Worded Problems �Years 2 - 6

28 October 2025

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MACS Mathematics Webinar Series 2025

Acknowledgement of Country

We acknowledge that MACS offices and Catholic schools in the Archdiocese of Melbourne are situated on the lands of the five language groups that make up the Kulin Nations, who have walked upon and cared for this land since time immemorial. We acknowledge their continued deep spiritual connection and relationship to Country.

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We pay respects to their Elders past, present and future, and commit to the ongoing journey of truth-telling and deep listening, working together for reconciliation and justice.

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Chelsea Sporle

St Anne’s School, Sunbury, Year 4

Amen

Giver of all wisdom and greatest of all teachers, look upon our teachers with love.

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Bless their hearts for they rejoice when we succeed and encourage us too when we fall and bless them with gentle patience for the path of learning is never easy.

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Instil in them a commitment to keep on learning, it shows us to not fear new knowledge and experiences.

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Inspire them to touch the future, they influence how big a dream we dream for ourselves.

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Let the light of your example shine upon all teachers

Pour Your Love

Year 1/2 Collaborative Artwork

Sacred Heart Primary School, Oakleigh

MACS Creative Art Show 2023

Attendance

Welcome

Please keep your microphone on mute.

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Please register your attendance using the QR code at the top of this slide.

�A copy of the slides will be provided to all registered participants after the presentation.

�This webinar will finish at approximately 4:30pm, followed by an optional Q&A session.

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Questions will be addressed during the Q & A session

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Attendance

Learning Intentions����

In this webinar, we will:

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• define worded problems and unpack its place in the Victorian Curriculum Mathematics V2.0 in Years 2-6 and the MACS Vision for Instruction

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• explore keywords - the impact on understanding worded problems and the importance of explicit instruction of vocabulary and language

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• explore attack strategies to support approaching worded problems

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• unpack the different worded problem types

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• share possible resources for teaching worded problems.

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Lee, B., & Powell, S. (2024 – Present) [Audio podcast] S02E05 - Sarah Powell On Effective Word Problem Instruction - Learning with Mr. Lee

…word problems help students apply the mathematics they are learning, develop critical thinking skills, and begin to connect mathematics to a variety of scenarios or contexts.

Institute of Education Sciences. (2021, March). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades. Institute of Education Sciences. Retrieved June 13, 2025, from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/WWC2021006-Math-PG.pdf

• Use problem-solving strategies: Explicitly teach problem-solving and reasoning strategies. Teach students how to read problems and organise work according to the structure of the problem.

Victorian Curriculum Mathematics V2.0

Proficiency in Mathematics

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• Understanding
• Fluency
• Reasoning
• Problem-solving

Worded problems

Victorian Curriculum Mathematics V2.0

Strands

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• Number
• Algebra
• Measurement
• Space
• Statistics
• Probability (3 -6)

Worded problems

Possible Problem-Solving Strategies

Key words and vocabulary

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Attack strategies

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Word problem types

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Challenges of Worded Problems in Mathematics

What do students need to do?

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• Read the problem
• Understand the problem context
• Identify the important versus the extraneous information
• Identify the unknown information to be solved
• Translating words into number equations
• Understand vocabulary
• Identify appropriate operations
• Choose a strategy to solving the problem
• Solve the problem correctly

Stevens, E. A., Leroux, A. J., Mowbray, M. H., & Lee, G. S. (2022). Evaluating the Effects of Adding Explicit Vocabulary Instruction to a Word-Problem Schema Intervention. Exceptional Children, 89(3) https://doi.org/10.1177/00144029221112290

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Key Words as a Problem-Solving Strategy

NAPLAN Year 3 Question 9 2016

https://kmhs.typepad.com/files/math---keywordsusedinmathwordproblems.pdf

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Key Words as a Problem-Solving Strategy

NAPLAN Year 5 Question 35 2015

https://kmhs.typepad.com/files/math---keywordsusedinmathwordproblems.pdf

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Key Words as a Problem-Solving Strategy

https://kmhs.typepad.com/files/math---keywordsusedinmathwordproblems.pdf

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NAPLAN Year 3 Question 3, 2016

Sample Key Words, Associated Operations and Key Word Fails

Powell, S& Fuchs, L Effective word problem instruction using schemas to facilitate Mathematical Reasoning EJ1190453.pdf

Regardless of the problem type, students need an “attack” strategy for working through the problem….

Sarah Powell

“Attack” Strategies

• An attack strategy is an easy-to remember series of steps students use to guide their approach to solving word problems.

