Checking Decimal Calculations

Overview

In this eighth lesson of the unit Decimal Fractions and Operations, students develop reliable ways to check decimal calculations. They apply estimation, inverse operations, mental strategies and calculators to identify errors and justify whether answers are reasonable.

Learning intentions

• WALT estimate before calculating with decimals.
• WALT use inverse operations, mental strategies and digital tools to check calculations.
• WALT identify errors in worked examples.
• WALT explain whether a decimal answer is reasonable and justify our thinking.

Success criteria

• I can estimate an answer before calculating.
• I can use an inverse operation or another strategy to check a calculation.
• I can identify and explain an error in a worked example.
• I can justify whether an answer is reasonable.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge questions with previously taught mathematical content.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Mathematical thinking and communication: explaining strategies, evaluating reasonableness and justifying conclusions.

Lesson structure (60 minutes)

1. 0–7 min · Hook and activate prior learning. Display a deliberately incorrect calculation, such as (4.8 + 2.37 = 7.07), using the hook and quick-check slide. Ask, “How could you know this answer is wrong without recalculating it?” Students make a quick estimate, discuss with a partner and share possible checking strategies. Record ideas such as rounding, inverse operations and using a calculator.

2. 7–17 min · Explicit teaching: estimate first. Model a calculation such as (6.29 \times 3.8): round to (6 \times 4 = 24), calculate accurately, then compare the exact answer with the estimate. Use the estimation model slides to show a number-line visual from 0 to 30 and discuss why an answer such as 2.394 or 239.4 would be unreasonable. Students complete two estimates on mini-whiteboards and explain which nearby whole numbers they chose.

3. 17–27 min · Explicit teaching: check in more than one way. Model (12.6 - 4.75 = 7.85), checking by adding (7.85 + 4.75), and then demonstrate a calculator check. Model a mental check for (0.6 \times 0.4), asking whether the product should be greater or less than either factor. Refer to the checking-strategies slides. Students classify each strategy as estimation, inverse operation, mental reasoning or digital checking, then explain when it is useful.

4. 27–43 min · Paired error analysis. Distribute the decimal error-analysis worksheet. In pairs, students estimate each problem, inspect the worked solution, identify the first error and correct the calculation. They must write a brief justification, using prompts such as “I know this is unreasonable because…” and “The error occurred when…”. Include examples involving addition, subtraction, multiplication and division by decimals. Confer with pairs, asking, “What did your estimate tell you?” and “Can you check this without repeating the same method?”

5. 43–52 min · Independent application and discussion. Students complete the final worksheet questions independently, choosing a checking strategy for each calculation and labelling it. Invite selected students to present contrasting methods using the strategy-comparison slides. The class compares efficiency and reliability, considering when a calculator confirms an answer but does not explain why it is reasonable.

6. 52–60 min · Extension and exit reflection. Students complete an exit response on the worksheet: estimate and check (7.2 \div 0.6), then state whether the answer is reasonable and why. Advanced learners create an erroneous decimal calculation, write two or three clues about the mistake, and exchange it with a partner to solve and explain. Finish with the plenary and exit-question slide and ask students to name the most convincing checking strategy they used.

Resources

• the decimal checking slide deck
• the decimal error-analysis worksheet
• Mini-whiteboards and pens
• Calculators, one per pair
• Place-value charts or number lines
• Exercise books and pencils
• Projector or interactive display

Assessment

• Listen to partner explanations during the hook and check that students estimate before calculating rather than simply recompute.
• Use questioning and the worksheet to assess whether students can locate the first error, correct it and justify reasonableness.
• Collect the exit response to identify students needing further support with decimal magnitude, inverse operations or division.

Differentiation

• Provide an error-analysis template with separate boxes for estimate, calculation, checking method, error and explanation. Offer sentence starters: “My estimate is…”, “The answer is reasonable because…” and “The mistake was…”.
• Use an open number line, place-value chart and enlarged worked examples for students who need visual support. Allow calculators for checking after students have first made an estimate.
• Confer with individuals or pairs, modelling one example and gradually removing prompts. Read questions aloud and reduce the number of examples without reducing the reasoning requirement for students with literacy or processing needs.
• Support EAL learners with illustrated vocabulary and paired rehearsal of terms such as estimate, inverse, reasonable, error and product. Accept oral explanations before students record a written justification.
• Extend advanced learners by requiring two different checking methods, comparing their efficiency, and creating an erroneous calculation with clues for a peer to diagnose.