Mathematics · Class 5

Active learning ideas

Introduction to Decimals: Tenths

Active learning helps students grasp the abstract concept of tenths by making it concrete and visual. When learners manipulate grids, number lines, and currency models, they connect the unfamiliar decimal notation to familiar fractions and place values, which builds a strong foundation for future work with decimals.

• CBSE Learning Outcomes
• NCERT: D-1.1

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

Activity 01

• Carousel Brainstorm
• 30 min · Pairs

Manipulative Task: Tenths Grids

Give students 10x10 grid paper. Instruct them to shade tenths for decimals like 0.3 by colouring 3 squares out of 10 in a row. Pairs compare grids by placing one over the other and note which covers more area. Record findings in notebooks.

Explain how the decimal point separates whole numbers from fractional parts.

Facilitation Tip

During the Tenths Grids activity, circulate to ensure students shade exactly 6 squares to represent 0.6, not 6 out of a different total like 100 for hundredths.

What to look for

Present students with a set of cards showing fractions with a denominator of 10 (e.g., 4/10, 9/10). Ask them to write the equivalent decimal for each fraction on a mini-whiteboard. Review responses to check for understanding of the fraction-decimal link.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Collaborative Problem-Solving
• 40 min · Small Groups

Collaborative Problem-Solving: Decimal Number Lines

Small groups draw number lines from 0 to 2, marking tenths. Distribute decimal cards (e.g., 1.2, 0.8). Students place and justify positions through discussion. Groups share one line with the class for verification.

Compare the representation of tenths as a fraction and as a decimal.

Facilitation Tip

While using the Decimal Number Lines, ask each pair to explain their placement of 0.7 relative to 0.5 and 0.9 before moving on.

What to look for

Give each student a slip of paper. Ask them to draw a number line from 0 to 1, marking 0.5. Then, ask them to write one sentence explaining how the decimal 0.5 relates to the fraction 5/10.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Carousel Brainstorm
• 25 min · Whole Class

Hands-On: Rupee-Paise Model

Use 10 paise coins as tenths of a rupee. Demonstrate 1.5 rupees with 1 rupee note and 5 coins. Students replicate amounts like 0.7 rupees with coins, then write as decimals. Circulate to check conversions.

Construct a number line that accurately places various decimal tenths.

Facilitation Tip

In the Rupee-Paise Model, remind students that 1 rupee equals 100 paise, so 0.2 rupees is 20 paise, not 2 paise, to avoid confusion with tens and units.

What to look for

Pose the question: 'Imagine you have a chocolate bar broken into 10 equal pieces. If you eat 3 pieces, how can you write the amount you ate as both a fraction and a decimal?' Facilitate a brief class discussion to hear different explanations and clarify concepts.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 20 min · Individual

Sorting Game: Fraction-Decimal Pairs

Provide cards with fractions (3/10) and decimals (0.3). Individually match pairs, then explain one match to a partner. Collect cards for class tally of correct matches.

Explain how the decimal point separates whole numbers from fractional parts.

What to look for

Present students with a set of cards showing fractions with a denominator of 10 (e.g., 4/10, 9/10). Ask them to write the equivalent decimal for each fraction on a mini-whiteboard. Review responses to check for understanding of the fraction-decimal link.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with familiar fractions like halves and quarters to build intuition, then connect them to tenths. Use consistent language: always say 'two point three' instead of 'two decimal three' to reinforce the place value meaning. Avoid rushing to rules like 'move the decimal point'—focus on the value of each digit in its place.

Students who succeed will confidently explain that 0.3 means 3 tenths, 2.5 is 2 wholes and 5 tenths, and equivalent values can be written as both fractions and decimals. They will use visual tools to compare tenths and justify their reasoning during discussions with clear place value language.

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Watch Out for These Misconceptions

• During Tenths Grids, watch for students who shade 6 out of 100 squares for 0.6, thinking it represents hundredths instead of tenths.

  Prompt them to count aloud: 'Each big square is one whole, divided into 10 parts. Shade 6 small parts to show 6 tenths, or 6/10.' Ask another student to verify the shading before they record the decimal.

• During Decimal Number Lines, watch for students who place 0.10 after 0.9, believing it is larger than 0.9.

  Have them label the line from 0.1 to 1.0 in steps of 0.1 and compare 0.10 to 0.1 on the same line, noting that the zero does not add value. Use peer discussion to correct the order.

• During Rupee-Paise Model, watch for students who treat 2.3 as 23 paise instead of 2 rupees 30 paise.

  Model trading with real or play currency: give 2 one-rupee coins and 3 ten-paise coins to represent 2.3 rupees. Ask them to explain why 2.3 rupees is less than 3 rupees, using the physical coins as evidence.

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Methods used in this brief

• Carousel Brainstorm
• Collaborative Problem-Solving