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Using Manipulatives: Beginning to Understand Stage

Math is so much more fun when it can be played! Dominoes and counting bears, M&M candies and fun blocks, activities and hands-on learning games all take the sting out of learning how to count, sort, add, and subtract. What a great way to enjoy school!

Then come the middle school years. Although visual and tangible learning tools are no less valuable during middle school, ideas become more elusive as our children outgrow the early learning resources and suggestions. During this stage, your student should be moving from concrete numbers that can be easily represented by objects to more abstract numbers that require the imagination. Students will move from simple shapes to 3D solids and will begin finding perimeter, area, surface area, and volume. Math problems become more complex and sometimes include unknowns (x). These are the foundations for algebra, and it can be hard to grasp how manipulatives can still be useful with these concepts. But, there are age-appropriate options that can help older kids better grasp math concepts and have some fun in the process. Here are some tips for using manipulatives during the Beginning to Understand stage.

Tips for the Beginning to Understand Stage

5th - 8th Grade

If your student is feeling frustrated with the idea of using the same type of manipulatives that they used in the younger grades, consider these more mature games and activities:


Although the actual construct of this dice game is one of chance, many middle school math concepts are natural components of the game. An understanding of Yahtzee can go a long way toward teaching the principle of probability, for instance. Make this game a part of family game night or non-school play time, then refer back to it as you encounter concepts that can be illustrated by the game.

Three-Dimensional Shapes

Shape blocks often come into the picture in the toddler years, so by middle school students really think of them as baby toys. But, three-dimensional shapes remain quite helpful even in high school geometry! Consider how much easier it is for students to comprehend angles and relationships such as similarity and congruency if they can actually hold the shapes instead of just seeing them in two-dimensional format.

Instead of using childish plastic shapes, show your student how to use firm cardstock to create his or her own shapes. The process of making the shapes can help show just how the various sides and corners interact with one another.

Base Ten Blocks

As parents and teachers, we set aside base ten blocks far too early, as these handy manipulatives are very helpful for early algebraic concepts. Although your student may feel he or she has outgrown base ten blocks, there are a couple of ways to make them feel a little more grown-up.

Turning the blocks over and using the underside of the blocks to represent negatives can help tremendously as students begin to work more with negative numbers – and make it feel like there is a “special” way for older students to use the blocks!

Companies such as Math-U-See and Didax offer algebraic overlays that help explain how we have to determine the value of “x” in an algebraic equation. By making these a middle-school-only resource, you can help your student see that the blocks grow with him or her.

The abstract concepts that begin to filter into math during middle school are challenging for concrete minds to comprehend, and base ten blocks help make sure those concepts—even concepts such as square roots and polynomials!—have a tangible expression. So don’t give up on them too early!

Here are some additional manipulative upgrades for middles schoolers:

  • Buy your student his or her own compass, protractor, and ruler. A pack of graph paper would also be handy.
  • Use dice to calculate the odds of rolling a certain number. What numbers are most likely to be rolled?
  • Use fraction and pie graph manipulatives to work out concepts such as budgets. This will also help demonstrate the correlation between fractions, percentages, and decimals and how those concepts work in real life (like budgeting!).
  • Square patty paper is an incredibly inexpensive resource that can help with introducing geometry concepts. Cut and fold the paper to help demonstrate angles, sides, and other foundational geometry concepts in a hands-on manner.

Don’t forget that real life offers great manipulative usage! Here are some ways to take life experiences and utilize them as manipulatives, of a sort, to make abstract concepts more tangible.

  • Next time you take a road trip, tell your student the mileage you have to travel and the speed at which you will travel. Walk him or her through the processes needed to mentally estimate how long the trip will take you.
  • Choose a wall to paint. Calculate the square footage of the wall and how much paint will be required.
  • When you eat out, help your child calculate the tip.
  • Help your child calculate the sales tax on your next bill of groceries.
  • Find different objects around the house and let your child find the surface area and volume of them.
  • Pick a room to rearrange, even if just “on paper.” Measure the room and the objects and create a scale of each on graph paper. Then use the pieces to rearrange and see how each item might fit into the room. Be sure to account for windows and doors!
  • Shop the sales racks and help your child calculate how much the discount is and how much the sale price is.
  • Record daily temperatures. Each month, find the mean, median, and mode of your temperatures.

With five kids in their teen and early adult years, Rebecca shares the many ups and downs of parenting, homeschooling, and keeping it all together. As the Well Planned Gal she mentors women towards the goal of discovering the uniqueness Christ has created in them and their family and how to best organize and plan for the journey they will travel.

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