New Zealand
Level 6 - NCEA Level 1

# Check reasonableness of calculations

Lesson

Checking if an answer is reasonable means we check to see whether an answer is a good approximation or estimate to the question. This is really important because it allows us to check whether our calculations make sense.

For example, if I said $\$10$$10 was shared between 22 people and they both got \50$$50, this would NOT be a reasonable estimate as my answer ($\$50$$50) is even more money than the total at the start (\10$$10)!

## How do we check if an answer is reasonable?

Well, one of the best things to do is to round the numbers in the question so you can do a quick mental calculation. If the given answer is close to your estimate, then it is a reasonable calculation.

You can also put the answer into context, ask yourself does it make sense that the answer is this big, or this small?

#### Worked Examples

##### Question 1

Is $6000$6000 a reasonable estimate for $57\times11$57×11?

Think: Let's round both these numbers to the nearest ten and see if it's close to $6000$6000.

Do: If we round $57$57 to the nearest ten, it's $60$60 and if we round $11$11 to the nearest ten, it's $10$10.

So, our estimate can be rewritten as $60\times10$60×10.

$60\times10=600$60×10=600

$600$600 is way less than $6000$6000 so NO $6000$6000 is not a reasonable estimate.

#### Worked Examples

##### Question 2

Ursula collects beetles. She knows that she has exactly $169$169 of them. Ursula has to move house this week, and must buy storage boxes to transport them.

1. Which of the following should Ursula buy?

$3$3 boxes that hold $180$180 beetles each.

A

$4$4 boxes that hold $40$40 beetles each.

B

$2$2 boxes that hold $10$10 beetles each.

C

$9$9 boxes that hold $20$20 beetles each.

D

$3$3 boxes that hold $180$180 beetles each.

A

$4$4 boxes that hold $40$40 beetles each.

B

$2$2 boxes that hold $10$10 beetles each.

C

$9$9 boxes that hold $20$20 beetles each.

D

##### Question 3

Is the following calculation reasonable?

$9352+47=479352$9352+47=479352

1. Yes

A

No

B

Yes

A

No

B

##### Question 4

Is this statement accurate?

"$4\times88$4×88 will be less than $320$320."

1. Yes

A

No

B

Yes

A

No

B

##### Question 5

Is the statement reasonable?

$9352\times4761$9352×4761 will be greater than $36000000$36000000.

1. Yes

A

No

B

Yes

A

No

B

### Outcomes

#### NA6-6

Generalise the properties of operations with rational numbers, including the properties of exponents

#### 91027

Apply algebraic procedures in solving problems