Mathematics · Grade 5

Active learning ideas

Multiplying Decimals by Whole Numbers

Students need to see how decimal multiplication connects to whole number work they already trust. Active learning lets them test predictions with tools like grid paper and base-ten blocks, turning abstract rules into visible patterns they can explain themselves.

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

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 35 min · Pairs

Manipulative Match: Base-Ten Blocks

Provide base-ten flats, rods, and units to represent decimals like 0.3 or 2.4. Students multiply by a whole number using repeated addition on mats, then record the product and decimal placement. Partners verify each other's work and adjust models as needed.

Predict the placement of the decimal point in the product of a decimal and a whole number.

Facilitation Tip

During Manipulative Match, ask partners to verbalize each step of their base-ten block arrangement to reinforce place value connections.

What to look for

Provide students with the problem: 'A recipe calls for 2.5 cups of flour per batch. If you make 4 batches, how many cups of flour do you need?' Ask students to show their work and write one sentence explaining how they determined the decimal point's placement in their answer.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 40 min · Small Groups

Grid Paper Arrays: Visual Multiplication

Students draw decimal rectangles on grid paper, such as 1.5 by 4 units, shading to show the decimal. They count total shaded squares to find products and predict decimal positions first. Groups share arrays on chart paper for class comparison.

Explain how multiplying decimals is similar to multiplying whole numbers.

Facilitation Tip

For Grid Paper Arrays, have students label each row and column with the correct place value before multiplying to prevent skipping steps.

What to look for

Present students with three multiplication problems: 3.4 x 5, 0.7 x 6, and 12.1 x 2. Ask them to solve each problem and then circle the one where they felt most confident predicting the decimal point's location, writing one reason why.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 30 min · Whole Class

Problem Design Relay: Real-World Scenarios

Teams line up and solve a decimal multiplication problem at the board, like 2.75 times 6 for recipe scaling. Correct answer passes baton with a new problem they create. Whole class discusses strategies after each relay.

Design a real-world problem that requires multiplying a decimal by a whole number.

Facilitation Tip

In Problem Design Relay, set a strict time limit for each round so students focus on clear, realistic scenarios rather than overly complex setups.

What to look for

Pose the question: 'Imagine you need to multiply 1.8 by 7. How is this calculation similar to multiplying 18 by 7? How is it different? Explain your reasoning using place value.' Facilitate a brief class discussion where students share their comparisons.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 45 min · Pairs

Budget Builder: Shopping Simulation

Give catalogs with decimal prices. Pairs select items totaling under a budget, multiplying quantities by unit prices. They explain decimal placements and adjust selections collaboratively.

Predict the placement of the decimal point in the product of a decimal and a whole number.

What to look for

Provide students with the problem: 'A recipe calls for 2.5 cups of flour per batch. If you make 4 batches, how many cups of flour do you need?' Ask students to show their work and write one sentence explaining how they determined the decimal point's placement in their answer.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start by reminding students that multiplying decimals is the same as multiplying whole numbers until they place the decimal point, which depends on the decimal factor alone. Avoid teaching shortcuts like counting decimal places before they understand why those places matter. Research shows students grasp place value better when they build and measure physical models before moving to paper calculations.

Students will confidently predict where the decimal point lands by connecting place values to visual models. They will justify their reasoning with clear language and apply the skill to practical situations like shopping or gardening without relying on memorized steps.

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Watch Out for These Misconceptions

• During Manipulative Match, watch for students who move all blocks to the product side without tracking the decimal factor's place value.

  Ask them to rebuild the decimal factor using a different color block and verbally explain how many tenths or hundredths it represents before multiplying.

• During Grid Paper Arrays, watch for students who place the whole number multiplier in the array instead of the decimal factor.

  Have them outline the grid to match the decimal's tenths or hundredths and label each square before counting, so they see the product's size clearly.

• During Budget Builder, watch for students who ignore the decimal and treat amounts like 3.50 as 350 when calculating totals.

  Prompt them to write each price with a decimal point and use play money to model multiplication, reinforcing that 3.50 times 4 is not 1400 but 14.00.

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Methods used in this brief

• Problem-Based Learning