Fraction Problem Solving

Overview

In this small-group lesson, students solve mixed-operation word problems involving fractions. The lesson uses a consistent “I do, We do, You do” structure so students learn to identify the operation, record an equation, solve it, and check whether the answer makes sense.

Learning intentions

• WALT identify what a fraction word problem is telling us and what information is known.
• WALT choose the correct operation: addition, subtraction, multiplication or division.
• WALT represent a word problem as a mathematical equation.
• WALT solve and explain fraction problems using appropriate strategies.

Success criteria

• I can identify the important information and the operation needed.
• I can write an equation before solving.
• I can use a common denominator when adding or subtracting fractions.
• I can simplify or convert my answer and explain how I know it is reasonable.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge is connected to relevant mathematical content.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, problem solving and mathematical communication.
• Te Mātaiaho mathematical practices: representing, reasoning, communicating and checking mathematical thinking.

Lesson structure (60 minutes)

1. 0–8 min · Activate prior knowledge. Display the prior-knowledge slides. Teacher briefly revises mixed numbers, improper fractions, converting an improper fraction to a mixed number, and finding a common denominator. Students complete four quick responses on mini-whiteboards:

• Convert (2\frac{1}{3}) to an improper fraction.
• Convert (\frac{11}{4}) to a mixed number.
• Identify a common denominator for (\frac{2}{3}) and (\frac{5}{6}).
• Explain what the numerator and denominator tell us. Correct misconceptions immediately and keep the examples visible as reference.

2. 8–18 min · Explicit teaching: choosing and solving. Teacher models a simple fraction word problem and uses the repeated routine: Read, Know, Operation, Equation, Solve, Check. Display the operation-choice and worked-example slides. Explain:

• Addition: amounts are joined or combined. Find a common denominator, add numerators, then simplify.
• Subtraction: an amount is taken away or a difference is found. Find a common denominator, subtract numerators, then simplify.
• Multiplication: finding a fraction of an amount or equal groups. Multiply numerators and denominators, then simplify.
• Division: sharing or finding how many fractional groups fit. Keep the first fraction, change ÷ to ×, and invert the second fraction; then simplify. Students identify the operation and equation for each example using mini-whiteboards before the teacher completes the calculation. Emphasise that the wording helps, but students must also consider the relationship between the quantities.

3. 18–26 min · Addition: I do and We do. Give each student the fraction word-problem practice sheet. Teacher reads Addition Question 1 aloud, highlights the known information and operation, writes the equation, and solves it while narrating each step. Students watch, identify the common denominator and copy the model. For Addition Question 2, teacher and students solve together: students suggest the operation, equation and next step, while the teacher records a clear shared solution. Students explain why addition is appropriate.

4. 26–31 min · Addition: You do. Students independently solve Addition Question 3 using the routine. Teacher checks each student’s equation before they continue and asks: “What does your answer represent?” Students may use a fraction strip drawing or number line to support their explanation. Briefly compare methods and correct errors before moving on.

5. 31–40 min · Subtraction: I do, We do, You do. Teacher models Subtraction Question 1, including renaming a mixed number if needed and finding a common denominator. Students then solve Question 2 with the teacher, explaining why subtraction is needed and checking whether the result should be smaller than the starting amount. Students independently solve Question 3 and show an equation, working and simplified answer. Teacher uses quick prompts rather than doing the calculation for them.

6. 40–52 min · Multiplication and division: I do, We do. Teacher models Multiplication Question 1 and Division Question 1, using a visual representation and the equation before calculating. For multiplication, connect “fraction of” to multiplication. For division, use a sharing or grouping interpretation before demonstrating “keep, change, flip”. Students complete Multiplication Question 2 and Division Question 2 with the teacher, taking turns to identify the operation, state the equation, complete the calculation and check the answer. Pause after each question to address misconceptions.

7. 52–60 min · Review and exit check. Display the reflection and exit-check slides. Students complete the final box on the fraction word-problem practice sheet: “A recipe uses (\frac{3}{4}) cup of flour and another (\frac{2}{3}) cup. Write the equation and solve.” They also circle the first step they find most useful: Read, Know, Operation, Equation, Solve or Check. Discuss one successful strategy and one common error. Collect the worksheet and exit response.

Resources

• the fraction word-problem teaching deck
• the fraction word-problem practice sheet
• Mini-whiteboards, pens and erasers
• Fraction strips or fraction circles
• Fraction wall or multiplication chart
• Highlighters for marking known information and operation clues
• Teacher model sheet or whiteboard
• Calculators for checking only, if appropriate

Assessment

• Listen for students accurately identifying the known information and operation during the shared examples.
• Check that students write an equation before calculating and can explain why the operation fits the context.
• Use the independent questions and exit response to identify whether students need further support with common denominators, multiplication/division procedures or interpreting answers.

Differentiation

• Provide a six-box prompt card on the worksheet: Read, Know, Operation, Equation, Solve, Check. Read each word problem aloud and allow students to highlight key information.
• Use fraction strips, a fraction wall and partially completed equations for students who need concrete or visual support. Offer sentence starters: “I know…”, “The operation is… because…”, and “My answer means…”.
• Reduce writing demands by allowing students to explain their operation orally before recording it. Pair students strategically, but require each student to complete the independent questions.
• For students ready for challenge, ask them to create a second word problem with the same equation, or explain how changing the order of the numbers would change the answer.