Mathematics · Grade 5

Active learning ideas

Understanding Place Value to Millions

Active learning deepens understanding of place value by engaging students in physical and collaborative representations of numbers. When students move, discuss, and manipulate digits, they internalize the multiplicative relationships between places that static worksheets often fail to convey. This hands-on approach is particularly effective for numbers up to a million, where abstract ideas can feel overwhelming.

• Ontario Curriculum Expectations
• 5.NBT.A.1

• 20–60 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: The Human Place Value Chart

Students move through stations where they act as digits in a large floor-sized place value chart. At one station, they must physically shift positions when the 'multiplier' calls out a power of ten, observing how their value changes. Other stations involve using digital tools to zoom into number lines between 0 and 1.

Explain how the position of a digit determines its value in large numbers.

Facilitation Tip

During The Human Place Value Chart, ensure each student holds a digit card and a place value label so they can physically see how their digit’s value changes with its position.

What to look for

Provide students with the number 7,452,916. Ask them to: 1. Write the value of the digit 5. 2. Write the place value of the digit 4. 3. Explain in one sentence how the value of the digit 7 compares to the value of the digit 5.

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

Activity 02

• Inquiry Circle
• 60 min · Small Groups

Inquiry Circle: The Million Dollar Walk

Groups use base ten blocks to model 1, 10, 100, and 1,000. They then work together to calculate and describe the physical size of a block representing 1,000,000. They present their findings using a gallery walk format to compare different visualization strategies.

Compare the value of a digit in the thousands place versus the hundred thousands place.

Facilitation Tip

For The Million Dollar Walk, place number cards in order along a hallway and have students walk backward to emphasize the decreasing value of digits to the right.

What to look for

Display a large number on the board, such as 3,805,124. Ask students to hold up fingers to indicate the place value of a specified digit (e.g., 'Show me the place value of the 8'). Then, ask them to write the value of that digit on a mini-whiteboard.

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

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Decimal Symmetry

Students examine a place value chart and discuss why there is no 'oneths' place. They work in pairs to find the 'mirror' of the tens place (tenths) and the hundreds place (hundredths). They share their theories with the class to build a collective understanding of the decimal point as an anchor.

Analyze how grouping by tens simplifies the representation of large quantities.

Facilitation Tip

During Decimal Symmetry, provide base ten blocks for students to build each decimal before comparing, reinforcing the visual connection between tenths and hundredths.

What to look for

Pose the question: 'Imagine you have 10,000 ones blocks. How many ten thousands blocks would you need to represent the same quantity? Explain your reasoning using the concept of place value.'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach place value by starting with concrete models before moving to abstract notation. Use manipulatives like base ten blocks and place value sliders to show that the decimal point is a fixed marker, not a moving one. Avoid rushing to algorithms; instead, let students discover the patterns themselves through guided exploration and discussion. Research shows that students who construct their own understanding of multiplicative relationships retain the concept longer and apply it more flexibly.

By the end of these activities, students should confidently explain how each digit in a number relates to the others through multiplication or division by ten. They should fluently compare, represent, and justify the value of digits in whole numbers and decimals. Mastery is visible when students can reason beyond memorization and articulate their thinking clearly.

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Watch Out for These Misconceptions

• During The Human Place Value Chart, watch for students who think the decimal point moves when a number is multiplied or divided by ten.

  Use a place value slider with a fixed decimal point during the activity. Have students slide the digits left or right while keeping the decimal stationary, then ask them to describe how the value of each digit changes in relation to its new position.

• During The Million Dollar Walk, watch for students who assume longer decimals are always larger in value.

  Provide base ten grids for students to shade the tenths and hundredths places of each decimal. During the activity, have them justify their rankings by comparing the shaded areas, focusing on the tenths place as the primary indicator of size.

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Methods used in this brief

• Stations Rotation
• Inquiry Circle
• Think-Pair-Share