Mathematics · Year 4

Active learning ideas

Decimal Discovery: Hundredths

Active learning with concrete models and real-world contexts helps students grasp hundredths because the concept requires visualizing tiny partitions of a whole. When students manipulate grids, coins, and number lines, they build mental images that make abstract place value meaningful and memorable.

• ACARA Content Descriptions
• AC9M4N01
• AC9M4N02

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 35 min · Pairs

Modelling Station: Hundredth Grids

Provide decimal grids divided into 100 squares. Students shade sections for numbers like 0.47, then compare to 0.4 by overlaying grids and counting differences. Partners explain why 0.47 needs hundredths. Record findings on mini whiteboards.

Compare the value of a tenth and a hundredth using models.

Facilitation Tip

During the hundredths grids activity, circulate and ask students to point to a single square and explain what 0.01 represents before they shade any area.

What to look for

Present students with a decimal grid shaded to represent a number. Ask them to write the decimal and the equivalent fraction. Then, ask: 'If this grid represented 1 dollar, how many cents would be shaded?'

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

Activity 02

• Stations Rotation
• 40 min · Small Groups

Money Hunt: Cent Scenarios

Distribute play money and scenario cards, such as 'Buy items totalling $1.23'. Students select exact coins, noting how cents represent hundredths. Groups create their own shopping problems and solve peers'. Discuss precision over tenths.

Construct a scenario where hundredths are more precise than tenths.

Facilitation Tip

During the money hunt, provide real coins so students can physically group cents to model dollars and decimal amounts.

What to look for

Pose the question: 'Imagine you are timing a race. One runner finishes in 10.5 seconds, and another finishes in 10.52 seconds. Who won and by how much? Explain why using the terms tenths and hundredths.'

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

Activity 03

• Stations Rotation
• 30 min · Small Groups

Ordering Relay: Decimal Line-Up

Write decimals to hundredths on cards. Teams line up in order on a floor number line, justifying placements with models. Switch roles for verification. Whole class reviews errors as a group.

Explain how hundredths relate to percentages (informally).

Facilitation Tip

During the ordering relay, assign roles like 'reader,' 'writer,' and 'verifier' to keep all students engaged in the comparison process.

What to look for

Give each student two cards. On one card, they write a number with tenths (e.g., 0.7). On the other, they write a number with hundredths that is equivalent to the tenths number (e.g., 0.70). They then draw a simple picture showing the relationship.

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

Activity 04

• Stations Rotation
• 25 min · Pairs

Fraction Link-Up: Matching Pairs

Create cards with fractions (e.g., 23/100), decimals (0.23) and money amounts ($0.23). Students match in pairs, then build models to prove equivalence. Share one match with the class.

Compare the value of a tenth and a hundredth using models.

Facilitation Tip

During the fraction link-up, require students to state both the decimal and fraction form aloud when they match cards to reinforce the equivalence.

What to look for

Present students with a decimal grid shaded to represent a number. Ask them to write the decimal and the equivalent fraction. Then, ask: 'If this grid represented 1 dollar, how many cents would be shaded?'

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

A few notes on teaching this unit

Teach hundredths by starting with what students already know about tenths, then gradually reducing the size of partitions to show how 0.01 fits into 0.1. Avoid rushing to abstract rules; instead, let students discover patterns through repeated, hands-on experiences. Research shows that students need 6 to 10 meaningful exposures to new decimal concepts before internalizing them, so plan activities that revisit hundredths in different contexts over time.

Students will confidently represent hundredths using multiple forms: shaded hundredths grids, decimal notation, and fraction equivalents. They will order decimals with hundredths correctly and explain the value of place in money and measurement contexts. Peer discussions will reveal their growing precision with the concept.

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Watch Out for These Misconceptions

• During the hundredths grids activity, watch for students who believe a hundredth is larger than a tenth because they see more parts on the grid.

  Have them shade 0.1 first, then shade a single hundredth square on the same grid. Ask them to compare the two shaded areas directly and explain why ten hundredths equal one tenth.

• During the fraction link-up activity, watch for students who treat decimals and fractions as separate concepts with no connection.

  Encourage them to shade the hundredths grids to match their fraction cards, then write the decimal equivalent side-by-side. Peer pairs must explain why 45/100 equals 0.45 before moving on.

• During the ordering relay activity, watch for students who add digits without considering place value, such as treating 0.2 and 0.03 as 0.23 instead of comparing values.

  Use base-ten rods renamed as hundredths flats to model the numbers. Students must physically regroup and compare the values before writing any sums or comparisons.

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Methods used in this brief

• Stations Rotation