Math Manipulatives

Math Manipulatives; Make Your Own DIY Kit FREE

Over the past four decades, studies conducted in several different countries across multiple grade levels indicate that math manipulatives substantially improve mathematical understanding and ability. Math manipulatives help children to understand abstract concepts by equating them to something concrete, using the manipulatives.

Young children think of their world in concrete ways.  They collect facts about objects they experience in daily life and organize those facts as they classify objects. Concrete thinking is focused upon gathering pieces of information about tangible objects.

Abstract thinking typically doesn’t develop until children are older. As children develop the skill of abstract thinking, they learn to deal with concepts they haven’t directly experienced, learning to draw their own conclusions from previous experiences.

Math manipulatives have improved mathematical understanding so greatly that several curriculum developers have begun selling math curricula entirely based on math manipulatives. Learn more about them in my Homeschool Math Curriculum Comparison Guide.

Math manipulatives are so important that every homeschool family should have a set. If you can’t afford $150 or more to buy a ready-made set of math manipulatives, or if you just don’t want to pay that much, you can certainly create your own with things you have around the house (or a quick trip to the dollar store) and your printer.

I store all of our math manipulatives in a simple plastic file box from the organization aisle at Walmart. I love that everything is in one place and I can easily remove it to a high shelf, away from my kids, when we’re not using it. Not that that always works. Somehow they search out (and lose or destroy) everything, but this still helps.

15 Math Manipulatives Your Kit Should Include:

1. Craft Sticks and Rubber Bands

You can find huge packages of craft sticks and rubber band at the dollar store. Craft sticks are easy to group, which makes them perfect for learning place value.

You’ll want at least 350 craft sticks and 20 or so rubber bands, so you can bundle the craft sticks into ten groups of 10, two groups of 100, and have some left over as ones. I like to teach place value by having my child trade me ten ones for a bundle of ten, or ten bundles of ten for a bundle of 100, so they fully understand the concepts of “borrowing” and “carrying”.

That number will allow you to work on two-digit addition and subtraction, and demonstrate 3-digit, though only having 2 bundles of 100 limits you to three-digit numbers starting with 1 or 2. But it demonstrates the concept in a concrete, easily understood way.

Math concepts to teach with craft sticks:

  • Place value
  • Borrowing and carrying
  • Addition and Subtraction
  • Multiplication and Division

2. Counters 

A pile of small, countable items will help your child recognize that written numbers represent real items (number recognition and correspondence). They can also help your child learn to count by rote. Those are some of the earliest learned concepts.

Dried beans, legos, wooden blocks, pennies, colored beads or anything you have around the house will work. It’s best, though, if they are identical, so your child is just working on one concept and not confused by trying to sort colors or shapes.

I keep a small container of coins (to use as both counters and to learn about money) and a couple of small bags of assorted counters in our math manipulative bin. Occasionally, for added interest and fun, I add edible counters, like m&m’s, jelly beans, marshmallows or cheerios to our kit. You wouldn’t want to use edible counters all the times, since they’re consumable, but they provide a fun change.

Later, your child can use these to master ordinal numbers (first, second, third…), addition and subtraction, compare numbers (more, less and equivalence) and eventually group them for multiplication, division and fractions.

This set of printable Rainbow Bear Counters with fun math games and activities includes bear counters in six colors, plus 18 fun math games to play with the bear counters. Use coupon code ‘Math25’ to download your rainbow bear counters and fun math games for only $3.

Math concepts to teach with counters:

  • Counting
  • Number recognition
  • Number correspondence
  • Ordinal numbers
  • More, less and equivalence
  • The concept of ten (use counters with ten frames)
  • Addition and subtraction
  • Multiplication and division

3. Dice are fun math manipulatives

You’ll need multiple dice for all the math games you’ll be playing. You can either rob your game closet, or you can pick up a package of these at the dollar store. I bought these, 6 dice for $1, at my local dollar store.

Dice are also a fun way to work on subitization, or the ability to “see” numbers at a glance. They can be used all by themselves to drill math facts or practice mental math in a fun and interesting way.

Math games to play with dice:

Pig: You’ll need a pair of dice, paper and pencil for scoring. The goal is to be the first player to reach 100.  The first player rolls both dice, calculates the sum, then rolls again if he or she wants to. The next sum is added to the first. The player can roll as many times as he chooses, but if he rolls a one on either die, he scores 0 for that round and it’s the next players turn. If he rolls 1’s on both dice, his entire total is scrapped and he starts over again at 0.

