Mathematics · Grade 5

Active learning ideas

Multiplying by Powers of Ten

Active learning helps students see the concrete changes in place value when multiplying by powers of ten. Moving digits with manipulatives or grids makes the abstract rule visible. Students connect the shift to the value increase, rather than memorizing rules without understanding.

• Ontario Curriculum Expectations
• 5.NBT.A.2

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 30 min · Pairs

Manipulative Shift: Base-10 Blocks

Give students base-10 blocks to represent decimals like 0.45. Instruct them to multiply by 10 or 100 by regrouping blocks and shifting positions. Pairs record before-and-after sketches and share patterns with the class.

Predict the outcome when a decimal is multiplied by 100.

Facilitation Tip

During Manipulative Shift, circulate to ensure students correctly regroup blocks when multiplying decimals, noting how ten unit blocks become one rod.

What to look for

Present students with a series of problems like '3.14 x 10 = ?' and '56 x 100 = ?'. Ask them to write the answer and then briefly explain the rule they used to get it.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Inquiry Circle
• 35 min · Small Groups

Pattern Hunt: Number Grids

Small groups create grids with numbers from 1.23 to 12.3, multiplying each by 10, 100, and 1,000. They highlight digit shifts and decimal movements. Groups present one key pattern to the class.

Explain the relationship between moving the decimal point and multiplying by powers of ten.

Facilitation Tip

In Pattern Hunt, ask students to circle patterns in the grid before explaining them aloud, building confidence in their observations.

What to look for

Give students a decimal, for example, 0.75. Ask them to calculate the product of this decimal multiplied by 10, 100, and 1000. On the back, they should explain how the decimal point moved for each calculation.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Inquiry Circle
• 20 min · Pairs

Relay Race: Decimal Multipliers

Prepare cards with decimals and powers of ten. Pairs line up; one solves a card, tags partner to run next. First pair finishing all correctly wins. Review answers whole class.

Analyze how the value of a digit changes when it shifts places due to multiplication by a power of ten.

Facilitation Tip

For Relay Race, assign mixed whole numbers and decimals to each team to prevent pattern memorization without understanding.

What to look for

Pose the question: 'How does multiplying 25 by 100 change the value of the digit '2'?' Guide students to explain that the '2' in 25 represents 2 tens (20), but in 2500, it represents 2 thousands (2000), a change of 100 times its original value.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 04

• Inquiry Circle
• 40 min · Small Groups

Scale Models: Classroom Measures

Small groups measure objects like desks in cm, multiply by 10 or 100 for meters or larger scales. Plot scaled versions on graph paper. Discuss real-world applications.

Predict the outcome when a decimal is multiplied by 100.

What to look for

Present students with a series of problems like '3.14 x 10 = ?' and '56 x 100 = ?'. Ask them to write the answer and then briefly explain the rule they used to get it.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teachers should start with whole numbers to establish the pattern of zeros, then transition to decimals to highlight the decimal shift. Avoid teaching tricks like 'just add zeros,' as this leads to misconceptions with decimals. Use consistent language, such as 'multiplying by 100 shifts digits two places to the left in terms of place value,' to reinforce the concept.

Students will confidently multiply whole numbers and decimals by powers of ten, explaining how digits move and why the value changes. They will use place value language to justify their answers, such as 'The 4 in 4.5 moves two places right to become 450.' Observations and written work show this understanding.

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Watch Out for These Misconceptions

• During Manipulative Shift, watch for students who incorrectly regroup blocks when multiplying decimals, treating them as whole numbers.

  Have students verbalize each regrouping step, using base-10 language like 'Ten unit blocks become one rod, so the decimal moves right one place.'

• During Pattern Hunt, watch for students who describe the decimal point moving left when multiplying by powers of ten.

  Use the number grid to trace the point moving right with a highlighter, asking students to describe the shift in terms of place value columns.

• During Scale Models, watch for students who add zeros to decimals as if they were whole numbers.

  Have students measure classroom objects and multiply by powers of ten, recording the exact changes on a place value chart to clarify the decimal shift.

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Methods used in this brief

• Inquiry Circle