New
New
Year 10
Foundation

Problem solving with rounding, estimation and bounds

I can use my knowledge of rounding, estimation and bounds to solve problems.

New
New
Year 10
Foundation

Problem solving with rounding, estimation and bounds

I can use my knowledge of rounding, estimation and bounds to solve problems.

Lesson details

Key learning points

  1. Rounding and estimation are practical maths skills.
  2. They can be used to quickly estimate the cost of a project.
  3. Sometimes you will need to apply common sense to rounding in context.

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

Get pupils to estimate the length and width of different things around the classroom.
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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6 Questions

Q1.
An interval for a number x shows the range of possible values of x.
Correct Answer: error
Q2.
Considering the maximum number of boxes to safely fit onto a lorry. Which of the following should be used? (Where $$l$$ represents the capacity of the lorry and $$b$$ represents the mass of a box?
Correct answer: $$LB_l\div{UB_b}$$
$$UB_l\div{LB_b}$$
$$LB_l\div{LB_b}$$
$$UB_l\div{UB_b}$$
Q3.
A sack contains 50 kg of rice correct to the nearest kg. What are the lower and upper boundaries of the rice?
Correct Answer: 49.5 kg and 50.5 kg, 49.5 kg & 50.5 kg, 49.5kg and 50.5kg, 49.5kg & 50.5kg, 49.5 and 50.5
Q4.
A sack contains 50 kg of rice correct to the nearest kg. This is put into smaller bags containing 1 kg correct to 0.01 kg. What are the lower and upper boundaries of the bags?
Correct Answer: 0.995 kg and 1.005 kg, 0.995 kg & 1.005 kg, 0.995kg and 1.005kg, 0.995kg & 1.005kg, 0.995 and 1.005
Q5.
A sack contains 50 kg of rice correct to the nearest kg. This is put into smaller bags containing 1 kg correct to 0.01 kg. Which calculation is correct to find the minimum number of bags produced?
$$LB_r\div{LB_b}$$
$$UB_r\div{LB_b}$$
Correct answer: $$LB_r\div{UB_b}$$
$$UB_r\div{UB_b}$$
Q6.
A sack contains 50 kg of rice correct to the nearest kilogram. This is put into smaller bags containing 1 kg correct to 0.01 kg. What is the minimum number of bags produced?

6 Questions

Q1.
A quick estimate for a calculation is obtained from using values, often rounded to 1 significant figure.
Correct Answer: approximate, rough, close
Q2.
Match each to the appropriate measure.
Correct Answer:Height of a house,metres

metres

Correct Answer:Mass of an dog,kilograms

kilograms

Correct Answer:Time taken to eat your tea,minutes

minutes

Correct Answer:Distance from London to Dover,kilometres

kilometres

Correct Answer:Area of a rugby pitch,$$m^2$$

$$m^2$$

Correct Answer:Volume of a fish tank ,$$cm^3$$

$$cm^3$$

Q3.
Which of the following are reasonable approximations?
The height of a tree $$\approx$$ 5 km
Correct answer: The distance between London and Manchester $$\approx$$ 300 km
Correct answer: Area of a football pitch $$\approx$$ 7000 $$m^2$$
The length of a cats tail $$\approx$$ 0.03 m
Q4.
Using estimation only which of the following is the correct answer to $${{106^2\times1.587}\over35.06}$$
50.86004564
Correct answer: 508.6004564
5086.004564
50860.04564
508600.4564
Q5.
Estimate the value of $${23.87\times105.7}\over38.942$$
Correct Answer: 50, fifty
Q6.
Andeep's dog is fed twice a day. Each meal weighs 175 g. A bag of food contains 7.5 kg. Estimate how many days the bag of food will last.
Correct Answer: 20 days, 20