Limits of accuracy – Developing Understanding Mastering Mathematics © Hodder and Stoughton 2014 Recognising a range of values Calculating within a range

Limits of accuracy – Developing Understanding Mastering Mathematics © Hodder and Stoughton 2014

Recognising a range of values

Calculating within a range

STEPS

Mastering Mathematics © Hodder and Stoughton 2014

Limits of accuracy – Developing Understanding

© Elaine Lambert


Menu Opinion 1Back Forward Cont/d More Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

Adam’s bag is weighed at the airport check-in.

It weighs 17 kg to the nearest kg.

1. What is the a) minimum and b) maximum weight that the bag could be?

2. Which of these three statements mean the same thing?

A 17 kg, to the nearest kgB 17 kg ±0.5 kgC 16.5 kg ≤ weight < 17.5 kg

If it was only 16.5 kg it would still be rounded up to 17 kg. … and it could be up to 17.4 kg.

Opinion has given the correct lower limit.

Opinion is not fully correct because a weight like 17.499 kg would still be rounded down as 17 kg to the nearest kg.

They all mean the same thing.

B is different. Because if you add 0.5 you would have 17.5 and that rounds up to 18.

A and C don’t include 17 kg.

Opinion is not strictly correct.

However, although Opinion is right about B these three statements are all commonly used to mean the same thing.

The intention is to show that the weight is 17 kg to the nearest kg. It can be anywhere from 16.5 kg up to (but not including) 17.5 kg

Check that you know how to use the signs ± , < and ≤.

The minimum is 16.5 kg. But the maximum could be 17.49 kg.



© Elaine Lambert

Menu Vocabulary Opinion 1

The lowest is 20.5 kg …and the upper limit is 21.5 kg.

It could be any weight from 20.5 kg up to 21.499999 kg.

Back Forward Cont/d Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

1. What is the lowest and highest weight that her suitcase could actually be?

2. How would you write the weight of Tina’s bag using inequality signs?

Tina’s suitcase is checked in as 21 kg to the nearest kg.

It’s 20.5 ≤ 21 ≤ 21.5.

It’s 20.5 < 21 < 21.5.

The opinions are correct in describing the boundaries; but you could carry on adding the 9s in Opinion forever! But of course that is just theoretical. Most check-in scales give the weight to the nearest 0.1 kg.

The upper and lower bounds are 21.5 kg and 20.5 kg.

The value that a number or measurement can exceed is called its called its upper bound. Similarly the value that it cannot be less than is called its lower bound.


Both opinions are wrong.The correct answer is 20.5 ≤ 21 < 21.5. Notice that the sign ≤ means ‘is less then or equal to’ and the sign < means just ‘is less than’.



Menu Opinion 1

The lowest that Adam’s could be is 16.5 kg and the lowest that Tina’s could be is 20.5 kg.

16.5 kg + 20.5 kg = 37 kg.

Opinion is correct, you need to find the lowest weights first before adding them together.

Back Forward Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

1. What is the lowest combined weight that Adam’s and Tina’s luggage could be?

2. And what is the upper bound for the combined weight?

The upper bound for Adam’s bag is 17.5 kg…

…and the upper bound for Tina’s case is 21.5 kg.

Opinions and have given the pair of upper bounds. So the combined upper bound is 17.5 + 21.5 = 39 kg.

So 37 kg ≤ combined weight < 39 kg.

17 kg

21 kg


© Elaine Lambert

21 kg + 17 kg = 38 kg

The weight is to the nearest kg, so the lowest it can be is 37.5 kg.



© Anne Wanjie


Menu Opinion 1

Each jug is 250 ± 10 ml.

Back Forward Cont/d Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

Lee and Suzi are preparing cream of chicken soup.

They don’t have a large jug to measure

2 litres of milk. So Lee uses a small jug to measure 250 ml ten times.

Each small jug he uses contains 250 ml to the nearest 10 ml.

1. What are the maximum and minimum volumes that each jug of milk could be?

2. What are the maximum and minimum volumes possible for the total amount of milk that Lee adds?

I’ll add 10 lots of 250 ml.That will be the same.

You need to add 2 litres of milk.

Opinions is correct but Opinion is wrong. Another way is to say

245 ml ≤ volume < 255 ml Opinion has found the minimum and maximum possibilities. But it would be unusual for every jug to be exactly the same.

Opinion is wrong. It was the content of each jug that was to the nearest 10 ml not the total content.

The lowest amount is 245 ml and the upper bound is 255 ml.

If every jug of milk was the lowest then they’d have 245 x 10 = 2450 ml.

In the same way the upper bound is245 x 10 = 2450 ml.

You expect the volume to be 10 x 250 = 2500 ml.

So to the nearest 10 ml,2405 ml ≤ volume < 2505 ml.



6.3 cm

© DougLambert


Menu Opinion 1

Using the measurements in the picture,2(6.25 + 8.65) < perimeter < 2(6.35 + 8.75)So 29.8 cm < perimeter < 30.2 cm.

Back Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

Look at this photograph.The measurements are accurate to the nearest millimetre.

1. Write the possible values of its perimeter using inequalities.

2. What are the upper and lower bounds for its area?

The width is at least 6.25 and less than 6.35. The height is at least 8.65 and less than 8.75.So 29.8 ≤ perimeter < 30.2.

8.7 cm

Opinion is correct. Opinion has got the bounds for the width and height wrong.

The area is between6.25 x 8.65 and 6.35 x 8.75

So, in cm2, 54.0625 ≤ Area < 55.5625.

The width is between 6.2 cm and 6.4 cm.The height is between 8.6 cm and 8.8 cm.

So the lower bound for the area is 6.2 x 8.6 = 53.32 cm2. The upper bound is 6.4 x 8.8 = 56.32 cm2.

Neither opinion is quite right.

In Opinion the left hand inequality sign should be ≤ not <.

Opinion has forgotten the units.

The correct answer is 29.8c l ≤ perimeter < 30.2 cm.



Editable Teacher Template

Menu Vocabulary Opinion 1Back Forward More Opinion 2 Answer Opinion 1 Opinion 2 AnswerQ 1 Q 2

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2. Task – appears

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Q1Opinion 1

Q1Opinion 2

Q1Answer

Q2Opinion 1

Q2Opinion 2

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Limits of accuracy – Developing Understanding Mastering Mathematics © Hodder and Stoughton 2014 Recognising a range of values Calculating within a range