--- title: "Estimating to check" subtitle: "Number Foundations · Place value and estimating · Lesson 19" --- # Estimating to check **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** You type 3.2 × 48 and the calculator shows 15.36. Looks plausible. But before you trust it, how big should the answer be? :::teacher-note **In one sentence:** Students estimate by rounding each number to its first digit, compare the estimate with the exact answer, and use it to catch slips such as a misplaced decimal point (AC9M7N05, node 3). **Students should be able to say:** I can estimate a calculation by rounding each number to its first digit. I can compare an estimate with the exact answer and say whether it is reasonable. I can use an estimate to find a slip, such as a decimal point in the wrong place. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Is the exact answer going to be a bit more or a bit less than 2000? Why? :::keep-together **Which is the best estimate for $38 \times 52$?** ☐ 90 ☐ 200 ☐ 2000 ☐ 20 000 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 2000. 38 is about 40 and 52 is about 50, and 40 × 50 = 2000. 90 is 38 + 52. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Estimates catch slips :::keep-together ### Round, then calculate **Estimate $6.8 \times 31$ by rounding each number to its first digit.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 210 6.8 ≈ 7 and 31 ≈ 30, so 7 × 30 = 210. ::: :::keep-together ### Find the mistake **Lina estimates 19.6 × 4.1. Click the line where her working goes wrong.** ``` 1 Estimate 19.6 × 4.1. 2 Round each number to its first digit: 19.6 → 2, 4.1 → 4. 3 2 × 4 = 8 4 So 19.6 × 4.1 is about 8. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: 19.6 is about 20, not 2: rounding keeps the size. 20 × 4 = 80, so 19.6 × 4.1 is about 80. ::: :::keep-together ### Is it reasonable? **You type $3.2 \times 48$ and the calculator shows 15.36. Is that reasonable?** ☐ No: 3 × 50 = 150, so the decimal point is in the wrong place ☐ Yes: a calculator is always right ☐ Yes: 3 × 5 = 15 is close ☐ No: the answer should be a whole number ::: :::teacher-note **Answer:** No: 3 × 50 = 150, so the decimal point is in the wrong place 3.2 × 48 ≈ 3 × 50 = 150. The real answer is 153.6: the calculator shows 15.36 only if the 3.2 was typed as 0.32. ::: :::typical ## Other operations, other sizes **Add them.** **Keep the size.** **Divide.** **Bigger or smaller?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Estimating :::keep-together ### Two numbers **Estimate $58 \times 19$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1200 58 ≈ 60 and 19 ≈ 20, so 60 × 20 = 1200. ::: :::keep-together ### A decimal times **Estimate $7.9 \times 4.2$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 32 7.9 ≈ 8 and 4.2 ≈ 4, so 8 × 4 = 32. ::: :::keep-together ### Check the calculator **The calculator shows $504 \div 6.3 = 8$. Is that reasonable?** ☐ Yes: 50 ÷ 6 is about 8 ☐ Yes: 504 ÷ 6 is about 8 ☐ No: 500 ÷ 6 is about 80, so 8 has lost a zero ☐ No: you cannot divide by a decimal ::: :::teacher-note **Answer:** No: 500 ÷ 6 is about 80, so 8 has lost a zero 504 ÷ 6.3 = 80. Estimating 500 ÷ 6 ≈ 80 shows 8 has lost a zero. ::: :::keep-together ### Review: rounding **Review: round 6.45 to 1 decimal place.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6.5 The next digit is 5, so 6.5. ::: ## Make: close but under Then find a pair where the exact answer is more than 2000, and write which rounding you used and why. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Estimate 4.8 × 31. The calculator shows 148.8. Is it reasonable?** {{lines-3}} ::: :::teacher-note **Answer:** 5 × 30 = 150, so yes. :::