Mathematical objects

Build a foundation for math with simple objects like shells.

Learning Stages

By Candace Lindemann

Children's Author & Education Consultant

Candace Lindemann is a published children’s writer and educational consultant. She holds a B.A. from Yale University and an M.Ed. from the Harvard Graduate School of Education. You can also find Candace blogging at While Candace’s degrees prepared her for a career in education, she’s found that the best preparation for parenting is on-the-job training.

My son is struggling with a math concept. I scoop up some of his baby brother's building blocks and we use the blocks to figure out the problem. Suddenly, the abstract becomes concrete—this makes sense! This problem is solved and, more importantly, he understands the concept.

Mathematics education has been moving away from rote memorization towards a deeper understanding of mathematical functions. This mathematical reasoning starts in infancy and lays down strong foundations during the toddler years.

The way young children learn is through play and fortunately these two concepts work together: learning through play and building mathematical reasoning go great together. Math manipulatives are the link.

What are math manipulatives?

Math manipulatives are objects that a learner can manipulate (move around) to gain a better understanding of a mathematical problem or concept.

You can purchase items designed as math manipulatives or just use items from around the house. Small toys like blocks, natural items like rocks or acorns, or even food items like cereal O's make great math manipulatives.

How can you use math manipulatives with toddlers?

  • More or less. Which pile has fewer O's? Which pile has more?
  • Counting. How many pine cones did you collect?
  • Simple addition. We have two red blocks and two blue many blocks do we have all together?
  • Sorting. Let's sort all the cereal by color into this muffin tin!
  • Measuring. How many building blocks is it from the couch to the toy box?

By using math manipulatives, toddlers gain an intuitive understanding of math and a method of solving problems that will help them as they encounter more advanced concepts later in school.