Fraction Problem Solving

Overview

Lesson 5 of 15 in Number Connections: Fractions, Decimals, Percentages. Students apply fraction knowledge to real-life sharing, measurement, sport and classroom contexts, choosing useful representations and explaining how they know their answers are reasonable.

Learning intentions

• WALT apply fraction understanding to real-life problems.
• WALT choose a useful representation or operation.
• WALT explain my reasoning using mathematical language.
• WALT check whether my answer is reasonable.

Success criteria

• I can identify the important information in a fraction problem.
• I can choose and use a diagram, number line, fraction strip or operation.
• I can solve accurately and explain my method.
• I can check whether my answer makes sense in the context.

Curriculum links

• Number: use fractions to describe, compare and solve problems involving quantities and measures.
• Number: connect visual, written and symbolic representations of fractions.
• Mathematical practices: reason, communicate, represent, calculate and check.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect

Open with the fraction problem hook. Display: “A sports team used three-quarters of its 24 drink bottles. How could we work out how many were used?” Students think, pair-share and describe possible methods without calculating yet. Revisit the WALT and success criteria.

2. 5–12 minutes – Model a problem-solving process

Use the problem-solving steps to introduce: read and visualise, identify the whole, choose a representation or operation, solve, explain and check. Model a sharing problem such as: “Four friends share two-thirds of a 12-piece tray of fruit. How many pieces do they share altogether?” Draw a bar model, identify the whole, calculate and check that the answer is less than 12.

3. 12–17 minutes – Guided example

Display the measurement problem from the guided example: “A 2-litre jug is three-quarters full. How much water is in it?” Solve together using a bar model or fraction strip. Ask: “What is the whole? What does one quarter represent? Does our answer seem reasonable?” Invite students to explain more than one method.

4. 17–32 minutes – Paired problem solving

Distribute the fraction problem-solving review to pairs. Students solve a selection of contexts involving sharing, measures, sport and classroom quantities. They must show a representation, operation or labelled diagram, write an explanation, and complete a reasonableness check. Use the guided template and reduced-number questions with students needing support. Circulate and ask, “What is the whole?” and “How could you represent this?”

5. 32–39 minutes – Compare and communicate methods

Select two or three different solutions to discuss. Use the strategy discussion prompts to compare methods, such as repeated addition, finding a unit fraction, multiplication or a bar model. Students explain why their answer fits the context and identify one possible error, such as treating the numerator as the whole.

6. 39–45 minutes – Independent check and reflection

Students complete the final problem on the fraction problem-solving review independently, then use the plenary and exit reflection to respond to: “Which representation helped you most today, and how did you check your answer?” Collect the worksheet or photograph selected work for assessment. Revisit the success criteria with a quick thumbs-up, sideways or not-yet response.

Resources

• the fraction problem-solving slide deck
• the fraction problem-solving review
• Mini-whiteboards and pens
• Pencils, rulers and coloured pencils
• Fraction strips or manipulatives
• the fraction wall and strip cards
• Guided problem-solving template prepared on the board
• Chart paper or board space for sharing methods

Assessment

• Listen for students identifying the whole, selecting an appropriate representation and explaining their operation during paired work.
• Check worksheet responses for accurate calculations, labelled models, explanations and reasonable answers.
• Use the final independent problem and reflection to identify students needing further support with representation, operations or checking.

Differentiation

• Support: read problems aloud, pre-teach words such as whole, share, of and remaining, reduce the numbers, and provide a guided template: “I know… I need to find… I will show… My answer is reasonable because…”
• Support: work with a teacher-led group using the fraction wall and strip cards to build and compare fractions before recording on the worksheet. Allow oral explanations, drawing and manipulatives.
• Extension: create and solve a multi-step fraction problem involving at least two operations or contexts. Students must show more than one possible method and explain which is most efficient.
• EAL and SEN: pair students strategically, chunk written questions, highlight key information, provide visual models and sentence stems, and check understanding privately before independent work.