Fraction Addition Strategies

Overview

This is lesson 5 of 6 in Fraction Foundations and Operations. Students apply prior learning about equivalent fractions, simplifying and mixed numbers to add and subtract fractions with like and unlike denominators, including improper fractions and mixed numbers.

Learning intentions

Students will:

• add and subtract fractions with like denominators efficiently
• find equivalent fractions and common denominators for unlike fractions
• calculate with proper fractions, improper fractions and mixed numbers
• simplify answers and explain whether their solutions are reasonable

Success criteria

• I can identify a suitable common denominator.
• I can convert fractions to equivalent fractions before operating.
• I can add or subtract numerators while keeping the denominator unchanged.
• I can convert, simplify and communicate my answer in an appropriate form.

Curriculum links

• Number — use the four operations with rational numbers, choosing efficient strategies and digital tools where appropriate.
• Number — model and solve practical problems involving rational numbers and percentages, explaining and reviewing solutions.
• Measurement — use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts.
• Mathematical reasoning and problem-solving are developed through explaining strategies, checking answers and interpreting results.

Lesson structure (60 minutes)

1. 0–5 min · Hook and diagnostic. Open with the fraction challenge hook and display: “Without calculating exactly, which is greater: ( \frac{3}{4}+\frac{2}{5} ) or 1?” Ask the student to estimate, explain their thinking and complete two quick examples: ( \frac{2}{7}+\frac{3}{7} ) and ( \frac{5}{6}-\frac{1}{6} ). Use responses to identify whether a reminder about numerator and denominator roles is needed.

2. 5–15 min · Explicit teaching: like denominators. Use the like-denominator modelling slides to model ( \frac{3}{8}+\frac{2}{8}=\frac{5}{8} ) and ( \frac{7}{9}-\frac{4}{9}=\frac{3}{9}=\frac{1}{3} ). Emphasise that the denominator names the equal parts and remains unchanged; only the numerators are added or subtracted. The student annotates the first section of the fraction operations practice worksheet and explains each step aloud.

3. 15–27 min · Explicit teaching: unlike denominators. Use the common-denominator modelling slides to demonstrate ( \frac{2}{3}+\frac{1}{4} ). Identify 12 as a common denominator, rewrite the fractions as ( \frac{8}{12}+\frac{3}{12} ), then calculate ( \frac{11}{12} ). Model subtraction with ( \frac{5}{6}-\frac{1}{4}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12} ). The student completes two guided questions on the worksheet, using multiplication to generate equivalent fractions and checking that the answer is sensible.

4. 27–40 min · Mixed numbers and improper fractions. Use the mixed-number modelling slides to show two valid approaches for (1\frac{1}{2}+2\frac{2}{3}): add whole and fractional parts using a common denominator, or convert to improper fractions first. Model (1\frac{1}{2}=\frac{3}{2}), (2\frac{2}{3}=\frac{8}{3}), then calculate ( \frac{9}{6}+\frac{16}{6}=\frac{25}{6}=4\frac{1}{6} ). Also model subtraction where regrouping is required, such as (3\frac{1}{4}-1\frac{2}{3}). The student chooses a strategy, records each line clearly and explains why the final answer is written as a mixed number.

5. 40–53 min · Independent application and conferencing. Direct the student to complete the differentiated worksheet tasks: like denominators, unlike denominators, mixed numbers and two practical problems. One problem may involve combining ingredient quantities; another may involve comparing distances or portions. Confer individually, asking: “What denominator will make both fractions easy to compare?”, “Have you simplified?”, and “Does the size of your answer fit the situation?” The student may use a calculator only after showing the fraction model and calculation.

6. 53–60 min · Review and exit ticket. Return to the review and exit-ticket slides. The student corrects one earlier response and explains one error or improvement. Complete an exit response on the final worksheet section: ( \frac{7}{8}-\frac{2}{3} ), (2\frac{1}{5}+1\frac{3}{10}), and a sentence explaining why denominators cannot simply be added. Finish by revisiting the hook estimate and confirming the exact result.

Resources

• the fraction addition and subtraction teaching deck
• the fraction operations practice worksheet
• Whiteboard and markers
• Student exercise book and pencil
• Fraction strips or a fraction wall displayed by the teacher
• Basic calculator for checking, if appropriate
• Visualiser or screen for modelling written working

Assessment

• Use the opening diagnostic to check fluency with like denominators and estimation.
• During guided and independent work, assess common-denominator selection, equivalent-fraction accuracy, operation accuracy, simplification and written explanations.
• Collect the worksheet and use the exit ticket to identify whether the next lesson should focus on fluency, mixed-number subtraction or problem interpretation.

Differentiation

• Support with a displayed four-step scaffold: choose a common denominator, rewrite equivalent fractions, operate on numerators, simplify and check. Provide multiplication facts or a list of useful common denominators.
• Use colour coding to connect each original fraction to its equivalent fraction and permit fraction strips or a fraction wall for visual confirmation.
• For EAL/D or students requiring language support, provide sentence starters: “The common denominator is…”, “I multiplied the numerator and denominator by…”, and “My answer is reasonable because…”.
• Extend through an open investigation: find two different fractions whose sum is (2\frac{1}{4}), then explain whether more than one solution is possible. Ask the student to create and solve a practical fraction problem.