Free Printable Year 2 Mathematical Modelling Worksheets

About This Year 2 Maths Topic

Mathematical modelling means using mathematics to understand and solve practical situations.

Children learn that solving a real-life problem involves more than completing a calculation. They need to understand the situation, decide which information is important, choose a suitable operation and explain what the answer means.

The practical situations in this unit may involve:

• buying items and calculating totals or change;
• collecting equal whole-dollar contributions;
• forming teams for games or sporting activities;
• sharing food or money equally;
• making equal groups;
• deciding what to do with a remainder;
• using a calendar to count days;
• representing grouping and sharing situations with number sentences.

Children may use addition, subtraction, multiplication or division depending on the relationship between the quantities.

These activities support Australian Curriculum Version 9.0 content descriptor AC9M2N06 and its associated elaborations.

The Big Idea for Parents

For example, a shopping problem might require:

• addition to find the total cost of several purchases;
• subtraction to find how much money remains;
• multiplication to find the cost of several equal-priced items;
• division to share an amount equally.

A complete solution should include the calculation and an explanation of what the answer represents.

The Year 2 Mathematical Modelling Process

1. Understand the practical situation.
2. Identify the known and unknown information.
3. Represent the problem with objects, drawings, diagrams or number sentences.
4. Choose an appropriate operation and calculation strategy.
5. Complete the calculation.
6. Check whether the answer is reasonable.
7. Interpret the answer in the context of the problem.
8. Communicate the solution clearly.

Learning Intentions

Children will learn to:

• identify the important information in a practical problem;
• decide what needs to be found;
• represent situations using objects, diagrams and number sentences;
• choose between addition, subtraction, multiplication and division;
• justify the choice of operation;
• select an efficient calculation strategy;
• solve whole-dollar money problems;
• calculate totals and amounts remaining;
• solve equal contribution problems;
• form teams and equal groups;
• share quantities equally;
• interpret remainders in practical situations;
• use calendars to count days;
• check whether an answer is reasonable;
• communicate a solution using the correct unit and context.

Student Success Criteria

Key Vocabulary

Teacher Guide for Parents

Teachers encourage children to think about the meaning of a problem before beginning a calculation.

At home, follow this sequence: understand it, represent it, choose, calculate, check and explain.

1. Read and Retell the Problem

Ask your child to read the problem and explain it in their own words.

Avoid beginning with: “Is this addition or subtraction?”

Instead ask:

• What is happening?
• What quantities are involved?
• What do we already know?
• What do we need to find?

2. Identify the Known and Unknown Information

Underline or list the quantities that are known.

Circle or describe the unknown quantity.

For example:

“A child has $20 and spends $7. How much money remains?”

• known starting amount: $20;
• known amount spent: $7;
• unknown amount: money remaining.

3. Decide Whether the Situation Is Additive or Multiplicative

Additive situations involve joining, separating or comparing quantities.

Multiplicative situations involve repeated equal quantities, equal groups or sharing.

Examples:

• combining the costs of two purchases is additive;
• finding the cost of 4 items at $5 each is multiplicative;
• sharing $36 equally among 4 people is multiplicative;
• finding money left after spending is additive.

4. Choose and Justify the Operation

Ask your child to explain why the chosen operation matches the relationship in the problem.

Other explanations may include:

• “I used addition because two amounts were being combined.”
• “I used multiplication because there were equal groups with the same amount in each group.”
• “I used division because the total was being shared equally.”

5. Represent the Situation

Children may represent practical problems using:

• physical materials;
• play money;
• drawings;
• bar models;
• part-part-whole diagrams;
• arrays;
• equal-group diagrams;
• number lines;
• calendars;
• number sentences.

A representation should show the mathematical relationship, not simply decorate the page.

6. Solve Shopping Problems

Create a pretend shop using whole-dollar prices.

Ask questions such as:

• What is the total cost of two items?
• How much money remains after a purchase?
• How much do 4 identical items cost?
• How many equal-priced items can be purchased?

Encourage your child to explain which operation is needed for each question.

7. Solve Whole-Dollar Addition Problems

Example:

“A book costs $8 and a game costs $12. What is the total cost?”

The amounts are being combined:

$8 + $12 = $20

The answer should be communicated as: “The total cost is $20.”

8. Solve Whole-Dollar Subtraction Problems

Example:

“Sam has $30 and spends $18. How much money remains?”

The amount spent is removed from the starting total:

$30 − $18 = $12

The answer is: “Sam has $12 remaining.”

9. Solve Equal-Contribution Money Problems

Example:

“Each of 6 children contributes $5. How much money is collected?”

Represent the problem as equal groups:

$5 + $5 + $5 + $5 + $5 + $5 = $30

Children may use repeated addition, skip counting or multiplication reasoning.

10. Form Teams for a Game

Give your child a class total and a proposed team size.

For example:

“There are 24 children. Each team needs 4 players. How many teams can be formed?”

Make groups of 4 until all 24 children have been placed:

6 teams can be formed.

11. Decide How Many People Should Be in Each Team

The question may instead provide the number of teams.

Example:

“There are 24 children and 6 teams. How many children should be in each team?”

Share 24 equally among 6 teams:

There should be 4 children in each team.

Compare this problem with the previous example. The same quantities are involved, but the unknown is different.