Multiplication Tetris: You’ll need a pair of dice, a sheet of graph paper and pencil per player, and a box of crayons. Players take turns rolling both dice and drawing arrays on their graph paper, according to the numbers rolled, then color it. For example, if 4 and 3 are rolled, the player draws a 4 x 3 rectangle on the graph paper. Players should draw rectangles strategically so they fit together like in Tetris. The first player with a full paper wins.

4. Blocks

Blocks can be used to teach multiple mathematical concepts. Blocks that are all one shape or color make it simpler to learn a single concept at a time.

Blocks can be used to teach patterns, they can be used as counters, and they can help your child to learn to compare sizes such as taller, bigger, or shorter. You can use any type of blocks to build towers, comparing heights, walls or snakes to compare length.

Concepts to teach with blocks:

  • Comparison (Build towers or walls and compare the sizes: tall, taller, tallest, long, longer, longest).
  • Pattern (if you have different colors or shapes)
  • Counting
  • Place Value

5. Pattern Blocks

Pattern blocks are different than building blocks. They’re comprised of 6 shapes in 6 colors (green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons).

Disregarding the thickness, pattern blocks are two dimensional shapes. They are designed so the sides are all the same length except for the trapezoid, which has 1 side that is twice as long, making it easy to nest the shapes together to build figures.

Pattern blocks help students develop spatial reasoning. As students become more familiar with composition and decomposition of shapes, they recognize patterns more easily.  This feature makes it possible for the shapes to nest together and provides for a wide range of explorations

Jessica Brown has printable pattern blocks and tons of fun patterns for using them. When I use paper pattern blocks I don’t laminate them because that makes them hard to nest together. I prefer to just print them on cardstock.

Container of pattern blocks.

Concepts to teach with pattern blocks:

  • Patterns
  • Geometric designs
  • Spatial Relations
  • Area and other geometry concepts

6. Deck of cards for math games

Cards with numbers on the face are such a fun way drill math facts without it seeming like drill! Here are several fun games to play with cards that will teach mathematical concepts from number recognition to drilling math facts.

Memory: Lay multiples of each number out, face down, on the table and scramble them around. Players take turns choosing two cards at a time. Players keep matching pairs and take an additional turn following each match. Alternately, you could match cards that add up to ten, so 7 and 3 match or 6 and 4 match.

War: The deck is divided evenly between two players, with cards face down on the table. Each player should have a stack of 26 cards face down in front of him.  Each player turns up a card at the same time and the player with the higher card takes both cards and places them on the bottom of his stack, face down.

In the event that the cards are the same rank, you have ‘War’. Each player turns up one card face down and one card face up. The player with the higher cards takes both piles. If the turned-up cards are again the same rank, each player places another card face down and turns another card face up. The player with the higher card takes all of the cards, and so on until one player has all of the cards.

Ten: Play this math card game alone or as a team. Lay out a deck cards on the table, face up (number cards only — leave out face cards). Players take turns removing sets of cards that add up to 10, trying to accumulate as many cards as possible. So 1+3+2+4 is preferable to 5+5. The player with the most cards wins. Alternately, you could decide that fewer cards are preferable. Or you could decide to only choose pairs.

Number Bingo: Lay out a 4 x 4 array of cards, face up (number cards only — leave out face cards) in front of each player. This is is ‘bingo card’. Remaining cards  are placed face down in front of the caller. The caller flips over a card. All players with that number on their board turns the card face down. Play continues until one player has a row flipped over horizontally, vertically, or diagonally and calls “Bingo!”

Twenty-one: This is traditionally a gambling game (aka Blackjack), but we don’t bet. This is a great way to practice arithmetic skills. The objective is to get to 21 or as close as possible. Number cards are worth their face value, jacks, kings and queens are worth 10. Aces can be either 1 or 11 — the holder of the card gets to choose. To start, the dealer deals two cards from his face-down deck to each player. After all cards are dealt, all players may look at their two cards and add up their total. In order, players may request a “hit” (another card from the dealer). You may hit any number of times in one turn. Do this until you are satisfied with your card total or bust (over 21). Once you’re satisfied with your card total, you “stay”.  The winner is the person closest to 21 without going over, or busting.

