Year 11 have been looking at a variety of Paper 1 (non calculator) questions ahead of their exam on Tuesday. One question seemed to be challenging for the students in my class. They were given a number line from 0 to 2 marked at every quarter and they were to find the FRACTION that was halfway between two given fractions. Here is a sample of the answers year 11 gave. This is a foundation class but targets of 4s and 5s.

Most if not all of the students converted the fractions to decimals and then subtracted the two decimals but then struggled to halve 0.75.

I spent some time with a small group of students and we looked at splitting the scale further and in doing so the students spotted an easier way to find the half way point. What I found interesting was that students didn’t see that the halfway fraction between 1/2 and 1 1/4 was the same as the halfway fraction between 3/4 and 1.

It made me think about finding the numbers in the middle of these pairs of numbers

8 and 10

7 and 11

5 and 13

1.5 and 16.5

I made the following for the next lesson and I wonder if students can make the connections between the 3 questions