WCCS JUNIOR SCHOOL MATHEMATICS SYLLABUS NUMBER YEAR 3

Transcription

1 WCCS JUNIOR SCHOOL MATHEMATICS SYLLABUS NUMBER TOPIC 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 SKILL YEAR 3 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

2 Sequences Money Introduction to fractions Place value Counting Addition Subtraction Multiplication Division Functions Inequalities 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 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

3 Negative numbers Sequences Money Fractions Introduction to decimals Decimal addition and subtraction Multiplication and division by 10, 100,1000 Place value Factors Number properties Decimals, fractions and percentages 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 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 4 2 and 7 3 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

4 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 , 0.5, 0.5 etc. - Fibonacci sequence, Powers of 2, 3 etc.

5 SHAPE, SPACE AND MEASURE TOPIC 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 SKILL YEAR 3 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

6 2D Shapes An introduction to line symmetry 3D shapes Scales, estimation and rounding Metric Measurement Lines Position co-ordinates Angles and direction 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 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 YEAR 4 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

7 2D shapes Symmetry and reflection 3D shapes Perimeter (and area) Angles Translation Rotation Area (and perimeter) 3D shapes 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 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 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 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 Know that angles round a point always add up to Know that vertically opposite angles are always the same (scissor angles) Know that angles in a triangle always add up to 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 90 0, 180 0, or 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

8 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

9 DATA HANDLING TOPIC SKILL YEAR 3 Carroll & Venn diagrams Handling data Arithmetic mean, range, mode and median 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 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 YEAR 5 Probability 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 Advanced data handling Can draw and interpret decision trees Can draw and interpret pie charts Can interpret grouped data