Structure of HSNP Numeracy - Four Levels of Proficiency

Subtraction 6 Decomposition–pairs of 4-digit numbers

Objectives

Use decomposition to subtract pairs of four-digit numbers (two, then three ‘carries’)
Choose a mental strategy or decomposition to subtract pairs of four-digit numbers

For this unit you will need:

Expanded decomposition at

Watch out for pupils who:

make frequent place value errors when using compact decomposition, especially when needing more than one ‘carry’; they may need to return to using expanded decomposition or use counting up on the number line to solve subtractions;
use decomposition for all subtractions, even those that can be easily worked out using a mental method;
having made a mistake, do not notice that their answer seems unreasonably large/small, encourage them to make estimates using rounding and mental methods.

Subtraction 6 Session 1

Objective: Use decomposition to subtract pairs of four-digit numbers (two ‘carries’)

Teacher input with whole class

Use Expanded decompositionat choosing ThHTU – ThHTU from the left column. Use the toggles to change the given numbers so that the last two digits of the smaller number are greater than the last two digits in the larger number. Ask pupils to use rounding to estimate the answer. Take some estimates and record them on the board. Click on the yellow arrow to show the partitioning of each number. Discuss what exchanges might be necessary to carry out the subtraction. Click on ‘take 10’ and ‘take 100’. Can we carry out the subtraction now? Click on the arrows below to carry out the subtraction, then the = sign to show the answer. Compare with pupils’ estimates.

Show the same using compact decomposition on the board.
Repeat for other subtractions which need ‘carries’ from 100s to 10s and 10s to 1s.

Individual practice

Pupils choose either expanded or compact decomposition to work out 8745 – 4268, 8607 – 3239, 9736 – 3647 and 7635 – 4368. They estimate each answer first. Ask pupils how they could check their answers. Draw out using addition. Ask them to choose three subtractions to check.

Subtraction 6 Session 2

Objective: Use decomposition to subtract pairs of four-digit numbers (two ‘carries’)

Teacher input with whole class

Use Expanded decompositionat ThHTU – ThHTU from the left column. Use the toggles to change the given numbers so that only the 100s digit of the smaller number is larger than the 100s digit in the larger number. Click on the arrow to show the partitioning of each number. Discuss what exchanges might be necessary to carry out the subtraction. Click on ‘take ‘1000’. Can we carry out the subtraction now? Click on the arrows beneath each column to carry out the subtractions and ‘=’ to show the answer.

Repeat, this time choosing numbers where you need to take 1000 and either take 10 or 100.

Individual practice

Pupils make an estimate and then choose either expanded or compact decomposition to work out 5283 – 2557, 7371 – 3653, 8362 – 3635 and 4435 – 2861. They choose one to check using addition.

Subtraction 6 Session3

Objectives: Use decomposition to subtract pairs of four-digit numbers (three ‘carries’); Choose a mental strategy or decomposition to subtract pairs of four-digit numbers

Teacher input with whole class

Use Expanded decompositionat choosing ThHTU – ThHTU from the left column. Use the toggles to change the given numbers so that only the 1000s digit of the larger number is more than the 1000s digit in the smaller number. Click on the arrow to show the partitioning of each number. Discuss what exchanges might be necessary to carry out the subtraction. Click on ‘take 10’, ‘take 100’ and then ‘take ‘1000’. Click on the arrows beneath each column to carry out the subtractions and ‘=’ to show the answer.

Show the same using compact decomposition on the board.
Repeat for other subtractions which need three ‘carries’.

Individual practice

Pupils choose either expanded or compact decomposition to work out 7223 – 2357, 7521 – 3852, 8313 – 3638 and 6335 – 2368. They estimate each answer first.
Write the following subtractions on the board and ask which of them pupils could solve mentally: 9350 – 2999, 7532 – 3469, 4005 – 3996, 4728 – 3100, 8273 – 2432.
Take feedback and ask them to work these out.