Make Sense of Numbers to Solve Problems

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Number facts progression

The number facts progression describes the number facts that learners need to recall and apply to solve number problems. At the earliest steps, learners need to be able to fluently recall the basic addition, subtraction, multiplication and division facts. At the highest step, learners know the conversions between common fractions, decimals and percentages.

Most adults will be able to: Activities
1.
  • addition facts with sums of 5 or 10 and the decade facts.

Learners know addition facts with sums of 5, for example, 1 + 4 = 5, 2 + 3 = 5, 4 + 1 = 5.

Learners know addition facts with sums of 10, for example, 1 + 9 = 10, 2 + 8 = 10, 7 + 3 = 10.

Learners know the “decade facts” (that is, how to add any single digit to any multiple of 10), for example, 10 + 4 = 14, 40 + 7 = 47.

2.
  • basic addition and subtraction facts up to 10 + 10.

Learners know the basic addition and subtraction facts up to 10 + 10, for example:

  • 3 + 4 = 7, 4 + 3 = 7
  • 7 – 3 = 4, 7 – 4 = 3
  • 9 + 9 = 18, 18 – 9 = 9.

Addition and subtraction facts

Learners develop strategies that will help them remember and recall the basic addition and subtraction facts.

3.
  • basic multiplication and division facts up to 10 x 10.

Learners know the basic multiplication and division facts up to 10 x 10. For example, a learner knows that:

  • the 5 times table is used to multiply: 1 x 5 = 5, 2 x 5 = 10
  • the 5 times table is used to divide: 50 ÷ 5 = 10, 45 ÷ 5 = 9
  • 6 x 4 = 24, 3 x 7 = 21, 8 x 4 = 32
  • 56 ÷ 7 = 8, 42 ÷ 6 = 7.

Understanding multiplication

Learners use already-known multiplication facts to develop quick recall of unknown facts.

Deriving multiplication and division facts

Learners extend their repertoire of multiplication and division facts by using already-known facts to derive unknown facts.

Multiplication and division facts

Learners develop strategies that will help them remember and recall the basic multiplication and division facts.

4.
  • basic multiplication facts with tens,
    hundreds and thousands
  • fraction and decimal groupings that
    make 1.

Learners know multiplication and division facts with tens, hundreds and thousands, for example:

  • 20 x 300 = 6,000
  • 400 x 800 = 32,000
  • 5,000 ÷ 10 = 500
  • 10 million ÷ 200 = 50,000.

Learners know the fraction and decimal groupings that make 1, for example:

  • 3/4 + 1/4 = 1
  • 2/7 + 5/7 = 1
  • 0.6 + 0.4 = 1.

Estimating facts

Learners apply their basic multiplication facts to problems involving multiples of tens, hundreds, thousands.

5.
  • common factors of numbers up to 100
  • fraction, decimal and percentage conversions for halves, thirds, quarters, fifths and tenths
  • the convention for exponents.

Learners know common factors, for example:

  • that the common factors of 48 and 64 are {1, 2, 4, 8, 16}.

Learners know the fraction, decimal and percentage conversions for halves, thirds, quarters, fifths and tenths. For example, a learner knows that:

3/4 = 0.75 = 75%.

Learners understand and can use the convention for exponents. For example, a learner knows that: 24 (2 to the power of 4) = 2 x 2 x 2 x 2 = 16.

Connecting percentages decimals and fractions

Learners explore the connections between percentages, decimals and fractions.

Decimal number place value

Learners develop their understanding of the place value system to include the decimal numbers tenths, hundredths and thousandths.

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