Following on this month's article on mastery, Caroline Clissold has put together some ideas for how you could help teach your children mastery in fractions. These ideas can be adapted for any Year Group.
First of all consider:
- What is the ‘big picture’ in this concept?
- How will you explore whole/part relationships?
- What will be your starting point?
- How will you explore equivalence?
- How can you make the link with division?
- How can you make connections with scaling up and down?
- What vocabulary will you introduce?
- What activities could you give the children to develop their understanding?
- What activities could you give the children to deepen their understanding?
- What activities will offer variance (intelligent practice)?
- What is the progression in addition and subtraction of fractions?
- How can this be accessed by all?
The concept of whole/part relationships is key to the children’s conceptual understanding of fractions. Generally speaking, this is not a focus in the primary curriculum in this country and it needs to be.
Simple ways of introducing this idea:
This is England. If England is the whole, London is one part, so is Devon, Surrey and Cumbria. What other parts can you see?
What whole/part relationship can you see in this picture?
The whole is five smiley faces. One part is one red smiley face. The other part is four white smiley faces.
What about in this picture?
The whole is eight birds. One part is white chickens. The other part is yellow chickens.
I like to introduce the Latin word fractio as the word that means fractions. The children can tell us that fractio sounds a little like fracture and they know that this means break. So a fraction is an object or quantity that has been broken up.
When we introduce what a fraction looks like, we draw the fraction bar first to indicate that something has been broken and that there are going to be two parts.
We then write the denominator to show how many parts there are and the numerator to show how many parts we need.
This is a useful model which helps make the link to division:
I ask children to act this out. A Year 1 class I was working with made the fraction bar symbol and then punched the denominator in place and then the numerator. They happily used the correct numbers and some of them said, ‘it’s like division’!
Often, practice looks something like this:
This isn’t helpful because children begin to develop the misconception that the parts of a fraction are all the same shape. It’s about the size or area of the shape.
When dealing with fractions we need to help the children make connections, so, for example, they look at half in lots of different ways:
Ask them to find unit and no-unit fractions of shapes and quantities.
You could carry out some of the activities suggested in the fractions challenge
Practice within a context
Give the children a strip of paper. Ask them to measure its length. They then find a half, one quarter, one-tenth, three-fifths and so on, of the length and draw lines of these new lengths. They could explore adding and subtracting the different fractions that they have made.
Use a tangram puzzle such as this and ask the children to find the fraction of the whole that each part is. They could then explore which shapes are the same fraction and prove it. This reinforces the idea that fractions are areas not shapes.
We hope that you can make use of some of these ideas when considering the mastery of fractions in your teaching. Let us know of any other ideas you have!
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