6 math concepts you can practice at home (no textbook needed)

Though your 2-year-old may not seem like a mathematician yet, they’re actually practicing math concepts all the time—and they’ve been doing it from the very beginning of their lives. Jan Greenberg of the The National Association for the Education of Young Children (NAEYC) explains:

“Babies tell us—often dramatically—that they know the difference between familiar and unfamiliar adults (sorting and classifying). Toddlers try to climb into boxes of various sizes (spatial relationships) and say words and phrases from familiar stories or songs that use repetition (patterns).”

Though number identification and counting are among the most important math concepts young children learn, there are other foundational skills that form the basis of their understanding. These skills can be enriched and supported with your help.

Here’s how to support early math concepts for your 2-year-old:

Compare size, weight, height, and other properties

Asking questions that invite comparisons introduces key math vocabulary like “less,” “more,” “bigger than” and “smaller than,” and other relational terms.

Use exaggerated hand gestures when you ask:

• “Which ball is heavier, this one or this one?”
• “Which door is open, and which one is closed?”
• “What’s bigger, the dog or the cat?”
• (Pointing at only two flowers) “Which flower is taller?”
• “Which cracker is whole, and which one is broken?”
• “Which hand is dirty? Which hand is clean?”
• “Which glass is full of water? Which one is empty and has no water?”

Learn how to measure

Your child is probably years away from understanding standard units of measurement (minutes, inches, teaspoons), but that doesn’t mean they can’t have fun measuring everyday objects. Measuring and comparing are closely related.

Here are a few ways to involve your child in measurement at this age:

• If you have a bathroom scale, let your child stand on it and see the numbers change. You can also stack objects on the scale like a stack of books or a container of blocks. Explain that the scale is weighing how big they are, and that number will change as they grow.
• Make a growth chart somewhere in your home where you can track your child’s height. This is not only a fun way to see how they grow over time, it also introduces them to the concept (and vocabulary) of measuring with inches, feet, or meters.
• Two-year-olds love to pour. Put out a tray with different-sized containers and some water, and ask your child to fill the biggest container with the smallest one: how many scoops does it take? They also may want to explore the pouring kit on their own without direction. 
• Help your child visualize weight with a balance scale. Give them a supply of objects to weigh: rocks, pom poms, feathers, small toy cars or animals. Point out that when the buckets are filled, the heavier side goes down, while the lighter side goes up.
• Giving your child access to simple tools is a great introduction to measurement. Rulers, yardsticks, measuring tape, and measuring cups and spoons from the kitchen can all be fun for them to explore. Watch little fingers if you’re using a measuring tape that snaps back hard.

Teach your child about spatial concepts 

The way we see certain objects in physical relation to one another (above, below, behind, next to) is also a critical early math skill. This is a precursor to geometry, and helps your child make sense of the physical world around them. Here are some ways of using spatial vocabulary in everyday life. Use descriptive language and hand gestures to make the terms come alive and give them meaning:

• “The cat is under the chair. Sometimes, he sits on top of the chair, like this.”
• “That tree is really close to us—see, we can reach out and touch it. That tall tree with the blue flowers is far away—we can’t reach it and we would have to walk awhile to get to it.”
• “I’m walking up the stairs; can you try walking down the stairs, that way?”
• “Your shoe is behind the couch; let’s go get it and put it here. Now it’s in front of the couch and we can see it.”

Other relational terms to point out and practice include in and out (filling and emptying containers), inside and outside (a ball inside and outside of a box), next to, and between.

Shapes 

Your two-year-old is also ready to deepen their understanding of basic shapes. Between 26 and 30 months, many children are able to start matching circles, triangles, and squares—meaning they can identify and match two shapes that are exactly alike, whether or not they can name them. Between 30 and 36 months, children often begin to sort those same three shapes, grouping them together with (usually) some adult help.

Here are some ways of pointing out these shapes in everyday life; as much as you can, try to point with obvious, clear gestures at what you’re talking about:

• “Your sandwich is the shape of a square! See, it has one, two, three, four sides.”
• “This plate is in the shape of a circle. It has no straight lines and goes all the way around, like this” (while tracing your finger around the circumference; hand over hand, have your child do it after you)
• “That street sign is a triangle; let’s count the sides together, one, two, three.”

Conservation practice 

Conservation is a form of logical thinking ability that children learn as part of their cognitive development. Being able to conserve means knowing that a quantity doesn’t change if it’s been altered (by being stretched, cut, elongated, spread out, shrunk, poured, etc). 

Your child won’t be able to “conserve” until at least age 5, but practicing some concepts now will help them make sense of it all later. Here are a few ways to do it:

• Break a cracker in half and show your child that the amount of cracker hasn’t changed—in their mind, two smaller pieces of cracker are now a greater amount than the whole. Put it back together and take it apart a few times to demonstrate.
• Take three pieces of food (something small, like blueberries) and put them close together. Count them slowly, touching each one as you go, and invite your child to join you. Then, spread them far apart; at this point, children will believe that there are now more berries. Count them again to show that the amount hasn’t changed, and clearly explain why.

• Pour water into a tall, narrow glass. Then, empty the water (with your child watching) into a low, wider glass. Your child won’t be ready to understand that the amount of water has stayed the same, but you can still give them words and rationale that will support their eventual understanding of such a tricky concept: “even though the water looks smaller, it’s still the same amount. Watch me pour it back into the tall glass.”

Patterns

Recognizing patterns is foundational to understanding math, and it’s also one of the most accessible concepts for young children. Here are some ways to notice patterns in everyday life:

• When you walk on floor tiles that alternate color, narrate as you go: “let’s step on black, then white, then black, then white.” 
• Set up a line of blocks that alternate heights in an obvious, contrasting way: “tall block, short block, tall block, short block.” 
• Make a necklace with cereal that alternates between different colors. 
• Sing songs like “Head, Shoulders, Knees, and Toes,” which involve repetitive pattern-matching.
• Point out simple patterns in the world around you: bricks in a chimney, the wings of a butterfly, the petals of a flower.

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