Maths Curriculum Overview
Maths Curriculum Overview | ||||
Term | Year 5 | Year 6 | Year 7 | Year 8 |
1 | Place Value Roman numerals to 1,000 Numbers up to 1,000,000 Read and write numbers 1,000,000 Powers of 10 10, 100, 1000, 10,000 and 100,000 more or less than Partition numbers to 1,000,000 Number line to 1,000,000 Compare and order numbers to 100,000 Compare and order numbers to 1,000,000 Round to the nearest 10, 100 or 1000 Round numbers within 100,000 Round numbers within 1,000,000 Addition & Subtraction Mental strategies Add and subtract whole numbers with more than four digits Round to check answers Inverse operations (addition & subtraction) Multi-step addition and subtraction problems Compare calculations Find missing numbers | Place Value Numbers to 1 million Numbers to 10 million Read and write numbers to 10 million Powers of 10 Number line to 10 million Compare and order any integers Round any integer Negative numbers Addition, Subtraction, multiplication & Division Add and subtract integers Common factors Common multiples Rules of divisibility Primes to 100 Square and cube numbers Multiply up to a 4-digit number by a 2-digit number Solve problems with multiplication Short division Division using factors Introduction to long division Long division with remainders Solve problems with division Solve multi-step problems Order of operations Mental calculations and estimation Reason from known facts | Place Value Recognise place value, write integers in words and figures up to 1 billion Work out and position intervals on a number line Compare and order integers up to 1 billion using = ≠ < > ≤ ≥ Understand place value of decimals and position on a number line Compare and order decimal numbers and any number up to 1 billion Round integer to nearest power of 10 Write 10, 100, 1000 etc as powers of 10 (E) Write positive integers in the form Ax10n (E) Investigate negative powers of ten (E) Write numbers between 0 and 1 in standard form (E) Four Operations Add and subtract integers Add and subtract decimals Multiply and divide by 10, 100, 1000 Multiply by 0.1 and 0.01 (E) Multiply integers Divide integers Multiply decimals Divide decimals by integers Divide by a decimal (E) Order of operations Averages and range Mode, mean, median, range Solve problems with averages and range Rounding and Estimation Round to 1 significant figure Round to 2 or more significant figures Estimate answers to calculations Solve problems with estimation Understand and use error interval notation (E) | Ratio Understand the meaning of ratio and use ratio notation Simplify ratios Solve ratio problems Divide in a given ratio Express ratios in the form 1:n and n:1 (E) Compare ratio and fractions Understand pi as a ratio Understand gradient as a ratio (E) Proportion and scale Solve problems involving direct proportion Explore conversion graphs Convert between currencies Explore direct proportion graphs Explore relationships between similar shapes Convert metric units Understand scale factors and use to interpret scale diagrams and maps Algebraic manipulation Form algebraic expressions Simplify expressions Use directed number with algebra Substitution with directed number Multiply out and factorise into a single bracket Expand multiple single brackets and simplify Expand a pair of binomials (E) Factorise quadratic equations (E) Identify and use formulae, expressions, identities and equations
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2 | Multiplication and division A Multiples and common multiples Factors and common multiples Prime numbers Square numbers Cube numbers Multiply and divide by 10, 100 and 1,000 Multiples of 10, 100 and 1,000 Fractions A Find fractions equivalent to a unit fraction Find fractions equivalent to a non-unit fraction Recognise equivalent fractions Convert improper fractions to mixed numbers Convert mixed numbers to improper fractions Compare fractions less than 1 Order fractions less than 1 Compare and order fractions greater than 1 Add & subtract fractions with the same denominator Add fractions within 1 Add fractions with total greater than 1 Add to a mixed number Add 2 mixed numbers Subtract fractions Subtract from a mixed number Subtract from a mixed number – breaking the whole Subtract 2 mixed numbers | Fractions A Equivalent fractions and simplifying Equivalent fractions on a number line Compare and order (denominator) Compare and order (numerator) Add and subtract simple fractions Add and subtract any 2 fractions Add and subtract mixed numbers Multi-step problems with fractions Fractions B Multiply fractions by integers Multiply fractions by fractions Divide any fraction by an integer Mixed questions with fractions Fraction of an amount Fraction of an amount - find the whole Converting units Metric measures Convert metric measures Calculate with metric measures Miles and kilometres Imperial measures | Sequences Describe and continue sequences in tables, graphs and diagrams as well as numbers Identify and continue linear and non-linear sequences Explain the term to term rule Find missing terms (E) Algebraic notation Find input and output using a single function machine Use diagrams and letters to generalise number operations & single function machines Given simple expressions find the function machine Substitute values into 1 step expressions Find functions, substitute values and generate sequences using 2 step expressions Represent one and two step functions graphically Equality & equivalence Understand the meaning of equality and use fact families, numerically and algebraically Solve 1 step and 2 step linear equations using inverse operations Understand like and unlike terms and equivalence Simplify expressions using ≡
