives to implement in your classroom

1. Dominoes

Dominoes are much more than just a fun game. They're also one of the best foundational math manipulatives. Dominoes can be used to teach a variety of math skills - like addition, multiplication, division, and subtraction. And they're particularly helpful in younger grade levels.

They're easy for even the youngest students to grasp and move, and they can help math learning feel like a game.

Dominoes work well for both individual and small group problem-solving. They also allow you to take a quick trip around the room, gauging student understanding at a glance.

During your math manipulative time, encourage your students to create and solve their own math problems by arranging the dominoes in different ways. There are loads of math games you can play with dominoes. If you need some ideas, a quick Google search can pull up enough ideas for the entire school year.

2. Pattern blocks

Pattern blocks are a math manipulative perfect for geometry lessons. These blocks are made of either plastic or wood and come in a variety of shapes - like triangles, squares, rectangles, and trapezoids.

Your students can experiment with how these shapes fit together to make new shapes or images. These blocks often come with pattern cards. These can guide your student in how to make a picture, or encourage them to be creative and create their own pattern.

Pattern blocks are also great for basic math learning. Lessons in fractions, counting and patterns can all be enhanced with pattern blocks. With so many diverse applications, many educators feel these blocks are an important and necessary component of their teaching toolkit - especially in younger grade levels.

3. Online math games

Regardless of your classroom setup - traditional, virtual, homeschooling or hybrid - digital math manipulatives are a great option! They allow students to engage with math in a unique and fun way. And there's a huge variety of online math games online, targeting whichever math skills you're currently teaching.

Online math games can even support student learning over the summer months or during school breaks. The fun nature of online games keeps students excited and learning at home - because they don't feel like homework.

Looking for a math game for your class, try Prodigy Math!

A lot of my higher level students are really motivated by Prodigy, but the part that I like the best is when my students can work cooperatively. My lower level math students can play with my higher level ones and they both are engaged in their math work and having fun. It's a great supplementary tool to help keep math fun and engaging, and it works.

William Stenross

4th Grade Classroom Teacher

4. Cuisenaire rods

Cuisenaire rods are rectangular rods of various lengths. They're often made of wood, and each length corresponds to a different color. For example, all red rods are 10 units long, while all yellow rods are 5 units long.

These colorful manipulatives can help bring the otherwise boring number line to life. Students can visualize the distance between numbers, and see the relationship numbers have with each other. How many times does 5 go into 10? Grab the number rods and find out!

Cuisenaire rods are a math favorite, mostly due to their versatility. They can be used to teach everything from basic number sense to fractions and patterns. Whether you teach Pre-K or 8th grade, you can find a use for Cuisenaire rods.

5. Two color counters

Another popular manipulative in math classrooms is two-color counters. Color counters are simple plastic circles with one color on each side. You'll see them most often used to demonstrate fractions, basic addition, subtraction and counting skills.

Two color counter's simplistic nature means they're most popular in lower grade levels. And even better, two-color counters are often magnetic, making them the perfect choice for whiteboard activities and math games. Use them to demonstrate lessons when you're front of class, or divide students into small groups so they can experiment and learn.

6. Fraction tiles & fraction circles

Fraction tiles and fraction circles are two different math manipulatives with a similar purpose.

Fractions can be particularly difficult for students to understand and work with. These manipulatives can help students deepen their conceptual understanding of fractions with two different math visuals - making them a perfect pair.

Fraction tiles are often flat, rectangular pieces of plastic or cardboard made of different colors and varying lengths. They usually have the corresponding fraction printed on them so kids can quickly look and compare. The varying lengths allow students to experiment with how fractions work together to create not just whole numbers, but also different fractions within the whole.

Fraction circles are very similar, but instead of rectangles, they use parts of a circle. This is the manipulative version of the pie or pizza example. Students can use differently sized pieces to understand how fractions can add up to 1.

Bonus - both of these math manipulatives are easy to DIY with paper print outs if you're on a time or budget restraint.

See how to make your own fraction tiles below!

7. Rekenreks counting frames

Rekenreks counting frames are often one of the first math manipulatives a student will use. In fact, many use similar bead counters before they ever come to school.

These simple arithmetic frames combine the concepts of the number line, individual counters, and base-ten models to create a useful learning tool. Students move the beads from one end to the other to practice counting or assist with basic addition and subtraction problems.

