Comparing Fraction Values

Overview

In this third lesson of Fraction Foundations and Operations, students compare and order proper fractions using benchmarks, equivalent fractions, common denominators and number lines. The lesson builds on prior work representing and simplifying fractions, with emphasis on selecting and explaining an efficient strategy.

Learning intentions

Students will:

• compare proper fractions using the symbols <, > and =
• use benchmarks such as 0, ½ and 1 to estimate and compare values
• generate equivalent fractions and use common denominators
• represent fractions on a number line and order them
• explain and review the strategy used to reach a conclusion

Success criteria

• I can compare two fractions and use <, > or = correctly.
• I can explain my comparison using a benchmark, equivalent fraction, common denominator or number line.
• I can order a set of fractions from least to greatest or greatest to least.
• I can check whether my answer is reasonable.

Curriculum links

• Number — operations with rational numbers using efficient strategies and digital tools where appropriate.
• Number — mathematical modelling involving rational numbers and percentages, including interpreting and communicating solutions.
• Measurement — mathematical modelling involving ratios and rates, including formulating and reviewing solutions.
• Algebra — representing and interpreting relationships on the Cartesian plane, supporting accurate number-line representations.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Open with the fraction comparison hook and display: “Which is greater: (\frac{3}{8}) or (\frac{5}{12})? How can you know without a calculator?” The student gives an initial answer and explains their thinking; the teacher records the strategy and identifies any misconception about larger denominators.

2. 7–17 min · Connect to benchmarks. Use the benchmark comparison slides to revisit that proper fractions lie between 0 and 1, then model comparisons with ½ and 1, such as (\frac{3}{10}<\frac12) and (\frac78>\frac12). The student places examples on a drawn 0–1 number line and explains whether each is closer to 0, ½ or 1.

3. 17–29 min · Model comparison strategies. Model (\frac{3}{8}) and (\frac{5}{12}) in three ways: estimate with a benchmark, rename using a common denominator, and locate both on a number line. Show that (\frac{3}{8}=\frac{9}{24}) and (\frac{5}{12}=\frac{10}{24}), so (\frac{3}{8}<\frac{5}{12}). Emphasise that cross-multiplication may be used as a compact strategy only when the student can explain why it works. The student completes a worked example with teacher questioning.

4. 29–44 min · Guided and independent practice. Distribute the fraction comparison and ordering worksheet. The student completes comparison questions, first choosing an appropriate strategy, then orders groups such as (\frac14,\frac23,\frac38,\frac56) from least to greatest. The teacher prompts with: “What benchmark could help?”, “Can the fractions be renamed?”, and “Where would each fraction sit between 0 and 1?” The student records reasoning, not only symbols.

5. 44–53 min · Reasoning challenge. Return to the ordering and reasoning challenge and present: “Place (\frac{2}{5},\frac{7}{10},\frac{3}{4}) in order. Can you prove your order using two different strategies?” The student solves independently, then checks the result using a second method. Discuss which method is most efficient and when a number line is more informative than a common denominator.

6. 53–60 min · Review and exit check. Use the plenary slides to revisit the key question: “How do you decide which fraction is greater?” The student completes an oral exit response: compare (\frac{5}{6}) and (\frac78), write the correct symbol, and explain the choice using either equivalent fractions or a benchmark. The teacher records the response for the next lesson’s grouping and support.

Resources

• the fraction comparison lesson deck
• the fraction comparison and ordering worksheet
• Whiteboard and markers
• Student exercise book and pencil
• Ruler for drawing number lines
• Optional calculator or digital fraction tool for checking, not replacing, reasoning

Assessment

• Listen during the hook and guided modelling for misconceptions, especially the belief that a larger denominator always means a larger fraction.
• Check the worksheet for correct symbols, ordered sets, strategy selection and written justification.
• Use the final comparison and explanation as an exit check; note whether the student can verify an answer with a second representation.

Differentiation

• Support with a pre-drawn 0–1 number line, benchmark prompts and sentence starters: “I know ___ is greater because…” and “Both fractions are equivalent to…”.
• Reduce the number of worksheet items while requiring complete explanations for each comparison; begin with fractions sharing a denominator before using unrelated denominators.
• Provide an explicit worked example and colour-code numerator and denominator when renaming fractions. Read instructions aloud and allow the student to explain reasoning verbally before writing.
• Extend through the two-strategy challenge: ask the student to create two different fractions between (\frac35) and (\frac23), then justify that both are correctly placed.