Part-part-whole explained for parents (Australia)

Homework shows a bar with a number on top and two blanks underneath - or two circles joined to a bigger circle - and your child is asked to "fill the parts" or "find the whole". Schools call this part-part-whole (sometimes part–part–whole or PPW). Same idea: two parts make a whole, and the whole can be split back into parts. This guide unpacks the model for Australian parents - concrete bars and circles first, how it underpins number bonds and addition / subtraction, how it differs from split-add-join and make-ten bridging, Prep–Year 2 mix-ups, and short home games.

It is a model page, not a strategy page. Split-add-join and make-ten are moves that use part-part-whole thinking. Bonds are the pairs that sit inside the model. Year maps: Prep–Year 2 maths.

The big idea: two parts make a whole

Part-part-whole means a total (the whole) is made of smaller amounts (the parts). With two parts:

• Part + part = whole (joining)
• Whole − part = other part (taking away or finding the missing piece)

Example: whole 8, parts 5 and 3.

• 5 and 3 make 8.
• 8 take away 5 leaves 3.
• 8 take away 3 leaves 5.
• If you know the whole is 8 and one part is 5, the other part must be 3.

Say it aloud: "Two parts make a whole - and the whole can split into parts." That sentence is the heart of the model. Number sentences and worksheets are later jackets for the same idea.

Australian Curriculum Mathematics (version 9) builds partitioning and part–part–whole reasoning strongly across Foundation to Year 2 (Foundation–Year 2). Classroom labels vary (part-part-whole, part–whole, partitioning, bar model, cherry model); echo your child's teacher.

Concrete first: bars, circles, and counters

Counter story. Put eight crackers on a plate (the whole). Slide five to one side and three to the other. Name: "Whole is eight. Parts are five and three." Push them back together. Split differently: six and two, four and four, seven and one. Same whole, different parts.

Bar (or strip) model. Draw a long rectangle for the whole. Draw a line that splits it into two sections. Write the whole above; write each part in a section. Leave one box blank for "missing part" stories. Many Australian worksheets look like this.

Circles / cherry model. Two small circles (parts) connected to a larger circle (whole). Fill any two; find the third. Useful when the worksheet wants a "diagram" rather than a bar.

Ten-frame as a part-part-whole stage. Seven counters on a ten-frame leave three empty spaces - one part shown, the other part visible as empty. That picture feeds number bonds and later make-ten.

Keep sessions under ten minutes. Celebrate the relationship ("five and three make eight, so eight take away three is five"), not only filling boxes.

Not the same as split-add-join or make-ten

Parents often hear three labels in one week and wonder if they are the same thing.

• Part-part-whole is the picture / relationship: parts join to a whole; the whole splits into parts. It works for addition and subtraction stories.
• Number bonds are the known pairs that live inside that picture (especially friends of ten: 7 + 3, 8 + 2, and so on).
• Make-ten bridging is a strategy: split one addend toward ten (8 + 5 → take 2 from the 5 to make 10, then add 3). It uses part-part-whole and bonds; it is not the model itself.
• Split-add-join is a wider partitioning addition habit: split an addend into friendly chunks, add the parts, join the total (not only bridge-to-ten).

This page owns the model. Bonds own the pairs. Make-ten and split-add-join own the strategies that lean on the model. Link them gently: "First see parts and whole; then use a strategy when the numbers get bigger."

How part-part-whole fuels addition and subtraction

Addition is often "parts → whole": you know both parts; find how many altogether (addition explained).

Subtraction is often "whole and one part → other part": you know the whole and what was taken (or how many are left); find the missing piece (subtraction explained).

Same diagram, different blank. That is why teachers draw one bar for both operations. Children who only memorise "plus means put together" without the reverse story struggle when worksheets hide a part.

Comparing sits nearby but is a different job: more / less / same between two amounts (comparing numbers). You might use part-part-whole when asking "how many more?" (the difference is a part), but comparing itself is the more-less-equal page.

Place value later treats tens and ones as parts of a larger whole (place value): 47 is 4 tens and 7 ones - partitioning with bigger parts. Early PPW trains that "numbers can split and rejoin" muscle.

