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Foundation

Decomposing Numbers

Break a whole number into parts and work out the missing part.

In a nutshell

Decomposition is the ability to break a whole number into smaller parts in different ways.

In decomposition tasks, students are shown a whole amount, one visible part, and one hidden or missing part. Students work out the missing part using understanding of part-part-whole relationships.

In Foundation, decomposition tasks often involve small quantities using blocks, counters, fingers, dot patterns, five-frames, ten-frames, or part-part-whole mats alongside numerals. Students first solve smaller decomposition tasks within 5 before progressing towards larger quantities within 10.

As students develop, they increasingly recognise small number combinations automatically and rely less on counting-by-ones. For example, they may know that 5 can be 2 and 3, 4 and 1, or 5 and 0.

Decomposition supports later addition and subtraction because students learn that numbers are made of parts and wholes. This understanding helps them solve missing-part problems, understand fact families, and use known number combinations flexibly.

As students move into Year 1, decomposition skills are increasingly represented through addition and subtraction number facts.

This guidance is designed for classes where ENSSA results indicate a class-wide need to strengthen part-part-whole understanding and missing-part reasoning.

See also: Addition and Subtraction

Teaching guidance

For schools and teachers using Ochre curriculum materials

Choose the curriculum used by your school, then find the relevant Foundation or Year 1 resource.

This section is for teachers using Ochre units as part of Tier 1 mathematics instruction in Victorian Curriculum settings, including MACS and CESL schools.

Use Ochre unit lessons when students need teaching or reteaching. Use Ochre Daily Review when students have already been taught the skill and need practice, reactivation or fluency-building.

Step 1: Where does this sit in your teaching sequence?

If

The skill has not yet been taught and is coming up soon

Then

Let the scheduled Ochre lesson address it. Consider brief pre-teaching for students flagged by ENSSA.

If

The skill has not yet been taught and is scheduled much later this year

Then

Consider bringing the relevant lesson section forward for flagged students only — check prerequisite lessons first.

If

The skill has already been taught

Then

Go to Step 2 below.

If

The skill was taught a while ago, last term or last year

Then

Start with Daily Review as a quick reactivation and accuracy check. If students are still inaccurate, go to Step 2.

Step 2: How are students performing right now?

Use this once you’ve confirmed the skill has already been taught.

If

Students are inaccurate or unsure

Then

Use the Ochre unit lesson section first — not Daily Review.

If

Most students are inaccurate

Then

Reteach the relevant modelling/guided-practice section to the whole class.

If

A few students are inaccurate but most are secure

Then

Use the lesson section for small-group reteaching with flagged students only.

If

Students are accurate but slow or inconsistent

Then

Use Daily Review — do not run a full reteach.

Foundation

Build foundations for this skill.

3 resources
Unit PlanPrimary FN02V Part-wholeUse this when students are inaccurate or unsure with parts and wholes, partitioning, missing parts, or recognising combinations.
Open Ochre Foundation Mathematics page ↗
After logging in, look for

FN02V Part-whole

Skill link

This is the primary Foundation Ochre resource for decomposition. Teaches partitioning numbers to 5 and 10 into two and three parts, identifying parts and whole, subitising parts, five-/ten-frame combinations, ‘how many more’ prompts, number pairs to 5 and 10, and making 10 from smaller parts.

Best section to use

Use the lesson matching the specific gap — partitioning, identifying parts/whole, subitising parts, five-/ten-frame combinations, ‘how many more,’ or number pairs.

If…then decision
  • If students confuse the part and the whole → use identifying parts/whole sections.
  • If students count every item each time → use subitising and frame-based sections.
  • If students cannot find missing parts → use ‘how many more’ and number pair sections.
Daily Review Number–Addition and Subtraction Daily Review deck, Part-whole slidesUse this when students have already had explicit part-whole teaching and need practice or reactivation.
Open Ochre Foundation Mathematics page ↗
After logging in, look for

Daily Review Topic Deck: Number – Addition and Subtraction, Part-whole section

Skill link

Mirrors FN02V — partitioning to 5/10, combinations, subitising parts, frame-based parts and ‘how many more.’

Use with care

Do not use when students are not yet accurate identifying the whole and parts — return to FN02V lesson sections first.

Unit PlanFollow-on FN04V Addition and SubtractionUse this when students are secure with decomposition and ready to apply part-whole knowledge to addition and subtraction contexts.
Open Ochre Foundation Mathematics page ↗
After logging in, look for

FN04V Addition and Subtraction

Skill link

Follow-on unit that applies part-whole understanding to number stories, take-away situations and difference on a number track.

Do not use when

Students need initial teaching of decomposition — use FN02V first.

Year 1

Extend this skill through Year 1.

1 resource
Daily Review Number–Addition and Subtraction Daily Review deck, Part-whole slidesUse this when students have already had explicit part-whole teaching and need practice or reactivation.
Open Ochre Foundation Mathematics page ↗
After logging in, look for

Daily Review Topic Deck: Number – Addition and Subtraction, Part-whole section

Skill link

Mirrors FN02V — partitioning to 5/10, combinations, subitising parts, frame-based parts and ‘how many more.’

Use with care

Do not use when students are not yet accurate identifying the whole and parts — return to FN02V lesson sections first.

Coming soon

Intervention resources (Tier 2 & Tier 3)

Targeted supports for students or small groups when classwide teaching is not enough.