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Curriculum Planning Guidelines – Progression Points – Familiarisation tools
Mathematics – Number (Level 5)
Students multiply by powers of 10, link division by powers of 10 to multiplication by decimals
and use these in estimation. They know that the position of the digit zero affects the size of
numbers, such as 00.070 = 0.07. They explain dividing by a number between one and zero, such
as dividing by 0.1 is finding out how many tenths.
Students determine prime factors and use them to express any whole number as a product of
powers of primes and to find its composite factors.
Students use mental estimation to check the result of calculator computations. They use written
and/or mental methods to divide decimals by single digit whole numbers, interpreting the
remainder. They use knowledge of perfect squares to determine exact square roots.
Students convert between fraction, decimal and percentage forms, and use them to calculate and
estimate, such as estimate 63% of 300 by finding two thirds. They describe ratio as a comparison
of either subset to subset (part to part) or subset to set (part to whole), using simple whole number
ratios. They find equivalent ratios.
Students use ‘equal division by 10’ to simplify division by whole numbers, such as
240 ÷ 40 = 24 ÷ 4 = 6. For estimation in division, they mentally use ‘division fact rounding’. They
divide by powers of 10, and multiplication by powers of 10, in mental estimation, such as 30 ÷
0.01 is the same as 30 x 100 = 3000.
Students use a model to subtract one integer, positive or negative, from another and show its
equivalence to adding the opposite (additive inverse). They estimate the square roots of whole
numbers using nearby perfect squares.
Students describe ratio as a comparison of either subset to subset or subset to set, where the scale
factor is greater than 1 such as 2 : 5 = 1 : 2.5.
Students use equal multiplication by 10 to divide by decimals, such as 0.24 ÷ 0.04 = 24 ÷ 4 = 6.
They use a range of strategies for estimating multiplication and division calculations with
decimals, fractions and integers.
Students use efficient mental and/or written methods to multiply or divide by two-digit numbers.
They estimate and use a calculator to find squares, cubes, square and cube roots of any numbers.
They multiply negative numbers together, and give a reasonable explanation of the result.
Students describe ratio as a comparison of either subset to subset or subset to set, where the scale
factor is less than 1, such as 5 : 2 = 1 : 0.4 . They convert between decimals, ratios, fractions and
percentages, such as compare 3 out of 4 to 5 out of 7.
Office of Learning and Teaching
DE&T
Curriculum Planning Guidelines – Progression Points – Familiarisation tools
At Level 5, students identify complete factor sets for natural numbers and express these
natural numbers as products of powers of primes (for example, 36 000 = 25 × 32 × 53).
They write equivalent fractions for a fraction given in simplest form (for example, 2/3 = 4/6
= 6/9 = … ). They know the decimal equivalents for the unit fractions 1/2, 1/3, 1/4, 1/5, 1/8,
1/9 and find equivalent representations of fractions as decimals, ratios and percentages (for
example, a subset: set ratio of 4:9 can be expressed equivalently as 4/9 = 0.4 ≈ 44.44%). They
write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of
accuracy.
Students use knowledge of perfect squares when calculating and estimating squares and
square roots of numbers
(for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30). They evaluate natural
numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2
= 4/9). They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125). They
calculate squares and square roots of rational numbers that are perfect squares (for
example, √0.81 = 0.9 and √(9/16) = 3/4). They calculate cubes and cube roots of perfect cubes
(for example, 3√64 = 4). Using technology they find square and cube roots of rational
numbers to a specified degree of accuracy (for example, 3√200 = 5.848 to three decimal
places).
Students express natural numbers base 10 in binary form, (for example, 4210 = 1010102), and
add and multiply natural numbers in binary form (for example, 1012 + 112 = 10002 and 1012
× 112 = 11112).
Students understand ratio as both set: set comparison (for example, number of boys :
number of girls) and subset: set comparison (for example, number of girls : number of
students), and find integer proportions of these, including percentages (for example, the
ratio number of girls: the number of boys is 2 : 3 = 4 : 6 = 40% : 60%).
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 π in related measurement calculations
(for example, π × 52 = 25π = 78.54 correct to two decimal places).
They use technology for arithmetic computations involving several operations on rational
numbers of any size.
Office of Learning and Teaching
DE&T