Younger students, like those in Pre-K and elementary school, benefit the most from Rekenrek counting frames. Once students have mastered counting and single-digit math problems, they're ready to move on to more diverse manipulatives.

8. Bear counters

Bear counters are another great option for younger students.

These fun and colorful plastic bears will keep your little learners excited to play with math. The bears are perfect for teaching the foundational math skills of counting and sorting. They can also be paired with a scale to teach measurement and weight.

If you don't have bear counters in your classroom, look for other small toys that can serve the same purpose. It's helpful for them to be similar in type, but that's not a necessity. Students can practice counting zoo animals, cotton balls, or erasers just the same.

9. Place value blocks or base ten blocks

Place value blocks, also called base-ten blocks, are used in classrooms from Pre-K all the way to 8th grade. These little plastic blocks connect to each other, making them a fun option for teaching a variety math concepts - like addition, subtraction, fractions, measurement, counting and more.

Most sets are colorful and can help students visualize different parts of an equation. They're perfect for exploring place value as well. Once students move up to solving double-digit problems, different colors can be used to represent the tens and even hundreds place.

Bonus tip: You can also use this place value chart as another in-class supplement!

10. Geoboards

Looking for something besides blocks for your geometry activities in class? Geoboards are the answer.

Geoboards are small wooden or plastic pegboards that use string or rubber bands to create a variety of shapes. They're a great hands-on activity for practicing shape recognition and names.

Geoboards can double as a fun brain break for young students. Pre-K and elementary students are often still working on the fine motor skills needed to draw shapes and write numbers. And manipulating the rubber bands or strings can be a welcome departure from the frustration of writing.

Like pattern blocks, you can have students use these in a structured way by making specific shapes. Or give them the freedom to create whichever shapes they'd like. You're sure to end up with some fantastic, mathematical art!

See how one teacher used a geoboard to explain basic shapes to her first grade students below!

Physical vs. virtual math manipulatives

Classrooms today don't look the same as they did twenty years ago, or even 3 years ago. The number of students in virtual or hybrid classrooms has increased dramatically. So, when you can't physically hand your students math manipulatives, what are your options?

There's actually quite a few! In the last few years, many free, online programs offering virtual math manipulatives have popped up. These may not be manipulatives in the traditional sense, but online games stretch the brain using a variety of learning models. They help students nail down complicated concepts in much the same way as the manipulatives mentioned above.

And it's not just virtual classrooms that can benefit from these tools. Homeschooling rates are on the rise. But many parents may not have the budget to purchase a large variety of math manipulatives. Online options provide a budget-friendly way to teach math at home or in the classroom.

It's easy to see how virtual manipulatives are beneficial for both students and teachers. Teachers now have a wide variety of effective teaching tools at their fingertips. And learners can gain a deeper understanding of math concepts on a platform they already enjoy. That means less frustration and more opportunity. Let's dive deep into a few more benefits of math manipulatives, whether virtual or physical.

3 Key benefits of using math manipulatives in the classroom

Increase interactive learning

In a classroom of 15-30 students, no two students are alike. They all learn in unique ways. And trying to make one lesson fit all those students is impossible.

For students who are struggling with math, hands-on learning activities with manipulatives can be a huge help. Not everyone can make sense of math on paper alone. Hands-on activities give learners a deeper understanding of how numbers work. And this understanding will continue to help them as they progress through school.

Students need to have a full understanding of basic concepts. Math builds on itself, so have a strong foundation will only help them as they gain more knowledge and advanced skills.

Also, manipulatives keep math learning exciting. Students grow bored of always using the same learning method. There's little to love about lectures and equations on a whiteboard. Math manipulatives can help you diversify your teaching style. You'll reach more students by using more methods, and that means more engagement and more learning. Awesome!

Develop problem-solving skills

Math manipulatives help students develop more complex problem-solving skills. When a student fully understands a math concept, they're better able to apply that concept to real-world problems. We want to teach students how to apply math skills across all of life, not just to next week's test.

Also, math manipulatives allow for a variety of problem solving methods. Students often interpret and think about problems in different ways. And that means they'll approach the solution differently too. Math manipulatives give your students the freedom to explore multiple paths to a solution. And if it doesn't work, it's easier for them to see why.

Build confidence in each math lesson

All of this problem solving with math manipulatives can give your students a major confidence boost! Activities with math manipulatives allow students to take the reins of their learning process. And because many math manipulatives are self-correcting, they can work individually on their problems. When they reach the right answer, all on their own, they'll feel an amazing sense of pride and accomplishment.

