I similar the bounds content inwards the novel GCSE. I retrieve that the introduction of error intervals has provided some clarity. Previously some students merely couldn't larn their caput around why nosotros utilisation 3.65 equally the upper saltation for 3.6 ("but Miss, 3.65 rounds to 3.7. This doesn't brand sense!"). The utilisation of inequality symbols (in conjunction amongst teaching using pose out lines) actually helps amongst conceptual agreement here.
3.55 ≤ x < 3.65
Of course of teaching error intervals aren't novel - they merely weren't previously assessed at GCSE. Upper bounds together with error intervals are clearly explained inwards this extract from the CIMT MEP textbook chapter on Estimation together with Approximation from the belatedly 1990s:
Truncation
I likewise similar the inclusion of truncation inwards the novel GCSE specification, because it agency that students demand to retrieve to a greater extent than carefully earlier answering a bounds question. Previously, bounds questions at GCSE were predictable, together with students entirely actually needed a superficial, procedural agreement of the topic. Things possess got changed.
Age is a skillful way to learn truncation, given that students volition already live on really used to truncating their ain age, rather than rounding it to the nearest integer.
Age is a skillful way to learn truncation, given that students volition already live on really used to truncating their ain age, rather than rounding it to the nearest integer.
Ed is 36 years old. His historic menstruum is represented yesteryear x. Give the error interval for x.
36 ≤ x < 37
My Year 11s actually struggled amongst a bounds enquiry inwards their mock exams this year. It's from a recent AQA newspaper together with then I can't part the actual enquiry here, but this enquiry is similar:
Two integers are rounded to the nearest 10. The rounded numbers are added to laissez passer on to 40. What's the maximum sum value of the orginal numbers?
Let's tell that both numbers were xx when rounded. The maximum each pose out could live on is 24, together with then the highest possible sum is 48. The mutual error hither is to accept the upper saltation to live on 25, giving an wrong in conclusion reply of 50. So why was this such a mutual mistake? I facial expression it's because most of us learn bounds inwards a context of measurement, non counting. We pass a lot of fourth dimension on continuous bounds, together with really niggling (if any) fourth dimension on discrete bounds.
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has one enquiry on discrete bounds:
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has one enquiry on discrete bounds:
The pose out of people on a omnibus is given equally 50, right to the nearest 10. What is the lowest together with highest possible pose out of people on the bus?
The OCR Check-In Test on Approximation together with Estimation has this question:
Explain why the error interval of 400 cars to the nearest l cars could live on written as 375 ≤ c ≤ 424 or 375 ≤ c < 425.
together with the AQA Rounding Topic Test has a twosome of discrete bounds questions, including this one:
Two performances of a present are each attended yesteryear 175 people, to the nearest 5. Work out the maximum possible departure betwixt the numbers of people attending.
It's worth noting that the Government's GCSE dependent land content doesn't specifically refer to discrete bounds. This is the official content for bounds at GCSE:
"15. circular numbers together with measures to an appropriate score of accuracy (e.g. to a specified pose out of decimal places or pregnant figures); use inequality annotation to specify unproblematic error intervals due to truncation or rounding
16. apply together with translate limits of accuracy, including upper together with lower bounds"
OCR's specification does refer discrete bounds though, proverb that students must "Understand the departure betwixt bounds of discrete together with continuous quantities".
AQA's fantabulous Teaching Guidance has this:
"Upper bounds produce non necessarily require utilisation of recurring decimals. For example, if the reply to the nearest integer is 7, the maximum could live on given equally 7.5, 7.49.... , or 7.49.
If this value of vii represented £7, £7.49 would live on expected for the maximum.
For continuous variables, students may live on asked for the lower together with upper limits rather than the minimum together with maximum values."The coin instance hither is interesting - it's non something I possess got explicitly covered amongst my students. Don Steward has a skillful post nearly truncation resources.
Discrete Bounds
My Year 11s actually struggled amongst a bounds enquiry inwards their mock exams this year. It's from a recent AQA newspaper together with then I can't part the actual enquiry here, but this enquiry is similar:
Two integers are rounded to the nearest 10. The rounded numbers are added to laissez passer on to 40. What's the maximum sum value of the orginal numbers?
Let's tell that both numbers were xx when rounded. The maximum each pose out could live on is 24, together with then the highest possible sum is 48. The mutual error hither is to accept the upper saltation to live on 25, giving an wrong in conclusion reply of 50. So why was this such a mutual mistake? I facial expression it's because most of us learn bounds inwards a context of measurement, non counting. We pass a lot of fourth dimension on continuous bounds, together with really niggling (if any) fourth dimension on discrete bounds.
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has bounds exercise including coin questions - I'll brand certain I utilisation this adjacent fourth dimension I learn this topic.
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has bounds exercise including coin questions - I'll brand certain I utilisation this adjacent fourth dimension I learn this topic.
Edexcel doesn't specifically refer to discrete bounds inwards either their specification or supporting material, but of course of teaching that doesn't necessarily hateful they won't come upwardly up inwards an Edexcel exam.
Exam Questions
Bounds questions involving calculations tin live on fairly challenging for students, especially equally sometimes it's non forthwith obvious that the enquiry involves bounds. Here's an instance from an former Edexcel Linked Pair paper:
Another type of challenging GCSE enquiry is 1 that says "by considering bounds, run out the value of x to a suitable score of accuracy, justifying your answer". For examples of questions similar this, meet Dr Frost's 'Full Coverage: Bounds' resources which has an instance of every dissimilar enquiry type from yesteryear Edexcel papers.
Resources
"Sian is driving on a motorway.
Sian drives for 2.8 miles, right to the nearest 10th of a mile.
It takes her 200 seconds, right to the nearest v seconds.
The average speed boundary on this purpose of the expressway is l miles per hour.
Did Sian drive at a speed inside the average speed limit? You must explicate your answer."
Another type of challenging GCSE enquiry is 1 that says "by considering bounds, run out the value of x to a suitable score of accuracy, justifying your answer". For examples of questions similar this, meet Dr Frost's 'Full Coverage: Bounds' resources which has an instance of every dissimilar enquiry type from yesteryear Edexcel papers.
Resources
I've already mentioned Don's fantabulous resource, the CIMT resources together with Dr Frost's sum coverage GCSE questions. For a comprehensive listing of bounds resources, meet my resources library.
It's worth noting that John Corbett has helpful videos, textbook exercises together with practise questions on post nearly truncation resources.
Discrete Bounds
Discrete Bounds
My Year 11s actually struggled amongst a bounds enquiry inwards their mock exams this year. It's from a recent AQA newspaper together with then I can't part the actual enquiry here, but this enquiry is similar:
Two integers are rounded to the nearest 10. The rounded numbers are added to laissez passer on to 40. What's the maximum sum value of the orginal numbers?
Let's tell that both numbers were xx when rounded. The maximum each pose out could live on is 24, together with then the highest possible sum is 48. The mutual error hither is to accept the upper saltation to live on 25, giving an wrong in conclusion reply of 50. So why was this such a mutual mistake? I facial expression it's because most of us learn bounds inwards a context of measurement, non counting. We pass a lot of fourth dimension on continuous bounds, together with really niggling (if any) fourth dimension on discrete bounds.
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has here.
Interestingly, my GCSE textbook doesn't incorporate a unmarried enquiry on discrete bounds. Influenza A virus subtype H5N1 fighting of network searching shows that BBC Bitesize has here.
