Number facts progression

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.

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.

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.

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.

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.