WCCS JUNIOR SCHOOL MATHEMATICS SYLLABUS
NUMBER
TOPIC
SKILL
YEAR 3
Place value
Counting
Addition
Subtraction
Multiplication
Division
Know the value of a digit placed in the units, tens or hundreds columns
Can write numbers in words and digits
Can organise numbers in order of increasing or decreasing size
Can count in ones, twos, threes, fours, fives, tens, multiples of 10 and multiples of 100
Can count on and back in nines
Can count on and back in elevens
Know the number bonds to 10
Can use a variety of mental methods for addition and are familiar with all vocabulary associated with addition
Can use the column method for written addition, including carrying, for up to 3 digit numbers
Can solve word problems which require addition
Can subtract single digits from 10
Can use a variety of mental methods for subtraction and are familiar with all vocabulary associated with subtraction
Can use the column method for written subtraction, including borrowing, for up to 3 digit numbers
Understand subtraction as the inverse or opposite of addition
Know how to check their answers by inverse operations
Can solve word problems which require subtraction
Understand that multiplication is repeated addition
Know the terms product and multiple and can suggest some multiples of a given number
Can multiply by 10 and by 100
Can use the partition method for multiplication
Can use a variety of mental methods for multiplication and are familiar with all vocabulary associated with multiplication
Can use the formal written method of multiplication for a 2-digit number multiplied by a 1-digit number
Can solve word problems which require multiplication
Know the 2x, 3x, 4x, 5x, 6x and 10x tables
Understand that division can be thought of as repeated subtraction, splitting into groups or sharing out
Understand the link between ‘a fraction’ of something and ‘dividing something’ e.g. a quarter of / dividing by 4
Can divide by 10 and by 100
Can divide by repeated subtraction – ‘chunking’
Know that division is the inverse of multiplication
Can use multiplication to check answers to division questions
Can use a variety of mental methods for division and are familiar with all vocabulary associated with division
Can use the formal written method of division to divide a 2-digit number by a 1-digit number – ‘the one-legged table’, including remainders as
rem X
Can use context to determine sensible way to round answer
Sequences
Money
Introduction to
fractions
Can solve word problems which require division
Know the sequence of even and odd numbers
Can find the rule in a number or pattern sequence and continue it or find any missing terms
Know the values of British coins and notes and can work out which coins/notes are needed to make a given total
Can use correct notation for writing money
Can convert between pounds and pence
Can add and subtract amounts of money, using formal and informal methods
Can mental methods for multiply amounts of money by single digit
Can solve simple word problems involving money
Can identify a fraction and name the parts of a fraction
Can add fractions with the same denominator
Can recognise and generate equivalent fractions
Can simplify a fraction to its lowest terms
Can find simple fractions of a number
YEAR 4
Place value
Counting
Addition
Subtraction
Multiplication
Division
Functions
Inequalities
Know the value of a digit placed in the thousands, ten thousands and hundred thousands columns
Can order numbers up to 1 million
Can count in tens, hundreds and thousands
Can use a variety of mental methods for addition and are familiar with all vocabulary associated with addition
Can use the column method for written addition for up to 3-digit numbers and for adding more than two numbers
Can solve word problems which require addition of large numbers
Can use a variety of mental methods for subtraction and are familiar with all vocabulary associated with subtraction
Can subtract informally using complementary addition
Can use the column method for written subtraction for up to 4-digit number
Can solve word problems which require subtraction of large numbers
Can use a variety of mental methods for multiplication and are familiar with all vocabulary associated with multiplication
Know the term product and multiple and the link to the times tables
Can multiply by 1000
Can define and recall the square numbers up to 100
Can use the informal partition method for multiplying a 2-digit number by a 1-digit number
Can multiply 2 and 3 digit number by a 1-digit number using a written method
Can solve word problems which require multiplication of 2 and 3 digit numbers by a 1-digit number
Know all times tables up to and including 12x tables
Can use a variety of mental methods for division and are familiar with all vocabulary associated with division
Can divide by 1000
Can use informal strategies for division
Can use a formal written method for division by a 1-digit number – ‘the one-legged table’
Can give answers to divisions as a mixed number e.g. 26/8 = 4¼
Can use inverse operations to check division calculations
Can solve word problems which require division by a 1-digit number
Can find an output from a given input into a simple function machine
Can find an input from a given output from a simple function machine
Can define and recognise an inequality
Can insert the correct inequality sign between a pair of numbers
Negative numbers
Sequences
Money
Fractions
Introduction to
decimals
Decimal addition
and subtraction
Multiplication and
division by 10,
100,1000
Can recognise negative numbers
Can order a set of positive and negative numbers
Can find the difference between two numbers when one or both of the numbers is negative
