Partitioned Fractions…
Huh??
I know. Weird name … but there is a really good reason for it.
Let’s go back a step.
Partitioning is dividing or splitting a quantity into parts.
When students create a fraction by equally segmenting a ribbon, or a strip of paper or group of objects, they are partitioning, so when we talk about partitioned fractions, we mean that they are going to break up a whole into even sized pieces.
So why the name change?
Good question.
When you hear or read the word ‘fraction’, what do think of? Probably the notation for a fraction, like 1/2, right?
We want your child to think slightly differently, with the notation being only one of the things they think about, and probably not the first thing, at this stage anyway.
We want them to think of a whole something - a strip of paper, an apple, a pizza, a window - being divided up into equal parts.
(In that case, a pizza may not be the best example - have you EVER seen one cut up evenly?? But you get the idea!)
We want them to understand that when we divide something into equal pieces, we create fractions, and eventually the fraction notation comes with it, but not to start with, not until Stage 2, but they do start thinking and talking about all of this in Kindergarten.
Let’s explore this further… one step at a time…
There are many steps involved in learning about fractions.
In Kinder, fractions are not discussed, nor is division, but they form groups of equal size by sharing objects. Let’s say they have a group of 20 pegs, and they make 4 equal groups - later in their learning journey, this will be discussed as quarters, and later than that, they will record it in fractional notation.
At this stage - usually Year 1 - they learn to recognise and represent division, by modelling a half of a collection of objects. They will talk about one half, two halves and the whole, but they don’t record anything using fractional notation.
They move onto model doubling and halving, they recreate the whole given half, and they model halves, quarters, and eighths. This can be done through repeated halving. Nothing is recorded in fractional notation.
In Year 3, your child will start to think, talk about and create thirds and fifths of a length, which are divisions that cannot be made by repeated halving. They will also use fraction strips to model halves, quarters, eighths and thirds, work out the complementary fractional part needed for halves, quarters, eighths, thirds, to complete one whole and recreate the whole if they are given a fractional part. The fractions they work with will now be recorded in fractional notation as ONE way to record what they are doing.
Now they’ll use lengths to model and compare equivalent fractions, using concrete materials (or hands-on materials), diagrams and number lines. Again, they’ll use fractional notation as a way to record their thinking. They will also rename 2 halves, 3 thirds, 4 quarters, 5 fifths, 6 sixths, 8 eighths and 10 tenths as one whole and regroup fractional parts beyond one.
The name changes again - now we talk about representing quantity fractions.
As a part of this, your child will recognise the role of the number 1 as representing the whole and compare halves and quarters of different sized wholes. They’ll compare and order common fractions using benchmark values and number lines, and solve problems involving addition and subtraction of fractions with the same denominator, using a range of strategies and record their thinking in various ways.
And finally, your child will learn to recognise that a fraction is a representation of division, compare common fractions with related denominators, build up to and beyond the whole, add and subtract using equivalent fractions and find fractional quantities of whole numbers, including expressing remainders as decimals.
It’s a lot …
but it’s a journey …
a journey of 7 years.
Your child is on a mathematical journey towards understanding and efficiency. Let’s not rush them.
This makes it important to know what your child is learning so that you don’t ‘jump ahead’ … that you don’t expect something from them that they have not yet come across, or do not fully understand.
As adults, we know what we know. We have forgotten the multiple steps that we made towards our current understanding of any mathematical concept, because we no longer NEED all of those building blocks.
But, our children are still on this journey.
Racing towards the ‘end’ point with little understanding is not the goal. The goal is to build such a deep understanding of the concept, that they are never worried or confused by fractions…EVER.
I want that for your child, don’t you?
Right!
So, let me help.
