Jonathan Robinson, TES Author Mr Mathematics, discusses how he teaches students to divide fractions using visuals
How to visualise dividing with fractions
I start with my dividing with fractions lesson pack*. To help students visualise what is happening when we divide one fraction by another, I do two things. I keep the fractions simple and I use proportions of a circle because it is much easier for students to see one circle as a whole.
The best way to keep the fractions simple is to use those which are easy to visualise, such as halves, thirds and quarters or those where the denominators have more factors, such as eighths and twelfths.
Scaffolding the questions
I set the scene by using a circle to represent the whole. I split the whole into a number of sectors, relevant to the question in hand, as shown in this video. For example, when looking at a question such as 3/4 ÷ 2, I would split the circle into eighths, then remove a quarter of the circle. Students can see that by dividing the 3/4 circle in half, you are left with 3/8.
For the next series of questions, I get students to sketch a circle split into 6 equal sectors and to wipe off one third. Now we have two thirds of a circle split into four equal sectors.
I ask the class to attempt 2/3 ÷ 4. Most present 1/6 as their answer. Some present 1/4 with the argument the shape has been split into four equal sectors. We discuss that while their argument has some validity, we need to look at 2/3 of the whole circle and the whole circle is split into sixths.
Getting the plenary right is crucial to ensuring a positive and purposeful end to the lesson. Students want to feel they have achieved something and have had the chance to apply their learning.
Dividing with fractions lesson*
Mr Mathematics’ TES Shop
*This resource is being sold by the author
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