Mental Strategies for Division - Progression Points

Number

2.75

• representation of multiplication as a rectangular array and as the area of a rectangle

2.75

• use of fact families (5 × 7 = 35, 35 ÷ 7 = 5) to solve division problems

3.0 Standard

… They round numbers up and down to the nearest unit, ten, hundred, or thousand.

They skip count forwards and backwards, from various starting points using multiples of 2, 3, 4, 5, 10 and 100.

They estimate the results of computations and recognise whether these are likely to be over-estimates or under-estimates. They compute with numbers up to 30 using all four operations. They provide automatic recall of multiplication facts up to
10 × 10.

They devise and use written methods for:

• multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70)
• division by a single-digit divisor (based on inverse relations in multiplication tables).

3.25

• appropriate selection and use of mental and written algorithms to add, subtract, multiply and divide (by single digits) natural numbers

3.75

• multiplication by increasing and decreasing by a factor of two; for example,
  24 × 16 = 48 × 8
  = 96 × 4 = 192 × 2
  = 384 × 1 = 384

4.0 Standard

… They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

5.0 Standard

… Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding
(for example, 925 ÷ 34 ˜ 900 ÷ 30 = 30).

Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. They use approximations to p in related measurement calculations

Structure

2.25

• knowledge of the effect of multiplying by ten on the location of the decimal point in a number

2.75

• use of distributive property in calculations; for example, 6 × 37
  = 6 × 30 + 6 × 7

3.5

• use of division and multiplication as inverses; for example, multiplication by 25 can be carried out as ‘multiplication by 100 followed by division by 4’

Working Mathematically

2.5

• explanation and comparison of alternative computation methods