| Coordinates and graphs Draw, plot and find coordinates in all 4 quadrants Identify and draw parallel lines to the axes Table of values Recognise and use the line y = x and y = mx Link y=mx to direct proportion (E) Introduce gradient (y=mx) Lines with negative gradient Lines of the form y=x+c and y=mx+c Find the midpoint of a line segment (E) Solve problems with coordinates and graphs (E) Quadratic graphs (E) Multiply & divide fractions Multiply and divide fractions by unit fractions and integers Understand and use the reciprocal Multiply and divide improper fractions and mixed numbers Multiply and divide algebraic fractions (E) Symmetry & reflection Recognise line and rotational symmetry Reflect a shape in a horizontal or vertical line Reflect a shape in a diagonal line Reflect a shape given equation of a line (E) Describe a reflection (E)
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3 | Multiplication & Division B Multiply up to a 4 digit number by a 1 digit number Multiply a 2-digit number by a 2-digit number (area model) Multiply a 2-digit number by a 2-digit number Multiply a 3-digit number by a 2-digit number Multiply a 4-digit number by a 2-digit number Solve problems with multiplication Short division Divide a 4-digit number by a 1-digit number Divide with remainders Efficient division Solve problems with multiplication and division Fractions B Multiply a unit fraction by an integer Multiply a non-unit fraction by an integer Multiply a mixed number by an integer Calculate a fraction of a quantity Fraction of an amount Find the whole Use fractions as operators | Ratio Add or multiply? Use ratio language Introduction to the ratio symbol Ratio and fractions Scale drawings Use scale factors Similar shapes Ratio problems Proportion problems Recipes Algebra 1-step function machines 2-step function machines Form expressions Substitution Formulae Form equations Solve 1-step equations Solve 2-step equations Find pairs of values Solve problems with two unknowns Decimals Place value within 1 Place value – integers and decimals Round decimals Add and subtract decimals Multiply and divide by 10, 100 and 1,000 Multiply and divide by integers Multiply and divide in context | Graphing data Pictograms Bar charts Dual bar charts Composite bar charts Coordinates in the first quadrant Scatter graphs Correlation Line of best fit Time-series graphs Non-linear relationships Fractions, decimals & percentages Represent factions on diagrams and number lines Number lines with decimals Convert fractions and decimals using tenths, hundredths, fifths, quarters Convert between fractions and decimals – eighths and thousandths Understand the meaning of percentage using a hundred square Convert fluently between fractions, decimals and percentages identify & use equivalent fractions Understand fractions as division Explore fractions above one, decimals and percentages (E)
| Area, volume and density Name 2-D and 3-D shapes Area Area of a 2-D shape Area of a compound shape Recognise prisms (inc. language of edges and vertices) Volume of cubes and cuboids Convert metric units of mass and capacity Understand the units of mass/density and volume Solve problems with density, mass and volume Area and volume in similar shapes (E) Equations and inequalities Solve simple 1 and 2 step equations Solve more complex equations Solve fractional equations Form and solve equations Solve equations with unknowns on both sides Understand and use inequalities Inequalities on a number line Solve simple inequalities Form and solve inequalities Solve inequalities with unknowns on both sides (E)
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4 | Decimals and percentages Decimals up to 2 d. p. Equivalent fractions and decimals (tenths) Equivalent fractions and decimals (hundredths) Equivalent fractions and decimals Thousandths as fractions Thousandths as decimals Thousandths on a place value chart Order and compare decimals (same number of decimal places) Order and compare any decimal with up to 3 decimal places Round to the nearest whole number Round to 1 decimal place Understand percentages Percentages as fractions Percentages as decimals Equivalent fractions, decimals and percentages Perimeter and area Perimeter of rectangles Perimeter of rectilinear shapes Perimeter of polygons Area of rectangles Area of compound shapes Estimate area Statistics Draw line graphs Read and interpret line graphs Read and interpret tables Two-way tables Read and interpret timetables | Fractions, decimals and percentages Decimals and fractions equivalents Fractions as division Understand percentages Fractions to percentages Equivalent fractions, decimals and percentages Order fractions, decimals and percentages Percentage of an amount – one step Percentage of an amount – multi-step Percentages – missing values Area, perimeter and volume Shapes – same area Area and perimeter Area of a triangle – counting squares Area of a right-angled triangle Area of any triangle Area of a parallelogram Volume – counting cubes Volume of a cuboid Statistics Line graphs Dual bar charts Read and interpret pie charts Pie charts with percentages Draw pie charts The mean | Directed number Use representations of directed number Compare and order directed number Directed number and zero pairs Perform calculations that cross zero Add, subtract, multiply, divide Use directed numbers with order of operations Use a calculator to solve directed number calculations Fraction & percentage of amounts Find fraction and percentage of a given amount (with /without calculator) Use a given fraction to find the whole and/or other fractions Percentage increase and decrease Use a percentage to find the whole (E) Solve problems with fractions greater than 1 and percentages greater than 100% (E) Perimeter and Area Convert metric units of length Perimeter of a polygon Perimeter of a compound shape Area of rectangles and parallelograms Area of triangles Area of trapezium Solve problems with perimeter and area Form expressions with perimeter and area (E)
