When a student’s face lights up with understanding, it’s pure joy. Especially for guest teachers, whose “aha” moments may be few and far between.
I’ve been privileged to glimpse a couple of these moments. It’s so great to see 2nd graders become more fluent in double-digit subtraction and regrouping, which can be challenging. In one of the 2nd grade classes, one little girl raised her hand and said, “Hey, this is a good math strategy!” Here’s the story:
Start with a quick sketch depicting the Ones and Tens as families who live next door to each other:
Then point to the sketch while telling the story:
Once upon a time, there were two families who lived right next door to each other, the ONEs family and the TENs family. Both families loved eating apples and making treats from apples, such as caramel apples, apple dumplings, candy apples, all sorts of good things…mmm…
The ONEs family only had one apple tree. Sometimes the ONEs family members would go outside, look UP into their tree, and find out they didn’t have enough apples for everyone in the house. So they had to go next door and borrow some from the TENs family, who had lots of apple trees.
The TENs family was happy to share because they had lots of apples. In fact, they had so many apples that they collected baskets of apples. The TENs family always put 10 apples in each basket.
(Then hold up a drawing. OK, so it’s not picture perfect, it works!)
When the TENs family talked about apples, they never talked about single apples, they always talked about BASKETS of apples. So the ONEs family had to learn the secret language of the TENs family so they could borrow apples. For example, when Mrs. Ones asked to borrow 1 from the TENs family, she knew she was borrowing one BASKET, which was really 10 apples.
Now the stage is set and we go back to the ONEs and TENs house sketch and fill in a subtraction problem, such as 22 – 5.
So one day there were 5 people home at the ONEs house and they each wanted an apple. They went outside to their tree, looked UUUPPPPP into the tree, and saw there were only 2 apples. If there are 2 apples, can 5 people each have their own apple? (Students are shaking their heads no). So what do they have to do? They have to go next door and borrow from the TENs family, right?
Remember, they are talking in the secret language of the TENs family. When they ask to borrow 1, how many apples are they really borrowing?
I hold up the basket picture and write the regrouped numbers in the roof of the house, e.g., 12 on the ONEs’ roof and 1 on the TENs’ roof. We continue with problems, getting slightly more complex as we go, e.g. 24 – 9; 30 – 11; 46 – 27; etc. Once students start catching on, throw in subtraction problems that don’t require borrowing or regrouping, such as 24 – 3 ; 20 – 0 ; 42 – 1 ; etc.
Be sure to talk it out, asking questions such as “how many people are in the ONEs house?” and “where do they look to find out how many apples are in their tree?” (UP!), “how many apples do they have?” and “do they have enough apples or do they need to borrow some?” The questions target when to borrow and regroup and when not to, along with where to find the starting point to solve the problem (the bottom number in the ones column).
The basket analogy reminds students that numbers in the tens column represent larger numbers and to think through why they’re borrowing and regrouping. Seeing students talking it out and quickly becoming versed in the strategy is heartwarming!
Of course, I understand that my role in students’ “aha” moments is small. Teachers invest so much time and effort in planting the seeds for such learning; my one-day role is doesn’t warrant major credit. Yet sometimes a fresh perspective is just what students need.
As a guest teacher, I’d love to hear from teachers and guest teachers on this.
- Have you used similar stories that you’ve found successful?
- Teachers, would you find it helpful for a guest teacher to use such stories in your classroom, if they shared a copy of the story with you?
All considerate, collaborative discussion is appreciated. Please share your thoughts!