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Year 10
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Using upper and lower bounds practically

I can consider a context and decide whether it is suitable to use the upper or lower bound for each value in a calculation.

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New
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Year 10
Higher

Using upper and lower bounds practically

I can consider a context and decide whether it is suitable to use the upper or lower bound for each value in a calculation.

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Lesson details

Key learning points

  1. When considering safety contexts, you want to be able to guarantee safety limitations (weight of materials).
  2. When considering costs, you may wish to know the maximum cost to you.
  3. When training in sport, you may wish to know the time you need to beat in order to win a race.

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

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.

Give pupils time to think and discuss situations where it is best to use the upper or lower bound for safety. This opportunity allows pupils to reflect on where they have seem or experienced the need for bounds in safety e.g fairground rides, elevators, parkour, special effects, etc
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
The bound for a rounded number is the smallest value that would round up to the next rounded value.
Correct Answer: upper
Q2.
$$x$$ = 5.2 correct to 1 decimal place. What is the error interval?
$$5.15\leq{x}>5.25$$
Correct answer: $$5.15\leq{x}<5.25$$
$$5.15\leq{x}\leq5.25$$
$$5.15<{x}\leq5.25$$
$$5.15\geq{x}<5.25$$
Q3.
$$y$$ = 45 correct to 2 significant figures. What is the error interval?
$$44.5\geq{y}<45.5$$
$$44.5<{y}\leq45.5$$
$$44.5\leq{y}>45.5$$
$$44.5\leq{y}\leq45.5$$
Correct answer: $$44.5\leq{y}<45.5$$
Q4.
The error interval of $$x$$ is $$5.15\leq{x}<5.25$$. The error interval of $$y$$ is $$44.5\leq{y}<45.5$$. What are the lower and upper bounds of $$xy$$? (Give you answers to 3 decimal places)
Correct Answer: 229.175 and 238.875, 229.175 & 238.875, 238.875 and 229.175, 238.875 & 229.175, 229.175 238.875
Q5.
The error interval of $$x$$ is $$5.15\leq{x}<5.25$$. The error interval of $$y$$ is $$44.5\leq{y}<45.5$$. What are the lower and upper bounds of $$xover{y}$$? (Give you answers to 3 s.f.)
Correct Answer: 0.168 and 0.178, 0.168 & 0.178, 0.178 and 0.168, 0.178 & 0.168, 0.168 0.178
Q6.
Which calculation will give the upper bound of $$x={{a^2}\over{b+c}}$$
$$UB_x={LB_{a^2}\over{LB_b+LB_c}}$$
$$UB_x={LB_{a^2}\over{UB_b+UB_c}}$$
Correct answer: $$UB_x={UB_{a^2}\over{LB_b+LB_c}}$$
$$UB_x={UB_{a^2}\over{UB_b+UB_c}}$$
$$UB_x={UB_{a^2}\over{UB_b+LB_c}}$$

Exit quiz

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6 Questions

Q1.
The degree of determines the upper and lower bounds of a number or measurement.
Correct Answer: acurracy
Q2.
Considering the maximum number of boxes to safely fit in a lift. Which of the following should be used? (Where $$l$$ represents the capacity of the lift and $$b$$ represents the mass of a box?
$$UB_l\div{UB_b}$$
$$UB_l\div{LB_b}$$
Correct answer: $$LB_l\div{UB_b}$$
$$LB_l\div{LB_b}$$
Q3.
A sack contains 16 kg of flour correct to the nearest kilogram. What are the lower and upper bounds of the mass of the flour?
Correct Answer: 15.5 kg and 16.5 kg, 15.5 kg & 16.5 kg, 15.5kg and 16.5kg, 15.5kg & 16.5kg, 15.5 and 16.5
Q4.
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. What are the lower and upper bounds of the mass of the bags?
Correct Answer: 495 g and 505 g, 495 g & 505 g, 495g and 505g, 495g & 505g, 495 and 505
Q5.
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. Which calculation is correct to find the minimum number of bags produced?
$$UB_f\div{UB_b}$$
Correct answer: $$LB_f\div{UB_b}$$
$$LB_f\div{LB_b}$$
$$UB_f\div{LB_b}$$
Q6.
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. What is the minimum number of bags produced?
Correct Answer: 30, 30 bags, thirty, thirty bags