Can find the rule in a number or pattern sequence and continue it or find any missing terms
Can use a rule to generate numbers in a sequence
Can find the rule in a number sequence containing fractions and continue it or find any missing terms e.g. 1/3, 3/6, 5/9…
Can convert between pounds/pence, euros/cents and dollars/cents
Can add and subtract amounts of money
Can multiply amounts of money by 2-digit number
Can divide amounts of money by 1-digit number
Can solve one-step and two-step word problems which involve working with money
Can convert improper fractions into mixed numbers
Understand the relationship between division and fractions
Can convert mixed numbers into improper fractions
Can find the lowest common denominator of a pair of fractions
Can order fractions with different denominators
Can add and subtract fractions with different denominators
Can identify the value of a digit in the tenths, hundredths and thousandths columns
Can order decimals with up to 3 decimal places
Can convert decimals to fractions
Can round numbers to the nearest tenth*
Can find a number half way between two decimals
Can add decimals with up to three decimal places
Can subtract decimals with up to three decimal places
Can multiply decimals by 10, 100, 1000
Can divide decimals by 10, 100, 1000
YEAR 5
Place value
Factors
Number
properties
Decimals, fractions
and percentages
Know the value of a digit placed in all columns up to and including the millions column
Can write very large numbers in words
Can write very large numbers in figures
Can use the divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, 20, 25, and 100
Can find all the factors of any number (up to 100) by finding pairs of numbers that multiply to give the number
Can define ‘square numbers’ and ‘square roots’ and know the square roots of all the square numbers up to 100
Can define ‘cube numbers’ and ‘cube roots’ and know the cube roots of all the cube numbers up to 216
Understand index notation such as 42 and 73
Can define ‘prime numbers’ and know the prime numbers up to 100
Can express a number as a product of its prime factors using a factor tree and ladder division
Can use knowledge of number properties to tackle number puzzles
Can use confidently all the following terms: even, odd, sum, difference, product, prime, multiple, factor, square, square root, consecutive
Know the properties of even and odd numbers and their sums, differences and products e.g. odd+odd=even, oddxodd=odd etc
Can convert decimals into fractions using tenths
Can convert decimals into fractions using hundredths
Can convert fractions into decimals
Can convert percentages into fractions
Can convert fractions into percentages
Fractions of
quantities
Percentage
Introducing
investigations
Ratio and
proportion
Functions
Inequalities
Decimal
multiplication
Decimal division
Long multiplication
Division using
factors
BIDMAS
Introduction to
algebra
Advanced number
work
Advanced number
sequences
Can convert decimals into percentages
Can convert percentages into decimals
Can order a group of numbers given as fractions, decimals and percentages
Can find a unitary fraction of a quantity
Can find any fraction of a quantity
Can write one quantity as a fraction of another quantity
Can use reverse fractions to find the whole amount of a quantity from only knowing the value of a fraction
Can write one quantity as a percentage of another quantity
Can find 50%, 25% and 75% of a number
The 10% method - Can find 10% of a number
The 10% method - Can find multiples of 10% of a number
The 10% method - Can find fractions of 10% of a number
The 10% method – Can find further percentages using combinations of multiples and fractions of 10%
Can find the VAT charged on an amount
Can use 1% method to find any percentage of a number
Can identify, discuss, explore and extend patterns in numbers
Can identify, discuss, explore and extend patterns in shapes
Can express quantities in two groups as a ratio
Can find a missing quantity by multiplying up a ratio
Can express the amount of one of a group of items as a proportion of the whole group, giving the answer as a fraction
Can find outputs for a given input into a double function machine
Can find inputs for a given output from a double function machine
Can solve word puzzles involving function machines
Can find the largest and smallest values that satisfy an inequality
Can find the range of values that satisfy an inequality and show them on a number lines
Can multiply decimals by 10, 100 and 1000
Can multiply decimals by multiples of 10, 100 and 1000
Can multiply a decimal by a decimal
Can divide decimals by a whole number with no remainder
Can divide decimals by a whole number giving an answer with a remainder
Can divide by multiples of 10, 100 and 1000
Can divide by a decimal
Can multiply informally by multiplying by factors in successive steps
Can multiply informally by using the partition method
Can use the formal written method for multiplication to multiply a 2 or 3-digit number by a 2-digit number
Can divide informally by dividing by factors in successive steps
Can divide informally by writing division as a fraction and simplifying
Know the order in which mixed operations should be carried out including brackets
Can interpret simple algebraic expressions and formulae to solve problems
Calculation by comparison: Can use a given number fact to calculate a related calculation e.g. 12 x 35 = 420. Find 1.2 x 3.5
Long division: Can divide by any two digit number
Can recognize, describe and extend advanced number patterns and sequences, including:
- increasing in steps of 0.1. 0.2, 0.5, 0.5 etc.
