Review of Fractions: Equivalence and Comparison

Active learning works well for fractions because students often struggle with abstract symbols alone. When they manipulate physical or visual models in activities like Manipulative Matching or Paper Folding, they build strong mental images of equivalence and size. This hands-on work turns confusion about denominators into clear understanding through repeated, meaningful practice.

• Class 7
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Compare two unlike fractions by converting them to equivalent fractions with a common denominator.
2. Simplify a given fraction to its lowest terms by identifying and dividing by the greatest common divisor.
3. Classify fractions as proper, improper, or mixed based on the relationship between their numerator and denominator.
4. Justify the equivalence of two fractions using visual representations such as fraction bars or number lines.
5. Calculate the value of a mixed fraction by converting it into an improper fraction and vice versa.

Think-Pair-Share

⏱ 30 min·Pairs

Manipulative Matching: Equivalent Fractions

Provide fraction strips or printed bars representing fractions like 1/4, 2/8, 3/12. Students in pairs match equivalents by aligning strips to show equal lengths, then simplify by grouping units. Discuss findings as a class.

Prepare & details

Analyze how common denominators facilitate the comparison of fractions.

Facilitation Tip: During Manipulative Matching, circulate with fraction tiles and ask pairs to explain why two fractions match before they record the pair.

Setup: Works in standard Indian classroom seating without moving furniture — students turn to the person beside or behind them for the pair phase. No rearrangement required. Suitable for fixed-bench government school classrooms and standard desk-and-chair CBSE and ICSE classrooms alike.

Materials: Printed or written TPS prompt card (one open-ended question per activity), Individual notebook or response slip for the think phase, Optional pair recording slip with 'We agree that...' and 'We disagree about...' boxes, Timer (mobile phone or board timer), Chalk or whiteboard space for capturing shared responses during the class share phase

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Comparison Strategies

Set up three stations: visual shading for like denominators, benchmark fractions on number lines, and cross-multiplication cards. Small groups rotate, solving five problems per station and recording strategies used.

Prepare & details

Justify why 1/2 is equivalent to 2/4 using visual models.

Facilitation Tip: In Station Rotation, place a timer at each comparison station so students practise both methods without rushing but with focus.

Setup: Designate four to six fixed zones within the existing classroom layout — no furniture rearrangement required. Assign groups to zones using a rotation chart displayed on the blackboard. Each zone should have a laminated instruction card and all required materials pre-positioned before the period begins.

Materials: Laminated station instruction cards with must-do task and extension activity, NCERT-aligned task sheets or printed board-format practice questions, Visual rotation chart for the blackboard showing group assignments and timing, Individual exit ticket slips linked to the chapter objective

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Think-Pair-Share

⏱ 35 min·Whole Class

Game Show: Simplify and Compare

Divide class into teams for a buzzer game with fraction cards. Teams simplify first, then compare pairs using chosen strategies. Award points for correct justifications with drawings.

Prepare & details

Differentiate between proper, improper, and mixed fractions and their representations.

Facilitation Tip: For Game Show, prepare a mix of simple and tricky fractions so all students experience both success and the need to revise their thinking.

Setup: Works in standard Indian classroom seating without moving furniture — students turn to the person beside or behind them for the pair phase. No rearrangement required. Suitable for fixed-bench government school classrooms and standard desk-and-chair CBSE and ICSE classrooms alike.

Materials: Printed or written TPS prompt card (one open-ended question per activity), Individual notebook or response slip for the think phase, Optional pair recording slip with 'We agree that...' and 'We disagree about...' boxes, Timer (mobile phone or board timer), Chalk or whiteboard space for capturing shared responses during the class share phase

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Think-Pair-Share

⏱ 25 min·Individual

Paper Folding: Fraction Types

Each student folds A4 paper to create proper, improper, and mixed fractions, labels them, and converts between types. Share models in pairs to verify conversions.

Prepare & details

Analyze how common denominators facilitate the comparison of fractions.

