AC9M1N05_E1
Model addition and subtraction problems presented in stories using a Think Board, solve the problem with physical materials and explain the connections between the materials, the Think Board diagram and the numbers in the story.
About This Year 1 Maths Topic
Mathematical modelling helps students use mathematics to solve practical problems from everyday life. In Year 1, students represent additive situations with diagrams, physical and virtual materials, number sentences and spoken explanations.
Students use Think Boards to organise their thinking and show the same problem in several ways. They identify the important numbers in a story, decide whether to add or subtract, choose a suitable strategy and explain how their representation connects to the context.
Simple money problems provide meaningful opportunities to use addition and subtraction. Classroom shops, buying and selling role-play, whole-dollar prices and play money help students see how mathematics is used in familiar situations.
Other practical contexts include people getting on and off a bus, entering and leaving a lift, joining a group, sharing classroom resources and keeping track of changing quantities.
These activities support the Australian Curriculum Version 9.0 content descriptor AC9M1N05 and its associated elaborations.
Australian Curriculum Alignment
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.
AC9M1N05_E2
Model simple money problems involving addition and subtraction using whole-dollar amounts, including classroom shops, buying and selling role-play, play money and practical money stories.
AC9M1N05_E3
Model a variety of additive situations to solve practical problems, such as tracking the number of people on a bus as passengers get on and off or the number of people entering and leaving a lift.
Learning Intentions
Students will learn to:
- identify the important information in a practical problem;
- decide whether a situation involves addition or subtraction;
- represent a problem using physical and virtual materials;
- use diagrams and Think Boards to organise their thinking;
- choose a suitable calculation strategy;
- solve simple money problems using whole-dollar amounts;
- use play money to model buying and selling;
- track changing quantities in real-life situations;
- connect the story, materials, diagram and number sentence;
- explain and check a solution.
Student Success Criteria
I can identify what the problem is asking.
I can find the important numbers in a story.
I can decide whether to add or subtract.
I can model a problem using materials.
I can use a Think Board.
I can solve a simple money problem.
I can use play money to show buying and selling.
I can track how a quantity changes.
I can explain how my model matches the story.
I can check whether my answer makes sense.
Key Vocabulary
problem
model
represent
strategy
diagram
Think Board
addition
subtraction
money
dollar
price
buy
sell
total
change
altogether
left
solution
Teacher Guide
Recommended Materials
- counters, cubes, buttons or bottle caps;
- toy people, vehicles and classroom objects;
- Think Board templates;
- story problem cards;
- number lines and ten-frames;
- part-part-whole mats;
- play Australian one-dollar coins;
- classroom shop items and price labels;
- shopping baskets or paper bags;
- bus and lift picture mats;
- mini whiteboards and markers;
- virtual manipulatives or digital modelling tools.
Suggested Teaching Sequence
- Begin with practical stories using familiar classroom contexts.
- Ask students to identify what is changing in the situation.
- Highlight the important numbers and the question being asked.
- Model the story with physical materials.
- Represent the same problem on a Think Board.
- Choose and apply an addition or subtraction strategy.
- Connect the materials, diagram and number sentence.
- Introduce whole-dollar money problems through shop role-play.
- Use bus, lift and group stories to model changing quantities.
- Ask students to explain and check whether the answer makes sense.
Teacher Questions
- What is happening in the story?
- What do we need to find out?
- Which numbers are important?
- Is the quantity increasing or decreasing?
- Should we add or subtract?
- How can you model the problem with materials?
- What could you draw on the Think Board?
- Which calculation strategy will you use?
- What does each number represent?
- How does your number sentence match the story?
- Does your answer make sense?
- Can you solve the problem another way?
Common Misconceptions
Choosing an operation from a single keyword
Focus on what is happening to the quantity rather than relying only on words such as more, left or altogether.
Using every number in the story without checking relevance
Ask students which numbers help answer the question and whether any information is unnecessary.
Drawing a diagram that does not match the story
Compare each part of the diagram with the people, objects or actions described in the problem.
Confusing the number of coins with their total value
Begin with one-dollar coins so one coin represents one dollar. Match each coin to one dollar in the price or total.
Forgetting that quantities can increase and decrease during one scenario
Use a bus or lift mat and physically add or remove figures at each stage before calculating the final amount.
Giving an answer without explaining the model
Ask students to describe how the materials, diagram and number sentence each represent the same situation.
Year 1 Maths Word Problems and Money Activities
Activity 1: Build the Story Problem
Read a simple addition or subtraction story. Students use counters, cubes or toy figures to model what happens.
