Aligning Decimal Sums

Overview

In this fifth lesson of the unit Decimal Fractions and Operations, students build on their understanding of decimal place value and comparing decimals. They use place-value knowledge to align decimal points, add tenths and hundredths accurately, estimate before calculating, and check whether answers are reasonable.

Learning intentions

• WALT add decimals accurately by aligning corresponding place values.
• WALT use estimation to predict the size of a sum.
• WALT explain why decimal points and place-value columns must be aligned.
• WALT check an answer using estimation and inverse thinking.

Success criteria

• I can estimate a sum before calculating.
• I can align decimal points and corresponding place values.
• I can add tenths and hundredths accurately.
• I can check whether my answer is reasonable and explain my thinking.

Curriculum links

• Mathematics and Statistics — Number: decimal place value and addition.
• Mathematics and Statistics — using representations, symbols and mathematical language to communicate reasoning.
• Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathsteasers / Alignment: challenge questions connected to relevant mathematical content and prior learning.

Lesson structure (60 minutes)

1. 0–7 min · Number talk and hook. Teacher displays the question, “Which is more likely: (2.4 + 1.35 = 3.75) or (2.4 + 1.35 = 2.595)? Explain without calculating formally,” using the opening estimation slide. Students estimate, discuss with a partner, and justify which answer is reasonable.

2. 7–17 min · Revisit place value. Teacher uses the place-value teaching slides to model (2.4) and (1.35) on a place-value chart, making the zero in (2.40) explicit. Students represent both numbers with a place-value chart, grid or base-ten materials, then explain what each digit represents.

3. 17–27 min · Explicit modelling. Teacher models the sequence: estimate, rewrite with matching decimal places, align decimal points, add from right to left, and check. Use colour-coded columns to solve (2.40 + 1.35), then contrast it with the incorrect layout (2.4 + 1.35). Students identify the error and use a mini-whiteboard to solve two guided examples: (3.20 + 0.46) and (5.7 + 2.18).

4. 27–44 min · Supported practice. Teacher distributes the decimal addition practice worksheet and works through the first question with the class, prompting students to estimate before calculating. Students complete paired and independent questions involving tenths and hundredths, showing aligned columns and a reasonableness check; the teacher conferences with students and pauses for a quick reteach where needed.

5. 44–53 min · Reasoning challenge. Teacher displays the reasoning and challenge slides with the statement, “A student says (4.6 + 2.37 = 6.97) because the digits were added in the order shown. Is the answer correct? Prove it.” Students use a place-value chart or grid to explain the reasoning, correct any error, and then attempt the thousandths extension (1.275 + 2.48), explaining why (2.480) is needed.

6. 53–60 min · Plenary and exit check. Teacher revisits the success criteria using the plenary slides and asks students to complete the final reflection on the worksheet. Students solve (6.35 + 1.8), record an estimate, show aligned working, and write one sentence explaining how they checked the answer.

Resources

• the decimal addition teaching deck
• the decimal addition practice worksheet
• Place-value charts
• Place-value grids or squared paper
• Base-ten decimal materials
• Mini-whiteboards and pens
• Pencils, rulers and highlighters
• Enlarged place-value chart for modelling

Assessment

• Listen for accurate use of terms such as tenths, hundredths, decimal point and equivalent decimal.
• Check mini-whiteboard responses for alignment, accurate regrouping where required, and sensible estimates.
• Collect or scan the final worksheet question and reflection to assess whether students can independently estimate, calculate and justify reasonableness.

Differentiation

• Support students with a place-value chart, squared paper, base-ten materials and colour-coded columns. Encourage them to rewrite (2.4) as (2.40) before adding.
• Provide a worked example and sentence starters: “My estimate is…”, “I aligned the decimal points because…”, and “My answer is reasonable because…”.
• Pair students strategically for discussion, read questions aloud where appropriate, and reduce the number of practice questions without reducing the reasoning requirement.
• Extension students solve sums involving decimals to thousandths, including (1.275 + 2.480), and explain why adding zeroes maintains value but supports correct alignment.