It sure looks like they are adding the same number to both side lengths. 72 – 16 = 56, and then 56+12 = 68. So I would probably try and do some more examples, probably using grid paper so that they have another way of checking their answer besides the similar triangles algorithm they are using.

First, the student is using additive reasoning instead of multiplicative reasoning. Multiplicative reasoning is usually considered more developmentally advanced so a good question to ask “Is the student developmentally ready?”

An even better question to ask is, “Is multiplicative reasoning needed?” Based on the given information, I do not see anything to indicate that these two shapes are similar, or that the sides are proportional. As such, it would be difficult to predict the poster’s height without more information or making some assumptions.

David:
Working on a grid is offered to students as one possible way to combat the additive reasoning (good suggestion). There are a few others such as scaling it down: is 3 the answer to 1/2 = ?/4 as additive would suggest. Or is 99 the answer to 1/2 = ?/100. But these examples might not work if we address
Chris:
Your first question, “Is this student developmentally ready?”
Thankfully this lesson included more ways than one to solve this problem and lead to lots of discussion.
And yes, we are working on proportions so the assumption was the photograph were enlarged proportionally. In isolation though it is not clear.

Thanks

Draw a 3 by 5 rectangle and tell the student to double it in size. They can usually come up with 6 by 10. So just because 3+3=6, does that mean that we do 5+3 as well?

## 4 replies on “Similar Figures”

It sure looks like they are adding the same number to both side lengths. 72 – 16 = 56, and then 56+12 = 68. So I would probably try and do some more examples, probably using grid paper so that they have another way of checking their answer besides the similar triangles algorithm they are using.

First, the student is using additive reasoning instead of multiplicative reasoning. Multiplicative reasoning is usually considered more developmentally advanced so a good question to ask “Is the student developmentally ready?”

An even better question to ask is, “Is multiplicative reasoning needed?” Based on the given information, I do not see anything to indicate that these two shapes are similar, or that the sides are proportional. As such, it would be difficult to predict the poster’s height without more information or making some assumptions.

David:

Working on a grid is offered to students as one possible way to combat the additive reasoning (good suggestion). There are a few others such as scaling it down: is 3 the answer to 1/2 = ?/4 as additive would suggest. Or is 99 the answer to 1/2 = ?/100. But these examples might not work if we address

Chris:

Your first question, “Is this student developmentally ready?”

Thankfully this lesson included more ways than one to solve this problem and lead to lots of discussion.

And yes, we are working on proportions so the assumption was the photograph were enlarged proportionally. In isolation though it is not clear.

Thanks

Draw a 3 by 5 rectangle and tell the student to double it in size. They can usually come up with 6 by 10. So just because 3+3=6, does that mean that we do 5+3 as well?