Section B Section B Checkpoint

Sample response: $\frac68$ and $\frac{9}{12}$.  Each $\frac14$ is the same size as two $\frac18$s. So, three $\frac14$s is the same size as six $\frac18$s.  Each $\frac14$ is the same size as three $\frac{1}{12}$s.  So, three $\frac14$s is the same size as nine $\frac{1}{12}$s. 

Sample response: $\frac68$ and $\frac{9}{12}$.  Each $\frac14$ is the same size as two $\frac18$s. So, three $\frac14$s is the same size as six $\frac18$s.  Each $\frac14$ is the same size as three $\frac{1}{12}$s.  So, three $\frac14$s is the same size as nine $\frac{1}{12}$s. 

Sample responses: $\frac16$ and $\frac{2}{12}$. There are 6 equal parts on the number line and the point is the first tick mark, so that’s $\frac16$.

The point is the second tick mark when I divide each $\frac16$ into 2 equal parts. Those parts are $\frac{1}{12}$s because there are 12 in 1 whole. So, the point is also $\frac{2}{12}$.

Sample responses: $\frac16$ and $\frac{2}{12}$. There are 6 equal parts on the number line and the point is the first tick mark, so that’s $\frac16$.

The point is the second tick mark when I divide each $\frac16$ into 2 equal parts. Those parts are $\frac{1}{12}$s because there are 12 in 1 whole. So, the point is also $\frac{2}{12}$.

Yes, I agree with Kiran. Sample response: $\frac{7}{12}$ is 7 equal parts when there are 12 of those parts in 1 whole. If I partition each of those 12 parts into 2 smaller parts, then I get $2 \times 7$ of the smaller parts with $2 \times 12$ of them in the whole. That’s $\frac{2 \ \times \ 7}{2 \ \times \ 12}$.

Yes, I agree with Kiran. Sample response: $\frac{7}{12}$ is 7 equal parts when there are 12 of those parts in 1 whole. If I partition each of those 12 parts into 2 smaller parts, then I get $2 \times 7$ of the smaller parts with $2 \times 12$ of them in the whole. That’s $\frac{2 \ \times \ 7}{2 \ \times \ 12}$.