There is something about counting that feels good. It’s rhythmic, it’s fun, and it’s a well-practiced skill. When given a set of objects like a box of chocolates or silverware, even adults resort to counting one by one. It works…until it doesn’t. Second graders solve problems with 2 and 3-digit numbers, thus requiring them to use more efficient strategies. For example, if faced with a problem requiring students to find the sum of 34 and 23, students do not want to count from 1 to 57. However, they may still need to “see” the amounts before they are ready to use the symbols.
My students had seen models of 10s and 1s as part of our daily tally of the days in school. The model consists of 10s sticks (made up of 10 small squares) and ones (single squares). However, they had not created their own representations. I asked them to think about how they could use nature to show 5. Hands shot up and they talked about using leaves, acorns, rocks, pinecones, and small sticks. Then I asked them how they could show 10. Many thought to just add 5 more to the 5 they already had. One student said, “We could do like we do in the morning and use 10s and 1s. We could break branches to make sticks. They can be our 10s.” I could see the lightbulbs turn on, as others were nodding in agreement. One child said, “That will be much more efficient.” They decided to use sticks and acorns because they are plentiful. They also thought it would be more accurate if everyone used the same materials.
So, off we went to the outdoor classroom. After sprinting to the woods and gathering bits of nature on the ground, the students used their 10s and 1s to make 2-digit numbers. After successfully representing a few numbers, I asked them to challenge themselves to solve a math problem with the materials. I had to hold back from just presenting them with a problem. I was willing to trust that they had ideas that may not only be more motivating, but more diverse and challenging as well. They did not disappoint.
One child showed 9 sticks and 3 acorns and explained that it would take 7 more acorns to make 100. I asked how many would need to be subtracted from the 93 to be left with 50. At first, the answer was 40, then it changed to 43. A pair of students were working to figure out the sum of 1st and 2nd graders. They had to add 13 and 19. They thought to make one stick and 3 acorns and another stick and 9 acorns, but then they included a plus and equal sign. I asked what would happen if they left out the signs and combined the 10s together and the 1s together. You would have thought I had given them candy! They quickly combined the sticks and then the acorns and shouted, “32.” Someone came up with the idea of combining sticks and acorns and soon they were working in small groups representing in the 100s.
To finish the lesson, I asked their advice about the counting all strategy. What do you think we should do with that strategy? That’s when we decided it was time to let it go. We wrote, “counting all” on paper and literally dug a hole and buried it in the outdoor classroom.
Laura Waite, Otisfield Community School, Grade 2