Here’s a little gem of an activity that will count as a big mathy moment and isn’t on a screen. I’ll begin with the instructions, then add a bit about what I saw and how I adjusted when my own 8-year-old did this. Materials needed are a piece of paper, a ruler, and a pencil. Add colored pencils or markers for excitement. (That applies to most of life, doesn’t it? Add color for excitement.) This could be as short as 5 minutes or extend as long as your child is interested.
Set up: Use the ruler to draw two lines that look like an x and a y axis. Mark off dots along the lines at 1 centimeter intervals. In my example, I chose to go up to 15 on each axis. (See the photo of the final product below for clarification.)
Activity: Hand your child the paper, the ruler, and the pencil. Give instructions to begin connecting the dots on each axis with straight lines using the ruler. To clarify which dots to connect, you might say “Connect dots that add to 16, like 15 and 1.” Or you can say “Connect the top-most dot on the vertical axis with the left-most dot on the horizontal axis.” (I was inclined at first to give the latter instruction to my child because it fit my understanding of the activity, but then I stumbled into the former instruction and discovered it was much more effective and sustainable. It allowed me to give only one instruction and then to sit back and let the kid work independently.)
That’s it. When your child is done, observe the finished product together. Note the shape you both see. Perhaps extend the activity by working with the colored pencils. Or by drawing more axes and connecting more lines. Add doodles and drawings based on what you see…a skate ramp? a sail boat? a bridge? Make it a mathy arty moment. Maybe extend the entire project by creating string art (same activity, but with a block of wood, nails, and colorful string. There are a lot of places to go with this. I just let my kid take me where he was interested…which wasn’t very far (time-wise), but was pretty cool nonetheless.
Reflect: What was fascinating to me was that my child did not at first see the curve he had created. He was focused on the straight lines he had drawn. When I said, “Isn’t it cool how straight lines can look like a curve?”, he paused…and then exploded in excitement.
“That is CRAZY, Mom! That is so awesome! How did that happen?”
Then he leaned in closer to his work and examined what he was seeing. He used his eyes to confirm the straight lines he really had drawn, and he noted that the way they crossed each other caused the entire drawing to look curved. Then he did a little jig and ran away. Because he is 8.
In his wake, he left me and his 11-year-old brother looking at the drawing together. I leaned into my older son and commented that his brother didn’t stick around long enough to see that if we drew more axes and added more lines, we could create all sorts of visual effects.
“Like an eyeball,” I suggested.
“Or a football,” commented the 11-year-old.
“And what if we extended the axes into what would be the negative numbers?”
“Then it would like kind of like a star, Mom. And, Mom, this reminds me of those pictures of a ball or a hole in a grid space that looks like its bending down.”
“Yeah, like space-time warping.”
“Totally.”
Okay, he didn’t say “totally,” but it would have been totally awesome if he had.
Mathematically speaking…this activity became more than just an arty moment that I was hoping would anchor the 8-year-old to his seat for another 5+ minutes. In the process of using a ruler on a traditionally aligned x and y axis, he was developing the skills for recognizing precision in measurement, working with graphs, and using fine motor manipulation skills. In the process of figuring out which dots to connect, he was working through the 15 fact family (all the numbers that combine to make 15). In the moment he saw the curve, he had an “ah-ha” that fueled his curiosity and inspired him to review and reflect on what he had created in light of new information. And the 11-year-old, who was simply looking on, visualized other shape possibilities. Maybe when he is introduced to graphing curves and thinking about calculus, this will have laid a little bit of the foundation. And maybe he’ll muse a little more over the curvature of space-time…
mathy moments 
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