# Partitioning

The ability to partition is essential to be at the maths standard for Year 4.

In Year 4 students are working towards being proficient at Strategy Stage 5 (Early Additive) in maths by the end of the year. One of the main skills of Strategy Stage 5 is the ability to add and subtract numbers by partitioning (breaking up) them rather than counting on or counting back (i.e. 5, 6, 7, 8, 9, 10, 11 … OR 12, 11, 10 9, 8…).

Partitioning numbers means we know that we can break a number up into its basic facts to help us solve problems. For example 7 can be broken up (partitioned) into two numbers:

`7 = 3 + 4, or 5 + 2, or 6 + 1`

## Understanding Partitioning

### Year 4 = Stage 5: Early additive

Students at the Early Additive stage solve number problems by simple splitting of the numbers (partitioning) and by using groupings of hundreds, tens and ones (simple place value).

Students at this stage need to recognise that numbers can be split into parts and recombined in different ways. This is called part-whole thinking. Problems at this stage are usually limited to numbers less than 20, or where one of the numbers is a single digit.

Strategies used at this stage include:

• using doubles
7 + 8 as (7 + 7) + 1
• up through a ten
38 + 7 as (38 + 2) + 5
• compensation
24 – 9 as (24 – 10) + 1.

## Slideshow explaining partitioning from Teacher Tools

Here is a video demonstrating Stage 5 Early Additive thinking (Year 4) by a Year 4 student.

# Partitioning with the Tidy Number Strategies

Note: We can make either number a tidy number in the addition tidy number strategy.

Note: We do the OPPOSITE to each number, i.e. if we subtract on one of the numbers we add on the other number. The reason for this is because we take away some numbers from one of the numbers to round the other number.

For example if our addition problem was:

`48 + 17 =`

STEP 1: Making a Tidy Number

We first round the 48 up to 50 (because it is closest to a tidy number) by taking 2 off the 17. We are then left with the easier problem of:

`50 + 15 =`

The 15 is what is left after taking the 2 off the 17.

We can then partition up the numbers and add them together:

50 + 10 + 5 = 65

So we haved solved our problem:

```48 + 17 = 65.

```

### SUBTRACTION Tidy Number Strategy

Note: We only make the second number a tidy number in the subtraction tidy number strategy. By making the second number a tidy number it becomes an easier problem to solve as there are less digits to subtract from the first number.

Note: We do the SAME to each number – both sides get bigger or smaller by the same amount. We are trying to work out the distance between the two numbers so we must do the same to both numbers to keep this gap the same.

For example, if our subtraction problem was:

`48 - 17 =`

STEP 1: Making a Tidy Number

We first round the second number which is 17 up to 20 by adding 3 to the 17.

We need to make sure we add 3 to the 48 as well so that the  gap between the two numbers remains the same
(i.e. there is always a gap of 31 between the numbers in our example).

We are then left with the easier problem of:

`51 - 20 =`

STEP 2: Using our basic facts to help us solve the problem

We could now approach this problem by using our basic fact of

```5 - 2 = 3
Therfore:
51 - 20 = 31```

So we have solved our problem:

`48 - 17 = 31`

Here is a video explaining the addition tidy number strategy.

Here is a video explaining the subtraction tidy number strategy.

Here is a pdf that explains the tidy number strategy for addition.