- Fibonacci sequence, Powers of 2, 3 etc.
SHAPE, SPACE AND MEASURE
TOPIC
SKILL
YEAR 3
Scales, Estimation
and Rounding
Measurement Length
Measurement –
Mass
Measurement –
Capacity
Time
Position –
co-ordinates
Drawing,
measuring lines
accurately
Angles and
direction
Can read simple scales
Can fill in suitable numbers on an unmarked scale
Can round numbers to the nearest 10 or 100
Know the terms mm, cm, m and km and can convert between them
Can write length measurements using correct notation
Can estimate lengths of everyday objects
Can measure objects proficiently
Know the terms g and kg and can convert between them
Can read and mark scales on weighing scales
Can weigh objects proficiently
Can estimate masses of everyday objects
Know the terms millilitre and litre and can convert between them
Can read and mark scales on measuring jugs
Can measure capacity of objects proficiently
Can estimate capacity of everyday objects
Can tell the time using an analogue clock
Understand that time can be given using the 24-hour clock
Can convert between 12-hour and 24-hour clock
Can write times given in words
Can convert times given in hours into minutes
Can convert times given in minutes to hours and minutes
Can add a period of time onto a given time
Can subtract a period of time from a given time
Can read and extract information from a travel timetable
Can solve word problems which involving time
Know the relationship between hours, days, weeks, years, decades, centuries and millenia
Can find a square on a grid given its (letter,number) co-ordinates and can name a given square (only first quadrant)
Can draw and measure lines accurately (to the nearest half centimeter)
Know the angle description for a full turn, half turn and quarter turn
Can identify 90° angles and use the term ‘right-angle’
Know the names of the main four points on a compass
2D Shapes
An introduction to
line symmetry
3D shapes
Can define and identify circles and semi-circles
Can define and identify triangles and can use the term vertex or vertices
Can define and identify quadrilaterals
Can define and identify polygons
Can identify symmetry in everyday objects
Can draw lines of symmetry on a 2D shape
Can recognize horizontal and vertical lines of symmetry
Can complete partial shapes to create a symmetrical shape, including diagonal mirror lines
Know the terms faces, edges and corners (vertices) and can identify them on a 3D shape
Can define and identify prisms
Can define and identify cones, cylinders, spheres and hemi-spheres
YEAR 4
Scales, estimation
and rounding
Metric
Measurement
Lines
Position –
co-ordinates
Angles and
direction
Can read numbers using a variety of scales
Can mark numbers on a variety of unmarked scales
Can round numbers to the nearest whole number or 1000
Know the relationship between mm, cm, m and km and can convert between the different length units
Know the relationship between mg, g, kg and metric tonne and can convert between the different mass units
Know the relationship between ml and litres and convert between the different capacity units
Can solve word problems which require working with metric measurements
Know and can convert between the following imperial measurements:
- inch-foot-yard-mile
- ounce-pound-stone
- pint-gallon
Know and can use the following metric-imperial conversions:
- cm-inch and km-miles,
- g-ounces and kilos-pounds
- litres-pints
Can draw and measure lines accurately (to the nearest millimetre)
Know the terms x-axis, y-axis and origin on a one quadrant co-ordinate grid
Can give the co-ordinates of a point given on a grid
Can plot a point given its co-ordinates on a grid
Can use the co-ordinates of the vertices of a shape to draw the shape on a grid
Can use vertices named with letters to join up points in the correct order to make a shape
Can identify acute and obtuse angles and can use the term right angle
Can identify a reflex angle
Can use a protractor to measure an angle
Can use a protractor to draw a given angle
Can find the angle between hands of a clock and can find the angle a clock hand sweeps through in a given period of time
Know the names and angles of the 8 main points of a compass
2D shapes
Symmetry and
reflection
Understand and use the terms parallel and perpendicular to describe pairs of lines