When students are able to understand and apply mathematical concepts, they're filled with that I did it feeling. Mastering the steps of a complicated math process gives students the confidence and encouragement to keep moving forward.

Students can then translate this deeper conceptual understanding to tests, quizzes, and standardized tests. They won't need a last minute cram session to succeed. They can stress less knowing they have the knowledge to tackle a variety of math and life problems.

Whether physical or virtual, math manipulatives can create a ripple effect that helps students throughout their entire educational journey.

Develop your student's math skills in a fun and engaging way

Math manipulatives are fantastic tools for helping your students understand and engage in their math lessons. And there are so many math manipulatives to choose from - something to fit every lesson and each student's unique needs.

Even if you don't have physical math manipulatives at your disposal, you can easily find virtual and online options that are just as helpful.

And some of them come at no-cost to teachers and schools! 👇

A no-cost, virtual math manipulative that's fun!

When you're exploring virtual options for math manipulatives, be sure to check out Prodigy Math. Prodigy's online math game is a stress-free way to help students master standards-aligned math skills. It's safe, fun and engaging, keeping your students excited and ready for their next lesson.

And with a free teacher account you can:

Set up engaging math practice in just a few clicks

Easily find out any learning gaps your students may have

Track how your students are progressing through your local or national curriculum

Sign up for free

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Math Manipulatives: How Can They Be Used to Enhance the Classroom Experience?

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Math is all around us. We can see it in nature and in our homes. We use math skills every day, even if we don't realize it. And you can help your students see math in all of its forms with fun and engaging math manipulatives.

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Meet Marcy Cook Master Educator, Author and Math Specialist, Marcy has presented workshops and seminars for teachers throughout the USA as well as in over two dozen foreign countries. Read More See All Tile Packets Involve All Students in Mathematical Thinking

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Place Value Pockets are amazing tools for developing strong number sense and place value understanding. This is a tool that will quickly become a daily routine in the elementary classroom. It is also an excellent tool for middle school students to practice divisibility rules and algebraic thinking. This product includes 30 sets of 0-9 digit cards in light pink cardstock and 30 place value pockets for ones, tens, hundreds and thousands in blue cardstock. Included are directions with games, questions and activities to facilitate the daily use of this tool. These place value pockets and digit cards are very powerful with Kim Sutton’s book, Place Value with Pizzazz.

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Unleash your creativity with the world's best virtual manipulatives!

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Using fraction circles to teach fractions is as easy as pie! Using the idea of pie is actually a great way to familiarize students with the idea of fractions. With fraction circles, children can imagine dividing a pie into equal pieces and show that visually.

To use the fraction circles, simply click and drag the colored pieces onto the circles. You can remove pieces by simply clicking them and dragging them out of the circles. By using different colors for each fraction, we made it easy for students to compare them.

Use these interactive fraction circles with your students to explore equivalent fractions, common denominators, and mixed numbers. You can show students a mixed, simple, or improper fraction and then ask students to model it using the fraction circles. Students can also model operations with fractions using fraction circles.

Looking for more fraction resources? Check out our fraction bars and fraction strips

Visit classplayground.com for more resources and printables related to fraction circles.

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Fraction Circles | Free Virtual Manipulatives | Toy Theater

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These interactive manipulative online fraction circles make teaching fractions as easy as pie! Model from 1/12th to 1 whole.

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Demonstrate key math concepts in your classroom using our new virtual manipulatives!

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Improving Science Education Through Three-Dimensional Learning

Quick Search Next Generation Science Standards

THE THREE DIMENSIONS OF SCIENCE LEARNING

Within the Next Generation Science Standards (NGSS), there are three distinct and equally important dimensions to learning science. These dimensions are combined to form each standard-or performance expectation-and each dimension works with the other two to help students build a cohesive understanding of science over time.

Crosscutting Concepts help students explore connections across the four domains of science, including Physical Science, Life Science, Earth and Space Science, and Engineering Design.

When these concepts, such as "cause and effect", are made explicit for students, they can help students develop a coherent and scientifically-based view of the world around them.

Science and Engineering Practices describe what scientists do to investigate the natural world and what engineers do to design and build systems. The practices better explain and extend what is meant by "inquiry" in science and the range of cognitive, social, and physical practices that it requires. Students engage in practices to build, deepen, and apply their knowledge of core ideas and crosscutting concepts.

