Mathematics · Year 5

Active learning ideas

Fractions to Decimals Conversion

Active learning works because converting fractions to decimals relies on concrete understanding of place value and partitioning. When students manipulate physical or visual models, they connect abstract symbols to real quantities, which strengthens their ability to generalise across denominators like 10, 100, and 1000.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions, Decimals and Percentages

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Flipped Classroom
• 20 min · Pairs

Pairs: Fraction-Decimal Matching Cards

Prepare cards with fractions (e.g., 3/10, 7/100) and matching decimals. Pairs sort and match them, then justify each pair using mini place value charts. Pairs share one justification with the class.

Justify why 3/4 can be easily converted to a decimal.

Facilitation Tip

During Fraction-Decimal Matching Cards, circulate and listen for pairs justifying their matches using place value language like ‘tenths’ or ‘hundredths.’

What to look for

Present students with a set of fractions (e.g., 5/10, 23/100, 7/1000, 1/4). Ask them to write the decimal equivalent for each on a mini-whiteboard and hold it up. Observe for common errors related to place value.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 02

• Flipped Classroom
• 30 min · Small Groups

Small Groups: Place Value Relay Race

Divide class into groups of four. Call a fraction; first student writes decimal on board and passes baton. Next student verifies and adds justification. First group finished correctly wins.

Analyze the relationship between fractions like 7/100 and their decimal equivalents.

Facilitation Tip

In the Place Value Relay Race, stand close to the team area to model how to read denominators aloud before converting, reinforcing attention to place value.

What to look for

Pose the question: 'Why is it easier to convert 7/100 to a decimal than 1/3?' Facilitate a class discussion where students explain their reasoning, focusing on the role of denominators that are powers of 10 and the concept of repeating decimals.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 03

• Flipped Classroom
• 25 min · Whole Class

Whole Class: Interactive Grid Shading

Display 10x10 grids on board or screen. Students call fractions with denominators 10 or 100; class votes on decimal and shades collectively. Discuss patterns observed.

Predict the decimal form of a fraction like 1/8 by understanding its relationship to 1/2 and 1/4.

Facilitation Tip

For Interactive Grid Shading, demonstrate zero tolerance for leading zeros by shading 3/10 as three tenths blocks, not thirty hundredths.

What to look for

Give each student a card with a fraction like 3/4 or 6/10. Ask them to write the fraction as a decimal and then explain in one sentence how they arrived at their answer, referencing either the denominator or an equivalent fraction.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 04

• Flipped Classroom
• 15 min · Individual

Individual: Prediction Journals

Students predict decimals for fractions like 1/8 or 3/4, sketch place value models, then verify by dividing. They note relationships to known fractions in journals.

Justify why 3/4 can be easily converted to a decimal.

Facilitation Tip

In Prediction Journals, remind students to show their partitioning steps for fractions like 1/8, not just the final answer.

What to look for

Present students with a set of fractions (e.g., 5/10, 23/100, 7/1000, 1/4). Ask them to write the decimal equivalent for each on a mini-whiteboard and hold it up. Observe for common errors related to place value.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teach this topic by starting with concrete models before moving to symbols. Research shows that students need repeated exposure to denominators that are powers of 10 before tackling non-tenth fractions like 1/8. Avoid teaching shortcuts like ‘add a zero’ before students understand why the decimal moves. Instead, focus on partitioning and equivalence, linking fractions to familiar measures like money or length.

Successful learning looks like students confidently converting fractions to decimals without relying on rules alone, explaining their reasoning using place value language, and correcting peers’ errors through collaborative discussion. They should justify conversions using grids, money, or partitioning strategies.

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Watch Out for These Misconceptions

• During Fraction-Decimal Matching Cards, watch for students matching 3/10 to 0.30 or 7/100 to 0.7. Redirect them by asking them to shade the fraction on a tenths or hundredths grid first, then write the decimal without leading zeros.

  During Place Value Relay Race, listen for teams converting 7/100 as 0.7. Stop the race and ask them to model 7p in £1 using a money mat, reinforcing that 7/100 is 0.07, not 0.7.

• During Place Value Relay Race, watch for students dividing the numerator by 10 regardless of denominator size. Redirect by asking them to read the denominator aloud and explain how many parts the whole is split into before converting.

  During Prediction Journals, if students predict 1/8 as 0.18, ask them to partition 1/8 into halves and quarters first, then relate it to 0.5 and 0.25 to find 0.125. Encourage them to record their steps and reflect on the process.

• During Interactive Grid Shading, watch for students shading 3/10 as 30 squares in a hundredths grid. Stop them and ask, 'Does 3/10 mean 30 parts out of 100?' Have them re-shade correctly in a tenths grid to see the difference.

  During Fraction-Decimal Matching Cards, if students struggle with 45/1000, ask them to first convert it to 45 thousandths and shade it on a thousandths grid, then write the decimal as 0.045, emphasising the three decimal places.

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Methods used in this brief

• Flipped Classroom