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 Recognising a range of values MenuOpinion 1BackForwardCont/dMoreOpinion 2AnswerOpinion 1Opinion 2Answer Q 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? A17 kg, to the nearest kg B17 kg ±0.5 kg C16.5 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 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 kg. 

Mastering Mathematics © Hodder and Stoughton 2014 Limits of accuracy – Developing Understanding © Elaine Lambert MenuVocabularyOpinion 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 kg.  BackForwardCont/dOpinion 2AnswerOpinion 1Opinion 2Answer Q 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 ≤ It’s 20.5 < 21 < 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. Recognising a range of values Both opinions are wrong. The correct answer is 20.5 ≤ 21 < Notice that the sign ≤ means ‘is less then or equal to’ and the sign < means just ‘is less than’.

Mastering Mathematics © Hodder and Stoughton 2014 Limits of accuracy – Developing Understanding MenuOpinion 1 The lowest that Adam’s could be is 16.5 kg and the lowest that Tina’s could be is 20.5 kg kg kg = 37 kg.  Opinion  is correct, you need to find the lowest weights first before adding them together. BackForwardOpinion 2AnswerOpinion 1Opinion 2Answer Q 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 = 39 kg. So 37 kg ≤ combined weight < 39 kg. 17 kg 21 kg Recognising a range of values © 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. 

Mastering Mathematics © Hodder and Stoughton 2014 Limits of accuracy – Developing Understanding © Anne Wanjie Calculating within a range MenuOpinion 1 Each jug is 250 ± 10 ml.  BackForwardCont/dOpinion 2AnswerOpinion 1Opinion 2Answer Q 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 is 245 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. 

Mastering Mathematics © Hodder and Stoughton 2014 Limits of accuracy – Developing Understanding 6.3 cm © DougLambert Calculating within a range MenuOpinion 1 Using the measurements in the picture, 2( ) < perimeter < 2( ) So 29.8 cm < perimeter < 30.2 cm.  BackOpinion 2AnswerOpinion 1Opinion 2Answer Q 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 The height is at least 8.65 and less than So 29.8 ≤ perimeter <  8.7 cm Opinion  is correct. Opinion  has got the bounds for the width and height wrong. The area is between 6.25 x 8.65 and 6.35 x 8.75 So, in cm 2, ≤ Area <  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 = cm 2. The upper bound is 6.4 x 8.8 = cm 2.  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.

Mastering Mathematics © Hodder and Stoughton 2014 Limits of accuracy – Developing Understanding Editable Teacher Template MenuVocabularyOpinion 1BackForwardMoreOpinion 2AnswerOpinion 1Opinion 2Answer Q 1 Q 2 Information 1.Task – fixed 2.Task – appears Vocabulary More Q1 Opinion 1 Q1 Opinion 2 Q1 Answer Q2 Opinion 1 Q2 Opinion 2 Q2 Answer