Top Math Manipulatives: Must-Have Math Tools
Math concepts can be challenging. It can be tough to comprehend a topic that can seem abstract. Teaching math concepts is made easier with manipulatives. They provide a multi-sensory experience that can help your child make sense of complicated topics. Math manipulatives are concrete tools that provide an opportunity to use a hands-on method to explore and learn. Kids get to see the problem and try different ways of reaching a solution. These tactile tools offer another method of making a connection and reaching that lightbulb moment when your kid suddenly understands!
Benefits of math manipulatives
Understanding why the solution works
Although the aim is to teach a child how to solve problems it is important to help them understand why the solution works. Manipulatives provide a visible and hands-on way to explore the why behind mathematical concepts.
Math manipulatives are fun!
Kids love moving things around and building a tactile picture of a problem. Maths can be a challenge but it doesn’t need to be boring. Manipulatives invite engagement and an opportunity to interact with math. The more your kid enjoys math the more they practice and the greater their proficiency.
They build confidence.
If your kid doesn’t understand a concept they can feel frustrated and disengaged or worse, develop a belief that they are not able to ‘do math’. By being able to take an abstract concept and make it concrete they can build comprehension and see their progress.
Encourage the use of trial and error.
Using tangible manipulatives allows your kid to test a theory, ‘If I add this, does it make that?’ By doing it themselves, seeing the problem and trying to work the solution, they develop important problem-solving and critical thinking skills.
Simplifying the problem
Breaking a concept down into parts is key for math progression. Not only does it improve understanding, but it also lays a foundation for higher-order math that requires the ability to work a problem into its components.
What ages are math manipulatives for?
While math manipulatives are an incredible tool for younger children, older children can benefit from engaging with them too! As manipulatives help make a concept easier to grasp, they can be used at all stages of the math journey, including high school.
Preschool and Kindergarten
The math journey usually starts in early childhood. Activities as simple as counting toys, arranging socks into pairs or even sharing candies into the ‘mine and yours’ groups are tactile exercises employing objects to grasp and practice a concept. Utilising these manipulatives can be particularly valuable for a child who cannot easily articulate their understanding through words.
When selecting manipulatives consider:
objects that are easy to grasp as your kid is developing their motor skills
are child-friendly without small parts that may be ingested, or sharp edges
are brightly colored and engaging (Lego is a good example)
While there are many wonderful math manipulatives you can purchase (check out our list below) they can also be cost-effective, everyday items you may already have in the pantry, your craft supplies or can source from thrift stores such as: popsicle sticks, cotton balls, playdough (click here for our no-cook homemade playdough recipe), board game pieces, toys, large beads, string, large buttons, pasta, pipe cleaners and candies. You won’t need a lot of items but it can be helpful to store them in a container for easy access and to encourage kids to explore independently.
Grade 1-3
By now your young learner is starting to build the fundamentals of math knowledge. At this stage, manipulatives such as Cuisenaire Rods, pattern blocks, analog clocks and even Lego will enable them to investigate concepts they are learning at school or home. Make the math manipulatives easily available to encourage exploration. By having items at hand, your kid can enjoy the process of building their knowledge. Don’t forget that craft items such colored paper, markers and even pipe cleaners will still have their place, as will kitchen staples like measuring cups and spoons.
Grade 4-6
At this stage, your kid is building the in-depth knowledge they will need for the complex concepts they will be taught in middle school and high school. You want to ensure they understand the basic concepts concretely before developing abstract understanding. It is important that they ‘do’ math in a tactile manner to strengthen the foundations needed before increasing the level of complexity. Consider base ten blocks, pattern blocks, protractors which can be purchased separately or as part of a geometry set, analog clocks and dice. Also consider items you may have at home like sand timers, calendars, rulers, and thermometers.
Middle and High School
The older child is starting to think abstractly, but there may be concepts they don’t feel they have grasped. The opportunity to investigate in a tactile manner engages both hemispheres of the brain providing creative solutions and additional pathways to unlock understanding. Algebra tiles, dice and balance scales can be offered in addition to the usual geometry sets and graph paper.
For useful tips on inexpensive homemade manipulatives for high school and how to use them check out this helpful post by Mrs E Teaches Math.
