Mathematics · Grade 5

Active learning ideas

Adding and Subtracting Decimals

Active learning transforms decimal addition and subtraction from abstract rules into visual, hands-on experiences. When students manipulate models, draw representations, and role-play real-world scenarios, they build a concrete understanding of place value that prevents common errors and deepens retention.

• Ontario Curriculum Expectations
• 5.NBT.B.7

• 30–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Place Value Mats: Decimal Addition

Provide mats divided into ones, tenths, and hundredths. Students represent two decimals with base ten blocks or drawings, align them, and combine blocks to find sums. They record the equation and draw their model.

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

Facilitation Tip

During Place Value Mats: Decimal Addition, circulate to ensure students label each column clearly and trade blocks for regrouping when sums exceed 9.

What to look for

Present students with two addition problems and two subtraction problems involving decimals to the hundredths. For example: 1. 12.34 + 5.67 = ? 2. 8.90 - 3.45 = ? Ask students to show their work, including aligning the decimal points, and to write one sentence explaining why aligning the points is important.

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

Activity 02

• Stations Rotation
• 45 min · Small Groups

Money Subtraction Stations

Set up stations with play money: students subtract prices from budgets using real coins and bills. They draw receipts showing alignment and explain steps to partners before rotating. Collect reflections on challenges faced.

Construct a visual model to represent the sum of two decimal numbers.

Facilitation Tip

In Money Subtraction Stations, encourage students to verbalize each trade (e.g., 'I have 3 dimes, but I need to subtract 5, so I exchange 1 dollar for 10 dimes') to reinforce place value thinking.

What to look for

Give each student a card with a subtraction problem like 7.50 - 2.25. Ask them to solve it, then write a brief explanation of how adding a zero (if needed) could help them solve a problem like 5.3 - 1.15.

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

Activity 03

• Stations Rotation
• 35 min · Pairs

Number Line Hops: Mixed Operations

Mark a large floor number line with decimal intervals. Pairs roll dice for addends, hop to solve, then subtract back. Record paths and discuss why alignment matters in jumps.

Analyze how adding zeros to the end of a decimal can help with subtraction.

Facilitation Tip

For Number Line Hops: Mixed Operations, ask students to explain their step size choices aloud to uncover misconceptions about tenths and hundredths spacing.

What to look for

Pose the question: 'Imagine you are adding 0.5 and 0.25. How could you use base ten blocks or draw a picture to show the answer?' Facilitate a brief class discussion where students share their visual strategies and explain how their models represent the sum.

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

Activity 04

• Stations Rotation
• 50 min · Small Groups

Decimal Shop Role-Play

Create a class store with priced items to hundredths. Students budget purchases, add totals, subtract costs, and verify with calculators. Switch roles as shopper and cashier.

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

Facilitation Tip

During Decimal Shop Role-Play, prompt the 'cashier' to justify change using place value language, such as 'Your total is $3.75, so I give back two quarters and two nickels to keep the dollars, dimes, and pennies separate.'

What to look for

Present students with two addition problems and two subtraction problems involving decimals to the hundredths. For example: 1. 12.34 + 5.67 = ? 2. 8.90 - 3.45 = ? Ask students to show their work, including aligning the decimal points, and to write one sentence explaining why aligning the points is important.

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

A few notes on teaching this unit

Teachers should start with concrete models before moving to abstract recording. Avoid rushing to algorithms; instead, use guided questions to help students discover rules through repeated exposure to correctly aligned models. Research shows that students who spend time constructing and discussing visual representations make fewer alignment and regrouping errors later. Always connect new learning to prior whole number knowledge to build on existing schemas.

Successful learning looks like students aligning decimal points without prompting, using zero placeholders naturally during subtraction, and explaining their reasoning with reference to models or diagrams. They should connect each step to place value language and correct their own work when misalignments occur.

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Watch Out for These Misconceptions

• During Place Value Mats: Decimal Addition, watch for students who shift numbers based on length, ignoring decimal alignment.

  Prompt them to compare their mat to a peer's and ask, 'Which tenths blocks are lined up in the same column?' Have them redraw the problem until all tenths are in the tenths column before adding.

• During Money Subtraction Stations, watch for students who believe adding zeros changes the value of the decimal.

  Ask them to model both versions with coins, then compare the physical amounts. Guide them to see that extra pennies equal zero while maintaining the dollar value, reinforcing that zeros only fill place value gaps.

• During Number Line Hops: Mixed Operations, watch for students who regroup incorrectly across the decimal point, treating tenths like ones.

  Have them decompose a problem like 4.3 - 1.5 using base ten blocks, trading a flat for rods when needed. Then, ask them to draw the trades on their number line to visualize the regrouping process.

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Methods used in this brief

• Stations Rotation