What Are Math Manipulatives?

The Trouble with Math

The importance of math literacy extends far beyond the classroom. It's a foundational skill that impacts critical thinking, problem-solving, and decision-making in day-to-day life. In 2022, the Nation's Report Card assessed that 25% of 4th graders and 38% of 8th graders^[1] did not meet grade level math benchmarks. The pandemic has set the next generation of Americans back. That means kids who lost ground need to make up for it.

Meet Math Manipulatives

Benefits of Math Manipulatives

Math manipulatives are physical objects students can use to model and solve mathematical concepts, making the intangible tangibly understandable. They are immensely helpful for students who struggle to connect the numbers and symbols on paper with tangible concepts. At its most basic level, math manipulatives give a physical form to what are often abstract concepts.

• Hands-on Learning Experience: Manipulatives invite students to touch, move, and interact with math concepts. This kinesthetic approach caters to various learning styles and helps to cement knowledge through action.
• Concrete Representation of Abstract Concepts: Math can often seem like a world filled with abstract ideas. Manipulatives bridge this gap, providing concrete examples of abstract concepts, which is especially beneficial in the early stages of cognitive development.
• Engagement and Focus: Students are naturally curious and eager to explore with their hands. Introducing manipulatives can transform a passive lesson into an interactive session that better engages students. More importantly, it can help students in a similar way to a fidget to focus better.
• Visual Representation of Problem-Solving: We process visuals 60,000 times faster than text. Manipulatives take advantage of this by allowing visual and spatial representations of mathematics, fostering deeper comprehension of problem-solving processes.

It Just Works

• A Common Tool for Math Intervention Programs: Math intervention programs help kids who fall behind to get to grade-level math. Among the common approaches are representing mathematical concepts in a variety of ways to help children connect the concept of numbers to a relatable framework. Not surprisingly, visualization and math manipulatives are common tools in math intervention programs. Instead of waiting until children need the intervention, we can pre-emptively incorporate these approaches into daily teaching.
• Manipulatives are a core component of Montessori Math: Successfully weaving manipulatives into teaching practices involves thoughtful lesson planning and understanding how these tools can support differentiated instruction. Teachers are often 1) not provided the tools and 2) are not provided the appropriate training to teach children with manipulatives. However, there are successful programs that have been tried and tested to do well. The Montessori and Saxon math methods rely heavily on math manipulatives for early math programs. In particular, Montessori math programs incorporate manipulatives in programs as early as primary programs (3-6 year olds), and have a demonstrated history of being successful.

Increasingly, these manipulatives are also cheaper and more accessible than they were historically. Amazon has increasingly cost-competitive options for a wide range of math manipulatives. Some simple manipulatives can be made with basic crafts at home or through other DIY guides on Pinterest.

Getting Started with Math Manipulatives

Counters and manipulative objects like cubes and beads make counting and arithmetic tangible. Number lines and number boards help conceptualize sequences and operations. Geometric shapes and pattern blocks solidify understanding of geometry and spatial relations. Fraction strips and tiles break down the daunting world of fractions into manageable portions.

Here are some examples of widely used math manipulatives that we have come to love.

1000 cube, 100 square, and 1 unit

1000 cube, 100 square, and 1 unit used in both Saxon and Montessori math programs help children understand the difference in magnitude. It is an early introduction to place value. They can also introduce parts of a whole, particularly the decimal system.

Montessori Chains

Montessori chains and beads help children learn to count by 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, and 10s to help visualize multiplication.

These chains are consistently color-coded across all Montessori materials, helping learners associate a color with a number. 

How to Use Montessori Chains to Teach Multiplication:

• Starting with the 1s chain, lay out chain after chain in a straight line
• Then lay out the tags that correspond to the total number of beads in the preceding chains. 

Fraction Circles

Fraction Circles can help illustrate fractions visually. It can help to explain concepts such as how 1/2 is larger than 1/3. This is non-intuitive for early learners because they think the number two is less than three. Therefore, one-half (½) should be less than one-third (⅓).

No Child Left Behind

Math manipulatives are more than just tools. They are catalysts for creating a more inclusive and effective math learning environment. They make learning visible and tangible, invite engagement, cater to diverse learners, and have the potential to turn mathematical bewilderment into a world of wonder and understanding.

In capable hands, the appropriate use of manipulatives can make all the difference between a child being left behind or becoming a future engineer because they love math.

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Sources:

^[1] Statistics pulled from Two Decades of Progress, Nearly Gone: National Math, Reading Scores Hit Historic Lows by Sarah D. Sparks, October 24, 2022.

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