# 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 one**s (**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.

### A video explaining addition partitioning (splitting numbers up) with a tens frame and a number line

### A video explaining addition subtraction (splitting numbers up) with a tens frame and a number line

## Partitioning subtraction & addition worksheet

Link to: Partitioning subtraction & addition worksheet

## Lesson on how to partition with three digit numbers

# Partitioning with the Tidy Number Strategies

### ADDITION Tidy Number Strategy

**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

### Useful Links

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.

### Partitioning using the Tidy Number Addition Strategy (Year 3 strategy)

### Partitioning using the Subtraction Tidy Number Strategy (Year 3 strategy)

### Partitioning using the Tidy Number Addition Strategy (Year 4 strategy)

### Partitioning using the Tidy Number Subtraction Strategy (Year 4 strategy)