Subtraction Methods

Subtracting on a numbered number line (individual jumps)

Subtracting on a numbered number line (tens and ones jumps)

Subtracting on a blank number line (tens and ones jumps)

Counting on to subtract (when numbers are close together)

Subtraction by partitioning the second number into tens and ones (double partitioning not suitable for subtraction at this stage)

Use base 10 or Numicon to model calculations. For 47 - 32, simply remove 3 tens and 2 ones. 47-32 = 15

Using place value counters, draw representations to support understanding

Intermediate step may be needed to lead to clear subtraction under- standing.

Begin with base 10 or Numicon. For 35 - 18, we don't have enough ones in 35 to do this calculation without going into negatives. We take one of the tens in 35 and move it next to the 5, making 15. Now we can do 15-8, so we have 7 in the the ones. There are two tens left from 35, so we subtract one ten from two tens. The answer to 35-18 = 17. This can be repeated with Dienes blocks.

Children may draw base ten or place value counters and cross off as they exchange between place value columns

Children model the process of exchange using Numicon, base ten and then move to place value counters. For 234-179, we need to exchange a 10 for ten 1s. Now the calculation in the 1s column is 14-9 = 5. In the 10s column, we need to exchange a 100 for ten 10s. Now we have 120-70 = 50 in the 10s column. In the 100s column, 100-100 = 0. So 234-179 = 55.

As Year 3. Children may draw base ten or place value counters and cross off as they exchange between place value columns

Children continue to exchange using formal method, including double exchanging (in this example, one 100 was used in the 10s column making the calculation in the 100s column 600-800. As this will result in a negative answer, we exhange with the 1000s column to create 1600-800 = 800.

CONCRETE

Reinterpret Dienes blocks in a decimal context.

PICTORIAL

Use decimal place value counters to model addition without carrying. E.g. above 3.21-1.11 =2.1

Children use the now-familiar column method for decimal subtraction. Decimal points must be alligned. Use zeros for place holders.

CONCRETE

Reinterpret Dienes blocks in a decimal context.

PICTORIAL

Use decimal place value counters to model addition without carrying. E.g. above 3.21-1.11 =2.1

Using column methods, children are reminded of the value of each digit when exchanging. Decimal points must be alligned. Some decimal calculations will involve differing number of decimal places, and zeros should be used as place-holders.

As Year 5 but with increasing numbers of digits, varied number of decimal places and the context of units of measure, for example.