Mathematics · Year 5

Active learning ideas

Introduction to Decimals: Tenths and Hundredths

Active learning works for decimals because visual models and manipulatives transform abstract symbols into concrete understanding. When students shade grids or sort money, they see how 0.3 is three parts of ten and 0.25 is twenty-five parts of one hundred, building mental images that persist beyond the lesson.

• ACARA Content Descriptions
• AC9M5N01
• AC9M5N02

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Hands-On: Decimal Grid Shading

Give each small group decimal grids divided into 10 or 100 squares. Students shade fractions like 4/10 or 23/100, record the decimal, and swap grids to read partners' work. Discuss equivalents as a group.

Explain the relationship between a tenth of a unit and a hundredth of a unit.

Facilitation Tip

During Decimal Grid Shading, circulate and ask students to say the decimal aloud as they shade, reinforcing place value vocabulary like 'three tenths' or 'forty-five hundredths'.

What to look for

Provide students with a hundred-grid. Ask them to shade 3 tenths and then shade another 4 hundredths. On the back, they should write the total amount shaded as a decimal and as a fraction.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Money Sort: Fraction-Decimal-Cents Match

Prepare cards showing fractions (e.g., 3/10), decimals (0.3), and money (30 cents). Pairs sort into matching sets three times, using play money to verify, then create their own sets to trade.

Compare the representation of a fraction and its decimal equivalent.

Facilitation Tip

While running Money Sort, listen for students to name coins as fractions (e.g., 'a quarter is one-fourth') before matching to decimals, bridging prior knowledge to new concepts.

What to look for

Present students with a number line marked from 0 to 1, with only tenths indicated. Ask them to place a marker for 0.05 and explain why they chose that position relative to 0.1 and 0.2.

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

Activity 03

• Stations Rotation
• 35 min · Small Groups

Number Line Parade: Ordering Decimals

Draw floor number lines from 0 to 2 with tape. Distribute decimal cards (e.g., 0.12, 0.9, 1.05) to small groups. Students position themselves, justify spots to the class, and adjust based on feedback.

Analyze how decimal notation extends the place value system to represent parts of a whole.

Facilitation Tip

In Number Line Parade, observe students’ placements and ask, 'Why did you put 0.15 here?' to prompt justification of place value reasoning.

What to look for

Pose the question: 'How is 0.7 the same as 0.70?' Guide students to discuss the concept of equivalent decimals and how adding a zero in the hundredths place does not change the value, relating it to fractions like 7/10 and 70/100.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Place Value Build: Expanded Form Towers

Provide base-ten blocks adapted for decimals (strips for tenths, squares for hundredths). Individuals build models for numbers like 0.47, write expanded form (4/10 + 7/100), then pair to compare sizes.

Explain the relationship between a tenth of a unit and a hundredth of a unit.

Facilitation Tip

During Place Value Build, challenge groups to build both 0.8 and 0.80 with place value blocks so they see the equivalence visually and physically.

What to look for

Provide students with a hundred-grid. Ask them to shade 3 tenths and then shade another 4 hundredths. On the back, they should write the total amount shaded as a decimal and as a fraction.

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

A few notes on teaching this unit

Research shows that integrating visual, auditory, and kinesthetic elements solidifies decimal understanding. Avoid rushing to abstract notation; let students grapple with models first. Use collaborative talk to normalize error and encourage peer correction. Emphasize reading decimals correctly ('zero point two five') to prevent place value confusion.

Students will confidently read, write, and compare decimals to hundredths using place value language. They will explain why 0.45 equals 0.450 and justify why 0.07 is less than 0.2, using models and number lines to support their reasoning.

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Watch Out for These Misconceptions

• During Number Line Parade, watch for students who order 0.19 before 0.2 because they compare 19 and 2 as whole numbers.

  Pause the group and have them align 0.19 and 0.2 vertically on a chart, then model regrouping 0.19 as 0.2 - 0.01 to show it is less than 0.2. Ask them to adjust the placement on the line based on this reasoning.

• During Place Value Build, watch for students who insist 0.5 must be written as 0.50 to have two digits after the decimal.

  Provide decimal strips and have students fold a tenth strip into ten equal parts to see 0.5 = 0.50. Then challenge pairs to prove equivalence by trading place value blocks: five tenths for fifty hundredths.

• During Decimal Grid Shading, watch for students who read 0.03 as 'three tenths' because they overlook the leading zero.

  Have students shade exactly three hundredths squares and count aloud, 'one hundredth, two hundredths, three hundredths,' matching the count to the decimal notation. Practice reading decimals aloud in pairs to reinforce correct pronunciation.

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Methods used in this brief

• Stations Rotation