12. Interpret Remainders

Some practical division problems do not divide evenly.

Example:

“There are 26 children and teams need 4 players.”

Six complete teams can be formed, with 2 children remaining.

Ask what should happen in the real situation.

• Could two teams have an extra player?
• Could the team size be changed?
• Could the remaining children take another role?
• Is an incomplete team acceptable?

13. Share Food or Money Equally

Use counters, pretend food pieces or play money to model equal sharing.

Example:

“Share $20 equally among 4 people.”

Each person receives $5.

Ask your child to explain:

• the starting total;
• the number of people;
• the amount each person receives;
• how they checked that the sharing was fair.

14. Use a Calendar to Count Days

Use a current or sample calendar to solve questions involving days, weeks and months.

To answer “How many days are left in the year?”:

1. identify today’s date;
2. count the remaining days in the current month;
3. add the days in each remaining full month;
4. decide whether today is included in the count;
5. state the final answer clearly.

15. Use First Nations Australian Games Respectfully

The curriculum includes opportunities to explore equal grouping and sharing through First Nations Australian children’s instructive games, including the example of Yangamini from the Tiwi Island Peoples.

Use trusted educational resources that explain the game and its cultural context accurately.

Focus the mathematical discussion on:

• the number of participants;
• how groups are formed;
• whether the groups are equal;
• the matching number sentence;
• what the solution represents in the game context.

16. Check Whether the Answer Is Reasonable

Ask your child to estimate or compare the answer with the quantities in the problem.

For example:

• if money was spent, the remaining amount should be less than the starting amount;
• if several equal contributions were combined, the total should be greater than one contribution;
• if a collection was shared, the amount in each group should be less than the original total.

17. Communicate the Solution in Context

Encourage complete answers rather than isolated numbers.

Instead of:

6

write:

Six teams can be formed.

Instead of:

$9

write:

Each person receives $9.

Recommended Teaching Sequence at Home

1. Read and retell the problem.
2. Identify the known and unknown information.
3. Decide whether the situation is additive or multiplicative.
4. Represent the situation with materials or a diagram.
5. Choose and justify an operation.
6. Select an appropriate calculation strategy.
7. Calculate the solution.
8. Check whether the answer is reasonable.
9. Interpret any remainder.
10. Write the answer using the correct unit and context.

Common Misconceptions and How Parents Can Help

Simple Home Mathematical Modelling Activities

Questions Parents Can Ask

• What is happening in this situation?
• What information do we know?
• What do we need to find?
• Which information is important?
• Is this an additive or multiplicative situation?
• Which operation matches the relationship?
• Why did you choose that operation?
• Can you represent the problem with objects?
• Can you draw a diagram or bar model?
• What number sentence matches the situation?
• Which calculation strategy will you use?
• What does each number represent?
• What does the answer represent?
• Is there a remainder?
• What should happen to the remainder?
• Does your answer need a dollar sign?
• Does your answer need another unit?
• Is the answer reasonable?
• How could you check the calculation?
• Can you communicate the solution in a complete sentence?

Mathematical Sentence Starters

Supporting Different Learners at Home

Children Who Need More Support

• use one-step practical problems;
• use small whole-number and whole-dollar amounts;
• read the problem aloud together;
• act out the situation with objects;
• highlight the known and unknown information;
• provide operation-choice cards;
• use play money and calendars;
• provide a partially completed diagram;
• use problems without remainders first;
• allow oral explanations before written responses.

Children Ready for Extension

• solve problems with unnecessary information;
• compare two possible operation choices;
• solve two-step practical problems;
• design their own shop and price list;
• create problems with different types of remainders;
• explain why different contexts require different remainder decisions;
• represent one problem in several ways;
• find and correct an unreasonable solution;
• create a calendar problem for another learner;
• write a complete mathematical modelling explanation.

Quick Parent Check

Use these questions to check whether your child understands the main ideas.

1. Two items cost $8 and $13. Choose an operation and find the total cost.
2. A child has $30 and spends $17. Find the amount remaining.
3. Five children each contribute $4. Find the total amount.
4. Share $24 equally among 4 people.
5. Form teams of 5 from a group of 22 children.
6. Explain what should happen to the 2 children remaining.
7. Draw a diagram for one of the practical problems.
8. Write a matching number sentence.
9. Use a calendar to count the days remaining in a chosen month.
10. Explain what the final answer represents in context.

A child shows secure understanding when they can interpret the situation, choose and justify an operation, calculate accurately and communicate the solution using the correct context and unit.

Quick Exit Ticket

1. Choose an operation to solve a whole-dollar shopping problem.
2. Solve a team-grouping problem and interpret any remainder.
3. Write one sentence explaining what the answer represents.

Printable Teacher, Parent and Student Resources

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Home Learning Summary

Mathematical modelling develops when children regularly solve meaningful problems and explain the connection between the calculation and the practical situation.

Use this simple routine:

1. understand the situation;
2. identify the known and unknown information;
3. represent the problem;
4. choose and justify an operation;
5. calculate and check;
6. interpret the answer;
7. communicate the solution clearly.

Related Foundation, Year 1 and Year 2 Maths Topics

Children who need additional support can revisit these earlier number, money, grouping and calculation topics.