Mathematics · Year 7

Active learning ideas

Fractions and Decimals Conversion

Active learning works for this topic because students need to repeatedly divide, observe patterns, and justify their reasoning to move from surface knowledge to deep understanding of fractions and decimals. Group activities create natural checks on overconfidence, while hands-on division builds fluency and speed.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number
• KS3: Mathematics - Ratio, Proportion and Rates of Change

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Sorting Relay: Terminating vs Recurring

Prepare cards with fractions like 1/2, 1/3, 3/5. In teams, one student converts a fraction using a calculator, runs to sort it under 'terminating' or 'recurring', then tags the next. Teams discuss predictions first and verify as a class.

Explain why some fractions result in terminating decimals while others recur.

Facilitation Tip

During Sorting Relay, circulate and listen for students verbalizing why 5/12 recurs while 7/25 terminates before they place the cards, correcting misclassifications immediately.

What to look for

Present students with a list of fractions (e.g., 1/8, 2/3, 5/16, 7/9). Ask them to write the decimal equivalent for each and label them as terminating or recurring. Check for accuracy in calculation and classification.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Prediction Pairs: Fraction Detective

Pairs receive fraction cards and predict if the decimal terminates or recurs based on denominator factors. They divide to check, record patterns in tables, then share one insight with the class.

Compare the efficiency of converting fractions to decimals versus decimals to fractions.

Facilitation Tip

In Prediction Pairs, hand out calculators only after students commit to a prediction and share their reasoning, preventing blind button-pushing.

What to look for

Give students a fraction like 3/11. Ask them to first predict if it will be terminating or recurring, explaining their reasoning based on the denominator's factors. Then, ask them to calculate the decimal to confirm their prediction.

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Conversion Circuit: Stations Challenge

Set up stations: one for fraction to decimal long division, one for decimal to fraction, one for predicting from factors, one for matching equivalents. Groups rotate, completing tasks and justifying answers.

Predict whether a given fraction will produce a terminating or recurring decimal.

Facilitation Tip

At Conversion Circuit stations, place a visible anchor chart of factor trees for denominators 2, 5, and 10 to guide students who freeze during division relays.

What to look for

Pose the question: 'When is it more efficient to convert a decimal to a fraction versus converting a fraction to a decimal?' Facilitate a class discussion where students share examples and justify their preferred methods for different types of numbers.

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

Activity 04

• Stations Rotation
• 20 min · Whole Class

Whole Class: Decimal Expansion Race

Project fractions; students race to write decimals to 10 places on mini-whiteboards, spotting recurrences. Discuss efficiencies and vote on quickest methods.

Explain why some fractions result in terminating decimals while others recur.

Facilitation Tip

In the Decimal Expansion Race, enforce a 3-second pause after each decimal is revealed so students can raise hands to signal termination or recurrence before moving on.

What to look for

Present students with a list of fractions (e.g., 1/8, 2/3, 5/16, 7/9). Ask them to write the decimal equivalent for each and label them as terminating or recurring. Check for accuracy in calculation and classification.

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

A few notes on teaching this unit

Teachers should start with short, timed drills to build automaticity, then layer in prediction tasks to make thinking visible. Avoid rushing to rules—let students discover the link between prime factors and decimal endings through repeated division. Research shows that students who predict before calculating develop better number sense and retain the concept longer.

By the end of these activities, students confidently convert fractions to decimals, classify them correctly as terminating or recurring, and explain their decisions using prime factors. They should also reverse the process, converting recurring decimals back to exact fractions with precision.

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Watch Out for These Misconceptions

• During Sorting Relay: Watch for students who assume all fractions terminate if they calculate far enough and stop checking for repeating patterns.

  In Sorting Relay, have teams hold up calculators only after they have written three decimal digits and circled any repeating digit or group, forcing early recognition of recurring patterns.

• During Prediction Pairs: Watch for students who claim any denominator that includes 10 automatically terminates, like 1/6.

  In Prediction Pairs, require students to draw a factor tree for each denominator and compare it to the chart of known terminating factors before making any prediction.

• During Conversion Circuit: Watch for students who believe recurring decimals cannot be converted back into exact fractions.

  During Conversion Circuit, place conversion cards at one station showing recurring decimals with their exact fractional forms, so students see the equivalence before converting others.

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Methods used in this brief

• Stations Rotation