| Percentages Percentage of an amount Convert between percentages and decimals Use multipliers to find percentages Convert between decimals and percentages greater than 1 Percentage increase and decrease using a multiplier Express one number as a fraction or percentage of another (calculator and non-calculator) Percentage change Find the original value given a percentage Choose appropriate methods to solve percentage problems Indices Add, subtract, multiply and divide expressions with indices Use the addition and subtraction law for indices Powers of powers (E) Negative indices (E) Fractional indices (E) Standard form Investigate positive and negative powers of 10 Work with numbers greater than 1 in standard form Work with numbers between 0 and 1 in standard form Standard form on a calculator Interpret and represent data Types of data Outliers and errors Averages and range Choose the most appropriate average Compare distributions using average and the range Averages from an ungrouped frequency table Represent and interpret grouped discrete data Represent and interpret continuous data grouped into equal classes Mean and mode from a grouped frequency table (E) |
5 | Shape Understand and use degrees Classify angles Estimate angles Measure angles up to 180 Draw lines and angles accurately Calculate angles around a point Calculate angles on a straight line Lengths and angles in shapes Regular and irregular polygons 3-D shapes Position and direction Read and plot coordinates Problem solving with coordinates Translation Translation with coordinates Lines of symmetry Reflection in horizontal and vertical lines Decimals Use known facts to add and subtract decimals within 1 Complements to 1 Add and subtract decimals across 1 Add and subtract decimals with the same number of decimal places Add and subtract decimals with different numbers of decimal places Efficient strategies for adding and subtracting decimals Decimal sequences Multiply and divide by 10, 100 and 1,000 Multiply and divide decimals – missing values | Shape Measure and classify angles Calculate angles Vertically opposite angles Angles in a triangle Angles in a triangle - special cases Angles in a triangle - missing angles Angles in special quadrilaterals Angles in regular polygons Circles Draw shapes accurately Nets of 3-D shapes Position and direction The first quadrant Read and plot points in four quadrants Silve problems with coordinates Translations Reflections
| Speed, distance and time Convert between milliseconds, seconds, minutes and hours Convert between hours, days and years Fractions of time Solve problems with tables and timetables Solve problems with time and the calendar Calculate speed Calculate time and distance Solve problems with speed, distance and time Interpret and draw distance-time graphs Calculate speed from a distance-time graph (E) Properties of number Find and use multiples Identify factors of numbers Recognise and identify prime numbers Write numbers as a product of prime factors Recognise square, cube and triangular numbers Square roots and cube roots Explore higher powers and roots (E) Highest common factor (HCF) Lowest Common multiple (LCM) HCF and LCM from a diagram (E) Use factors to simplify calculations (E)
| Angles in parallel lines & polygons Understand and use basic angle rules and notation Investigate angles between parallel lines and the transversal Identify and calculate alternate, corresponding and co-interior angles Solve complex problems with angles in parallel lines Properties of special quadrilaterals and their diagonals Find sides and angles in special quadrilaterals Exterior and interior angles of a polygon Interior angles in a regular polygon Prove simple geometric facts (E) Tables & probability Probability vocabulary The probability scale Probability of a single event Use the sum of probabilities being equal to 1 Probability experiments Sample spaces for 1 or more events Probabilities from sample space diagrams Two-way tables Probabilities from two-way tables Frequency trees Probabilities from frequency trees
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6 | Negative numbers Understand negative numbers Count through zero in 1s Count through zero in multiples Compare and order negative numbers Find the difference Converting units Kilograms and kilometres Millimetres and millilitres Convert units of length Convert between metric and imperial units Convert units of time Calculate with timetables Volume Cubic centimetres Compare volume Estimate volume Estimate capacity | Consolidation and themed projects. | Add and subtract fractions Simplify a fraction Convert between a mixed number and improper fractions Add and subtract fractions with the same denominator Add and subtract with fractions and integers Add and subtract fractions where denominators share a simple common multiple Add and subtract fractions with any denominator Add and subtract improper fractions and mixed numbers Use equivalence to add and subtract decimals and fractions (E) Add and subtract simple algebraic fractions (E) Substitution and solving equations with fractions (E) Angles and polygons Draw and measure lines and angles Understand and use geometric notation Understand and use the sum of angles at a point, on a straight line and vertically opposite Know and apply sum of angles in a triangle and a quadrilateral Solve angle problems using properties of triangles and quadrilaterals Recognise and name polygons Solve problems with angles Parallel and perpendicular lines (E) Angles in parallel lines (E) Angles in a polygon (E) Simple proofs (E) | Circles Circle vocabulary Pi as a ratio Circumference of a circle Perimeter of parts of a circle Area of a circle Area of parts of a circle Area and circumference of a circle Perimeter of compound shapes with circles Perimeter and area of compound shapes with circles Graphs and charts Pictograms and bar charts Vertical line graphs Draw and interpret pie charts Line graphs Choose the most appropriate graph or chart Compare distributions using graphs Misleading graphs and charts Sequences Generate sequences given a rule in words Generate a sequence given a simple algebraic rule nth term of a linear sequence Generate a sequence given a complex algebraic rule (E)
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