Disciplinary Core Ideas (DCIs) are the key ideas in science that have broad importance within or across multiple science or engineering disciplines. These core ideas build on each other as students progress through grade levels and are grouped into the following four domains: Physical Science, Life Science, Earth and Space Science, and Engineering.

More about 3D Learning

GET TO KNOW

The Next Generation Science Standards (NGSS) are K-12 science content standards. Standards set the expectations for what students should know and be able to do. The NGSS were developed by states to improve science education for all students.

A goal for developing the NGSS was to create a set of research-based, up-to-date K-12 science standards. These standards give local educators the flexibility to design classroom learning experiences that stimulate students' interests in science and prepares them for college, careers, and citizenship.

Get to Know the Standards

IMPLEMENT

The NGSS call for a three-dimensional approach to K-12 science instruction. This represents a significant transition from previous state standards. That's why effective implementation demands a great deal of collaboration and patience among states, districts, schools, teachers, and students.

Thoughtful and coordinated approaches to implementation will enable educators to inspire future generations of scientifically literate students. That is the vision of the NGSS. This website provides a range of high-quality resources that empower educators, administrators, parents, and the general public to help bring this vision to life.

Find Tools and Resources

WHY

Science-and therefore science education-is central to the lives of all Americans.

A high-quality science education means that students will develop an in-depth understanding of content and develop key skills-communication, collaboration, inquiry, problem solving, and flexibility-that will serve them throughout their educational and professional lives.

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Home Page | Next Generation Science Standards

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Improving Science Education Through Three-Dimensional Learning Quick Search Next Generation Science Standards Within the Next Generation Science Standards (NGSS), there are three distinct and equally important dimensions to learning science. These dimensions are combined to form each standard-or performance expectation-and each dimension works with the other two to help students build a cohesive understanding of science over time.

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5E Lesson Plan

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Before During and After Lesson Plan

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Before During After Lesson Plan Done PDF

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Checking for Understanding with White Boards

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How to Read the Next Generation Science Standards

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

Research has long linked strong reading skills with improved math achievement -which may seem obvious when it comes to typical math tasks like understanding directions on a test, or parsing word problems.

But literacy skills also support and deepen math understanding in unique and powerful ways.

"Reading and writing are complex, fundamental, integrative learning skills that should be used to their full potential in math class," writes Alessandra King, a middle school math teacher in Bethesda, Maryland. For all students, and especially those who "enjoy reading and writing more than the computational side of math," King says that finding ways to fold literacy into math class gives them "a deeper understanding and stronger appreciation of the usefulness and effectiveness of mathematics."

Blending the disciplines, when the lesson allows for it, also sets students up to "engage with math in a new-and often far more inviting-way," explains educator and tutor Chelsea Miro in an article about math read-alouds. "Kids who have struggled with geometry may love the opportunity to write a shape story, for instance-and it might even help them to remember that a square is a type of rectangle but a rectangle is not a type of square."

Here are six ideas, sourced from teachers and recent research, for merging math and literacy in ways that challenge students' abstract reasoning and build critical thinking and collaborative learning skills.

Explore Picture Books

Early-grade math problems tend to be straightforward and linear-much like the picture books that introduce them to literacy concepts. These shared properties make mathematical reasoning fertile ground for early-grade book authors.

But not all children's books that feature math are created equal. Just like in language arts classes, text selection is important, say educators Kathleen Crawford-McKinney and Asli Özgün-Koca. The trick is to find options that present a rich mathematical problem that students can work through alone or in groups, and then compare their answers to the solution in the book.

In one of their favorite examples, Molly Bang's When Sophie Thinks She Can't, main character Sophie is challenged to form as many different rectangles as possible using 12 tiles. It's a low-threshold, high-ceiling problem, offering a challenge for students across a range of skill levels. For some kids, a related exercise might involve creating their own rectangles using manipulatives and comparing solutions as a class; a more advanced exercise could involve asking them to create squares instead and discussing the differences between shapes.

When designing lessons around picture books, Crawford-McKinney and Özgün-Koca suggest creating content specific questions for students to answer, which will vary by book. But they also favor asking general questions about how math concepts shape the story and how the author establishes this understanding-which can teach students to think more like mathematicians.

