Fraction Problems Together

Overview

Lesson 9 of 10 in Understanding Fractions Together. Students apply their understanding of halves, quarters and other familiar unit fractions to solve practical word problems using pictures, concrete materials, equations and words. Activities are age-respectful for students aged 12–14, with mathematical language and tasks pitched at approximately Years 2–4.

Learning intentions

• WALT solve fraction word problems.
• Students will identify the whole, the fraction and the question in a problem.
• Students will represent fractions using objects, drawings or a fraction wall.
• Students will explain how they know their answer is reasonable.

Success criteria

• I can find the important information in a fraction problem.
• I can show the problem with a drawing, materials or an equation.
• I can accurately solve practical fraction problems.
• I can explain my answer using a sentence and check that it makes sense.

Curriculum links

• Recognising and representing halves, quarters and other familiar fractions as equal parts of a whole.
• Connecting fraction names, symbols, images and practical situations.
• Solving simple mathematical problems involving sharing, grouping and fractions.
• Communicating mathematical thinking using representations, materials, discussion and explanation.

Lesson structure (45 minutes)

1. 0–5 minutes – Connect and hook Open with the fraction problem hook. Present: “Four friends share one pizza equally. Sam eats one quarter. How much pizza is left?” Students make a quick prediction, then explain what information they would need to solve it. Establish that word problems require us to understand the story before calculating.

2. 5–12 minutes – Model a problem-solving routine Display the four-step routine from the four-step problem-solving routine: Read, Represent, Solve, Check. Model a problem such as: “There are 12 strawberries. One quarter are put in a bowl. How many strawberries are in the bowl?” Think aloud: identify 12 as the whole, divide into four equal groups, find one group, and write “One quarter of 12 is 3.” Demonstrate drawing four equal groups or using a fraction wall.

3. 12–17 minutes – Guided practice Solve a second problem together: “A class has 8 coloured pencils. One half are blue. How many are blue?” Use counters, a drawing or the fraction wall. Ask: “What is the whole? What does one half mean? How can we check?” Record more than one valid representation on the board.

4. 17–32 minutes – Partner problem solving Distribute the fraction word-problem worksheet. Students work in pairs, taking turns as reader and solver. The worksheet should include practical problems involving halves, quarters and thirds, with pictures and numbers within an accessible range. Students use the problem-solving template: underline the whole, circle the fraction, draw or build the situation, solve, and write an answer sentence. Confer with pairs and prompt rather than give answers.

5. 32–38 minutes – Share and compare strategies Return to the strategy discussion slides and select two problems for discussion. Invite students to show different methods, such as sharing counters into equal groups, drawing an area model or using a fraction wall. Emphasise that equal parts are essential and that an answer must match the story.

6. 38–43 minutes – Independent check Students complete one new problem independently: “A tray holds 16 muffins. One quarter are chocolate. How many chocolate muffins are there?” Students must show their strategy and complete the sentence, “There are ___ chocolate muffins because ___.” Collect responses for assessment.

7. 43–45 minutes – Plenary and preview Use the plenary reflection slide. Students complete the sentence orally: “When I solve a fraction word problem, I first…” Ask one student to explain how they checked an answer. Preview the final unit lesson, where students will apply these strategies in a mixed fraction challenge.

Resources

• the fraction word-problem slide deck
• the fraction word-problem worksheet
• Counters, linking cubes or small classroom objects
• Paper, pencils, coloured pencils and mini-whiteboards
• Board or display screen
• the fraction wall and strip cards
• Problem-solving routine displayed on the board

Assessment

• Observe whether students identify the whole and make equal groups during guided and partner work.
• Review worksheet responses for accurate representations, calculations and answer sentences.
• Use the independent check to identify students who can solve without a partner and explain their reasoning.

Differentiation

• Support students with a four-box problem-solving template: What do I know? What fraction? Show it. Answer and check. Read problems aloud and use counters or strip cards before recording symbols.
• Provide a reduced choice of problems using halves and quarters, visual prompts, enlarged print, pre-drawn equal-part models and sentence starters such as “The whole is…” and “One quarter of ___ is…”.
• For EAL/D learners, explicitly teach and display whole, equal parts, half, quarter, share and left. Pair each word with a picture, gesture and completed example; allow oral explanation before writing.
• Extend students by asking them to solve the same problem in two ways, create a matching word problem for a given fraction, or explain why an incorrect answer is unreasonable. Offer challenge problems involving the fraction left over.