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3. Mathematics

Mathematics

• Early Stage 1
• Stage 1
• Stage 2
• Stage 3

Mathematics develops students’ thinking, understanding, competence and confidence with numbers, shapes and measurement. Students learn to add, subtract, divide and multiply whole numbers, fractions and decimals. They learn to measure time and calculate with money. They learn geometry, algebra and how to work with data and graphs.

In Kindergarten

• count aloud to 30 and recognise numbers from 1 to 20
• manipulate objects such as counters to help add and subtract numbers
• recognise the value of currency, eg 20 cent piece, five dollar note
• count backwards from a given number in the range 0 to 20
• name the days of the week and seasons
• tell the time to the hour, eg four o’clock
• identify and name simple shapes, eg circles, squares
• use positional terms, eg between, under, right, left
• recognise that halves are equal parts

Some Year 1 examples

• state the place value of digits in two-digit numbers, eg ‘in the number 32, the 3 represents 30 or 3 tens’
• begin to model multiplication using concrete objects, eg 3 x 2 is the same as 3 groups of 2 or as an array with 3 rows of 2
• describe halves and quarters found in everyday life, eg quarters of an orange, half a glass of water
• begin to use metres and centimetres to estimate and measure length and distance, eg ‘My book is 30 cm long’, ‘My desk is more than a metre wide’
• count forwards and backwards by two, fives and tens
• use the terms ‘add’, ‘plus’, ‘equals’, ‘is equal to’, ‘take away’, ‘minus’ and ‘the difference between’

Some Year 2 examples

• read clocks on the half-hour
• count, read and write numbers up to 999
• begin to model division using concrete objects, eg 6 ÷ 3 is the same as sharing 6 objects into 3 equal groups
• record area by describing the number and type of units, eg the area of this surface is 20 tiles
• use a calendar to identify dates, months, seasons and birthdays
• begin to understand and draw graphs and diagrams of data, eg using simple picture graphs and column graphs
• recognise and explain numbers such as odds and evens, numbers ending with five and zero

Some Year 3 examples

• develop mental strategies to multiply a two-digit number by a one-digit number, eg using known facts, multiplying the tens and then the ones, repeatedly doubling when multiplying by an even number
• count, read, write and order numbers up to 9999
• identify, represent and compare fractions involving halves, quarters, and eighths
• interpret decimal notation for tenths and hundredths, eg 0.1 is the same as ¹/₁₀
• identify and measure the length, breadth, height and perimeter of objects in metres, centimetres and millimetres
• record area in square centimetres and square metres, eg 5 cm², 6 m²
• recall multiplication facts (‘times tables’) up to 10 x 10
• organise data to create and interpret tables and graphs

Some Year 4 examples

• read and record time in one-minute intervals
• record numbers up to four digits using expanded notation, eg 5429 = 5000 + 400 + 20 + 9
• develop mental strategies to divide by a one-digit number, eg ‘63 ÷ 9 = 7 because I know 7 x 9 = 63’
• determine factors for a given number, eg ‘factors of 12 are 1, 2, 3, 4, 6, 12’
• add and subtract decimals with the same number of decimal places (up to 2 decimal places), eg 0.10 + 0.33 = 0.43
• relate common percentages to a fraction or decimal, eg ‘25% means 25 out of 100 or 0.25’
• manipulate, compare and describe features of 2-D shapes, eg pentagons, octagons, parallelograms
• record volume and capacity using litres, millilitres and cubic centimetres, eg 5 L, 6 mL, 27 cm³
• use coordinates and compass points to describe position and to give and follow directions, eg ‘the lion cage is at B3’, ‘the treasure is north-east of the cave’

Some Year 5 examples

• read, write, and order numbers of any size
• identify and classify angles, eg right, acute, obtuse, reflex, straight, revolution
• multiply three-digit numbers by two-digit numbers using the written extended form (long multiplication)
• identify prime numbers, eg 13 has only two factors (1 and 13) and therefore is prime
• find equivalent fractions using diagrams and number lines, eg ³/₄ = ⁶/₈
• add and subtract simple fractions, eg ⁵/₆ + ³/₆ = ⁸/₆ or 1²/₆, ²/₃ + ¹/₆ = ⁴/₆ + ¹/₆ = ⁵/₆
• record lengths and distances using decimal notation to 3 decimal places, eg 2.753 km

Some Year 6 examples

• use 24-hour time and am/pm notation
• calculate simple fractions and percentages of an amount, eg ¹/₅ of 30 = 6, 10% of $200 = ¹/₁₀ of $200 = $20
• multiply simple fractions by whole numbers , eg 3 x ²/₅ = ⁶/₅
• record remainders as fractions or decimals, eg 25 ÷ 4 = 6¹/₄ or 6.25
• identify and construct 3-D objects on the basis of their properties, eg rectangular prisms, triangular pyramids
• record volume and capacity using decimal notation to 3 decimal places, eg 1.275 L
• interpret and draw a wider range of graphs using a scale, eg line graphs, divided bar graphs
• complete simple sentences by calculating missing values, eg 270 ÷ x = 9