They explain which objects represent each number in the story.
Curriculum connection: AC9M1N05_E1
Activity 2: Think Board Modelling
Students represent a story problem using materials, a picture, a number sentence and a written or spoken explanation.
Compare the four representations and identify how they are connected.
Curriculum connection: AC9M1N05_E1
Activity 3: Match the Story to the Model
Provide story cards, diagrams and number sentences. Students match the representations that describe the same problem.
Ask students to justify each match.
Curriculum connection: AC9M1N05_E1
Activity 4: Classroom Shop
Set up a shop with items priced in whole-dollar amounts. Students use play one-dollar coins to buy and sell items.
Create addition and subtraction questions based on each transaction.
Curriculum connection: AC9M1N05_E2
Activity 5: Birthday Money Problem
Model a story such as, “I had $14 and was given $15 for my birthday.” Students represent the two amounts and combine them.
Record and explain the addition strategy used.
Curriculum connection: AC9M1N05_E2
Activity 6: Buy Two Items
Students choose two whole-dollar items from the classroom shop and calculate the total cost.
They model the transaction with play money and record the matching number sentence.
Curriculum connection: AC9M1N05_E2
Activity 7: Bus Stop Problem
Use a toy bus and figures. Add passengers at one stop and remove passengers at the next.
Students keep track of the changing number and determine how many passengers remain.
Curriculum connection: AC9M1N05_E3
Activity 8: Lift In and Out
Place figures in a pretend lift. At each floor, some people enter and others leave.
Students model each change and record the final number of people in the lift.
Curriculum connection: AC9M1N05_E3
Activity 9: Create a Real-Life Problem
Students create their own practical addition or subtraction problem using a familiar classroom, playground, transport or shopping context.
A partner models and solves the problem using a Think Board.
Curriculum connection: AC9M1N05
Activity 10: Does the Answer Make Sense?
Present a solved practical problem with a correct or incorrect answer.
Students use materials, estimation or another strategy to check the solution and explain their decision.
Curriculum connection: AC9M1N05
Differentiation
Support
- use one-step problems with numbers within 10;
- read the story aloud one sentence at a time;
- use real objects and familiar classroom contexts;
- highlight the important numbers and question;
- provide partially completed Think Boards;
- use only one-dollar coins in money tasks;
- allow students to act out the problem;
- provide sentence starters and adult scribing;
- check each representation before calculating.
Extension
- include two-step practical problems;
- add irrelevant information to selected problems;
- ask students to compare two different models;
- use missing-number situations;
- create shop problems involving several items;
- solve problems using more than one strategy;
- write original Think Board problems for classmates;
- justify why a selected strategy is efficient;
- check solutions using inverse operations.
Mathematical Sentence Starters
The problem is asking me to find _____.
The important numbers are _____ and _____.
The quantity is increasing because _____.
The quantity is decreasing because _____.
I chose addition because _____.
I chose subtraction because _____.
My materials show _____.
My Think Board diagram shows _____.
The number sentence is _____.
The total cost is _____ dollars.
There are _____ people left.
My answer makes sense because _____.
Assessment Ideas
Observe whether the student can:
- identify the question and important information;
- decide whether to add or subtract;
- model a story problem using materials;
- represent the problem on a Think Board;
- choose and apply a calculation strategy;
- solve whole-dollar money problems;
- model buying and selling using play money;
- track changing quantities in a practical context;
- connect the story, diagram, materials and number sentence;
- check and explain whether the answer is reasonable.
Quick Exit Ticket
- Read a short practical addition or subtraction story.
- Model it using counters or play money.
- Draw one Think Board representation.
- Record and explain the solution.
Printable Teacher and Student Resources
Use the buttons below to open the available AC9M1N05 teaching materials and printable activities in a new browser tab.
Main Worksheets
Problem Solving Activities
Think Board Word Problems
Story Problem Modelling
Money Word Problems
Buying and Selling Activities
Real-Life Problem Solving
Bus and Lift Word Problems
Resources open in a new tab. Browser PDF settings may affect whether a file opens in the browser or downloads.
Home Learning Ideas
Families can practise mathematical modelling through everyday situations involving shopping, toys, food, transport, visitors and household objects.
Create a short problem, act it out with objects or play money and ask the child to explain how their model matches the story.
Ask questions such as:
- What is the problem asking?
- Which numbers are important?
- Are we adding or subtracting?
- How could you model the problem?
- What could you draw?
- How much do the items cost altogether?
- How many people are left?
- What number sentence matches the story?
- Does your answer make sense?