Comparing Decimal Numbers

Overview

Lesson 9 of 15 in Number Connections: Fractions, Decimals, Percentages. Students compare, order and justify decimal numbers to hundredths using money, measurement, place-value representations and number lines.

Learning intentions

• WALT compare and order decimal numbers to hundredths.
• WALT align place values when comparing decimals.
• WALT use <, > and = accurately.
• WALT explain why zeros can be added to the end of a decimal without changing its value.

Success criteria

• I can align the ones, tenths and hundredths places.
• I can use comparison symbols correctly.
• I can order decimals from smallest to largest and explain my reasoning.
• I can add a zero as a placeholder and explain why the value stays the same.

Curriculum links

• Number: recognise, represent, compare and order decimals in familiar contexts.
• Number: use place value to explain the relative size of numbers.
• Number: connect fractions, decimals and percentages through equivalent representations.
• Mathematical practices: communicate mathematical thinking, use representations, and justify conclusions.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook: Which is greater? Open with the decimal comparison hook. Display a price or measurement pair such as $3.50 and $3.05. Students silently decide which is greater, then show their answer with hand signals. Invite several explanations without confirming immediately.

2. 5–12 minutes – Explicit teaching: align place values Use the place-value teaching slides to model a place-value chart. Compare 4.7 and 4.65 by writing 4.70 and 4.65, then compare from left to right: ones first, then tenths, then hundredths. Emphasise that 4.70 and 4.7 represent the same amount because the added zero is a placeholder, not an extra tenth.

Model comparison symbols and read each statement aloud: “4.70 is greater than 4.65.” Link this to money ($4.70 and $4.65) and measurement (4.70 m and 4.65 m).

3. 12–20 minutes – Guided practice: prove it In pairs, students use mini-whiteboards or place-value mats to solve the examples on the guided comparison slides. Include 0.6 and 0.58, 2.04 and 2.4, and 7.25 and 7.205. Pause after each example for students to explain which place value decided the comparison.

Address the misconception that “more digits means a bigger number”. Ask: “Is 0.6 bigger or smaller than 0.58? How can we rewrite 0.6 to make the comparison clearer?”

4. 20–32 minutes – Pair practice: order and justify Distribute the decimal comparison and ordering worksheet. Students complete the place-value, comparison-symbol and ordering questions independently for the first five minutes, then compare methods with a partner. They should use a decimal number line for at least one question and write a short justification for one ordering decision.

Circulate and prompt: “Which place are you comparing first?”, “Could you add a zero?”, and “How does the number line show this?” Select two different strategies to share.

5. 32–40 minutes – Real-life challenge and feedback Use the real-life application slides. Groups of four order a set of prices or measurements from smallest to largest and prepare a spoken explanation. Include close comparisons such as $5.08, $5.80 and $5.18. Groups hold up their ordered list, then explain one common error and how to avoid it.

For rapid feedback, ask students to correct: “3.9 < 3.89” and explain the correction using 3.90.

6. 40–45 minutes – Plenary and exit check Return to the reflection and exit slides. Students complete the final two questions on the worksheet: compare 6.2 and 6.20, then order 1.09, 1.9 and 1.19. Students must add one sentence explaining why a zero may be added to a decimal. Invite two students to share different explanations.

Resources

• the decimal comparison lesson deck
• the decimal comparison and ordering worksheet
• Place-value mats or grids
• Decimal number-line strips
• Number cards showing tenths and hundredths
• Mini-whiteboards and pens
• Pencils and highlighters
• Displayed money and measurement examples

Assessment

• Observe pair explanations for accurate place-value language and correct use of <, > and =.
• Check worksheet responses, especially comparisons involving zeros and numbers such as 0.6 and 0.58.
• Use the final explanation and ordering task as an individual exit check to identify who needs further support before the next lesson.

Differentiation

• Support learners with a place-value grid, expanded notation, colour-coded columns and number cards. Explicitly teach that 0.6 can be written as 0.60, and rehearse reading each digit’s value.
• Reduce the initial task to numbers with the same ones digit, then introduce differing ones digits. Pair students strategically and provide sentence stems: “I know ___ is greater because…”.
• Support EAL learners with visual money and measurement contexts, gestures, repeated oral rehearsal and the terms “greater than”, “less than”, “equal to”, “tenths” and “hundredths”.
• Extend confident learners by ordering decimals to thousandths, including numbers such as 2.4, 2.39 and 2.405, and finding several decimals between two given numbers.