The subtraction model for comparing is quite different from that for take away. When modeling take away, we see the total and then remove items; we do not model both numbers in the subtraction. For example, for 8 – 2, we show 8 and then remove 2. But when we compare 8 and 2 to model how much more 8 is than 2, we normally show both the 8 and the 2 and then look at the “extra.”
Questioning about subtraction as comparison should focus on the model used, what each number in the subtraction sentence represents, and why subtraction can be thought of as comparison. In this case, we would look at how many more ladybugs than butterflies there are.”
QUESTIONS:
(to supplement the question and to include in a conversation about the picture)
Where do you see 12 in the picture? [We want students to associate the parts of the number sentence with the appropriate parts of the real-life situation.]
Where do you see 8?
Why do you think a subtraction sentence was used? [We want students to recognize that subtraction can tell how much more one amount is than another.]
When you take 8 away from 12, you see the 8 items within the 12 items. Why does it make sense to show all 8 + 12 (or 20) items to “compare the ladybugs to the butterflies? [We want students to understand why the models for take away subtraction and comparison subtraction might be different.]”
“Why is thinking about how many more ladybugs there are than butterflies like taking away 8 butterflies from the 12 ladybugs? [We want to build a connection between the various meanings of subtraction. For example, if we think of matching the ladybugs and the butterflies, we could take away the 8 ladybugs that have a matching butterfly and see how many ladybugs do not have a match.]
EXTENSION Ask students to put out 5 blue counters and a lot more red ones, and then to tell how many more are red than blue. Ask them how they know, and have them record the associated subtraction sentence.”
Excerpt From: Small, Marian. “Eyes on Math: A Visual Approach to Teaching Math Concepts"
Questioning about subtraction as comparison should focus on the model used, what each number in the subtraction sentence represents, and why subtraction can be thought of as comparison. In this case, we would look at how many more ladybugs than butterflies there are.”
QUESTIONS:
(to supplement the question and to include in a conversation about the picture)
Where do you see 12 in the picture? [We want students to associate the parts of the number sentence with the appropriate parts of the real-life situation.]
Where do you see 8?
Why do you think a subtraction sentence was used? [We want students to recognize that subtraction can tell how much more one amount is than another.]
When you take 8 away from 12, you see the 8 items within the 12 items. Why does it make sense to show all 8 + 12 (or 20) items to “compare the ladybugs to the butterflies? [We want students to understand why the models for take away subtraction and comparison subtraction might be different.]”
“Why is thinking about how many more ladybugs there are than butterflies like taking away 8 butterflies from the 12 ladybugs? [We want to build a connection between the various meanings of subtraction. For example, if we think of matching the ladybugs and the butterflies, we could take away the 8 ladybugs that have a matching butterfly and see how many ladybugs do not have a match.]
EXTENSION Ask students to put out 5 blue counters and a lot more red ones, and then to tell how many more are red than blue. Ask them how they know, and have them record the associated subtraction sentence.”
Excerpt From: Small, Marian. “Eyes on Math: A Visual Approach to Teaching Math Concepts"