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      Advanced problem solving with rounding, estimation and bounds

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      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. Sometimes you will need to apply common sense to rounding in context.
      3. Using your knowledge of arithmetic procedures, you can determine which bounds to calculate with.

      Keywords

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

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

      • 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

      Truncating the numbers rather than rounding when considering the suitable degree of accuracy.

      Emphasise that the numbers are being rounded and therefore the digit in the next decimal place must be considered.

      Teacher tip

      In pairs pupils challenge each other to estimate a calculation the other has made. Encourage the use of calculations given as fractions, exponents and roots.

      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

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      6 Questions

      Q1.
      A quick estimate for a calculation is obtained from using approximate values, often rounded to significant figure.

      Correct Answer: 1, one

      Q2.
      Round 508 273 to 2 significant figures.

      Correct Answer: 510 000, 510000

      Q3.
      A piece of string is measured as 6.8 cm correct to 1 decimal place. What are the lower and upper bounds?

      Correct Answer: 6.75 cm and 6.85 cm, 6.75 cm & 6.85 cm, 6.75cm and 6.85cm, 6.75cm & 6.85cm, 6.75 and 6.85

      Q4.
      Which of the following is not a correct formula for the area of a trapezium? [IMG]

      $${A} = {1\over2}{{(a+b)h}}$$
      Correct answer: $${A} = {{a+bh}\over2}$$
      $${A} = {{(a+b)h}\over2}$$
      $${A} = {1\over2}\times{{(a+b)\times{h}}}$$

      Q5.
      Which calculation will give the upper bound of $$a\times{b}$$?

      $$LB_a\times{LB_b}$$
      $$LB_a\times{UB_b}$$
      Correct answer: $$UB_a\times{UB_b}$$
      $$UB_a\times{LB_b}$$

      Q6.
      Which calculation will give the lower bound of $$a\div{b}$$?

      Correct answer: $$LB_a\div{UB_b}$$
      $$LB_a\div{LB_b}$$
      $$UB_a\div{UB_b}$$
      $$UB_a\div{LB_b}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      An error for a number $$x$$ shows the range of possible values of $$x$$.

      Correct Answer: interval

      Q2.
      Using estimation only which of the following is the correct answer to $${{214^2\times2.875}\over37.06}$$

      355.2711819
      Correct answer: 3552.711819
      35527.11819
      355271.1819
      3552711.819

      Q3.
      Estimate the value of $${{19.56^3}\over{37.06-16.2}}$$

      Correct Answer: 400

      Q4.
      Which of the following calculations will give the lower bound of $$a^2$$?

      $$a^2=UB_{c^2}-UB_{b^2}$$
      $$a^2=LB_{c^2}-LB_{b^2}$$
      Correct answer: $$a^2=LB_{c^2}-UB_{b^2}$$
      $$a^2=UB_{c^2}-LB_{b^2}$$

      Q5.
      If $$LB_x = 0.4562$$ and $$UB_x = 0.4569$$. Find the value of $$x$$ and the appropriate degree of accuracy in significant figures.

      $$x$$ = 0.45 (2 s.f.)
      $$x$$ = 0.45 (3 s.f.)
      Correct answer: $$x$$ = 0.46 (2 s.f.)
      $$x$$ = 0.46 (3 s.f.)
      $$x$$ = 0.456 (3 s.f.)

      Q6.
      $$a$$ = 2.64 (3 s.f.), $$b$$ = 1.655 (4 s.f.), $$c={\sqrt{a}\over{b^3}}$$. Work out the value of $$c$$ to a suitable degree of accuracy.

      $$x$$ = 0.35 (2 s.f.)
      $$x$$ = 0.35 (3 s.f.)
      $$x$$ = 0.36 (3 s.f.)
      Correct answer: $$x$$ = 0.36 (2 s.f.)
      $$x$$ = 0.358 (3 s.f.)

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