Mathematics · Year 5

Active learning ideas

Adding and Subtracting Decimals

Active learning helps students grasp decimal operations by turning abstract rules into concrete experiences. When students manipulate place value mats or race through relay problems, they internalize why decimal points must align and how estimation prevents errors. These hands-on moments build both accuracy and confidence before moving to paper-and-pencil work.

• ACARA Content Descriptions
• AC9M5N02

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

Activity 01

• Stations Rotation
• 35 min · Small Groups

Money Market: Addition Simulation

Provide play money in dollars and cents. Students in small groups select items with decimal prices, add totals on mini whiteboards while aligning points, then estimate first by rounding. Groups present one purchase to the class for verification.

Analyze the importance of aligning decimal points when adding or subtracting decimals.

Facilitation Tip

During Money Market, circulate with a checklist to watch for students who skip writing decimal points in their place value mats.

What to look for

Present students with three addition or subtraction problems involving decimals with varying places (e.g., 12.5 + 3.78, 25.05 - 1.2). Ask them to first estimate the answer, then solve the problem, showing their work. Review their work for accurate alignment and calculation.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Decimal Dash: Subtraction Relay

Line up pairs at the board with decimal subtraction cards. One student aligns and subtracts at the board while partner estimates aloud. Switch roles after each problem; first accurate pair to finish advances.

Construct a method for estimating the sum or difference of decimals before calculating.

Facilitation Tip

In Decimal Dash, assign roles so every student practices both writing and solving problems under time pressure.

What to look for

Give students a problem like: 'Sarah bought a book for $15.75 and a pen for $3.50. She paid with a $20 note. How much change did she receive?' Ask students to write down the steps they took, including their estimation, calculation, and final answer.

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Estimation Stations: Rotation Challenge

Set up three stations with decimal problems: one for rounding estimates, one for exact addition, one for error checking. Groups rotate every 7 minutes, recording strategies and comparing estimates to exact answers.

Evaluate common errors made when performing decimal operations and suggest corrections.

Facilitation Tip

At Estimation Stations, pause the rotation to debrief one group’s strategy before letting others proceed.

What to look for

Provide students with two solved decimal addition/subtraction problems, one correct and one with a common error (e.g., misaligned decimal points). Have students work in pairs to identify which problem is solved incorrectly, explain the error, and show the correct solution.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Place Value Puzzle: Individual Matching

Students match decimal addition problems to correct alignments and solutions using puzzle pieces. They explain one match to a partner, noting estimation checks, then create their own puzzle.

Analyze the importance of aligning decimal points when adding or subtracting decimals.

What to look for

Present students with three addition or subtraction problems involving decimals with varying places (e.g., 12.5 + 3.78, 25.05 - 1.2). Ask them to first estimate the answer, then solve the problem, showing their work. Review their work for accurate alignment and calculation.

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

A few notes on teaching this unit

Teach this topic by starting with visual models—place value mats and base-ten blocks—to show why alignment matters. Avoid rushing to the algorithm; let students discover the rules through guided errors and corrections. Use frequent low-stakes checks, like thumbs-up or whiteboards, to catch misconceptions early before they solidify.

Students will align decimal points correctly, estimate answers before calculating, and explain their reasoning using place value language. They will identify and correct errors in peer work, showing that they understand why misalignment or skipped steps lead to wrong answers.

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Watch Out for These Misconceptions

• During Money Market, watch for students who add 2.30 and 1.45 as 3.75 by ignoring the decimal point and treating them as whole numbers.

  Have students write each amount on a place value mat, using colored rods to show tenths and hundredths. Ask them to read their sum aloud, forcing attention to the decimal point placement.

• During Decimal Dash, watch for students who borrow without considering the decimal point, such as subtracting 1.5 from 3.02 by borrowing from the ones place incorrectly.

  Provide manipulative rods to model 3.02 as 3 ones, 0 tenths, and 2 hundredths. Students physically move rods to borrow, reinforcing that the decimal point stays fixed while borrowing crosses place values.

• During Estimation Stations, watch for students who skip estimation entirely, assuming exact calculations are always correct.

  Use a timer to make estimation a race: students must round each problem to the nearest whole number or tenth before solving. Then, they compare estimates to exact answers to spot discrepancies.

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Methods used in this brief

• Stations Rotation