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Guidance

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      Problem solving with standard form calculations

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      Lesson details

      Learning outcome

      I can use my knowledge of standard form to solve problems.

      Key learning points

      1. It can be useful to have very large or very small numbers written in standard form.
      2. Being able to perform arithmetic operations on numbers written in standard form reduces error during conversion.
      3. Standard form calculations can be done quickly with the use of a calculator.

      Keywords

      • Standard form - Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer).

      • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

      • Commutative - The commutative law states you can write the values of a calculation in a different order without changing the calculation; the result is still the same. It applies for addition and multiplication.

      • Associative - The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.

      Common misconception

      Incorrect use of the calculator when finding the mean of numbers. Omitting the brackets when summing the values.

      Encourage pupils to calculate the sum of the values and record this before dividing by the number of values. This also encourages a record of a method.

      Teacher tip

      To help with the second learning cycle you could have 'chocolate spheres' and toilet roll tubes to help pupils visualise the problem. They could also test out the theory of 64% of the volume of the cylinder being consumed.

      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.
      Standard form is when a number is written in the form $$A × 10^n$$. When numbers are written in standard form the value of $$A$$ must be greater than or equal to and less than 10.

      Correct Answer: 1, one

      Q2.
      Calculate $$(4.6\times10^6)\div(2\times10^2)$$.

      $$2.3\div10^3$$
      $$2.3\div10^4$$
      $$2.3\times10^3$$
      Correct answer: $$2.3\times10^4$$
      $$2.6\times10^4$$

      Q3.
      Calculate $$(5.4\times10^{5})\div(3\times10^{-2})$$.

      $$1.8\times10^3$$
      Correct answer: $$1.8\times10^7$$
      $$1.8\div10^7$$
      $$1.8\div10^3$$
      $$2.4\times10^7$$

      Q4.
      Calculate $$480\text{ } 000\div(4\times10^{-2})$$.

      $$1.2\times10^{-1}$$
      $$1.2\times10^{-2}$$
      $$1.2\times10^{2}$$
      $$1.2\times10^{3}$$
      Correct answer: $$1.2\times10^{7}$$

      Q5.
      Calculate $${(1.6\times10^4)\times(2\times10^{-5})}\over(6.4\times10^2)$$. Give your answer in standard form.

      $$0.5\times10^{-3}$$
      $$5\times10^{-3}$$
      Correct answer: $$5\times10^{-4}$$
      $$0.5\times10^{-4}$$

      Q6.
      A grain of sand has a mass of $$1.6\times10^{-5}$$ g. How many grains of sand are there in $$5$$ kg? Give you answer as an ordinary number.

      Correct Answer: 312 500 000, 312500000, 312,500,000

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      Which of the following is described here: The middle (or average middle) value in an ordered data set.

      Mean
      Correct answer: Median
      Mode
      Range

      Q2.
      What is the mode of the following? $$4.5\times10^3$$, $$4.5\times10^{-2}$$, $$4.5\times10^2$$, $$4.5\times10^3$$, $$4.2\times10^4$$.

      $$4.5\times10^{-2}$$
      $$4.5\times10^2$$
      Correct answer: $$4.5\times10^3$$
      $$4.2\times10^4$$

      Q3.
      Starting with the smallest number, put these numbers in ascending order.

      1 - $$4.5\times10^3$$
      2 - $$5.4\times10^3$$
      3 - $$4.5\times10^4$$
      4 - $$4.2\times10^5$$
      5 - $$4.5\times10^5$$
      6 - $$4.8\times10^6$$

      Q4.
      Find the median of: $$4.5\times10^5$$, $$4.5\times10^3$$. $$4.2\times10^5$$, $$5.4\times10^3$$ and $$4.5\times10^4$$.

      $$4.5\times10^3$$
      Correct answer: $$4.5\times10^4$$
      $$4.2\times10^5$$
      $$4.5\times10^5$$
      $$5.4\times10^3$$

      Q5.
      Convert $$4\times10^6 $$ m$$^3$$ into cm$$^3$$.

      $$4\times10^8 $$ cm$$^3$$
      $$4\times10^9 $$ cm$$^3$$
      $$4\times10^{10} $$ cm$$^3$$
      $$4\times10^{11} $$ cm$$^3$$
      Correct answer: $$4\times10^{12} $$ cm$$^3$$

      Q6.
      The volume of a football is $$4200$$ cm$$^3$$. The volume of Wembley is $$4\times10^6 $$ m$$^3$$. Assuming no gaps, approximately how many footballs will fit into Wembley stadium?

      100 billion
      10 billion
      Correct answer: 1 billion
      100 million
      10 million

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