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      Problem solving with rounding, estimation and bounds

      Lesson details

      Learning outcome

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

      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.

      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.

      Teacher tip

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

      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.

      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

      To help you plan your 10 maths lesson on: Problem solving with rounding, estimation and bounds, download all teaching resources for free and adapt to suit your pupils' needs...