Top Math Manipulatives
Number lines
Number lines are important for developing number sense. It strengthens your kid’s comprehension of mental representations of number magnitude, number relationships and mathematical operations. They can be homemade, a simple drawing on a piece of paper or a ruler will do, or you can purchase something like a dry-erase number line board for ease of use. You can access a free printable number line as part of our math strategy activity printables here.
Circle counters and animal counters
These are a great choice for building counting, addition and subtraction knowledge. They are versatile for number bingo, learning about groups, fractions or even patterning or probability.
Cuisenaire rods
These are a timeless set of math manipulatives that have helped generations of children understand math concepts. They are a set of 10 rectangular rods in 10 distinguishing colors. Each rod and its color correspond to a specific length. For example, white rods are the shortest and denote one unit and the orange rod is the longest. Each rod in the sequence is one unit more than the previous rod. This pattern is visible when the rods are arranged in a ‘staircase’. Cuisenaire rods are fabulous tools for simplifying complex concepts such as basic arithmetic, number theory (prime or composite numbers), and fractions. For simple math activities using Cuisenaire Rods take a look at this article by the University of Cambridge.
Base ten blocks
Freepix
Base Ten Blocks are coloured plastic or wooden blocks that are used to represent numbers. There are four different Base Ten Blocks blocks. They are usually used to represent 1000, 100, 10 and 1. These are versatile tools for exploring place value, number sense, and regrouping.
Dice
Dice are a staple tool for basic arithmetic, to practice mental math and probability but dice can be used creatively in a variety of activities and games that explore math concepts and promote problem-solving. More than this, using dice breaks away from the standard worksheets or flashcards providing an opportunity to learn in a fun and game-oriented environment. You can print the bingo card below here.
Dominoes
Not only do kids love math games but they also gain a lot of focused practice on math concepts. Dominoes can be used in a variety of interesting and fun ways to develop problem-solving skills and provide calculation challenges. Domino math games are not limited to basic arithmetic but can include probability, estimation, sequencing and even fractions.
Fraction bars and circles
Your kid will need to learn the concept of parts of a whole. It’s a big concept to grasp and these tactile tools make it a lot easier by representing wholes, halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths.
Algebra tiles
Algebra Tiles are a set of square and rectangular-shaped tiles used to represent integers (or constants) and variables. Although they look similar to base ten blocks, these tiles depict various components of algebraic equations and are labelled as unit 1, x, y, xy, x² and y² pieces depicting the area. The tiles can be used to teach a variety of concepts, including counting (for the younger student), area, perimeter, and arithmetic, as well as equations, factoring quadratics, algebraic long division, and simultaneous equations.
Geoboards
Geoboards are peg boards and the simplest use of a geoboard is to create different shapes. They are a great manipulative to visually demonstrate the concepts of area and perimeter. They are also useful for exploring angles and symmetry.
Pattern blocks
Pattern blocks are colorful shaped math manipulatives that help students explore concepts like symmetry, area, and fractions. Moreover, they also stimulate creativity and spatial reasoning so important for higher-order math.
Unfix Cubes
Unifix cubes are plastic cubes that connect on two opposing sides. These are great tools for counting, basic arithmetic operations, comparing, place value and patterning.
Linking cubes
These cubes interlock on all six sides. Again, great for basic arithmetic operations, sequencing, patterning but also useful for measurement and 3D operations.
Balance scales
A great way to explore inequalities. Your kid will have a lot of fun exploring inequalities with like and different materials.
Geometric solids
Understanding surface area and volume is made easier when your kid can visualise and touch 3D shapes. These particular items can be filled with water which means your kid can be hands-on when testing their understanding of volume.
Clocks
Although many children will have access to digital watches it’s still vital they learn to read an analogue clock if they are to understand time as a concept.
100’s chart
This tool is essential for the younger learner who is developing their understanding of counting and place value. A visual and tactile way of recognising number patterns.
Play money
In an age of cashless transactions, understanding the concept of money will be an essential life skill and an easy way to introduce the topic is with play money.
The Final word
The above math manipulatives can be used to develop understanding across a range of math topics. Incorporate these resources into your kid’s math environment to provide them with a concrete way to turn a sometimes confusing abstract concept into something that is both enjoyable and readily understood. Foster your kid’s interest in math and ensure they always think of themselves as someone who can ‘do’ math.