Powell, S., King, S., & Benz, S. (2024, February 1). Maths Practices You Can Count On: Five Research-Validated Practices in Mathematics. The Centre for Independent Studies. Retrieved August 22, 2025, from https://www.cis.org.au/publication/maths-practices-you-can-count-on-five-research-validated-practices-in-mathematics/

“Attack” strategies

• Ochre uses a variety of “attack” strategies
• One is the commonly used attack strategy CUBES

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Ochre Year 3_ Addition and Subtraction 3 - Using the CUBES strategy to solve addition problems

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“Attack” strategies

• Ochre uses a variety of “attack” strategies
• One is the commonly used attack strategy CUBES
• Another “attack” strategy outlines the key steps to solve a worded problem

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Ochre Year 5 – Fractions 2 - Solving addition and subtraction worded problems with fractions (related denominators)

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Key components of a good “attack” strategy

1. Read the problem

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• Plan

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• Solve

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• Check/Review

This needs to be the first component of any attack strategy

This may include:

• Drawing a diagram
• Using manipulatives
• Using a graphic organiser
• Talking through their thinking

Powell, S. (2018, October 3). Word Problem Attack Strategies. Retrieved from Project STAIR: Supporting Teaching of Algebra: Individual Readiness: https://blog.smu.edu/projectstair/2018/10/03/word-problem-attack-strategies/

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Some other “attack” strategies

1. Read the problem

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• Plan

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• Solve

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• Check/

Review

“Attack” Strategies

• Attack strategies help students address all parts of a word problem

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• Acronyms support memory of strategy steps.

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• Explicit teaching of each acronym component is essential.

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• Ongoing use of the strategy must be reinforced

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• Consistent attack strategies are recommended across the school

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Powell, S., King, S., & Benz, S. (2024, February 1). Maths Practices You Can Count On: Five Research-Validated Practices in Mathematics. The Centre for Independent Studies. Retrieved August 22, 2025, from https://www.cis.org.au/publication/maths-practices-you-can-count-on-five-research-validated-practices-in-mathematics/

Effective Use of Attack Strategies in Word Problem Instruction

• Model Explicitly: Clearly demonstrate the chosen attack strategy and explain how it works.

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• Scaffold Learning: Reduce support gradually to help students internalise the strategy.

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• Practice with Feedback: Provide frequent opportunities for application with corrective feedback.

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• Adapt to Student Needs: Tailor modelling, practice, and feedback based on student knowledge and instructional quality.

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Using Schemas or Problem Types to solve worded problems

Schemas

or

Problem Types

Powell, Sarah R., and Lynn S. Fuchs. “Effective Word-Problem Instruction: Using Schemas to Facilitate Mathematical Reasoning.” TEACHING Exceptional Children, vol. 51, no. 1, 7 June 2018, pp. 31–42, https://files.eric.ed.gov/fulltext/EJ1190453.pdf

Additive Schemas - Combine

Additive Schemas - Combine

15 apples are on the table. 3 apples are red and the rest are green. How many apples are green?

15

3

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12

3 + = 15

12

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12 apples are green

Additive Schemas - Compare

Additive Schemas – Compare/Difference

Caterina has 32 apples. Jan has 15 apples. How many more apples does Caterina have?

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15

Jan

32

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Caterina

17

32 - 15 =

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17

Caterina has 17 more apples than Jan

Additive Schemas - Change

Additive Schemas - Change

Linda had some money, and then she earned $24 babysitting. Now Linda has $53. How much money did Linda have to start with?

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$53

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+$24

$29

+ $24 = $53

Linda had $29 dollars at the start.

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$29

Multiplicative Schemas – Equal groups

Multiplicative Schemas – Equal Groups

Mark bought 60 eggs. The eggs were sold in cartons with 12 eggs in each carton. How many cartons of eggs did Mark buy?

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60

12

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5

Mark bought 5 cartons of eggs

Multiplicative Schemas - Comparison

Multiplicative Schemas – Comparison

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Kyla picked 3 times as many flowers as Jo. If Kyla picked 21 flowers, how many flowers did Jo pick?

21

3

?

7

Jo picked 7 flowers

Multiplicative Schemas - Proportions

Year 7 & 8

Secondary Mathematics

Multiplicative Schemas - Ratio

Year 7 & 8

Secondary Mathematics

Identifying Schemas – What do you ask yourself?

Powell, S., & Berry, K. (n.d.). Pirate Math Equation Quest Supplemental Materials. Retrieved September 3, 2025, from https://www.piratemathequationquest.com/docs/PMEQ-2C-Supplemental-Materials.pdf

The University of Texas. (2025). SPIRAL Word Problems with Set/Comparison Schema (Video). Youtu.be. https://youtu.be/oaGkVMIl1H0

Schema sort

In the chat identify which problem type each question is.

