Subtracting Decimals

Overview

This is lesson 6 of 12 in the unit Decimal Fractions and Operations. Students build on their understanding of place value and decimal addition to subtract decimals accurately, using estimation, visual models, regrouping and inverse operations to explain and check their thinking.

Learning intentions

• WALT subtract decimals using place value, regrouping and visual models.
• WALT estimate a difference before calculating.
• WALT explain and check a subtraction strategy using mathematical language.
• WALT choose an efficient method and justify why it works.

Success criteria

• I can estimate a difference before I calculate.
• I can align decimal points and place-value columns correctly.
• I can regroup when a digit cannot be subtracted.
• I can check my answer using addition and decide whether it is reasonable.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks connected to relevant textbook content and prior learning.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, multiple strategies and extension through non-routine problems.
• New Zealand Curriculum Refresh emphasis: mathematical reasoning, problem solving, communicating strategies and using representations to make sense of number.

Lesson structure (60 minutes)

1. 0–7 min · Launch and estimate. Teacher displays the problem 8.4 − 3.76 using the opening estimation slide and asks, “Will the answer be closer to 4, 5 or 6? How do you know?” Students estimate independently, compare with a partner and explain which digits influenced their estimate. Record several strategies without confirming the exact answer yet.

2. 7–18 min · Connect representations. Teacher models 8.40 − 3.76 with money or measurement, then represents it on a place-value chart and with a number line using the visual model and place-value slides. Make explicit that equivalent decimals can be written with zeros, so 8.4 becomes 8.40. Students use the place-value columns to describe what each digit represents and predict where regrouping will be needed.

3. 18–28 min · Explicit teaching and guided practice. Teacher models the vertical algorithm: align decimal points, subtract from right to left, regroup one whole or tenth when necessary, bring the decimal point straight down, and check by addition. Use the place-value slider the standard form place value slider to physically show a regrouping example such as 6.02 − 1.78. Students solve two guided examples on mini-whiteboards, showing either a visual model or written algorithm and explaining one step to a partner.

4. 28–45 min · Supported independent practice. Teacher distributes the subtracting decimals practice worksheet and conferences with individuals or pairs. Students complete estimation, calculation and checking questions, including money and measurement contexts. Pause after the first two questions to check decimal alignment and regrouping; students correct errors in a different colour and explain the correction.

5. 45–54 min · Strategy comparison and challenge. Teacher displays the strategy comparison and challenge slides and poses 12.5 − 7.86. Students solve it in two different ways, such as the standard algorithm and counting up on a number line, then compare efficiency, accuracy and ease of checking. Invite selected students to present contrasting methods and ask classmates to identify the mathematical reasoning used.

6. 54–60 min · Plenary and exit check. Teacher revisits the opening estimate and reveals the exact answer using the final reflection slide. Students complete an exit response: “Solve 10 − 3.47. Estimate first, show one calculation method, and check your answer using addition. Explain why your answer is reasonable.” Collect responses to group students for the next lesson.

Resources

• the decimal subtraction slide deck
• the subtracting decimals practice worksheet
• the standard form place value slider
• Mini-whiteboards and pens
• Place-value charts
• Rulers or metre strips for measurement contexts
• Play money or price labels
• Pencils, highlighters and scrap paper

Assessment

• Listen for accurate use of terms such as tenths, hundredths, regroup, estimate and inverse operation during partner explanations.
• Use mini-whiteboard responses to identify errors with aligning decimal points, regrouping across zero and placing the decimal point.
• Analyse the exit response for estimation, a correct method, addition checking and a reasonable explanation. Use results to plan a short regrouping workshop or move to multiplying decimals in the next lesson.

Differentiation

• Support learners with money and measurement contexts, place-value charts, a number line and the partially completed algorithms on the scaffolded practice section. Allow students to write zeros to make equivalent decimal places visible.
• Model one step at a time and provide sentence starters: “I estimated ___ because…”, “I regrouped from the ___ place because…”, and “I checked by adding ___ and ___.”
• Pair learners strategically for verbal rehearsal. Read problems aloud, clarify vocabulary and provide uncluttered copies or enlarged text for learners with visual, literacy or processing needs.
• Extension learners must solve selected problems using two different methods, compare their efficiency, and create a subtraction problem that requires regrouping across a zero. They explain how they know their answer is correct.