For more book ideas, see former elementary school teacher Chelsea Miro's list of favorite books for math read-alouds, including more abstract titles like Kate Hosford's Infinity and Me.

Connect Thinking Through Math Journals

Teachers in subjects like English and science often use journals or logbooks to give students space to record their learning progress, make observations, and brainstorm solutions in a low-stakes format.

In math class, however, the journals might look a little different, explains former high school math teacher Nell McAnelly, who used them often with her students. "It is a record of personal experience showing what a student tried, what worked and what didn't, what practices should be continued, and what improvements a student should focus on going forward," she says. "Consequently, journals can promote initiative and confidence, which we know are gateways to learning."

There's still space for written reflections, but also for illustrations, diagrams and charts-making math journals more formal than scrap paper but less polished than an exam paper.

In her experience, students use them to make connections across mathematical ideas and delve into the reasoning behind their answers-much like they might use a journal to analyze a poem or text in language arts. Entries can also be used as discussion prompts for group work, where students can learn directly from one another as they explore new strategies.

Design Math Magazines That Relate to Real-World Topics

In Alessandra King's math classroom, while writing prompt activities are helpful, she prefers assignments that create strong connections between what students are learning in math class and the real world. "Reading and writing are particularly effective in developing a quantitative understanding of the world around us because they can be used to lead students to reflect on everyday experiences," King writes.

To harness the benefits of reading and writing, King has students create math magazines, collaborative publications that they compile with summaries they've written of math-related articles and images from publications like Scientific American, The Economist, the New York Times' Upshot section, and the Atlantic. It's one of her most popular assignments of the year.

King keeps a thick file of articles she's clipped or printed out that touch on math-related topics-from political gerrymandering to fractals in modern art and using machine learning to predict March Madness upsets-and lets students choose ones that pique their interest. They compose a page-long summary of the piece with special emphasis on the math concepts discussed and package their work with related charts or graphics.

At the end of the assignment, everyone's contributions are compiled into a magazine, and King uses a simple rubric to assess their content understanding, clarity of communication, editing, critical thinking, initiative, and creativity.

Identify and Teach Math Vocabulary

When fifth-grade math teacher Kathleen Palmieri discovered that only about 40 percent of her students could accurately define key math vocabulary (of various levels of complexity), she realized she needed to make learning math terms a regular part of her instruction, Palmieri writes in an article for MiddleWeb.

But rather than simply memorizing a list of words, she found that students needed to understand how the mathematical concept worked before the term itself would stick. In other words, if her students didn't know how fractions work, learning the definition probably wouldn't mean much. Additionally, math concepts typically make the most sense when learned in sequential order.

Drawing on ELA vocabulary building skills, Palmieri began asking students to pull out key terms they don't understand at the beginning of a unit for a math glossary that they add to as they learn each concept. Students also used colorful Post-its to create a math word wall that they add to as they learn new words-and can refer to at any time. Lastly, the class regularly decides on a word of the day or even a word of the week, with students responsible for tallying every time they see the word and describing how it's used.

Identify Patterns and Connections Via Word Sorts

Another strategy inspired by ELA instruction, word sorts can easily be adapted to math class to help students recognize patterns and relationships between words. Working alone or in groups, students identify each term in a given vocabulary list and sort terms into categories-either ones created by the teacher (known as closed sorts) or that they come up with themselves (open sorts).

Word sorts can be implemented using mathematical terms, symbols, or even expressions. Students can sort these based on various attributes-say, operation type (addition, subtraction, multiplication, division), geometric shapes (circle, triangle, square), or algebraic properties (commutative, associative, distributive).

To sort a list of mathematical expressions, kids might separate them based on whether they involve addition, multiplication, or both (e.g., the expression 5𝑥+ 3).

Younger students might perform a similar sort by placing the word "rhombus" into multiple categories, including parallelogram, quadrilateral, and two-dimensional, write Miranda L. Sigmon, Kavin Ming, and Daniel Herring-the authors of a 2022 piece on word sorts for the journal Mathematical Teacher.

To drive meaning home, the authors suggest using sentence stems, such as "I think (insert term) goes under the (category name) category because . . ." -which gets students thinking more about the choices they're making. Model a few examples yourself and split students into small groups to encourage genuine discussion and comprehension.

