Adding Decimal Numbers

Overview

Lesson 10 of 15 in Number Connections: Fractions, Decimals, Percentages. Students add and subtract decimals accurately in meaningful money and measurement contexts, using place-value understanding, written methods and estimation.

Learning intentions

• WALT add and subtract decimals accurately.
• WALT connect decimals to money and measurement.
• WALT choose and explain a suitable calculation method.
• WALT estimate to check whether an answer is reasonable.

Success criteria

• I can align decimal points and place values correctly.
• I can calculate using a written or visual method.
• I can use zeros as placeholders when needed.
• I can estimate and explain whether my answer is reasonable.

Curriculum links

• Number: understand place value and use decimals to solve addition and subtraction problems.
• Additive thinking: select, represent and explain efficient strategies for additive problems.
• Measurement: use decimal quantities in contexts such as length, mass and capacity.
• Mathematical communication and reasoning: explain thinking, use estimates and check solutions.

Lesson structure (45 minutes)

1. 0–5 min – Hook and connect Open with the opening money problem: “You have $20.00. You spend $7.85 and then $3.60. How much is left?” Students estimate independently, then share strategies with a partner. Connect the decimal amounts to dollars and cents and explain that today’s focus is accuracy and reasonableness.

2. 5–13 min – Explicit teaching Use the place-value teaching slides to model:

• $12.40 + $3.75 = $16.15
• 8.50 − 2.76 = 5.74 Emphasise aligning decimal points, not simply lining up the digits. Show the same calculations on a place-value chart and with base-ten representations, then discuss why trailing zeros can be added. Model estimating $8.50 − $2.76 as about $9 − $3 = $6.

3. 13–18 min – Guided practice Display the guided examples from the worked-example slides. Students solve on mini-whiteboards:

• 4.6 + 2.35
• 10.00 − 3.48 Pause after each calculation to check alignment, regrouping and estimation. Invite students to explain where a zero is useful and how they know the answer is sensible.

4. 18–33 min – Differentiated workbook practice Distribute the decimal addition and subtraction practice sheet. Students work independently, then compare selected answers with a partner.

• Support: use the place-value chart, squared paper and base-ten representations; begin with tenths and money amounts with no regrouping.
• Core: solve mixed addition and subtraction problems involving tenths and hundredths in shopping and measurement contexts.
• Extension: solve multi-step budgeting and measurement problems, recording an estimate and explaining the most efficient method. Circulate to check that students align decimal points and ask, “What estimate did you make?”

5. 33–39 min – Context challenge Show the budgeting and measurement challenge. In pairs, students solve one problem such as: “A picnic costs $14.75 for food, $6.40 for drinks and $3.85 for fruit. What is the total? If the budget is $30, how much remains?” Measurement option: “A 2.5 m rope is cut by 0.85 m and then 0.4 m. How much remains?” Pairs must show a written or visual method and an estimate.

6. 39–45 min – Share and assess Use the discussion and exit prompt. Invite two students to compare methods and discuss which was efficient and why. Students complete the worksheet exit question: calculate 6.00 − 2.75, estimate first, and write one sentence explaining how they checked the answer. Revisit the WALT and success criteria.

Resources

• the complete decimal lesson slide deck
• the decimal addition and subtraction practice sheet
• Mini-whiteboards and pens
• Pencils and erasers
• Squared paper
• Place-value charts
• Base-ten blocks or decimal place-value equipment
• Projector or interactive whiteboard

Assessment

• Observe guided practice for decimal alignment, regrouping and use of place-value language.
• Check differentiated worksheet responses, estimates and explanations.
• Use the exit question to identify students needing further support with alignment, subtraction or checking reasonableness.

Differentiation

• Provide a colour-coded place-value chart, squared paper and base-ten materials; initially limit calculations to tenths and familiar money amounts.
• Read problems aloud, highlight key information and provide sentence stems such as “My estimate is… because…” for EAL learners and students needing language support.
• Allow students to explain orally, draw a model or use a written algorithm; pair strategically during the context challenge.
• Extend confident learners with multi-step budgeting, change and measurement problems requiring comparison of two methods and justification of efficiency.