Simplifying Fractions

Active learning works for simplifying fractions because students must physically manipulate materials to see how parts relate to wholes. This hands-on approach builds spatial reasoning and deepens understanding of equivalence between fractions, decimals, and percentages.

• Year 5
• Mathematics
• 3 activities
• 20 min–45 min

Learning Objectives

1. Identify the greatest common factor (GCF) for pairs of numbers up to 100.
2. Calculate the simplest form of a given fraction by dividing the numerator and denominator by their GCF.
3. Compare two fractions by simplifying them to their lowest terms and determining their equivalence.
4. Explain why a fraction is in its simplest form when the numerator and denominator have no common factors other than 1.
5. Justify the steps taken to simplify a fraction using the concept of common factors.

Simulation Game

⏱ 45 min·Pairs

Simulation Game: The 100-Square Shop

Students run a mock shop where every item is priced out of $100. They apply 'discount cards' (e.g., 20% off) and must use a 100-grid to color in the saving and calculate the new price, explaining their math to the 'customer.'

Prepare & details

Explain why simplifying fractions makes them easier to work with.

Facilitation Tip: During The 100-Square Shop, circulate to ensure each pair uses the grid to count units aloud as they ‘purchase’ simplified fractions of items.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Percentages in the Wild

Students find examples of percentages in news headlines or food packaging (e.g., '98% fat-free' or '60% of voters'). They think about what the 'whole' is in each case, pair up to discuss if the percentage sounds 'large' or 'small,' and share with the class.

Prepare & details

Compare different methods for simplifying fractions (e.g., dividing by common factors, prime factorization).

Facilitation Tip: In Percentages in the Wild, listen for students connecting real-world examples (like discounts) to the fraction and percentage forms they write on their cards.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Inquiry Circle

⏱ 30 min·Whole Class

Inquiry Circle: The Human Bar Graph

The class is asked a question (e.g., 'Who likes Vegemite?'). Students stand in a line of 10. If 7 students step forward, they discuss why that is 7/10 or 70%. They then try with different group sizes to see how the percentage changes.

Prepare & details

Justify when a fraction is in its simplest form.

Facilitation Tip: For The Human Bar Graph, stand back after assigning values to let students self-correct spacing errors by comparing their human bars to the class scale.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Teaching This Topic

Teach this topic with concrete-pictorial-abstract progression, starting with physical 100-squares before moving to grids and symbols. Avoid rushing to algorithms; let students discover the GCF through repeated halving and grouping. Research shows that students who connect visual models to symbolic notation retain concepts longer and make fewer errors in simplification.

What to Expect

Successful learning looks like students confidently identifying equivalent fractions, using visual models to justify their simplifications, and explaining why 10% and 1/10 represent the same value when applied to a quantity.

Watch Out for These Misconceptions

Common Misconception

During The 100-Square Shop, watch for students who insist that 150% cannot represent a real quantity because it exceeds 100 squares on the grid.

What to Teach Instead

Direct students to combine two 100-squares or use blocks to physically build a stack that shows 150%, explaining that 150% is one and a half times the original amount.

Common Misconception

During Percentages in the Wild, listen for students who confuse 5% with 1/5 when describing real-world examples like discounts or interest.

What to Teach Instead

Have students color 5 squares on a blank 100-grid and then color 20 squares next to it, prompting them to compare the two visuals and recognize that 5% is much smaller than 1/5.

Assessment Ideas

Quick Check

After The 100-Square Shop, give students a list of fractions (e.g., 4/8, 6/9, 10/15, 7/14) and ask them to simplify each fraction to its lowest terms and write the GCF they used for each.

Exit Ticket

During The Human Bar Graph, provide each student with a fraction like 12/18 and ask them to write the steps they took to simplify it to its simplest form and explain why their final answer is in simplest terms.

Discussion Prompt

After Percentages in the Wild, pose the question: ‘Imagine you have two fractions, 3/5 and 6/10. How can simplifying fractions help prove they represent the same amount?’ Facilitate a class discussion where students share their methods and reasoning.

Extensions & Scaffolding

• Challenge: Ask early finishers to create their own 100-square shop scenario with a 50% discount, then write the original and discounted prices as fractions and decimals.
• Scaffolding: Provide fraction strips for students who struggle to visualize equivalence, and have them lay strips side-by-side to find matching lengths.
• Deeper: Invite students to research and present how percentages are used in real-world contexts like interest rates or sports statistics, focusing on how simplification helps compare values.

Key Vocabulary

Factor	A number that divides exactly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Common Factor	A number that is a factor of two or more different numbers. For example, 3 is a common factor of 12 and 18.
Greatest Common Factor (GCF)	The largest number that is a factor of two or more different numbers. The GCF of 12 and 18 is 6.
Simplest Form	A fraction where the numerator and denominator have no common factors other than 1. It is also called the lowest terms.
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 fractions.