Encourage Collaboration With Math Circles

Inspired by literature circles, a common practice in ELA, history, and occasionally even science classes, math circles involve assigning roles to students that they perform as part of collaborative work in small groups. The goal is to foster math-related group learning, discussion, and advanced collaboration skills like leadership and flexible thinking.

In Patricia Kridler's middle school math classroom, student roles include Situation Summarizer, Vocabulary Master, Idea Guy/Gal, Model Maker, and Computation Kid, Kridler writes in the journal Mathematics Teaching in the Middle School. Since math topics can vary greatly, she often creates new roles depending on the assignment, and asks groups to complete a role worksheet that includes space for every student to share their contributions. After every cycle, she asks students to swap roles.

At first, she assigns simple word problems and lets students take turns in their roles before moving to more complicated or abstract projects that could take several class periods to complete. Typically, students use the role sheets to explain their thinking and their mathematical reasoning in depth, and the Situation Summarizer presents the findings to the entire class.

Math circles allow Kridler to structure a math task "so that all students get to focus on different aspects of how to solve a problem," she writes. "Students also develop the skills necessary to become better independent thinkers. In the process, I am learning much about how students think through problems."

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6 Ways to Merge Literacy With Mathematics

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

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The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics. They would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks. Progressions documents also provide a transmission mechanism between mathematics education research and standards.

For more information on the project, please visit the project website.

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Progressions Documents for the Common Core State Standards for Mathematics

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The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

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Depth of Knowledge handout for PD with stems on front and possible activities with roles on back-2

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English Learners (EL) Academic Language Function Toolkit | Missouri Department of Elementary and Secondary Education

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205 Jefferson St.
Jefferson City, MO 65101Map(link is external)

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Science Fieldwork 2

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Math Fieldwork 1

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Math Fieldwork 2

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Common Core Instruction: Exploring Dividing Decimals to the Hundredths

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Time for Class - Mr. Adler Science Lesson

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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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2016 Science Framework - Science Framework (CA Dept of Education)

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The curriculum framework was adopted by the State Board of Education on November 3, 2016. This is the final published version.

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STEM subjects - science, technology, engineering, and math - are a crucial part of a child's education both now and in the future. These STEM books are filled with great stories and cool project ideas that can help lay a foundation for any mixture of STEM disciplines. We hope the books recommended here spark excitement, teach something new, and make STEM accessible to your children.

STEM Books for Kids Ages 4 - 8

STEM Books for Ages 8 - 12
Editor's Note: This article was originally published in 2017 and updated in 2023.

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18 STEM Books That Make Science and Technology Fun for Kids | Brightly

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Science, technology, engineering, and math are crucial parts of a child's education. These STEM books are filled with great stories and project ideas.

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Outstanding Science Trade Books for Students K–12

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NSTA, in conjunction with the Children’s Book Council, is pleased to announce the list of Outstanding Science Trade Books for Students. Representing the best science trade books published in 2025 for students in kindergarten through 12th grade, the books featured on the list include captivating stories, compelling characters, and beautiful illustrations.

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Science Nonfiction Elementary Plus - Elementary - Categories

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Welcome to Junior Library Guild, the collection development and book review service relied upon by thousands of schools and public libraries across the country.

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Mathematics Instruction & Math Teaching Strategies

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NGSS Elementary School Science Classroom Activity

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A Project-Based Approach to Teaching Elementary Science

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Children's books often contain valuable lessons that can help young students begin to think like mathematicians.

monkeybusinessimages / iStock

Many students and teachers view math as a subject for numbers and computation, instead of one that benefits from discussion and interpretation. Based on our experience as children's literature and mathematics teacher-educators, we've found that providing the context to mathematical problems through literature supports students' learning-children's books can be used to integrate math and literacy and to provide context for math.

For example, the books When Sophie Thinks She Can't, a story about a little girl who discovers the importance of struggle, and , a story about the history of the color blue, are great examples of books that integrate mathematical thinking into storytelling.

USING LITERATURE TO SUPPORT MATHEMATICAL THINKING

1. Selecting books to support mathematical thinking: First, find books that have a worthy math problem to discuss or a story to connect to a math problem in your curriculum. Context is one of the most important parts of choosing a book. If the problem is not challenging or accessible enough for students, think about ways to revise the problem. We advocate for low-threshold, high-ceiling problems, which allow access for all students with their previous knowledge and build more knowledge and challenge all students.