Can identify and define circles and semi-circles and use the terms radius, diameter and circumference
Can identify and define equilateral, isosceles and scalene triangles
Can identify and define the features of the following quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium, isosceles trapezium, kite
and arrowhead
Can identify and define the features of polygons up to and including the decagon
Can identify and define ‘regular’ shapes
Can identify and define diagonals and vertices in 2D shapes
Can construct simple 2D shapes from given information with reasonable accuracy
Understand what we can say about a shape which from its lines of symmetry
Can reflect a shape across a mirror line on a grid, including diagonal mirror lines
3D shapes
Can identify relationships between faces, edges and corners (vertices) on 3D shapes through investigation
Can name prisms by cross-sectional shape, such as pentagonal and hexagonal prisms
Perimeter
(and area)
Understand the terms perimeter and area and know the difference between them
Can find the perimeter of a rectangle given length and width and can find a missing side given the perimeter and the other side
Can find the perimeter of any 2D shape given sufficient information
Can find the area of a shape by counting squares
YEAR 5
Angles
Translation
Rotation
Area
(and perimeter)
3D shapes
Can use a protractor to measure angles
Can use a protractor to draw angles
Know that angles on s straight line always add up to 1800
Know that angles round a point always add up to 360 0
Know that vertically opposite angles are always the same (scissor angles)
Know that angles in a triangle always add up to 1800
Can use angle laws and knowledge of the properties of the three types of triangles to find missing angles in triangles
Can describe a translation of a point on a grid
Can translate a point on a grid
Know that positive numbers indicate RIGHT/UP and negative numbers means LEFT/DOWN
Can translate and describe translations of shapes on a grid
Can rotate a line or a shape by 900, 1800, 2700 or 3600 on a grid
Understand the term rotational symmetry and can give the order of rotational symmetry of a shape
Can find the area of a rectangle using the formula A = L x W
Can find a missing length/width of a rectangle given the area
Can find the area of shapes composed of rectangle
Can find the area of a square given only one side
Can find the length of a side of a square given its area
Can find the area of a right-angled triangle
Can find the perimeters of rectangles, squares, right-angled triangles and composite shapes
Can recognise and draw the nets of a cube, cuboid, square-based pyramid, tetrahedron and triangular prism
Can find the surface area of a cube and a cuboid
Can find the volume of a cuboid using the formula V = LxWxH
Can find the volume of various 3D shapes by counting cubes on isometric drawings
Can find how many times small boxes of given dimensions will fit into a larger box of given dimensions
Line graphs
Speed-distancetime
Scale drawings and
grids
Can read and complete pictograms and bar charts
Can read and complete line graphs
Know that line graphs show how a single variable changes over time whilst pictograms/bar charts show a snapshot of many variables at one point
in time
Can solve problems involving speed-distance-time
Can interpret scale drawings including maps
Can plot co-ordinates in all four quadrants
DATA HANDLING
TOPIC
SKILL
YEAR 3
Carroll & Venn
diagrams
Handling data
Can sort items using a Carroll diagram
Can create a suitable Carroll diagram to sort a set of items
Can sort items using a Venn diagram
Can create a suitable Venn diagram to sort a set of items
Can read and complete a pictogram
Can read and complete a bar chart
Understand the term frequency and can use tally chart to keep a record of frequency
Can use a tally chart to create a frequency diagram
YEAR 5
Arithmetic mean,
range, mode and
median
Probability
Advanced data
handling
Can find the range of a data set
Can find the mode of a data set
Can find the median of a data set
Can find the mean of a data set
Understand and can use the terms certain, likely, unlikely, impossible, fair and unfair to describe the likelihood of given outcomes
Can express the probability of an outcome as a fraction
Can draw and interpret decision trees
Can draw and interpret pie charts
Can interpret grouped data