Mathematics · Primary 5

Active learning ideas

Subtraction of Fractions and Mixed Numbers

Active learning builds confidence with fraction subtraction by giving students physical and visual ways to see why procedures work. Fraction strips and number lines make abstract rules concrete, especially for borrowing, which many students find confusing when taught only with symbols.

• MOE Syllabus Outcomes
• MOE: Fractions - P5

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 35 min · Small Groups

Small Groups: Fraction Strip Borrow Challenge

Give each group colored fraction strips representing mixed numbers. Students build models for problems like 4 1/6 - 2 5/12, perform subtraction by aligning strips and borrowing wholes as needed. Groups record steps on mini-whiteboards and share one solution with the class.

Differentiate between the steps for adding and subtracting mixed numbers.

Facilitation Tip

During Fraction Strip Borrow Challenge, circulate and ask groups to explain how their strips represent the borrowed whole before proceeding to subtraction.

What to look for

Present students with the problem: 'Calculate 5 1/3 - 2 1/2.' Ask them to show their steps on mini whiteboards, focusing on how they found a common denominator and handled borrowing. Review responses to identify common errors.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 25 min · Pairs

Pairs: Subtraction Error Hunt

Provide cards with mixed number subtraction problems containing common errors, such as forgetting common denominators or improper borrowing. Pairs identify mistakes, correct them step-by-step, and create a correct version. Switch cards with another pair for verification.

Explain the concept of 'borrowing' when subtracting mixed numbers with unlike denominators.

Facilitation Tip

For Subtraction Error Hunt, give pairs two completed problems with different errors so they must diagnose and articulate the mistake in their own words.

What to look for

Provide students with two problems: 1) 7/8 - 1/4, and 2) 4 1/2 - 1 3/4. Ask them to write one sentence explaining the key difference in the procedure for solving each problem.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 40 min · Whole Class

Whole Class: Number Line Mixed Number Race

Draw large number lines on the board. Divide class into teams; each team sends a member to plot mixed numbers, subtract by jumping intervals, and borrow visually if needed. Correct teams score points; debrief as a class.

Design a word problem that requires subtracting mixed numbers and interpreting the result.

Facilitation Tip

In Number Line Mixed Number Race, require students to mark each step on the line so you can see their missteps in real time.

What to look for

Pose the question: 'Explain to a classmate why you need to borrow from the whole number when subtracting 3 2/5 from 5 1/5. What does the 'borrowed' whole become?' Facilitate a brief class discussion to solidify understanding of the borrowing concept.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 20 min · Individual

Individual: Word Problem Creator

Students design original word problems requiring mixed number subtraction with borrowing, such as dividing fabric lengths. Solve their own problem, then swap with a partner for peer checking using fraction circles.

Differentiate between the steps for adding and subtracting mixed numbers.

Facilitation Tip

When reviewing Word Problem Creator, check that students' scenarios require borrowing and that their solutions include clear fraction models.

What to look for

Present students with the problem: 'Calculate 5 1/3 - 2 1/2.' Ask them to show their steps on mini whiteboards, focusing on how they found a common denominator and handled borrowing. Review responses to identify common errors.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach subtraction of fractions by starting with concrete models before moving to symbols. Use fraction strips and number lines to show why denominators must match and why borrowing is necessary. Research shows students retain procedures better when they first understand the underlying concepts through hands-on work and peer discussion. Avoid rushing to abstract steps before students have internalized the visual models and language of equivalent fractions.

Students will confidently find common denominators, recognize when borrowing is needed, and execute subtraction steps correctly. They will explain their reasoning using precise vocabulary and correct notation in both written and verbal forms.

---

Watch Out for These Misconceptions

• During Fraction Strip Borrow Challenge, watch for students who try to subtract denominators directly. Redirect them to place their strips side by side to see why common denominators are needed.

  Ask students to find strips that match the size of the fractions they're comparing before proceeding. Have them explain how the strips represent equivalent fractions, emphasizing that the value stays the same even though the pieces look different.

• During Subtraction Error Hunt, watch for students who claim borrowing isn't necessary when the fractional parts are close in value. Redirect them to model the problem with fraction strips to see the gap.

  Have pairs model the problem with strips and observe where the pieces don't align. Guide them to convert one whole into equivalent fractions to bridge the gap, then subtract.

• During Word Problem Creator, watch for students who forget to subtract 1 from the whole number after borrowing. Redirect them to check their final mixed number against the original minuend.

  Ask students to write the original and final mixed numbers side by side and circle the whole number part in each. Prompt them to explain why the whole number decreases by one after borrowing.

---

Methods used in this brief

• Problem-Based Learning