Common misconception 1: understanding the denominator
Let’s start with the denominator, meaning ‘that which names’ in Latin.
The Latin translation identifies the denominator as a name, the same way one, two and three are names.
The denominator can also tell you the size of the parts. Children learn that:
*/2 shows us that each part is called a half and two of them will make one whole.
*/3 shows us that each part is called a third and three of them will make one whole.
*/4 shows us that each part is called a quarter and four of them will make one whole.
And so on.
Children need to use physical materials to discover this for themselves. Like in the following example from Maths — No Problem! Textbook 1B, Chapter 14, Lesson 1.
How do we know that Charles’ part is the same as Holly’s part?
We could put Charles’ piece on Holly’s piece to see if they are the same size.
How many parts are needed to make one whole piece of paper?
It would take two parts to make one whole piece of paper.
Children need to discover this using physical materials first and develop the language associated with the idea.
Or this example from Maths — No Problem! Textbook 1B, Chapter 14, Lesson 2.
If we concentrate on the size of the pieces and understand that each size has a name, in this case a quarter, the notation becomes easier to understand.
Once learners understand this we can find the name of the fraction.
What fraction of the shape is green?
Using the ideas that were first introduced in Year 1, this should be quite straightforward to answer.
It takes 6 green pieces to cover the yellow shape. There is one piece.
1/6 of the shape is green. We can develop the idea further and ask, “How many green pieces would it take to cover half of the shape?”.
If we concentrate on the denominator first the understanding of the numerator becomes easier to understand. The numerator is simply showing us the number of parts.
3/4 shows us that there are three parts and it takes four parts to make one whole.