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Problem solving with rounding, estimation and bounds
I can use my knowledge of rounding, estimation and bounds to solve problems.
Lesson 3 of 3
New
New
- Year 10
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
- Rounding and estimation are practical maths skills.
- They can be used to quickly estimate the cost of a project.
- Sometimes you will need to apply common sense to rounding in context.
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.
Get pupils to estimate the length and width of different things around the classroom.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz
6 Questions
Q1.An interval for a number x shows the range of possible values of x.
An interval for a number x shows the range of possible values of x.
Correct Answer: error
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?
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: $$LB_l\div{UB_b}$$
$$LB_l\div{UB_b}$$
$$UB_l\div{LB_b}$$
$$LB_l\div{LB_b}$$
$$UB_l\div{UB_b}$$
Q3.A sack contains 50 kg of rice correct to the nearest kg. What are the lower and upper boundaries of the rice?
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
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?
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
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?
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: $$LB_r\div{UB_b}$$
$$LB_r\div{UB_b}$$
$$UB_r\div{UB_b}$$
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?
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?
Assessment exit quiz
6 Questions
Q1.A quick estimate for a calculation is obtained from using values, often rounded to 1 significant figure.
A quick estimate for a calculation is obtained from using values, often rounded to 1 significant figure.
Correct Answer: approximate, rough, close
approximate, rough, close
Q2.Match each to the appropriate measure.
Match each to the appropriate measure.
Correct Answer:Height of a house,metres
Height of a house - metres
Correct Answer:Mass of an dog,kilograms
Mass of an dog - kilograms
Correct Answer:Time taken to eat your tea,minutes
Time taken to eat your tea - minutes
Correct Answer:Distance from London to Dover,kilometres
Distance from London to Dover - kilometres
Correct Answer:Area of a rugby pitch,$$m^2$$
Area of a rugby pitch - $$m^2$$
Correct Answer:Volume of a fish tank ,$$cm^3$$
Volume of a fish tank - $$cm^3$$
Q3.Which of the following are reasonable approximations?
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
The distance between London and Manchester $$\approx$$ 300 km
Correct answer: Area of a football pitch $$\approx$$ 7000 $$m^2$$
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 $${{106^2\times1.587}\over35.06}$$
Using estimation only which of the following is the correct answer to $${{106^2\times1.587}\over35.06}$$
50.86004564
Correct answer: 508.6004564
508.6004564
5086.004564
50860.04564
508600.4564
Q5.Estimate the value of $${23.87\times105.7}\over38.942$$
Estimate the value of $${23.87\times105.7}\over38.942$$
Correct Answer: 50, fifty
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.
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
20 days, 20
