Decimal Strategy Workshop

Overview

Students partition decimals using place value, then apply known whole-number, fraction, bridging and compensation strategies to add and subtract decimals. The lesson builds directly on understanding tenths, hundredths and thousandths, extending it to accurate calculation in money and measurement contexts.

Learning intentions

Students will:

• partition decimals into whole numbers, tenths, hundredths and thousandths;
• align place values when adding and subtracting decimals;
• choose and explain an efficient calculation strategy;
• estimate answers to check whether they are reasonable.

Success criteria

• I can represent a decimal in expanded form, such as 3.47 = 3 + 0.4 + 0.07.
• I can line up decimal points and matching place values.
• I can rename or regroup when a calculation requires it.
• I can explain my strategy and use an estimate to check my answer.

Curriculum links

• Number — interpret, compare, order and represent decimals using place value, including decimals with more than two decimal places.
• Number — apply place-value understanding to calculate with decimals.
• Number — check and explain the reasonableness of solutions using estimation strategies.
• Mathematical proficiencies — reasoning, problem-solving, fluency and communicating mathematical thinking.

Prior knowledge

Students should recognise tenths, hundredths and thousandths; read and compare decimals; use place-value charts and number lines; add and subtract whole numbers; understand equivalent fractions such as 0.5 = 5 tenths = 50 hundredths; and use dollars, cents and common metric measurements.

Vocabulary

Decimal point, place value, partition, expanded form, tenths, hundredths, thousandths, align, rename, regroup, bridge, compensation, estimate, reasonable, difference, total.

Lesson structure (90 minutes)

1. 0–8 min · Launch and estimate. Open with the launch and estimation slides showing a grocery receipt: $3.47 + $2.86, and ask, “Will the answer be closer to $5, $6 or $7?” Students estimate independently, share reasoning with a partner and identify what they already know about decimal places. Ask: “What must be lined up?” and record strategies without confirming the exact answer.

2. 8–25 min · Explicit teaching: partition and align. Use the place-value model slides and a large place-value chart to model 3.47 = 3 + 0.4 + 0.07. Show that 3.47 can also be renamed as 3.4 + 0.07 or 347 hundredths. Model 3.47 + 2.86 by partitioning: (3 + 2) + (0.4 + 0.8) + (0.07 + 0.06) = 5 + 1.2 + 0.13 = 6.33. Model the written layout with decimal points aligned, including placeholder zeros: 4.5 = 4.50. Then model 5.00 − 2.68, renaming 5 ones as 4 ones and 10 tenths, and one tenth as 10 hundredths, to obtain 2.32. Students explain each regrouping step using place-value language.

3. 25–40 min · Connect known strategies. Display the strategy comparison slides and think aloud through:

• whole-number partitioning: 6.38 + 2.41 = (6 + 2) + (0.38 + 0.41) = 8.79;
• fraction thinking: 0.6 + 0.25 = 60 hundredths + 25 hundredths = 85 hundredths = 0.85;
• bridging: 3.76 + 0.24 + 1.5 = 4 + 1.5 = 5.5;
• compensation: 8.00 − 3.98 = 8.00 − 4.00 + 0.02 = 4.02.

Students use mini-whiteboards to solve 2.7 + 1.45 and 6.2 − 3.85. Ask: “Which strategy did you choose? Why was it efficient?” Check estimates before accepting answers.

4. 40–58 min · Guided practice: money and measurement. Distribute the decimal partitioning and calculation worksheet. Complete the first money problem together: “A drink costs $3.47 and a sandwich costs $5.86. What is the total?” Students estimate $9.30, solve using a place-value chart or partitioning, and explain why $9.33 is reasonable. Pairs solve selected money and measurement problems, including 2.75 m + 1.8 m and 6.00 kg − 2.65 kg. Pause for checks: “Where is the hundredths digit?” “Can 8 hundredths be subtracted from 5 hundredths without renaming?” “What does the answer mean in this context?”

5. 58–75 min · Collaborative investigation. In groups of four, students use the worksheet’s strategy challenge: solve the same calculation in two ways, such as $12.50 − $7.85 or 4.6 + 2.78, then compare methods. Roles are calculator, recorder, checker and explainer. Groups must show an estimate, identify whether they partitioned, bridged, compensated or regrouped, and prepare one explanation. Visit groups and observe alignment, correct renaming and use of units. Invite contrasting strategies to share; emphasise that an efficient strategy is one that is accurate, explainable and suited to the numbers.

6. 75–86 min · Independent practice and assessment. Students complete the remaining worksheet questions independently, including one decimal with three places and one open choice of strategy. Teacher conferences with students who misalign columns or omit zeroes. Students circle one answer and write an estimate beside it.

7. 86–90 min · Plenary and exit ticket. Revisit the plenary and exit-ticket slides. Students complete the exit ticket: A. Partition 4.305. B. Calculate 3.47 + 2.86. C. Calculate 5.00 − 2.68. D. Explain why 3.47 + 2.86 is not likely to equal 5.33. Answers: A. 4 + 0.3 + 0.005; B. 6.33; C. 2.32; D. An estimate is about 6.3, so 5.33 is unreasonable; alternatively, the tenths and hundredths have been added incorrectly.

Resources

• the complete decimal strategies slide deck
• the decimal partitioning and calculation worksheet
• Place-value chart, including thousandths
• Mini-whiteboards and markers
• Base-ten decimal grids or place-value equipment
• Pencils, rulers and highlighters
• Calculators for checking selected answers only

Assessment

• During modelling, ask students to identify the value of each digit in 3.47 and explain why 4.50 and 4.5 are equivalent.
• Observe whether students align place values, rename/regroup accurately, attach units and choose an appropriate strategy.
• Use the exit ticket to identify students needing further practice with partitioning, regrouping or estimation.

Differentiation

• Support: provide a place-value chart, decimal grids, colour-coded columns, sentence starters (“I partitioned…” and “My estimate is…”), and calculations limited initially to tenths and hundredths. Work with a teacher-led group during independent practice.
• Core: solve money and measurement problems using at least one written or mental strategy and justify the estimate.
• Extension: include thousandths and ask students to find two efficient methods, compare which is clearer, and create a context in which compensation is more efficient than the written algorithm.
• EAL/SEN: pre-teach vocabulary with examples, read problems aloud, reduce written copying, use manipulatives and allow students to explain orally or with labelled diagrams.

Common misconceptions and teacher responses

• Digits are aligned from the right rather than by place value: write the decimal points in a vertical line and add placeholder zeroes.
• A longer decimal is assumed to be larger: compare whole numbers first, then matching place values; use 2.5 and 2.45 as an example.
• Decimal points are added separately or omitted: say, “The point marks the places; it is not an extra number to add.”
• Regrouping is treated as changing the value: rename one whole as ten tenths or one tenth as ten hundredths using the chart.
• An answer is accepted without checking: require an estimate and a sentence about reasonableness.

Follow-up

Students record one decimal addition and one subtraction from a real receipt, ruler or measuring jug at home, estimate each answer, solve accurately and explain the strategy used. Next lesson, use exit-ticket patterns to revisit regrouping or move towards multi-step decimal problems.