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Ma2 Number

Subtraction of two-digit numbers

Pupil's hand-drawn number line showing the subtraction of two-digit numbers.
Two number lines representing two separate subtraction problems. The first number line starts at 79, add 1, 80, add 20, 100, add 20, 120, add 20, 140, add 20, 160, add 5, 165. The sum says 165 minus 79 equals 86. The number line below starts at 98, add 2, 100, add 30, 130, add 30, 160, add 20, 180, add 1, 181. The sum says 181 minus 98, 6.

Teacher’s notes

  • Uses a number line to count on.
  • Rounds to the nearest 10 and then counts on in steps of 10, 20 or 30.
  • Adds the steps mentally.

Next steps

Use larger jumps for efficiency, aiming for significant numbers, for example nearest 10, 100 (101 – 33: 33 → 40 → 100 → 101).

Multiplication by 4

Pupil's handwritten work to show multiplication by 4, including partitioning to show amounts to be multiplied.
There are two lines of sums that have lines to show which figures are being multiplied. ᆪ1.60 multiplied by 4 equals 4.00 plus 2.40 equals 6.40. 0.60 multiplied by 4 points to 2.40 on the line below and 1 multiplied by 4 points to 4 on the line below.

Teacher’s notes

  • Partitions the amount to be multiplied.
  • Doubles and doubles again for each component.
  • Adds the answers together.

Next steps

Use the grid method for multiplication.

Halves and quarters

Pupil's handwritten work to solve calculations using halves and quarters.
The pupil has titled the page 'Fraxhen' with three problems written below. The first problem is: Half of 1118, half of 1000 equals 500, half of 100 equals 50, half of 10 equals 5, half of 8 equals 4. The answer is 559, which has a tick next to it. The second calculation is half of 2768, half of 2000 equals 1000, half of 700 equals 350, half of 60 equals 30, half of 8 equals 4. The answer is 1384, which has a tick next to it. The third calculation is one-quarter of 64 equals 16, half of 60 equals 30 half 30 equals 15, half of 4 equals 2 half of 2 equals 1, 1 plus 15 equals 16. There is a tick next to this.

Teacher’s notes

  • Understands halving as ÷ 2 .
  • Understands finding a quarter as halving and halving again.
  • If necessary, partitions the quantity to be halved or quartered in order to break down the calculation into more manageable amounts.

Next steps

  • Find other unit fractions of quantities, for example 1 3 of 24, 1 3 of 63, 1 5 of 75.
  • Find 34 of 24, 64, etc., having found 14 .

What the teacher knows about Darren’s attainment in Ma2

Darren recognises multiples of 2, 5 and 10, and uses his knowledge of place value to multiply and divide whole numbers by 10 and 100, with whole number answers (and occasionally with non-integers in context). He uses correctly the symbols <, > and =. He identifies number patterns and can continue them. He recognises negative numbers in the context of temperature.

He can find unit fractions of small quantities, where there is an integer answer, by mentally dividing the quantity by the denominator. To find a half he divides by two; to find a quarter he halves and halves again. To divide by 3 or 5 he uses multiplication tables facts. He also finds unit fractions of larger quantities, where there is an integer answer, by using a written method based on partitioning. He matches unit fractions to their percentage equivalents, for example 1 2 = 50 % , 1 4 = 25 % . He uses decimal notation in contexts such as money and length, and can add and subtract decimals that do not require carrying or decomposition. He is beginning to be able to place decimals in order: for example, he shows the position of 0.42 on a number line with intervals of 0.1, but marked only with 0, 0.5 and 1.0. Using a calculator where appropriate, he solves simple problems involving direct proportion: for example, he finds the weight of £1.20 worth of plums given that 100 g cost 80p.

Darren adds and subtracts small two-digit integers mentally and three-digit integers using a written method (partitioning). He understands that subtraction is the inverse of addition and uses this, with a calculator, to find missing numbers, such as complements to 1000. He uses a number line for counting on to find the difference. He has good recall of the 2, 3, 4, 5 and 10 multiplication facts and is beginning to know those for the ×6, ×7, ×8 and ×9 tables. He can multiply a two-digit number by 2, 3, 4 or 5, using partitioning to achieve this. To multiply by 4, he chooses to double and double again. When he tries to use partitioning for division, it often proves an inappropriate method. It also does not work fully for a two-digit number multiplied by a two-digit number, as he is not yet setting his work out on a grid. Darren is confident with one-step problems. He solves whole number problems that require using one operation, including those that give rise to remainders.