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Year 10
Higher

Upper and lower bounds in additive calculations

I can calculate upper and lower bounds for calculations involving rounded numbers.

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New
New
Year 10
Higher

Upper and lower bounds in additive calculations

I can calculate upper and lower bounds for calculations involving rounded numbers.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The biggest possible sum comes from adding the upper bounds.
  2. The smallest possible sum comes from adding the lower bounds.
  3. The biggest possible difference comes from subtracting a lower bound from an upper bound.
  4. The smallest possible difference comes from subtracting an upper bound from a lower bound.

Common misconception

For example if a measurement of 12 cm has been given to the nearest centimetre assuming the upper bound is 12.4 cm.

Emphasise the infinite nature of a measurement.

Keywords

  • Upper bound - The upper bound for a rounded number is the smallest value that would round up to the next rounded value.

  • Lower bound - The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.

  • Error interval - An error interval for a number x shows the range of possible values of x. It is written as an inequality a ≤ x < b

Allowing pupils time to create their own cross number puzzle using the addition or subtraction of bounds allows them to think carefully about degrees of accuracy and bounds so the numbers interweave.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
An error interval for a number shows the of possible values of the number.
Correct Answer: range
Q2.
Work out the lower and upper bounds of 560 rounded to the nearest 10
559 and 561
559.5 and 560.5
555 and 564
554 and 565
Correct answer: 555 and 565
Q3.
Work out the lower and upper bounds of 4.8 rounded to 1 decimal place.
4.7 and 4.9
Correct answer: 4.75 and 4.85
4.3 and 5.3
4.74 and 4.85
4.75 and 4.84
Q4.
rounded to the nearest integer. The lower bound is 8.5 and the upper bound is 9.5
Correct Answer: 9, 9.0
Q5.
rounded to 1 decimal place. The lower bound is 1.65 and the upper bound is 1.75
Correct Answer: 1.7, 1.70
Q6.
rounded to 2 significant figures. The lower bound is 1250 and the upper bound is 1350
Correct Answer: 1300, 1 300

Exit quiz

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6 Questions

Q1.
The numbers either end of an error interval are called the lower and upper .
Correct Answer: bounds, bound
Q2.
A piece of string is measured as 10.2 cm correct to 1 decimal place. What are the lower and upper bounds?
9.7 and 10.7
10.25 and 10.35
Correct answer: 10.15 and 10.25
10.15 and 10.24
Q3.
A piece of string is measured as 10.2 cm correct to 1 decimal place. The lower and upper bounds are 10.15 and 10.25. What is the error interval?
$$10.15\leq{x}\leq10.25$$
Correct answer: $$10.15\leq{x}<10.25$$
$$10.15<{x}\leq10.25$$
$$10.15\geq{x}<10.25$$
$$10.15\leq{x}>10.25$$
Q4.
The mass of a cat is 4.8 kg correct to 2 significant figures. What is the error interval?
$$4.75\leq{x}<7.849999999999$$
Correct answer: $$4.75\leq{x}<4.85$$
$$4.75\leq{x}\leq4.85$$
$$4.75<{x}<4.85$$
Q5.
Here are the error intervals for $$x$$ and $$y$$: $$24.5\leq{x}<25.5$$ and $$9.5\leq{y}<10.5$$. What are the lower and upper bounds of $$x + y$$?
34 and 35
Correct answer: 34 and 36
35 and 35
35 and 36
Q6.
Here are the error intervals for $$x$$ and $$y$$: $$24.5\leq{x}<25.5$$ and $$9.5\leq{y}<10.5$$. What are the lower and upper bounds of $$x - y$$?
15 and 16
15 and 15
14 and 15
Correct answer: 14 and 16