RATL 1 | Lesson 3 | Explore (Solution: Proportional Reasoning)

Proportional Reasoning

A cookie recipe make one dozen cookies and requires \(\Large \frac{2}{3}\) cups of milk.

1.  How many cookies can be made with 9 cups of milk?

Solution:  162 cookies


2.  What method did you use to solve this problem?

Methods vary.  Two methods are described below:

Method 1:  Additive Reasoning

If \(\frac{2}{3}\) cups of milk makes 12 cookies, then

  • 2 times \(\frac{2}{3}= \frac{4}{3}=1\frac{1}{3}\) cups of milk makes \(2(12)=24\) cookies
  • 3 times \(\frac{2}{3}=\frac{6}{3}=2\) cups of milk makes \(3(12)=36\) cookies
  • 6 times \(\frac{2}{3}=\frac{12}{3}=4\) cups of milk makes \(6(12)=72\) cookies
  • 13.5 times \(\frac{2}{3}= \frac{27}{3}=9\) cups of milk makes \(13.5(12)=162\) cookies

Method 2: Division and multiplication

\(\Large\frac{9}{\frac{2}{3}}\)\(=9(\frac{3}{2})=\frac{27}{2}=13.5\) dozens of cookies. \(13.5(12)=162\) cookies.

3.  Which of the two methods above did you use?   Did you use another method?


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