Learning target: students can model exponential situations.
Dispite the fact that I;ve been writting equations with ratios like this for some time students still want to multiply the 4 by 30% and add it back on to 4. Aside from the fact that such steps make it hard to see what the pattern is (are we multiplying or adding? Both?) the only problem I see with this is an economy of calculations, if a student makes a mistake they feel like they have to start over because they were balancing so many things in their head at the time.
On the worksheet students are asked to calculate how tall she would be if she ate 2 oz of cake. When students rush to calculate 2 oz without first calculating 1 oz they usually do 4(1.00+.60) because 30%+30%=60%.
When modeling this with an equation a common mistake is for students to write y=x(1.3), mixing up the recursive and explicit method of describing this pattern.
Then, every so often I can tell that students want to know this stuff. I find evidence of a student putting in EXTRA effort to make sense of a problem. #2 show the meaning of each part of this equation. Beautiful.
Here is an available version of the worksheet:
This was a good lesson for sorting out repeated multiplication issues.
Dispite the fact that I;ve been writting equations with ratios like this for some time students still want to multiply the 4 by 30% and add it back on to 4. Aside from the fact that such steps make it hard to see what the pattern is (are we multiplying or adding? Both?) the only problem I see with this is an economy of calculations, if a student makes a mistake they feel like they have to start over because they were balancing so many things in their head at the time.
On the worksheet students are asked to calculate how tall she would be if she ate 2 oz of cake. When students rush to calculate 2 oz without first calculating 1 oz they usually do 4(1.00+.60) because 30%+30%=60%. 
When modeling this with an equation a common mistake is for students to write y=x(1.3), mixing up the recursive and explicit method of describing this pattern.
Then, every so often I can tell that students want to know this stuff. I find evidence of a student putting in EXTRA effort to make sense of a problem. #2 show the meaning of each part of this equation. Beautiful.
Here is an available version of the worksheet:
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