Year by year: where part-part-whole shows up

Prep - after children can count a set and say how many (Prep maths), many classes partition small collections (make 5 or 6 in different ways) with counters and talk. Formal bars may be light; spoken "parts and whole" is the win.

Year 1 - part-part-whole diagrams and bonds to 10 become regular; missing-part stories; early make-ten appears (Year 1 maths, number bonds, make-ten bridging).

Year 2 - firmer use of the model for two-digit partitioning, bridging, and difference stories; strategies like split-add-join lean on the same picture (Year 2 maths, split-add-join).

If wobbles sit inside a broader worry, see Is my child behind in maths?, maths anxiety, and homework without tears.

Common mix-ups (and kinder fixes)

Thinking part-part-whole is only addition. Fix: hide one part. "Whole is 9, one part is 4 - what's the other part?" That is subtraction language on the same diagram.

Confusing the model with make-ten or split-add-join. Fix: ask "Are we naming parts and whole, or are we using a strategy to add?" Point to the right guide.

Only filling boxes without objects. If the child cannot show 6 and 2 making 8 with counters, pause the worksheet. Build the story first; then copy it onto the bar.

Assuming the two parts must be different. Equal parts are fine: 4 and 4 make 8. Doubles are a special case of the same model.

Racing to three-part wholes before two-part is steady. Some later sheets show three parts. Stay with two parts until "parts make whole / whole splits" is automatic.

Mixing with comparing symbols. < > = belong to comparing numbers. Part-part-whole is about composing and decomposing a single total, not deciding which of two totals is larger.

Home games that do not feel like worksheets

Plate split. Count a small snack pile (the whole). Child splits into two plates and names both parts. Rejoin. Split a different way.

Cover one part. Show eight counters; cover three with a cup. "How many are under the cup?" (Missing-part story.)

Bar blank. Draw a bar; write the whole on top; fill one part; child finds the other. Swap roles.

Story swap. You say an addition story ("5 red cars and 3 blue - how many?"); child draws the bar. Then you give a take-away story with the same numbers.

Bond flash inside the model. Flash a friends-of-ten pair; child places both parts under a whole of 10 on a ten-frame or bar - see number bonds.

Keep each game under ten minutes. Stop while it is still friendly.

A simple weekly home routine

1. Two minutes of naming - show a whole; name two parts (or hide one part and find it).
2. Five minutes of one game - plate split, cover one part, or bar blank.
3. Three minutes of a soft strategy link - for ready children, one make-ten or friendly split story that uses the same picture - see make-ten bridging or split-add-join.

If nights fray, shorten further - see homework without tears.

How this links to other guides

• Number bonds explained for parents - pairs that live inside the part-part-whole picture
• Addition explained for parents - parts → whole joining journey
• Subtraction explained for parents - whole and one part → other part
• Split-add-join explained - partitioning addition strategy that uses this model
• Make-ten bridging explained for parents - bridge-to-ten strategy that uses this model
• Place value explained for parents - tens and ones as parts of a larger whole
• Comparing numbers explained for parents - more/less/same between two amounts; different job
• Prep–Year 2 maths - year maps where partitioning sits
• Maths Help hub - more parent guides

Ask the teacher: "Do you introduce part-part-whole with counters and a bar or circle diagram first - and when do you link it to make-ten or split-add-join?" Matching language reduces crossed wires.

FAQ

Is part-part-whole the same as number bonds?

No. Part-part-whole is the model (parts and whole). Number bonds are the pairs that fit that model (especially to 10 and 20). Bonds live inside PPW (number bonds).

Is it the same as make-ten or split-add-join?

No. Those are strategies for adding that lean on part-part-whole thinking. This page owns the relationship picture; those pages own the moves (make-ten bridging, split-add-join).

Does part-part-whole help subtraction too?

Yes. Knowing both parts and the whole lets children find a missing part - the core of many subtraction stories (subtraction explained).

Do we need special materials?

No. Counters, pasta, snack pieces, a drawn bar, or two plates are enough. A ten-frame helps for bonds to 10.

A calm next step

When "two parts make a whole" feels settled and you want a wider number-skill snapshot at home, Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet early number skills at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.

Part-part-whole is the model; flexible splits of a number (e.g. 47 as 40+7) are partitioning explained for parents.

Part–part–whole diagrams help story problems — see word problems for parents.