Math Manipulatives

posted by Stephanie Forsman

All teachers are inherently hoarders of one kind or another. In the beginning of my teaching career, I would collect everything from eggshell cartons to the Styrofoam trays that are included in meat packaging to spending many of my weekends going garage sale-ing and buying books, games, cooking utensils, stickers… You name it and I had to have it and store it somewhere at home or in my classroom. Many times, I didn’t even have a specific project for these items. I just knew that some day, down the road, there would be an opportunity to use these items and I would be ready. Safe to say that 90% of those precious items I lovingly collected, were thrown out. And I am sure that, at the time, it pained me to throw it away. Now, after more than seventeen years of teaching experience, I am no longer an aimless hoarder. I have become a very specific hoarder; I hoard math manipulatives.

Math manipulatives are essential to math learning. According to Scholastic Parents, “Math has many areas — patterns, measurement, geometry, statistics, probability, and more — and they’re often unfamiliar, abstract, and confusing to students. We need to help children develop the ability and confidence to find their way around in each of these areas, see how they connect, and know what to do should they forget a fact or procedure.” Math manipulatives can help students learn in several ways: they help to make abstract ideas more concrete, they build confidence and aid in more clearly visualizing their reasoning, they are useful tools for problem-solving, and most importantly, they can be interesting and fun.

I have had the advantage of working in the same school for sixteen years and ten of those years have been in the same room. A couple of years ago, when it came time to remodel the classrooms and put in new cabinets and shelving, I asked for 5 x 5 shelving cubbies in which to neatly store my math manipulatives. Each cubby fits in a plastic shoebox container with lid, and is easily accessible. This collection of manipulatives and the way


that I have them stored is my pride and joy. I love having easy access to almost any manipulative a child might need to solve a problem or enough game pieces to play a spur of the moment math game. Math manipulatives help to make math accessible to everyone, all learners and they also help to take the anxiety out of math. And having the manipulatives on hand, at any given moment, help to make them part of the set-up and routine of student’s math practices.

One of my favorite manipulatives is number tiles.

And I especially love the magnetic number tiles. has a big selection of magnetic manipulatives (fractions sets, base ten numbers, money, geometric shapes) that I rely heavily upon. Back from my nondiscriminatory hoarding days, I collected a ton of tins in all shapes and sizes. I put the magnetic sets in the tins and clearly label the outside of the tin. Number tiles help children take risks and take away the stigma of making a mistake. Instead of erasing and using up paper to solve a number problem, the children can simply move numbers around until they figure out how to solve the problem. For my age group, the number tiles are very helpful for double-digit addition and subtracting with regrouping and finding the unknown. These number tiles also come with equation signs. The beauty of the magnetic manipulatives is that they are contained in a tin and the lid of the tin can be used to set up and calculate their number problems.

Our lower school uses TERC curriculum and the program comes with a lot of manipulatives and games. The games need to be assembled a head of time and now, after several years teaching 4th grade, I have my collection of math games neatly filed away in a bin on top of my manipulative shelving. Along with the actual game boards, instructions and recording papers, the games need cards or game pieces. I have a specific cubby for cards and a cubby for game pieces. Playing cards is one of the supplies I ask my students to bring in at the beginning of the year. I find that the playing cards take a beating each year and I like to start each year with fresh packs. The game pieces can be anything that will mark a spot. Anything from small, colored teddy bears to colored ones cubes. I keep the games out all year long and do not put them away once we have moved to another unit. Some children need refreshers throughout the year and I find that playing these skill- building games help to reinforce their skills.

Some of my cubbies also contain math stations onto themselves. I have one cubby that has Tangram Puzzles and Tangram activities. This is especially beneficial for my spatial learners. Years ago, I had a child in 3rd grade who really struggled in math. He was motivated but concepts and skills did not come easily to him and he slogged through math work and activities. One day, while studying China, I gave each child a Tangram Puzzle and asked them to make a square using all the shapes of the puzzle. This child solved the puzzle in a minute flat. He then went on to complete all of the most advanced configurations in the set. We called him the “Tangram King” and from then on, I have had activities that helped in building and complimenting spatial intelligence. is a great website that I use to download printables for the children to use as guides. I also have a cubby that has KenKen and Suduko puzzles and I encourage the children to use the number tiles to help them solve the puzzles.

Dice, small Judy clocks, calculators, paper money and plastic coins, Dominoes, colored tiles, pattern blocks, rules and tape measures, Unifex cubes, stamps (blank clocks, numbers) and ink pads, and geo blocks are some of the other manipulatives that I have in my collection. I start the beginning of each year by introducing the manipulatives and how and when to use them. I give them an exploration time in which they can “play” and use each manipulative and then steer them towards Use classroom materials and manipulatives in a respectful and appropriate manner as a class rule. I have found that the children love having the manipulatives at their disposal. During their free time after lunch or during Choice time, they will build with the blocks, make intricate designs with the pattern blocks, or calculate hard equations using the calculators.

Having a specific goal when going to garage sales in search of manipulatives has saved me a lot of money and makes the hunt that much more fun. My latest addiction has been multiplication and division flashcards and taking games (Sorry, Candyland) and using the rules, board, and pieces to make a new math game.

Stephanie Forsman

Stephanie Forsman—who wrote many of the math lessons on our Math at Home website—has been teaching in the New York City independent school system for more than 15 years. She is currently a fourth-grade teacher at The Berkeley Carroll School in Brooklyn, where she previously taught at the second- and third-grade levels. She has served as a facilitator for Mathematics in the City, a research and professional development center with a mission to "transform classrooms into communities of mathematicians, where children explore interesting problems and, like mathematicians, engage in crafting solutions, justifications and proofs." She has presented workshops on Math Puzzles & Logic Games, Technology and Math and Napier’s Bones at national conferences and served as the math subcommittee chair for the accreditation group conducting the New York State Association of Independent Schools’ 10-year school accreditation reviews in 2013. Stephanie earned her B.A. in art history and fine art at Trinity College in Washington, DC, and her M.Ed. in elementary education and museum education at Bank Street College in New York City. She also served as a Peace Corps volunteer in Mali, West Africa.

Read more posts by Stephanie Forsman

3 Replies to “Math Manipulatives”

  1. I agree that teachers are hoarders but most importantly I agree that manipulatives are very essential in each phases of math. These manipulatives help students with understanding process that teachers may never relate to some children.

  2. I like the idea of math stations. Math stations can easily be adapted for younger ages. Containers that contain objects can easily be packed into a diaper bag or young toddlers backpack for object sorting on the go. While waiting at the laundry mat a toddler can be given a math station container of goosh balls or various sizes. The parent can allow the toddler to manipulate the materials and use math vocabulary as the child explores the materials. Which ball is bigger? smaller? the same? different?

  3. Manipulatives are very important in a classroom. I have many different ones in separate bins.
    They love the puzzles, pegs, and numbers the best.

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