Question

a grade 6 4.8 problem solving: using double number lines and tape diag the double number lines below show the number of math problems that zoey does and the amount of time that she spends doing the problems. use the double number lines to determine the number of math problems that zoey does per minute. math problems 0 5 10 minutes (min) 0 10 20 zoey does blank math problems/min.

Explanation:

Step1: Analyze the number lines

The "math problems" number line has marks at 0, 5, 10. The "minutes" number line has marks at 0, 10, 20. Let's assume the intervals between marks are equal. For the "math problems" line, from 0 to 10, there are \( \frac{10 - 0}{\text{number of intervals}} \). Looking at the lines, the number of intervals between 0 and 10 (or 0 and 20) seems to be such that we can find the rate.

Step2: Find the rate

We need to find math problems per minute, so we can take a point. Let's say when time is 10 minutes (from the minutes line), how many math problems? From the math problems line, if we assume the relationship, let's see the ratio. If we consider that the number of math problems and minutes have a proportional relationship. Let's find the number of intervals. The minutes line: from 0 to 20, let's count the marks. Wait, maybe a better way: the rate is \( \frac{\text{math problems}}{\text{minutes}} \). Let's see the number of intervals between 0 and 10 on math problems: from 0 to 10, how many steps? Let's say the math problems line: 0 to 5 is some steps, 5 to 10 is some. Wait, maybe the key is that the number of math problems and minutes are related such that when minutes are 10, math problems are 10? No, wait, the problem is to find problems per minute. Wait, maybe the number lines are set so that for a certain time, the number of problems. Wait, maybe the first number line (math problems) has 0, then some marks, and the minutes line has 0, 10, 20. Wait, maybe the rate is 1 problem per minute. Let's check: if in 10 minutes, she does 10 problems, then rate is \( \frac{10}{10}=1 \). Or if in 20 minutes, 20 problems, rate is 1. So the rate is 1 math problem per minute.

Answer:

1