The diagram shows whether you are finding the total, a leftover, or a missing part.
Explain your thinking: Say what each part of the model represents, then explain why the answer or conclusion follows.
Choose an operation from the situation
Represent an additive problem, solve it and say what the answer means.
Worked example
A game needs 15 counters. There are 9 on the table. How many more are needed?
Draw a bar for the total of 15. Mark the 9 already there and leave the missing part blank.
Count on from 9 to 15: one to reach 10, then five more. That is six altogether.
Six more counters are needed. Check: 9 + 6 = 15.
Watch for this mistake: The words ‘more’ do not always mean add the two numbers given. Ask what is known and which part is missing.
Try it, then explain
A book costs $7. You pay with $10. How much change should you receive?
Hint
Find the missing part between 7 and 10.
Answer and explanation
$3. The $7 cost and $3 change together equal the $10 paid.
There are 8 red blocks and 5 blue blocks. Draw a model and find the total.
Hint
Both coloured groups are parts of one total.
Answer and explanation
13 blocks; 8 + 5 = 13.
Australian Curriculum elaborations
These curriculum examples extend the central model into varied contexts. They are learning contexts, not extra definitions to memorise.
E1
modelling problems involving addition and subtraction presented in stories, using a Think Board to represent the problem, solving the problem using physical materials and explaining the connections between any materials used, the Think Board diagram and the numbers within the story
Try and explain: A box holds 13 crayons. Eight are blue and the rest are red. How many are red?
Answer and teaching point
Five are red. Show a whole of 13 split into eight and the missing part; 13 − 8 = 5 or 8 + 5 = 13.
E2
modelling simple money problems involving addition and subtraction using whole dollar amounts; for example, setting up a shop and role-playing practical problems of buying and selling of goods, using addition and subtraction with play money and prices in whole dollar amounts; solving the problem “I had \$14 and was given \$15 for my birthday” using addition to answer the problem
Try and explain: At a pretend shop, a notebook costs $6 and a pen costs $3. You pay $10. How much change is due?
Answer and teaching point
The cost is $9, so the change is $1. Check that $9 + $1 equals the $10 paid.
E3
modelling a variety of different additive situations to solve practical problems; for example, keeping track of the number of people on a bus as it stops to pick up and drop off passengers or the number of people entering a lift
Try and explain: A bus has nine passengers. Four get off and six get on. How many are on the bus now?
Answer and teaching point
9 − 4 = 5, then 5 + 6 = 11 passengers. Account for both changes in the correct order.
Common misconceptions and traps
Number grabbing — Read the story before choosing an operation.
Money answer without units — Use cents or dollars in the answer.
Ignoring missing part problems — Sometimes subtraction is solved by thinking addition: 6 + ? = 10.
Guided learning activities
Shop model
Use play coins to solve a simple buying and change problem.
Model: 10c − 6c = 4c
Bar model
Draw parts and whole for an additive story.
Model: part + part = whole
Explain the operation
Say why you added or subtracted before giving the answer.
Model: I subtracted because...
Revision Notes
Key idea: Additive problems can involve joining, taking away, comparing or finding a missing part. Diagrams and materials help decide what to do.
Remember
Model additive stories
Use diagrams/materials
Solve money problems
Choose operations
Check units
Quick questions
A toy costs 8c. You pay 10c. What is the change?
What diagram helps with two parts and a whole?
When does a story need subtraction?
Why should the answer include units?
Return to the concept model if an answer is uncertain. Use the model to explain, not just to guess.
Official curriculum reference
AC9M1N05: use mathematical modelling to solve practical problems involving additive situations including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem
Use the Practice Sheet for written or hands-on work, Practice for supported feedback, and Test when the student is ready to demonstrate independent mastery.
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Khan Academy — Use a picture and addition to solve a small real-world joining problem.
As you watch: Which two groups are being joined, and what does the total count?
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Try it: Draw 4 apples and then 3 more. Write a matching addition sentence and explain the answer in words.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Additive problem solving and money
Mapped skill: use mathematical modelling to solve practical problems involving additive situations including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M1N05 — Additive Problem Solving and Money