Math Manipulatives: A Fun, Hands-On Way To Learn Math

Math can be a pretty abstract concept for kids. Giving them an opportunity to see the math they are working on can really help them understand what they are learning. That’s why math manipulatives can help. In this post, let’s learn more about what math manipulatives are, how to use them, and some ideas on what to use for various different math topics.

What are math manipulatives?

A math manipulative is a tangible item that you can use to explore, understand, develop, and master various mathematics skills. It helps students be able to visually see how math works in a hands-on, practical way.

Wikipedia defines it as “an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.” (reference)

Why use manipulatives to help with math skills?

Using math manipulatives can offer several benefits to students in their learning process. Here are some reasons why students should use math manipulatives:

1. Concrete Understanding: Manipulatives provide a concrete representation of abstract mathematical concepts. By physically interacting with objects, students can better grasp and understand math ideas that might otherwise be challenging in purely abstract form.
2. Visual and Tactile Learning: Different students have varying learning styles, and math manipulatives cater to visual and tactile learners. Seeing and touching physical objects can enhance comprehension and retention of mathematical concepts.
3. Engagement and Motivation: Hands-on activities with manipulatives make learning math more engaging and enjoyable for students. This increased engagement can lead to higher motivation to explore and understand mathematical concepts.
4. Problem-Solving Skills: Manipulatives encourage students to explore and experiment with mathematical ideas. This encourages problem-solving skills as students work through challenges using physical representations.
5. Communication and Collaboration: When students work with manipulatives, it often involves communication and collaboration. Explaining their thought process to others and working together on problem-solving tasks can enhance both their mathematical and interpersonal skills.
6. Real-World Applications: Many math manipulatives are designed to model real-world situations. This connection to practical, everyday scenarios helps students understand the relevance of math concepts in their lives.
7. Building Mathematical Vocabulary: Manipulatives encourage kids to develop and reinforce their math vocabulary because they can associate specific terms with physical objects, which helps language development related to mathematics.

Are there any downsides to using manipulatives?

In general, the addition of manipulatives to a math program is a benefit, but there can be some potential downsides as well. The main one is dependency – the need to have access to and use of a manipulative in order to complete specific math tasks because there hasn’t been a full connection between the abstract and the concrete. The hope of course is that, eventually, there will be a shift from needing to see a concept and fully understanding it.

I will admit that sometimes, manipulatives can be a distraction from the work at hand. Temptation to use them to play instead of do math does happen, which can derail a lesson or bring it to a crawl. Although I do advocate for the opportunity to free play with math manipulatives outside of lesson time, it can be frustrating when it’s not helping your child progress with their work.

What to use as math manipulatives?

There are lots of amazing resources that you can use as manipulatives for math. Some you can buy. Some you might have just around the house already. Let’s break down math into it’s main categories and consider the options of manipulatives that could be used for each.

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Numbers & Number Sense

This category is the understanding of … well, numbers. It’s understanding quantities, more / less, counting, ordering, comparisons, adding, subtracting, multiplying, dividing, etc.

Basic manipulatives for this topic tend to be groups of identical items that can be manipulated and moved around as counters. You can buy things for this – such as plastic bear counters or simple circular counters for kids. I personally love to pop into the dollar store and grab something fun based on the season (one year, I found some great little plastic leaves which were a big hit for example!) But you can also just use things from home, like milk / bread tabs or food items such as noodles, mini-marshmallows, dry beans, or chocolate chips.

For adding and subtracting, never underestimate the power of the manipulatives you have naturally – fingers!

Dominoes make great tools for addition (add up the dots on the top with those on the bottoms), as are dice – which are fantastic for turning math into games.

Linking math cubes allow you to use one colour for each part of the equation, but you can also use basic LEGO bricks from your collection at home.

As you move into concepts of ones, tens, hundreds, etc., resources like base ten blocks are helpful because they showcase exact differences between each. The curriculum Math-U-See comes with a similar resource of math manipulative blocks which are quite popular. Check out used sales for the best deals on these.

Money

Money can be a tricky one for kids – especially Canadian kids if they are using an American math program. Adding Canadian money to a curriculum doesn’t have to be difficult, but it can be really handy to have some actual things to use as they are learning.

The first, and maybe most obvious, is to use real money. If you have a stash of coins, pull them out and let your kids use them for math lessons. But, you can also purchase Canadian play money which gives the same basic experience (if a little cartoon-y.) This has always been popular in our house. The biggest challenge we’ve had is it not going missing while they play “store.”

Time

I recommend that you have multiple kinds of clocks in your house – making sure to have at least one analog and one digital clock so that kids can check both and start making the connection between them both. But while you are learning time facts, grab a student clock which children can use to change the time themselves with minutes marked so they can see how to count by fives to tell the current time, etc.

Another fantastic tool for learning time is a timer – specifically an analog timer that has a visual countdown of minutes. We always used these to give the kids a computer time limit and when they struggled to complete work. I’d set the timer for 15 minutes and promise that if they focused for those 15 minutes, when the timer went off, they could stop – even if they weren’t finished. They loved seeing the time they had left.

Fractions

Fractions can be really challenging to understand for kids. Thankfully there are some great resources that you can add to your manipulatives collection to help. For example, fraction strips and circles can be used to build fraction combinations. But you can also use measuring cups from your baking drawer. They already come in different fraction sizes – 1 cup, ½ cup, etc. Add in a larger measuring cup (like a 2 or 4 cup size) can make it even more meaningful.

I have a whole blog post about fractions with a free fraction strip printable.

Patterning / Shapes

Learning shapes can be easy with things like tangram / pattern blocks for 2D shapes and wooden building blocks for 3D ones. They let kids actually touch the shapes and discover the number of sides and corners (vertices).

Geoboards are small square boards with pegs sticking out and a set of elastics. Students stretch the elastics over the pegs to make a variety of shapes. Some sets come with idea cards for kids to replicate or blank dot cards to design their shapes before using the elastics.

For patterns, you can use the above blocks, or LEGO, or anything that has a selection of shapes or colours – like apples, coins, counters, etc. Tangram blocks, for example, are wonderful for creating symmetrical art!

Measurements

For measurements, kids typically start with non-standard measurements (like “how many paperclips long?” or “how many books tall?”) so you can use just about anything to measure with. A popular one at our house with younger kids was to use Hot Wheels cars. Once they get older, they can use things like rulers and measuring tapes. Bonus if it has both metric and imperial options for your kids to understand that we can use both systems for measurements.

For weight, scales are a great tool. You can use something official like a kitchen scale or a weight scale to demonstrate how much something weighs, or you can use a toy scale which requires children to put equal values on both sides to make it balance.

Volume manipulatives are easy. Just offer a variety of containers and some water. Put together a volume learning sensory play zone and let them explore.

What Grades / Ages Can Use Math Manipulatives?

Math Manipulatives are useful (and fun) for everyone from toddlers through to adulthood. Of course, the way they are used and the items themselves change as students grow, but they are a practical additions for all levels of math learning.

How to Use Math Manipulatives in Your Homeschool

It’s easy to add math manipulatives to your homeschool. First, you can simply pull them out whenever you are using your math curriculum so your child has access to them as they practice whatever skills they are developing. You can also use manipulatives AS the math lesson – without even opening a curriculum at all! Lastly, if you have them available for free play throughout the day, you might be surprised at what your child discovers on their own. Be prepared with open ended questions, ideas that inspire problem solving, and being willing to observe what skills are being covered in their play time.