What are math manipulatives? Why use them?
Math manipulatives are helpful tools for learning and practicing math! If you’ve ever counted on your fingers, you have used math manipulatives. Most manipulatives are physical objects – like cubes, beads, or magnets – that kids can arrange, pile up, sort, or otherwise move around.
If your math instruction growing up involved a lot of worksheets, flash cards, and memorization (like mine did) you may be puzzled as to why kids need math manipulatives. But manipulatives are incredibly important for helping children understand the deep ideas in math.
Manipulatives help children to think about math concepts through hands on exploration and visualization. They provide opportunities for practicing and discovering relationships between concepts. Using manipulatives will help you to avoid the angst that can come along with math instruction when concepts seem too abstract, or practicing calculation is “boring”.
When do you use math manipulatives?
As an elementary math teacher, I used math manipulatives to introduce every new concept or skill. I kept them out for student use until they could confidently perform the calculation or skill. The only reason I didn’t have them available all the time is that, in the school environment, having lots of little tiny loose parts is a big management challenge!
I pulled manipulatives out whenever a child seemed confused or was making conceptual mistakes. For example, if I noticed that a child was subtracting but getting an answer bigger than the numbers she started with, I’d say, “Let’s see what this looks like with the blocks.” Once the child “built” the math problem using manipulatives, she would notice her own process error and say, “Oh! I wasn’t taking away. I was adding more!”
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Math manipulatives for early childhood (Ages 3-5)
You don’t need to keep math manipulatives on a high shelf until your child is “old enough” for formal academics. Young children enjoy using loose parts like beads, cubes, small blocks, and found objects in their play. They might arrange them on a table or floor, count them, put them in groups, divide them up, etc. Your child will naturally begin to practice “math skills” just through using these objects in everyday play.
Some of my favorite math manipulatives for younger kids:
Shape sorter: Toddlers probably won’t realize that they’re learning basic geometry, but that’s the beauty of play. You can save the 3-D shapes for when they’re older and ready to learn formally about cubes, cylinders, pyramids, etc.
Pegboard: This works on multiple levels. Young children will love to see how many pegs they can stack before it falls over. My son also enjoys making patterns. You can use this when they’re older to teach multiplication – it’s super easy to see the similarity & difference between 4 x 5 vs. 10 x 2 when you’re making it on the pegboard!
Abacus: This was one of our first “math toys”, and we still use it often. Younger children might just enjoy flicking the beads around or moving them from side to side. But pretty soon, as children start to enjoy counting, they will enjoy having 100 beads to count. And you will enjoy not having 100 loose beads rolling all over your floor.
Math manipulatives for ages 5+
I hesitate to put an upper age range on this category, since I firmly believe that older students also need math manipulatives. The manipulatives suggested for younger kids absolutely would work for kids ages 5+. Plus these teaching tools, which are helpful when learning more formal math.
Hundreds chart: I can’t say enough about how great hundreds charts are. Whether your child is learning how to count past 20 or is trying to memorize times tables, hundreds charts are great! This one lays out on your floor, so your child can physically walk on it, drive trucks over it, seat dolls on it, whatever works. It comes with several games as well. You can certainly print out any number of hundreds charts onto paper, but you can’t play Twister on them!
Unifix cubes: These are great for learning addition and subtraction – especially once you start adding in different colors and comparing stacks. You can use them to make a 3-D bar graph too!
Base ten blocks: These are SUPER USEFUL for visualizing larger numbers and performing calculations with them. Especially once your child has to start “borrowing” – that concept really makes no sense unless it’s modeled with base ten blocks too. My students and I used to play games like “Race to 100” or “Race to o” so they could practice “exchanging” larger and smaller base ten pieces.
Ten frames: My first few years of teaching math, ten frames weren’t really a “thing”. But some of the newer math curricula out there really emphasize them. I like these bc they’re magnetic and they come with two different colors of dots, so it’s easier to keep track of your numbers.
Cash register: I got this for my kid purely for the play value – but he actually learned his coin values and some simple addition just by playing with it! As for coins as manipulatives, I’m a fan of using real coins rather than play money, but it’s great to have a set that your child can use & lose without worrying about them trashing a real $20 bill!
Fraction cubes: There are soooo many math manipulatives geared towards teaching fractions, but the one I’ll link here is pretty similar to regular unifix cubes – just helpfully arranged to help your child compare fractional parts. There are others that features similar concepts using a “pizza pie” style (sometimes literally).
Do I have to buy math manipulatives?
If you’re short on funds, don’t fear! You can recreate many manipulatives on your own, using toys and materials that you may already have. Legos are a great substitute for unifix cubes and base ten blocks. I have also used craft sticks, rubber bands, beads on pipe cleaners, and balls of playdoh. To make a floor hundreds chart, you can use masking tape to mark off tiles on your floor, or sidewalk chalk on your driveway. Get creative!
Should I allow my child to count on his fingers?
Yes! Fingers are a manipulative in the most literal sense. Even adults count (or skip count) on their fingers at times. My general rule is to always allow your child to use a strategy that is working. If your child is getting confused, you can offer other manipulatives as alternatives.
Contrary to popular belief, young kids CAN count higher than ten using their fingers. Simply tell them to put the first number “on your head” and keep going. For example, if I wanted to add 9 + 5, I would put 9 on my head, and then use my fingers to count five more. 10, 11, 12, 13, 14. Kids just starting to learn “what addition is” really benefit from this strategy!
My philosophy on learning math
Math doesn’t have to be torture, either for your kids or for you. It can be enjoyable! Who doesn’t love figuring out a puzzle or solving a mystery? The way we’ve traditionally taught math in schools gets abstract way too quickly and leaves the playfulness and joy far behind.
It’s possible to have fun, colorful manipulatives and still make learning math a sour, boring experience. So just having the right tools in the room isn’t enough. But you’re much more likely to have an enthusiastic child, and a fun open ended experience, if you start with manipulatives and let your child lead the way.