Estimate and Check

Overview

Students use rounding and benchmarks to estimate results, then check whether calculations are reasonable. The lesson builds on place value and decimal knowledge through a short, individual problem-solving sequence suited to one Year 8 student.

Learning intentions

• WALT round whole numbers to a specified power of 10.
• WALT round decimals to the nearest whole number, tenth, hundredth or thousandth.
• WALT use estimation and benchmarks to predict results.
• WALT check whether a calculation is reasonable.

Success criteria

• I can identify the place value I am rounding to.
• I can use the next digit to decide whether to round up or down.
• I can estimate a calculation before solving it.
• I can explain whether an answer is reasonable using a benchmark or range.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting mathematical challenge with relevant textbook content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: extending reasoning through estimation, checking and justification.
• Year 8 knowledge and practices: rounding, estimation and benchmarks support comparing numbers and checking the reasonableness of findings.

Lesson structure (15 minutes)

1. 0–3 min · Hook and diagnostic. Open with the estimation hook and opening question and ask: “Without calculating exactly, is 14.7 × 5 closer to 70, 75 or 100?” The student gives an initial estimate and explains which nearby whole numbers could be used.

2. 3–6 min · Model the strategies. Use the rounding and benchmark examples to model that 14.7 rounds to 15, so 14.7 × 5 is approximately 15 × 5 = 75; also show that the exact answer must be between 14 × 5 = 70 and 15 × 5 = 75. The student identifies the rounding place, names the benchmark numbers and repeats the reasoning in their own words.

3. 6–10 min · Guided practice. Distribute the rounding and estimation practice sheet and complete the first two questions together. Include examples such as 46,782 rounded to the nearest 1,000; 8.746 rounded to the nearest hundredth; and 3.98 × 6 estimated using 4 × 6. The student records the rounded value, estimate and a brief explanation for each answer.

4. 10–13 min · Independent reasoning challenge. Refer back to the prediction and reasonableness challenge and ask the student to solve: “A calculator gives 9.6 × 21 = 201.6. Is this reasonable?” The student estimates using 10 × 20, gives a sensible range using 9 × 20 and 10 × 21, then decides whether the calculator answer is reasonable and explains why.

5. 13–15 min · Plenary and exit check. Show the final reflection prompt. The student completes the final worksheet question: “Round 27.384 to the nearest tenth and explain how this could help check 27.384 × 4.” Ask the student to state one rounding rule and one way estimation can detect an unreasonable answer.

Resources

• the rounding, estimation and checking slide deck
• the rounding and estimation practice sheet
• Pencil and ruler
• Calculator for checking, not for replacing estimation
• Place-value chart or whiteboard

Assessment

• Listen for accurate identification of the rounding place and the use of the following digit to round up or down.
• Check that the student estimates before calculating and can use benchmarks to give a sensible range.
• Use the final worksheet response to assess whether the student can justify the reasonableness of a result, not just provide an answer.

Differentiation

• For support, provide a place-value chart, underline the target place and use sentence starters: “I rounded ___ to ___ because…” and “The answer is reasonable because…”.
• If needed, reduce the number of decimal places and work with a number line before returning to the multiplication examples.
• For extension, ask the student to create a multiplication calculation whose exact answer lies between two chosen benchmark products, then explain how rounding verifies it.
• Read questions aloud, present one step at a time and allow the student to explain orally before writing. Use clear spacing and avoid unnecessary visual information on the worksheet.