Halfway Fractions

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.

IMG_4342IMG_4341IMG_4340IMG_4339

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

Screen Shot 2019-05-16 at 22.50.11

 

decimals-fractions.pptx

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