Share and Solve Fractions

Overview

In this final lesson of “Equivalent Fractions in Action”, students apply equivalent fractions to fair-sharing and comparison problems. They represent solutions using fraction walls and number lines, explain their reasoning, and justify whether answers are reasonable.

Learning intentions

• WALT apply equivalent fractions to solve sharing and comparison problems.
• WALT represent fractions using diagrams, fraction walls and number lines.
• WALT communicate mathematical thinking using models, calculations and mathematical sentences.
• WALT check whether a solution is reasonable.

Success criteria

• I can represent a sharing problem as a fraction.
• I can use equivalent fractions to solve or check my answer.
• I can explain my strategy with a model, calculation and mathematical sentence.
• I can justify whether an answer is reasonable.

Curriculum links

• Fractions — represent and compare halves, quarters, thirds and fifths as lengths on a number line, including related fractions formed by halving.
• Fractions — model equivalent fractions as lengths and represent fractional quantities equal to or greater than one.
• Multiplicative relations — use known number facts and number sentences to solve contextual problems.
• Mathematical reasoning and communication — explain, compare and justify strategies.

Lesson structure (60 minutes)

1. 0–7 min · Hook and connect. Display the question, “Is 2/4 of a pizza the same amount as 1/2 of a pizza?” using the opening sharing problem. Students think-pair-share, then show an answer with fingers or a quick sketch; teacher revisits the meaning of numerator, denominator and equal parts.

2. 7–18 min · Model a fair share. Present: “Three friends share two identical sandwiches equally. What fraction of one sandwich does each friend receive?” Teacher models the problem-solving scaffold—understand, represent, solve, check—using the worked fair-sharing example and the fraction wall and strip cards. Students build or sketch the share, identify each person’s amount as 2/3, and connect it to the number line; discuss why 2/3 is reasonable and why the total is 3 × 2/3 = 2.

3. 18–30 min · Guided representation. Distribute the equivalent fractions problem-solving sheet. Teacher completes the first question with the class: “Four children share three litres of juice equally.” Students represent each share as 3/4 using a diagram and number line, then use the fraction wall to compare it with 6/8. Prompt: “What stayed the same? What changed?” Invite students to rehearse an explanation with a partner before sharing.

4. 30–43 min · Group problem solving. Place students in groups of four and provide the fraction scenario cards. Assign roles: reader, model builder, recorder and reporter. Each group solves two or three different sharing or comparison problems, recording the context, model, calculation, equivalent fraction and reasonableness check in a collaborative reasoning journal. Teacher conferences with groups, asking, “How do you know the parts are equal?” and “Can your number line prove your answer?”

5. 43–52 min · Compare and communicate. Groups select one solution and prepare a one-minute explanation using the strategy comparison prompts. Two or three groups present. Class identifies similarities and differences between area models, fraction walls and number lines, and respectfully gives one “clear because…” comment or question. Teacher reinforces that equivalent fractions name the same length or amount.

6. 52–60 min · Individual exit task and reflection. Students complete the final questions on the individual exit task independently: “A cake is shared equally among six children. What fraction does each child receive? Show an equivalent fraction by halving or doubling where possible, represent it on a number line, and explain whether 3/6 is equal to 1/2.” Students finish with a confidence rating and hand in the sheet.

Resources

• the equivalent fractions teaching deck
• the equivalent fractions problem-solving sheet
• the fraction wall and strip cards
• the fraction scenario cards
• Fraction strips or paper strips
• Individual whiteboards and markers
• Pencils, rulers and coloured pencils
• Collaborative reasoning journals
• Prepared group role cards
• Exit collection tray

Assessment

• Observe partner talk and group work for accurate representation of equal parts, use of equivalent fractions and appropriate number-line placement.
• Review collaborative journals and peer explanations for a model, calculation, mathematical sentence and reasonableness check.
• Use the individual exit task to assess independent understanding, including an unfamiliar fraction context and mathematical communication.

Differentiation

• Support students with the scaffold “Understand: What is being shared? Represent: Draw or build it. Solve: Find the fraction. Check: Does it make sense?”, worked examples and partially labelled number lines.
• Use real-life contexts, concrete fraction strips, illustrated instructions, simplified language and bilingual resources where available. Pre-teach and display: share equally, numerator, denominator, equivalent and reasonable.
• Provide EAL/D learners with sentence frames: “Each person receives ___ because…”, “/ is equivalent to / because…”, and “My answer is reasonable because…”. Allow rehearsal with a partner and responses through drawing, pointing, speaking or writing.
• Provide targeted teacher support during group work, pairing students strategically and reducing the number of problems without reducing the reasoning demand.

Extension

• Solve one scenario in two different ways, such as with a fraction wall and a number line.
• Write a new sharing problem that has an unfamiliar equivalent-fraction solution, then exchange and solve it with a partner.
• Generalise: explain how to decide whether two fractions are equivalent, using examples such as 2/4, 3/6 and 4/8.