Mathematics · Year 4

Active learning ideas

Decimal Discovery: Tenths

Active learning works for this topic because students need to physically manipulate representations of tenths to move beyond whole number thinking. When they see, touch, and compare decimal amounts in multiple forms, they build lasting connections between symbols, words, and visual models.

• ACARA Content Descriptions
• AC9M4N01
• AC9M4N02

• 25–50 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 40 min · Small Groups

Gallery Walk: Decimal Representations

Students create posters showing a decimal (e.g., 0.75) as a fraction, a shaded grid, a location on a number line, and a collection of coins. The class moves around the room with sticky notes to leave 'I notice' or 'I wonder' comments on each representation.

Evaluate when it is more useful to use a decimal instead of a whole number.

Facilitation Tip

During the Gallery Walk, place a timer at each station so students move at a steady pace without rushing through comparisons.

What to look for

Present students with a set of number lines marked with tenths. Ask them to circle the number 0.7 and write the fraction it represents. Then, ask them to shade a visual model (like a rectangle divided into 10 parts) to represent 0.7.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Simulation Game
• 50 min · Pairs

Simulation Game: The Decimal Shop

Set up a classroom shop with items priced in dollars and cents. Students use play money to pay for items, focusing on how 10 cents represents one tenth of a dollar and 1 cent represents one hundredth, recording their transactions in decimal form.

Design a visual representation to differentiate between a tenth and a whole.

Facilitation Tip

During The Decimal Shop, circulate with a small notepad to jot down authentic student language about prices and change.

What to look for

Pose the question: 'When might it be more useful to write 1.5 metres instead of 1 metre and 50 centimetres?' Facilitate a discussion where students compare the efficiency and clarity of using decimals for measurements.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Inquiry Circle
• 25 min · Whole Class

Inquiry Circle: Human Number Line

Give each student a card with a decimal or a fraction (e.g., 0.5, 1/10, 0.25). Without speaking, students must organize themselves into a physical number line from zero to one, justifying their position to their neighbors once the line is formed.

Justify the use of a decimal point to separate whole units from parts.

Facilitation Tip

During the Human Number Line, stand yourself on an even-numbered position so you can model movement left and right as students take their turns.

What to look for

Give each student a card with a picture of a whole divided into 10 equal parts, with some parts shaded. Ask them to write the decimal and fraction that represents the shaded part, and to explain in one sentence why the decimal point is important.

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

A few notes on teaching this unit

Experienced teachers approach this topic by anchoring new decimal notation to familiar fraction ideas. They avoid rushing to abstract rules and instead let students discover patterns through repeated visual comparisons. Research shows that students who build decimals from concrete tenths before moving to hundredths show stronger long-term retention and fewer misconceptions.

Successful learning looks like students confidently translating between decimals and fractions, using place value language for tenths, and recognizing decimals in real-world contexts like money and measurement. They should explain why 0.8 is greater than 0.10 and model both values accurately.

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Watch Out for These Misconceptions

• During Gallery Walk: Decimal Representations, watch for students who claim 0.10 is larger than 0.8 because 10 is greater than 8.

  Redirect them to the 10x10 grid stations where they must shade 0.8 as 80 squares and 0.10 as 10 squares, then compare the areas side by side with a partner.

• During Simulation: The Decimal Shop, watch for students who believe the decimal point moves when prices increase or decrease.

  Use the taped place value chart on the desk so students slide digit cards left or right while the decimal point stays fixed, reinforcing that the value changes but the point’s position does not.

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Methods used in this brief

• Gallery Walk
• Simulation Game
• Inquiry Circle