Facilitation Tip: With Paper Folding, insist students label each fold clearly to avoid confusion between halves, fourths, and eighths.

Setup: Works in standard Indian classroom seating without moving furniture — students turn to the person beside or behind them for the pair phase. No rearrangement required. Suitable for fixed-bench government school classrooms and standard desk-and-chair CBSE and ICSE classrooms alike.

Materials: Printed or written TPS prompt card (one open-ended question per activity), Individual notebook or response slip for the think phase, Optional pair recording slip with 'We agree that...' and 'We disagree about...' boxes, Timer (mobile phone or board timer), Chalk or whiteboard space for capturing shared responses during the class share phase

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teachers should start with concrete models before moving to symbols, as research shows this reduces errors in comparison tasks. Avoid rushing to rules; instead, let students discover patterns through guided play. Use small group discussions to surface misconceptions early, and repeat key activities like Simplify and Compare to build fluency. Always connect visual work back to the symbolic form to strengthen symbolic reasoning.

What to Expect

Successful learning looks like students confidently identifying equivalent fractions, simplifying without hesitation, and comparing unlike fractions using both methods. They should explain their reasoning clearly and use models or diagrams to justify their answers. Group discussions should show they can correct each other’s mistakes with evidence from their work.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Matching, watch for students who pair 1/3 with 1/6 because both have small denominators, ignoring that 1/3 is larger.

What to Teach Instead

Have them place both fractions on a number line strip to see the actual size difference and ask them to find equivalents of 1/3 that match 2/6 or 3/9 to correct the error.

Common Misconception

During Station Rotation, listen for students who say 2/5 and 4/10 are not the same because the numbers look different.

What to Teach Instead

Ask them to overlay fraction tiles or strips to see that both cover exactly half the same whole, then guide them to write the multiplication step that shows 2 x 2 = 4 and 5 x 2 = 10.

Common Misconception

During Paper Folding, notice students who fold a paper into 3 parts and label each as 1/3 but think the pieces are smaller than halves.

What to Teach Instead

Have them fold another sheet into halves and thirds and compare the sizes side by side, then ask them to write improper fractions like 4/3 to show that fractions can be larger than 1.

Assessment Ideas

Quick Check

After Manipulative Matching, present students with three fractions: 2/5, 4/10, and 3/7. Ask them to identify which are equivalent and explain their reasoning using their fraction tiles. Then, ask them to simplify 6/9 to its lowest terms on the same sheet.

Exit Ticket

During Station Rotation, give each student a card with two fractions, such as 5/8 and 7/12. Ask them to write the steps they used to compare these fractions and the common denominator they chose, then collect the cards to check for correct method use.

Discussion Prompt

After Game Show Simplify and Compare, pose the question: 'Why is it easier to compare 1/3 and 2/3 than 1/3 and 1/4?' Facilitate a class discussion where students use their game cards or whiteboards to show the role of the common denominator in making the comparison straightforward.

Extensions & Scaffolding

• Challenge students who finish early to create a set of three new equivalent fractions and explain the pattern to their group.
• Scaffolding for struggling students: Provide fraction strips with pre-marked denominators to help them compare visually before moving to symbolic work.
• Deeper exploration: Ask students to design a real-life scenario (like a recipe or craft project) where they must compare or simplify fractions to solve a problem.

Key Vocabulary

Equivalent Fractions	Fractions that represent the same value or proportion, even though they have different numerators and denominators. For example, 1/2 and 2/4 are equivalent.
Simplest Form	A fraction where the numerator and denominator have no common factors other than 1. It is obtained by dividing both by their greatest common divisor.
Common Denominator	A common multiple of the denominators of two or more fractions, used to make them ready for comparison or addition/subtraction.
Improper Fraction	A fraction where the numerator is greater than or equal to the denominator, indicating a value equal to or greater than one.
Mixed Fraction	A number consisting of a whole number and a proper fraction, representing a value greater than one.