Powell, S., & Berry, K. (n.d.). Pirate Math Equation Quest Supplemental Materials. Retrieved September 3, 2025, from https://www.piratemathequationquest.com/docs/PMEQ-2C-Supplemental-Materials.pdf

The University of Texas. (2025). SPIRAL Word Problems with Set/Comparison Schema (Video). Youtu.be. https://youtu.be/oaGkVMIl1H0

Schema sort

Powell, S., & Berry, K. (n.d.). Pirate Math Equation Quest Supplemental Materials. Retrieved September 3, 2025, from https://www.piratemathequationquest.com/docs/PMEQ-2C-Supplemental-Materials.pdf

The University of Texas. (2025). SPIRAL Word Problems with Set/Comparison Schema (Video). Youtu.be. https://youtu.be/oaGkVMIl1H0

Schema sort

Powell, S., & Berry, K. (n.d.). Pirate Math Equation Quest Supplemental Materials. Retrieved September 3, 2025, from https://www.piratemathequationquest.com/docs/PMEQ-2C-Supplemental-Materials.pdf

The University of Texas. (2025). SPIRAL Word Problems with Set/Comparison Schema (Video). Youtu.be. https://youtu.be/oaGkVMIl1H0

Schema sort

Powell, S., & Berry, K. (n.d.). Pirate Math Equation Quest Supplemental Materials. Retrieved September 3, 2025, from https://www.piratemathequationquest.com/docs/PMEQ-2C-Supplemental-Materials.pdf

The University of Texas. (2025). SPIRAL Word Problems with Set/Comparison Schema (Video). Youtu.be. https://youtu.be/oaGkVMIl1H0

Multi-step problems

Multi-step problems can;

• be solved using problem schemas,
• incorporate more than one problem schema,
• combine additive and multiplicative schemas.

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Year 5 NAPLAN example question 2025

Multi-step problems

Year 5 NAPLAN 2025

$11

$15

$450

1

12

12

$450

$132

$180

$132

$180

$450

$762

Explicit instruction of worded problems

1. Present the schema or problem type – one schema at a time

Introduce a Change problem

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2. Explore the schema or problem type with a story that contains all quantities

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There were 18 children on the bus. 7 children got off the bus at the first stop.

11 children are still on the bus.

Explicit instruction of worded problems

3. Explore the schema or problem type with a missing part (word problem).
4. Connect the quantities between the story and the word problem.
5. Support students to visualise the problem and identify relevant information (Role playing, gestures, concrete materials and/or representations ).

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There were 18 children on the bus. 7 children got off the bus at the first stop.

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How many children are still on the bus?

Explicit instruction of worded problems

6. Show students’ different examples of the schema or problem type using different scenarios – discuss how and why each problem belongs to the schema.

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Quantity increase

The rose bush has 15 flowers blooming.

Then 12 more bloomed.

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How many flowers are blooming on the rose bush now?

Quantity decrease

Selina had 24 cupcakes. At her birthday the next day, she and her friends ate 16.

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How many cupcakes does Selina have left to share with her family?

Explicit instruction of worded problems

7. Expand students’ ability to identify relevant information in word problems by presenting problem information differently.

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Selina had 24 cupcakes and 12 cookies. At her birthday the next day, she and her friends ate 14 cupcakes.

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How many cupcakes does Selina have left to share with her family?

Explicit instruction of worded problems

8. Once students have mastered the schema or problem type, engage students in solving worded problems using a variety of problem types.

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At her birthday party, Selina receive 9 presents in red wrapping paper and 5 presents in yellow wrapping paper. How many presents did Selina receive for her birthday?

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Selina received 12 presents at her birthday party. The next day her grandmother gave her some more presents. She then had 17 presents. How many presents did she receive from her grandmother?

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Change

Combine

A possible process for schema (problem type) instruction

1. Present the schema or problem type – one schema at a time.
2. Explore the schema or problem type with a story that contains all quantities.
3. Explore the schema or problem type with a missing part (word problem).
4. Connect the quantities between the story and the word problem.
5. Support students to visualise the problem and identify relevant information (role playing, gestures, concrete materials and/or representations).
6. Show students different examples of the schema or problem type using different scenarios – discuss how and why each problem belongs to the schema.
7. Expand students’ ability to identify relevant information in word problems by presenting problem information differently.
8. Once students have mastered the schema or problem type, engage students in solving worded problems using a variety of problem types.

Suggested schemas across the year levels

Resources

Evaluation