When Sophie Thinks She Can't, by Molly Bang, poses a worthwhile math task, asking Sophie and her friends to form as many different rectangles with 12 tiles as they can. Because she can't figure out the solution to the problem, her teacher says, "You can't figure it out yet," which encourages her to keep trying. This book is a perfect example of a mathematical problem that is easily seen in the context of the story and encourages the notion of the power of yet as a problem-solving technique.

In many books, the math problem is not as easily seen. As a teacher, you may not think that most books have some type of mathematical focus within them, but upon close examination, you can discover that many of them can be part of your math curriculum. For example, Blue, written by Nana Ekua Brew-Hammond and illustrated by Daniel Minter, can be connected to an examination of patterns and shapes in textile designs. Working with different shades of blue papers, students could be asked to create patterns by folding the papers and study the patterns that they created mathematically. Studying the relationships between the number of folds and partitions in the final shape would take this task to a higher ceiling.

1. Whose story is this? How might it relate to students' mathematical stories?

2. Through what point of view is this story told?

3. What mathematical concepts shape the story?

4. How are mathematical tasks and understandings established?

2. Critically examining literature: Teachers should spend time critically examining their texts; as Maria José Botelho and Masha Kabakow Rudman advise, teachers should read beyond the words in the text and make connections between local, sociopolitical, personal, and mathematical content. Teachers can ask questions like the following:

The first two questions help students relate to the issues, topics, and questions they may have about the story. The last two questions help students think like a mathematician. For example, Blue is told from a historical perspective and touches on classism throughout time. By examining the book closely, teachers can pull out the patterns in the illustrations and ask students to create mathematical patterns on their own-this is shown throughout this book and particularly on the endpapers.

This picture book provides so many historical background understandings of who cultivated the materials to make the color blue and who had access to textiles made from blue dyes. By leading the students through the questions above, teachers will help them begin to see math in all things and begin to think like mathematicians.

3. Designing a lesson to integrate literacy and mathematics: It's beneficial to think ahead about questions for both disciplines that can help students extend and guide their thinking; in previous work, we developed a full lesson with content-specific questions. Asking students to analyze or interpret their peers' mathematical work and making connections to the text would also extend students' thinking. After coming up with their own set of rectangles with 12 tiles, students can compare their rectangles with the rectangles created by their peers or by Sophie and her friends. This can lead to a discussion of how similar or different all of the rectangles are.

Circle Dogs, written by Kevin Henkes, illustrated by Dan Yaccarino. Exploring shapes through a day in the life of two dachshunds. Perfect read-aloud for a geometry unit! Pair this with Hot Dog (below) to help your students make text-to-text connections.

Bean Thirteen, written and illustrated by Matthew McElligott. This book explores the concept of division with the tribulations that the two characters encounter as they work their way through a problem. A great way to engage children in discussions of trying to work through problem-solving.

, written and illustrated by DougSalati. This 2023 Caldecott-winning book explores a day in the life of a dog as readers are taken on an adventure throughout an urban setting to find solitude for the owner and the dog in a noisy city. A wonderful way to look at mapping.

A Land of Books: Dreams of Young Mexihcah Word Painters, written and illustrated by Duncan Tonatiuh. This story focuses on the creation of books by the Indigenous people of Mexico, exploring their knowledge, culture, and history. Readers can dig deeply into the illustrations and see how precise measurement, geometry, and special relationships of mathematical concepts enhance the telling of this story.

We hope these ideas and books will support you as you provide meaningful conversations with your students by integrating mathematical understandings through children's literature.

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Using Stories to Support Mathematical Thinking in Young Students

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Children's books often contain valuable math lessons that can help young students begin to think like mathematicians.

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working with a partner to form 2-digit numbers; cooperative activities dealing with concepts before, after, and between DIGITAL FORMAT (view & accomplish tasks on computer, ipad, or other hand held device with google)

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Original Tiling Task Card Packets include 20 unique task cards on card stock, 3 backdrop cards , tracking sheets, suggestions and answer sheets. These are contained in a printed manila envelope for convenient storing. A set of number tiles 0 - 9 is needed for each task card.

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Bloom’s Taxonomy - Center for Instructional Technology and Training - University of Florida

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The original Taxonomy of Educational Objectives, commonly referred to as Bloom’s Taxonomy, was created by Benjamin Bloom in 1956, and later revised in 2001. Bloom categorized and classified the cognitive domain of learning into varying levels according to complexity and richness. As you travel up th…