With everything there are trade-offs. It’s the same for homeschooling. Sometimes when I am planning I come across an activity or discussion that I think would work so much better in a group dynamic. It doesn’t happen too often, but often enough. Sometime, like with physics for my 13-year-old son this year, I just decide to do the activity with a group of friends. Sometimes I end up putting the activity aside as it doesn’t feel worth the effort of organizing the group with which to do it. Every once in a while though, I have some epiphany or inspiration and find another way to do it.
I have wanted to do this activity I read about in Active Arithmetic by Henning Andersen for some time, but it required several children to perform it the way described in the book. In this game there are several raidi running out from a center each with a number of stepping stones. For instance, one might have 2 stepping stone, one might have 3, and one might have 4. You have the children hop on each stone as you count towards the center, running back to the furthest one out and hop towards the center again. You can see how this gives number sense to different common multiples for each of the numbers. You can switch up the numbers and see different multiples. I love the idea of this game, especially using the movement, but I have only one child that is within the age range for this.
One day while we were drawing numbers on our sidewalk around our pool, I had an inspiration. We were going to practice skip counting, which we did, but I decided to pull something that I got from a Gattigno study group with questions like “I wonder…?” and “I notice…” and the use of predictions. So after we had skip counted 2’s, 3’s, 4’s and 5’s, I said, “I wonder if you skipped 2’s and I skipped 3’s, if we would ever land on the same square.” She, thankfully, took the bait. “I don’t know. Let’s try.” She skipped her first number and I skipped enough 2’s to go ahead of her. She skipped her next number. You can see where this is going. We ended up on 6. She marked a colored X beside the six. Somewhere along the line, maybe on the 18 (we have written all the way to 100!) I said, “I notice that I there are six between each of the numbers we both land on. What do you think our next number will be?” From there she accurately predicted we would land on 24. After we went all the way around, I asked, “Do you think we could do that with another two numbers?”
We then proceeded to look for common multiples of 2 and 5. We noticed that each of time we landed on a number together it was a 10. I said, “How many jumps do I have for each 10?”
“And how many jumps do you have for each 10?”
“How interesting!!! I am 2 and I have 5 jumps. You are 5 and you have 2 jumps.”
“Yes, Mama. Don’t you remember from the skip counting number line we did last week?”
And I thought, “Oh, good. This stuff is sinking in.”
After we made it all the way around, I then asked, “So how many 10’s do you think were in our 100?” She already knew this one, but it was a great lead into the others. Sometimes, those inspirations really work out for us.