Number Scrabble: A dealer deals each player 10 cards (numbers only), then places one card face up in the center and the remaining cards face down in a pile on the edge of the table. Players take turns placing cards in sequential order, building off the card already in the center. For example, if the card in the center is a 3, a player could place a 2 or a 4 below, above or the the right or left. The next player would build on that sequence or start another in a different direction. Players can place more than one card at a time. If the center card is 3, and a player has a 2, a 4 and a 5, he could place them all at once. All cards that are next to each other must be sequential.

Solitaire for number sequencing.

7. Clock

You might have an old analog clock around the house you could use. It doesn’t need to be anything special, just a clock with moveable hands and numbers (not Roman numerals).

I’ve used this inexpensive clock in our homeschool for years. It’s geared on the back so the hands move together, helping kids see the way hands move together typically. But that isn’t necessary.

free math manipulative kit diy

You can make your own clock that will do in a pinch, using the free printable at the bottom of the page and a brad.

Games for learning to tell time:

Daily schedule: Create a visual schedule of your daily activities, with pictures of getting dressed at 6:30 am, pictures of breakfast at 7 am, pictures of practicing (instruments or whatever) at 8 am, pictures of school at 9 am, etc…

Stop the clock: We play this with at least two children, but you could play it non-competitively with one child. Each child has a clock with moveable hands (free printable at the bottom of this page). I yell out a time, or display the time on a digital device. Players have to make their clock hands match the specified time. I start with o’clock times, move to half past, quarter of, quarter after, then to more specific times.

8. Money 

Coins are essential for teaching children to count money. You might have a toy cash register that came with plastic coins and fake bills, or a game with money you can play with. Or you could just use real money. That’s what I do, because my kiddos kept losing the play money and I hate spending real money on fake money.

I just use the loose change I find in our pockets at the end of the day. It gets collected for awhile in a jar and then added to our manipulative kit, along with bills of all denominations, which I am more careful about.

Coins can also be used for:

  • Use pennies as counters
  • Use nickels, dimes, or quarters to practice counting by 5s, 10s, or 25s.
  • Use pennies and dimes to teach place value.
  • Use pennies and dimes to teach adding and subtracting 2-digit numbers, with or without regrouping.
  • Use pennies and dimes to stand for tenths and hundredths to teach decimals.

Pennies, dimes and 1 dollar bills (1s, 10s and 100s) are great for teaching place value. So are 1 dollar bills, 10 dollar bills and 100 dollar bills from your Monopoly set.

9. Ruler and other measuring tools

You probably already have rulers, yard sticks, measuring tapes, measuring spoons, measuring cups, quart/gallon pitchers and a kitchen scale around your house. If not, you can pick them up at the dollar store.

I actually don’t keep my kitchen tools in my math manipulative kit because I only have one set of them. Plus, they’d take up too much room, we only use them for math infrequently, and we homeschool at the kitchen table anyway (so they’re very accessible).

Concepts you can teach with measuring tools:

  • length
  • size
  • weight
  • metric system
  • unit conversion

10. Hundreds Chart

A hundreds chart is just a 10 x 10 array of all the numbers from 1 to 100 in order. It’s useful to have one with the numbers filled in and a blank one, laminated, for your child to practice filling in.

Dry erase markers can be difficult for little hands to manage, so I actually prefer to print several and not laminate them for my preK and kinders to practice with. Older, more dexterous kids do fine with the laminated, reusable version.

You’ll find two hundreds charts in the free printable at the bottom of this post, one blank and one with the numbers filled in.

Games to play with your hundreds chart:

Missing Digits: I’ll use a black dry-erase marker to black out multiple squares on the laminated hundreds chart with the numbers filled in. My child has to figure out the missing numbers then wipe off the marker to check his guess. Black out more numbers for more experienced children, or just write in a few numbers on the empty chart.

Hundreds Bingo: Give your child a couple of rolls of smarties or a handful of m&m’s or other small treat. Call out numbers and have him cover the corresponding number on his chart. Work to cover a whole row or go for blackout.

Mystery Numbers: You choose a number and give the other players clues, such as, “The mystery number has two digits.” “The mystery number is greater than 60.” ” They mystery number is even.” until the players guess your mystery number correctly.

