Comparing Decimal Amounts

Overview

Lesson 4 of 5 in Decimal Place Value Explorers. Students compare tenths and hundredths using visual models, equivalent fractions, place-value reasoning and comparison symbols. This lesson is designed for 20 Year 5–6 students working in pairs and small groups.

Learning intentions

• WALT compare tenths and hundredths represented as fractions and decimals.
• WALT rename tenths as hundredths when needed.
• WALT use place value to decide which decimal is greater, less than or equal to.
• WALT explain our mathematical reasoning using models and comparison symbols.

Success criteria

• I can compare decimals by checking the value of each place.
• I can recognise equivalent fractions and decimals, such as 0.3 = 0.30 = 30/100.
• I can use >, < and = correctly.
• I can explain my answer using a grid, fraction model, place-value chart or number line.

Curriculum links

• Number: understand, represent and compare decimals to at least hundredths.
• Number: connect fractions with denominators of 10 and 100 to decimal notation.
• Number: use place value and equivalence to solve and explain comparison problems.
• Mathematical practices: communicate mathematical thinking, use representations, justify conclusions and respond to others’ strategies.

Lesson structure (30 minutes)

1. 0–5 min – Daily review and activate prior knowledge Open with the review and hook slides. Students answer independently, then compare with a partner:

• Which is greater: 0.3 or 0.30? Explain.
• Which is greater: 4/10 or 35/100?
• Put 0.08, 0.8 and 0.18 in order. Take quick responses and address the misconception that a longer decimal is always larger.

2. 5–10 min – Model equivalent representations Display a 10-by-10 decimal grid and model 0.3, 0.30, 3/10 and 30/100. Use the place-value mat to place digits in the tenths and hundredths columns. Ask: “What has changed? What has stayed the same?” Emphasise that adding a zero to the right of a decimal does not change its value.

3. 10–15 min – Compare with concrete materials In pairs, students use teacher-prepared decimal grids and fraction strips to model comparison examples, including 0.4 and 0.35, 0.6 and 0.60, and 0.08 and 0.18. Partners rename tenths as hundredths where needed, then record a comparison using >, < or =. Prompt students to justify each answer rather than relying on appearance.

4. 15–20 min – Human number line Place 0 and 1 at opposite ends of the room, with 0.5 as a benchmark. Give selected students decimal cards and ask them to stand where they think their number belongs. Use examples such as 0.08, 0.18, 0.3, 0.35, 0.8 and 0.80. The class discusses and adjusts positions, explaining which place-value information helped.

5. 20–26 min – Paired practice Distribute the decimal comparison practice sheet. Students complete comparison questions independently for two minutes, then check and explain answers with a partner. Include straightforward tenths first, followed by mixed tenths and hundredths, equivalent representations and ordering three decimals. Circulate and ask: “Which place did you compare first?” and “Can you show this as hundredths?”

6. 26–30 min – Share, assess and preview Open the explanation and plenary slides. Invite two students to explain different strategies for one comparison. Students complete the final “prove it” question on the worksheet: compare 0.7 and 0.65 using a representation and a sentence. Preview the final unit lesson, where students will apply decimal comparison in a practical problem.

Resources

• the decimal comparison slide deck
• the decimal comparison practice sheet
• the place-value mat
• Decimal grids showing tenths and hundredths
• Fraction strips or paper strips divided into tenths and hundredths
• Decimal and fraction cards for the human number line
• Large labels for 0, 0.5 and 1
• Mini-whiteboards, markers and pencils

Assessment

• Listen during the review, modelling and number-line discussion for accurate use of place-value language and recognition of equivalent forms.
• Check the worksheet for correct symbols, ordering and explanations, particularly comparisons requiring tenths to be renamed as hundredths.
• Use the final “prove it” response to identify students needing targeted support in the next lesson.

Differentiation

• Support learners with comparison mats, the place-value mat, benchmark points of 0, 0.5 and 1, and decimal grids. Begin with numbers such as 0.2 and 0.5 before introducing mixed examples.
• Provide sentence frames: “I compared the ___ place first because…”, “___ is greater than ___ because…”, and “___ tenths is equivalent to ___ hundredths.”
• Use targeted partner practice, assigning confident explainers to model reasoning without completing the task for others. Allow students to point, build or draw before recording symbols.
• Extend advanced learners with missing-digit challenges, such as “0.__ > 0.45” or “0.3__ < 0.35”. Ask them to find and prove more than one possible answer.