# Playing with Math at the Playground

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 *smallercircles* within the *incomplete* *circles* — is also *all* about spatial relations.

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*top*—*two 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 bottom*.*Only 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. Incomplete37. 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.

Originally published on the DREME website: https://dreme.stanford.edu/news/playing-math-playground