Sharing Decimal Quantities

Overview

In this eleventh lesson of the unit Decimal Fractions and Operations, students divide decimals by whole numbers using sharing, grouping and place-value strategies. They connect concrete representations to written calculations, choose an appropriate place value for the quotient, and verify answers through multiplication.

Learning intentions

• WALT divide decimals by whole numbers using sharing, grouping and place-value strategies.
• WALT represent a division problem in more than one way.
• WALT calculate a quotient to an appropriate place value.
• WALT check a division answer using multiplication.

Success criteria

• I can represent a decimal division problem using a diagram, materials, a number line or an equation.
• I can divide a decimal by a whole number accurately.
• I can explain why my answer has the correct place value.
• I can check my quotient by multiplying it by the divisor.

Curriculum links

• Mathematics and Statistics — number, decimal fractions and operations.
• Multiplicative thinking — interpreting division as sharing and grouping, and relating division to multiplication.
• Mathematical and statistical practices — represent, reason, communicate, justify and check solutions.
• Mathsteasers — using higher-order thinking questions to deepen understanding and challenge advanced learners.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior learning. Open with the opening question and decimal-sharing image and ask: “Four people share $7.20 equally. How much does each person receive?” Students estimate, discuss whether the answer should be more or less than $7.20, and explain a possible method. Briefly revisit decimal place value and the inverse relationship between multiplication and division.

2. 7–17 min · Concrete modelling. Use place-value materials or a place-value chart to model $7.20 ÷ 4. Teacher first shares 7 ones, then exchanges the remaining 3 ones and 2 tenths as 32 tenths, sharing these to give 18 tenths to each person. Record $1.80 and check with $1.80 × 4 = $7.20. Students follow the model, describe the exchange, and identify why the quotient has two decimal places. Refer to the place-value modelling slides.

3. 17–27 min · Two connected strategies. Model 6.3 ÷ 3 as both sharing 63 tenths into three equal groups and grouping along a number line in jumps of 2.1. Emphasise that the decimal can be expressed in tenths to make the division easier. Students solve 8.4 ÷ 4 and 9.6 ÷ 3 with a partner, showing either a place-value representation or number line before writing the equation. Check strategies through a short class discussion.

4. 27–45 min · Supported practice. Distribute the decimal division practice worksheet. Students work in pairs for the first two problems, then independently on the remaining questions. Include practical contexts such as sharing 5.6 litres among 4 containers and grouping 12.75 metres into 5 equal lengths. Students must show a representation, calculate the quotient, and use multiplication to check. Circulate and prompt: “What unit are you dividing?” “Where is the decimal?” and “How can multiplication confirm your answer?” Use the practice instructions and checking prompts.

5. 45–54 min · Reasoning challenge. Display the reasoning and challenge slides. Groups solve and justify: “A student says 14.4 ÷ 6 = 2.4 because 24 ÷ 6 = 4. Is the explanation correct? Improve it.” Students compare methods, identify errors and write a clear explanation. Invite groups to present different representations and discuss whether each answer is reasonable.

6. 54–60 min · Plenary and exit check. Students complete the final question on the reflection and exit-ticket section: “Solve 7.5 ÷ 3. Show one representation and check using multiplication.” They add one sentence explaining how they know the decimal point is correctly placed. Teacher samples responses, addresses a common misconception, and previews the next lesson on applying decimal operations in multi-step problems.

Resources

• decimal division teaching and practice slide deck
• decimal division practice worksheet
• Place-value blocks, counters or decimal grids
• Place-value charts
• Whiteboards and pens
• Rulers for number lines
• Calculators for checking selected answers only
• Exercise books and pencils

Assessment

• Listen during the hook and modelling for students’ understanding of sharing, grouping, decimal place value and reasonable estimates.
• During paired and independent practice, check whether students represent the dividend in suitable units, place the decimal correctly and use multiplication to verify.
• Collect or quickly scan the exit response, grouping students for the next lesson according to whether they need support with representation, calculation or checking.

Differentiation

• Support students with practical sharing contexts, place-value materials, decimal grids, number lines and a place-value chart. Allow them to begin with tenths or hundredths represented as whole units.
• Provide chunking prompts such as “How many tenths are there altogether?” and “Share the whole-number part first, then exchange.” Use worked examples with selected steps completed.
• Pair students strategically and provide sentence starters: “I represented ___ as ___ because…” and “My answer is reasonable because…”. Read contexts aloud and clarify vocabulary for EAL learners.
• For advanced learners, investigate divisions such as 1 ÷ 3, 5 ÷ 6 and 7.25 ÷ 8. Decide whether the quotient terminates or continues, explain the pattern, and choose an appropriate rounding level for a stated context.