# Playing with Math at the Playground

May 19 2021

### Posted In:

General, Parents, Teachers

By Herbert P. Ginsburg

It is often said that math is all around us. Playgrounds, for instance, can be a great place for caregivers and children to explore the math around them as they play. Let’s see what that means for a young child and a caregiver. (I have italicized the everyday math words used in this blog post.)

## Notice Math Around You

Cassie, 2 years and 3 months old, is at her local playground. Math is all around her, whether she notices it or not. Some of this math would be easy for her; some would be hard and best saved for when she is older; and some will have just the right amount of challenge to be fun and promote learning.

For example, as Cassie is climbing steps on her way to the top of the play structure, the steps can be counted. There are about three steps to start, and then about four or five to get to the next level. This is a lot of steps to climb (especially for a young child!). The steps provide many opportunities for you to promote number learning by talking about counting and quantity (e.g., lots, more, and fewer) as she climbs.

At the start, Cassie climbs to the top, going up and up and up. Later, Cassie climbs to the bottom, going down and down and down.This is all about direction, which is an important part of spatial relations, a key early math topic.

When Cassie begins to climb again, she is at the bottom; when she reaches the top, she is up high, higher than she was at the beginning. This is all about understanding height and differences in height—again, a part of spatial relations.

Also, notice the white pole with the orange object that resembles a sunflower. It has a big circle in the middle, surrounded by six incomplete circles (partially cut-off circles). Within each of those six are seven smaller circles. The smaller circles and larger incomplete circles are shapes. Their arrangement—circle in the middle, incomplete circles surrounding it, and smaller circles within the incomplete circles—is also all about spatial relations.

There are many early math learning opportunities at the playground.

So, math is all around us in the sense that it’s there to be seen if you look for it. This everyday math is very different from the formal math you learned in school. But young children love to engage in and learn about everyday math, and it can serve as the foundation for their later learning and success in school.

## Talk About Math in Everyday Life

How can you use the math that is all around us to support your child’s math development? Help your child to see basic math in the everyday world, for example at the playground. The best way to do this is by using language to point out and explore the math in their world.

Here are some examples of what you can say to a 2- or 3-year-old in this setting (again, I have italicized the everyday math words):

• “Let’s count the steps: One, two, three. There are three steps. Look, now there are more steps.”
•  “Here’s one more step, and one moreagain. Almost at the toptwo more steps.”
• “We are going up, up, and up. Look down. We’re up high now.”
• “Now we’re going to go down. Take one step down. Now another step.
• “Now look back. Look how far down we’ve come. We’re almost at the bottomOnly two more steps left.
• “Look at the big orange circle over there on the white pole. Look at all these little circles. There are so many of them. Let’s count them.”

## Keep the Conversation Going

After making comments on the math, try to keep the conversation going. The child may make a reply that you will then want to respond to. For example, if you say, “Look, now there are more steps,” your child may say, “Lots of steps!” And then you can say, “Yes, lots of steps. Let’s count them.”

What’s the right number of comments to make? Saying all the examples above would be overwhelming. Say only as much as you feel comfortable saying and what you think your child will understand.

Keep in mind that everyday math conversations are not lessons. Math talk is meant to be a conversation about features of the world that your child will find interesting. Let children enjoy the playground. That, after all, is the primary goal!

## A Final Note

Here is a list of all of the everyday math words in this blog post (I hope I didn’t miss any)At the end, I was amazed at how many there were. There were so many that I decided to list them.

You may think that at least some of these words are iffy; that they are not very “mathy.” It’s true that they do not include words like “equation” or the “equals” sign. But informal math is so fundamental to our lives (and children’s too) that we may not recognize it in the words we speak, just as we are not aware of breathing air. A word like “any” as in, “Do you want any cookies?“ could be translated in formal math language as, “Do you want at least one cookie from the larger set of cookies?” Clearly “any” is intended to convey a mathematical idea. Think about that as you read my list.

Anyway, here are the informal math words. So many of them! Isn’t that amazing? Like totally! Did I miss any? (Math translation: Is there at least one other math word that could be included in this set?)

 1. A few2. A lot3. Above4. After all5. Again6. All7. Almost at the bottom8. Almost at the top9. Amount10. Another step11. Any12. Around13. Arrangement14. As much as15. At the end16. At the start17. Beginning18. Best19. Big20. Bottom21. Circle22. Count23. Differences24. Direction25. Down26. Down and down and down27. Each28. Fewer29. Final30. Four31. Height32. Higher33. How far down34. How many35. In36. Incomplete 37. Just the right (amount)38. Larger39. Lots40. Many41. Middle42. More43. Next level44. Number45. Often46. Older47. On48. One more again49. One step down50. One, two, three51. Only as much as52. Only two more steps left53. Partially cut-off54. Primary55. Quantity56. Ran out of57. Seven58. Shapes59. Six60. Smaller61. Some62. So many63. Spatial relations64. Surround65. Top66. Totally67. Two more68. Up and up and up69. Up high70. Very different from71. Within

Herbert P. Ginsburg is the Jacob H. Schiff Professor Emeritus of Psychology and Education at Teachers College, Columbia University. He is a member of DREME’s Family Math and Early Math Resources for Teacher Educators projects.

Recent News

## Preparing Teachers to Develop Young Children’s Spatial Skills

Thursday, August 4, 2022

Professional development materials that prepare teachers to grow young children’s geometry and spatial skills.

## Grow Math Skills While Playing Hopscotch

Thursday, July 21, 2022

Tips for having conversations about math while keeping hopscotch games interesting and challenging.

## What Early Math Topics Are Important for Children to Know and Why?

Friday, June 24, 2022

Preparing professionals to support family math is key to having families start and continue to engage in math learning together.