#### Understanding

Students use double number lines to solve questions that involve finding a value for x when a:b is equivalent to c:x.

### What to look for

At this level, students are investigating informal but useful strategies for solving problems involving proportions. Moving to the formal equation can lead to misunderstanding and support longstanding student misconceptions.### Sample Assessment

8 km is approximately 5 miles. How many km is 32 miles?

Answer: 32 miles is about 51 $\frac{1}{5}$ km. This is because 5:8 is equivalent to 1:( $\frac{8}{5}$ ) ; multiplying by 32 gives 32:( $\frac{\mathrm{256}}{5}$ ) .