Twenty Questions: You choose a number. Players may ask up to 20 yes/no questions to try to guess the number.

Don’t eat Pete!: Choose one player to be the guesser. He leaves the room. The remaining players choose a number to be Pete. Cover all 100 numbers with a smartie or other small candy, make sure everyone knows which is Pete, and invite the guesser back in. The guesser starts guessing numbers randomly. As he says the number out loud, he removes and eats the candy (or places it in his pile to save for later). When he finally reaches Pete, everyone shouts, “Don’t eat Pete!” and his turn is done. Another guesser is chosen and everything is repeated.

11. Ten Frames math manipulatives

A ten frame is just a 2 x 5 array of squares, used to visually represent ten in a simple way. Because our number system is based on ten, having a thorough understanding of ten and combinations that make ten or can be derived from ten is critical.

Concepts taught with ten frames:

Free printable ten frame

Ten frames are excellent ways to present sums and differences up to ten in a visual way. You can model addition with two different colors of counters, one per space. For example, six green counters and four red counters makes ten.

You can also model subtraction by filling the spaces with a single color of counters, then removing some. Stack two of the ten frames to create a 4 x 5 array when your child is ready to add and subtract into the teens.

Ten frames are also helpful when it comes to teaching multiplication and division. Model multiplication by grouping equal quantities of counters in each square. For example, 10 groups with 4 counters each is 40.

Division is just the opposite. “If I have 40 counters and divide them equally between the squares, how many will be in each square?” It’s a great way to teach remainders as well. And you don’t have to use all ten squares.

The free printable at the bottom of this post includes a couple of ten frames.

12. Fraction Strips and Circles

Both of these are excellent ways to visually represent division and fractions. Fractions can be hard to grasp until kids can actually hold the pieces in their hands and see that 1/4 is smaller than 1/3.

The free printable (watch for the big, blue button) math manipulatives at the bottom of this post include a set of fraction strips and a set of fraction circles from whole to 1/16.

DIY math manipulative kit homeschool

Concepts taught with fraction strips and circles:

  • Whole and part
  • Multiplication of fractions
  • Division of fractions
  • Fraction equivalents
  • Addition and subtraction of fractions

13. Base Ten Set

Base Ten Blocks provide hands-on ways to learn number concepts such as place value, regrouping and decimals. They physically represent mathematical concepts so students can develop a deeper understanding. The blue button at the bottom of this post will take you to a free printable that includes a base ten set.

Concepts to teach with a base ten set:

  • Adding and Subtracting
  • Multiplication and Division
  • Number sense
  • Place Value
  • Regrouping
  • Counting
  • Decimals

14. Picture Books make great visual math manipulatives

I constantly trade picture books in an out of my math manipulative kit, depending on the concepts we’re working on at the time. We visit the library weekly, so I just look ahead in my children’s math books and try to find a couple of math picture books to go along with upcoming concepts each week.

Picture books teach shapes, numbers, counting, prepositions, comparison words and so much more. Picture books are a fun way to learn concepts because they’re so visual.

15. A Chalkboard or Dry Erase Board

This is not a necessity, but if you have one around the house, this will make learning to write numbers more fun.

First you can just write a single number on the board and have your child count out the corresponding number of counters. Next, you can use it to write addition facts, placing the corresponding number of counters above each number.

My kids like the 9 x 12 size so they can work independently. They love having their own tools. I also appreciate that the smaller size boards fit into our math manipulative kit. I buy the 2-sided kind with a blank side for math and a lined side for writing.

Now That’s a (practically free!) Math Manipulatives Kit

There you have it! A very simple math manipulative kit that is every bit as effective as the expensive, commercial kits. You probably have most of the items you’ll need around your house already, except for the printables, which you may download free below.

Math manipulatives don’t need to be complicated!

Are you looking for a complete, gameified, FUN math curriculum?

Kids don’t hate math, they hate feeling stuck. We Play Math eliminates frustration through gamification. Short, animated videos teach concepts and games and puzzles provide practice. Our math arcade facilitates instant, automatic recall of critical math facts.

Sign up here for your 25-page FREE Math Manipulatives printable, which includes:
  • Ten Frames
  • Base Ten Set
  • Practice Clock
  • Hundreds Chart (1 blank and 1 filled in)
  • Fraction Strips
  • Fraction Circles




Pin this DIY Math Manipulatives kit for later!

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