Why are manipulatives so awesome? Here are some reasons:
- learn by doing
- hands-on, kinesthetic learning
- great for both individuals and small groups
- explore, develop reasoning and problem-solving skills
- understand concepts through manipulating them: learn abstract ideas through concrete representations
- personalised, individualised ways of learning
- create a positive learning environment–fun!
What are manipulatives? You might think of an abacus, plastic/paper money sets, tangram sets, Math U See blocks, dice, coins and bills, lego blocks and mega-blocks, analogue clocks, the 9 times multiplication facts finger method, beans or macaroni, and bundles of popsicle sticks. But there are so many more options…
Of course, you can go out and buy manipulatives. It’s quite the industry! It’s also expensive most of the time, so you might want to consider the free or low-cost alternatives below–but if you want to purchase them (or get ideas to create your own) here are a couple of sites you might want to check out:
So… Before you go out and empty your wallet (which would be too bad, because real coins and bills make great manipulatives for counting, math facts, handling money, learning to skip count [use pennies to count by 1s, nickels to count by 5s, dimes by 10s, quarters by 25s]….and they’re also fun to spend on things you really want instead of expensive plastic math manipulatives!), check around the house. You might be surprised how many math manipulatives you already have!
Start with the obvious math items: paper, pencils, graph paper, white board and erasable writers or blackboard and chalk, calculators, rulers (regular school ones, carpenters’ rulers out in the workshed, tape measures in mom’s sewing box…), sidewalk chalk…
Then start thinking about hands-on household items and activities that are lots of fun, are hands-on and kinesthetic: skip ropes and trampoline (for counting), home science experiments (especially “kitchen science” experiments like measuring and mixing vinegar and baking soda and then using the results to bake cakes or alternatively shoot off 2 litre pop bottle rockets or build volcanoes on the kitchen table…er… I mean, outside where it doesn’t matter if you make a mess), or practising fractions by dividing and eating pie), playing with measuring cups in the bathtub… well, you get the idea!
And then, of course, you can make your own math manipulatives:
- Counting cans to drop items in as you count: recycled yogurt-style plastic containers or tin cans (make sure the edges aren’t sharp)
- Square colour tiles: just use your lego type blocks, or go out and collect pebbles (different natural colours or can be painted), or you can check with craft or building supply stores for scrap mini-tiles
- Snap cubes, math link cubes: lego-style and mega blocks
- Sorting trays: recycled tinfoil pie plates, deli containers, etc. Use popsicle sticks or cardboard for dividers. Or use egg cartons or muffin pans or the containers for homemade popsicles!
- Plastic animal-shape counters: use animal, fish, or other shaped crackers–and allow the kids to eat them as a reward for finishing their math. Or count real things: silverware (while setting the table), sock and other laundry sorting (counting by 1s and 2s, patterns, pairs…)
- Plastic 2D geometric shapes: make your own with coloured paper, cardboard, etc. When the children measure, draw, and cut out their own shapes, they learn so much more about geometry than when they fill in mindless worksheets!
- Plastic 3D geometric shapes: use items from around the house. Examples: for rectangular prisms, use books or cereal boxes. For cylinders use canned food tins or toilet paper rolls. For cones, use ice cream cones (then fill them with ice cream and eat them–you deserve it after a successful math lesson, right?). At building sites or furniture building shops, ask permission to dig through scrap piles for smaller wood scraps in different shapes.
- Cuisenaire Rods or other base ten blocks: make your own using coloured paper or cardboard; or snap lego-style blocks together in groups of ones, tens, hundreds, etc.
- Dot dice: borrow from your collection of table games. (Just remember to put them back or your next table game session will get off to a frustrating start!)
- Number dice, number operations dice, picture dice: write numbers or operations or pictures on stickers on your kids’ wooden or plastic blocks (go to the dollar store and get those handy, cheap, round, coloured stickers meant for yard sales)
- Real geometry: measure tents, TV screens, cupboards, mattresses, table tops…and build real things to learn to use geometry in real-life applications.
- Fractions: use food! Increasing/decreasing recipes, cutting pies and fruit and cheese…and eat them, naturally.
- Timers for learning to tell seconds, minutes, etc.: use the kitchen timer (even the one on the microwave)…and real analogue clocks on the wall, alarm clocks, wrist watches, etc. (If you’re afraid of breaking your household ones, get used ones cheap from the thrift store!).
- Sand timers: Use the kitchen egg timer or boardgame timers (and yes, put them back right after, please).
- Magnetic or foam numbers: make your own with cardboard, or foam from that old mattress or from the foam in the computer packing box, or better yet, make them with sandpaper: the texture makes them extra-kinesthetic!
- Tangrams: Have your children make your own by cutting up coloured paper into shapes.
- Place value mats, number line mats, etc.: make your own–or download free ones online.
- Geoboards: Make your own with pegboard scraps, screws and nuts, and multi-colored elastic bands from the dollar store; or use a block of wood and nails and dollar store elastic bands (not sure what geoboards are, or how to use them? Check out: https://nrich.maths.org/10060
- Plastic buttons for counting: raid Grandma’s button box!
- Category sorting: Use ordinary household items; raid the toy box; go to yard sales or thrift stores and get bags of miscellaneous small toys to sort.
For excellent free PDFs on how to use different kinds of math manipulatives: http://www.edugains.ca/newsite/math/manipulative_use.html (The PDFs also include ones on how to use more advanced math manipulatives such as algebra tiles and a geometer’s sketchpad for the Pythagorean theorem. The site also has a 19-minute video on how to use hands-on manipulatives. Handy!)
What other tips do you have for using math manipulatives? Please share them in the comments. Thanks!