Be a Maths Detective: Does Your Answer Make Sense? Use an Estimate!

Hello Sharp Thinkers! You’ve been learning lots of cool ways to do maths, like adding and subtracting. But how do you know if your final answer is a sensible one? What if you made a tiny mistake? Today, we’re going to learn about a super-sleuth skill: using an estimate to check if your answers are reasonable. An estimate is like a smart guess that tells you if you’re in the right ballpark!

What’s an “Approximate Answer” and Why Is It Useful?

When you calculate something exactly (like 125 + 283 = 408), that’s your exact answer. An estimate gives you an approximate answer. “Approximate” means “close to the actual value, but not necessarily exact.” It’s a simpler, rounded number that’s easier to work with in your head.

For example, to estimate 125 + 283:

• You might round 125 to 100 (to the nearest hundred) or 130 (to the nearest ten).
• You might round 283 to 300 (to the nearest hundred) or 280 (to the nearest ten).
• If you rounded to hundreds: 100 + 300 = 400. So, 400 is an approximate answer.
• If you rounded to tens: 130 + 280 = 410. So, 410 is another approximate answer (and a bit closer!).

Both 400 and 410 are good estimates for the exact answer of 408.

How Estimates Help Us Check for “Reasonableness”

“Reasonable” means “makes sense” or “seems about right.” An estimate is your tool to check this!

Here’s the detective work:

1. First, you work out your exact answer to a problem using methods like column addition or subtraction.
2. Then, you make an estimate for the same problem (by rounding the numbers first, then doing the sum with the rounded numbers).
3. Finally, you compare your exact answer to your estimated answer.

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• If your exact answer is close to your estimate: Great! Your exact answer is probably reasonable. It makes sense!
• If your exact answer is VERY different from your estimate: Uh oh! This is a clue. It means your exact answer might not be reasonable. You might have made a mistake in your exact calculation, and it’s a good idea to check your work again!

Example: Checking an Addition Imagine you calculated: 318 + 195 = 613 (This is your exact answer, but is it right?)

Let’s estimate by rounding to the nearest hundred:

• 318 rounds to 300.
• 195 rounds to 200.
• Estimated sum: 300 + 200 = 500.

Now compare: Your exact answer was 613. Your estimate is 500. Are 613 and 500 close? Not very! This tells you that 613 is probably not reasonable. You should re-check your column addition. (The correct exact answer is 513, which is close to 500!)

Example: Checking a Subtraction Imagine you calculated: 789 − 211 = 578 (Your exact answer)

Let’s estimate by rounding to the nearest ten:

• 789 rounds to 790.
• 211 rounds to 210.
• Estimated difference: 790 − 210 = 580.

Now compare: Your exact answer was 578. Your estimate is 580. Are 578 and 580 close? Yes, very close! This tells you that 578 is a reasonable answer.

Be a Maths Detective: Is the Answer Reasonable? (18 Scenarios)

Ready to use your estimation skills to check some answers? For each scenario below, you might be given a sum and an “exact answer.” Your job is to make an estimate and decide if the given “exact answer” is reasonable or if it looks a bit suspicious!

(Your web app with the 18 questions will go here. Questions could provide a calculation, a proposed exact answer, and ask if it’s reasonable after the child estimates. Or, provide a calculation and ask for an estimate, then show possible exact answers to evaluate.)

Why is Checking for Reasonableness So Important?

• Catches Mistakes: It’s like having a built-in error detector for your maths work!
• Builds Number Sense: You get a better feel for numbers and what answers should look like.
• Saves Time in the Long Run: Finding a mistake early is quicker than having to redo lots of work later.
• Makes You a More Confident Mathematician: Knowing how to check your work gives you power!

Tips for Grown-Ups: Fostering the “Reasonableness Check”

Helping children understand that an estimate is a tool to check the reasonableness of an answer is a crucial step in developing their mathematical thinking and self-correction skills.

• Make it a Habit: After completing a calculation, always ask, “Does that answer seem reasonable? How can we make a quick estimate to check?”
• Model Your Own Estimation: When doing everyday maths, talk aloud about how you estimate. “I need to buy these two things… this one is about £3 and that one is about £5, so it should be around £8 altogether.”
• Focus on “Close Enough”: Explain that an estimate doesn’t have to be exact, just in the right ballpark.
• Discuss “Unreasonable” Answers: If an estimate is very different from a calculated answer, explore why. Was there a calculation error? Was the rounding for the estimate too rough?
• Use Real-World Contexts: “If there are 32 children in one class and 28 in another, would 160 children altogether be a reasonable answer for a school trip? Why or why not?”