Year 3

We can add and subtract numbers using an empty number line.
We can add and subtract numbers using partitioning.

Year 3 Unit 12a

What we are learning:

• A written method is generally needed for the addition and subtraction of two-digit and three-digit numbers as there are several parts to each calculation. This can be too much to hold in the memory.
• The column method (where numbers are written in hundreds, tens and units columns) is referred to as a FORMAL written method.
• The types of INFORMAL written methods usually taught in schools are: Partitioning and the Number Line.
• Partitioning is simply splitting a number into different parts (but retaining the same overall value). 52 can be partitioned into 50+2, 40+12, 30+22 etc
• Partitioning both numbers is often used in written addition to simplify the calculation:
  52 + 23 can be simplified through partitioning to
  50+20=70
  2 + 3 = 5
  And then re-combining the two separate totals to get 70+5=75
• Partitioning the smallest number to simplify taking away from the bigger number is often used in written subtraction methods:
  85 – 27 can be simplified through partitioning to
  85 -20 = 65
  65 – 7 (might be easier to do as -5 then -2) = 58

ACTIVITY 1: ADDITION USING A NUMBER LINE

ACTIVITY 2: SUBTRACTION USING A NUMBER LINE

ACTIVITY 3: ADDITION USING PARTITIONING

ACTIVITY 4: SUBTRACTION USING PARTITIONING

Activities you can do at home:

A number line is a simple diagram (quick to draw – no need for scaling accuracy) used to represent and support a calculation. It consists of a straight line (normally drawn horizontally. Key numbers should be added onto it.

Draw a horizontal line on a sheet of paper. Use the number line to support the calculation of 25 + 37. Mark 37 at the left hand side of number line (this is the highest number so the best place to start an addition).
Mentally partition the number that we are adding on (25) into tens and units (20+5). Begin by adding on the tens: 37+10 = 47, 47+10 =57, finish by adding on the units. In this instance it is simpler to split the 5 units into 3 and 2, as 57+3 = 60.

Practice finding the total of: 27+44, 53+28, 19+35, 57+25

Draw a horizontal line on a sheet of paper. Use the number line to support the calculation of 35 – 27. Mark 35 at the right hand side of the number line. Mentally partition the number that we are taking away (27) into tens and units (20+7). Begin by taking away the tens: 35-10 = 25, 25-10 =15,
finish by taking away the units. In this instance it is simpler to split the 7 units into 5 and 2, as 15 – 5 =10

Practise subtraction: 44 – 27, 53 – 28, 35 – 19, 57 – 25

Use partitioning to calculate 35 + 27.
Partition 35 into 30 + 5 and 27 into 20 + 7
Add the tens first 30+20 = 50
Add the units next 5 + 7 = 12
Combine the two parts of the calculation
50 + 12 = 62
Practice finding the total of: 27+44, 53+28, 19+35, 57+25

Use partitioning to calculate 35 – 27.
Keep the number we are taking away from (35) whole.
Partition the number we are taking away (27) into tens and units 20+7.
Take away the tens first from the whole number: 35 – 20 = 15
Take away the units now (in this calculation it is easier to split the 7 into 5
and 2)
15 – 5 = 10
10 – 2 = 8
Practice subtraction: 44 – 27, 53 – 28, 35 – 19, 57 – 25

Good questions to ask:

How can you partition these numbers to make the calculation easier?
Which bit are you going to do first?
What do you need to write down to help you remember?

If your child:

Prefers to use either the number line or partitioning method
Let them do this, but also show them the other method and talk about it so that they understand it and can make a choice