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Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] Band KS2 Assessment Objective Descriptors Target Grade All skills listed in band 2,3,4,5 and 6 sections plus: Year 7 Numbers - 1 Higher Attainers - Estimate calculations by rounding every number to 1 significant figure Solve complex questions in context involving multiplication and division Divide any number by a decimal between 0 and 1 and solve questions in context, e.g. money Use calculations and reasoning to decide which item is the ‘best value’ Show that a negative power means the base and power are in the denominator Show that a fractional power is a root Simplify and/or find the value of numerical expressions involving positive and negative powers, raising a power to a power, fractional powers (numerator = 1) Find the LCM and HCF of two numbers using prime factor decomposition and a Venn diagram Find the percentage of a quantity using a multiplier Increase/decrease an amount using a multiplier Algbra - Factorise complex algebraic expressions by taking out common factors Show that two algebraic expressions are equivalent, e.g. ‘Argue mathematically that 2(x + 5) = 2x + 10’ Derive a simple formula, including those with squares, cubes and roots Use substitution to find coordinates for simple quadratic functions, e.g. y = x2 + 4x - 1 Form and solve equations for problems involving: perimeter of a shape area of triangles, rectangles, parallelograms, trapeziums etc. 8+ Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - angles in triangles, quadrilaterals and other polygons) Solve and inclusive inequality and show the solution set on a number line (e.g. –3 < 2x + 1 < 7) Solve two linear inequalities and show both solution sets on the same number line to find the whole numbers that satisfy both inequalities Shapes - Identify the line of symmetry of a quadratic graph Use the graph to find other coordinates on the line (that are not in the table), e.g. ‘Use the graph to find the values of x when y = 2.5’ Understand proof that exterior angle of triangle = sum of interior angles at other two vertices Find missing angles in multi-step or worded problems Understand proof that angles in a triangle add up to 180° All skills listed in band 3,4,5 and 6 sections plus: Numbers 2 Core & Extend - - Rounding integers questions in context Round decimals in context questions (all types) Solve questions in context involving multiplication and division Divide: 2-, 3- and 4-digit numbers by a single digit number with remainders (written as decimal answers) 3- and 4-digit numbers by a 2-digit number with remainders (written as decimal answers) Divide: a decimal by an integer an integer by a decimal a decimal by a decimal 7 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - Use a ‘given’ multiplications/divisions to find other answers e.g. ‘Given 2.6 x 15.8 = 41.08, find 26 x 0.158’ Use a calculator to answer questions involving squares, cubes, roots, brackets and powers with all four operations Show that any number raised to the power of zero equals 1 Simplify numerical expressions involving positive powers, raising a power to a power and power of zero Use a calculator to find the value of a numerical expression involving positive powers, raising a power to a power and power of zero Use the given prime factor decompositions for two numbers to find the LCM and HCF using a Venn diagram Order fractions, decimals and percentages Find the amount a number has been increased/decreased by Find the value of an amount after simple interest Find the value of an amount after consecutive percentage increase/decrease Use the formula for the nth term of an arithmetic sequence to generate the terms of a sequence Algebra - - Factorise algebraic expressions by taking out common factors Simplify an expression using index laws Substitute positive and negative numbers into formulae involving more than two letters (e.g. v = u + at) Write expressions to solve problems representing a situation Solve simple equations involving: brackets, including with negatives, e.g. 2(x – 5) = 8 or 2(x + 3) = 4 – 3(x – 1) fractional coefficients, e.g. x/2 = 5 Form and solve an equation to represent a worded problem Write down the inclusive/exclusive inequality shown on a number line Write down the whole numbers that satisfy an inequality Solve a linear inequality (variable on both sides) and show the solution set on a number line Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] Shapes - Plot and draw straight line graphs of the form y = mx + c using table of values Use the graph to find other coordinates on the line (that are not in the table), e.g. ‘Use the graph to find the value of y when x = 2.5’ Find missing angles in a right-angled triangle using fact that ‘angles in a triangle add up to 180°’ Find missing angles in isosceles triangles using fact that ‘angles in a triangle add up to 180°’ Data Handling and Probability - Explain why a sample may not represent the whole population All skills listed in band 4,5 and 6 sections plus: Numbers - 3 - Solve addition/subtraction questions in context, including: multi-step problems, choosing the correct operation and problems involving negative numbers Write large integers to 1, 2 and 3 significant figures Round decimals to a given number of significant figures Multiply 3- and 4-digit numbers by a 3-digit number Divide 2-, 3- and 4-digit numbers by a single digit number with remainders and 3- and 4-digit numbers by a 2-digit number with remainders Multiply: an integer and a decimal two decimals any number with decimal between 0 and 1 6 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - questions in context, e.g. money Use BIRDMAS to carry out calculations using the correct order of operations (Brackets, Indices, Roots, Divide, Multiply, Add, Subtract) Multiply the powers to raise a power to a power Write any power of 10 in index form, including negative powers, and vice versa Solve questions in context involving the LCM of two numbers Identify all the common factors for two numbers and write down the HCF Find the prime factor decomposition of positive integers and write answers as a product using index notation (e.g. 2x2 x 3 x 5) Add/subtract/divide and multiply two fractions Change an improper fraction to a mixed number Change a mixed number to an improper fraction Multiply a fraction by an integer (and vice versa) Find a fraction of an amount in context Change a fraction to a percentage, a percentage to a decimal and a decimal to a percentage Increase/decrease a number by a percentage (without a calculator) Recognise the difference between arithmetic and geometric sequences Algebra - Factorise simple algebraic expressions by taking out common factors Simplify expressions involving brackets Simplify and expression using index laws Substitute positive and negative numbers into expressions involving two letters with powers and brackets (e.g. y = 4x2 – 3x + 2, find y when x = 2) Use substitution to find coordinates of a straight line graph Solve simple equations involving: integer coefficients with unknowns on one side, e.g. 2x – 6 = 4 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - integer coefficients with unknowns on both sides, e.g. 2x + 5 = 8x – 7 Solve a linear inequality (one variable) and show the solution set on a number line Shapes - Find missing angles in a scalene triangle using fact that ‘angles in a triangle add up to 180°’ Find a missing angle using each angle fact: Angles on a straight line add up to 180° Vertically opposite angles are equal Alternate angles are equal Corresponding angles are equal Co-interior angles add up to 180° Data Handling and Probability - Design a two-way table Explain why a source of data may be biased All skills listed in band 5 and 6 sections plus: Number 4 Core - Add 2-, 3-, 4- and 5-digit integers with carrying and solve questions in context Subtract 2-, 3-, 4- and 5-digit integers with carrying and solve questions in context Compare negative integers Add/subtract 1- and 2-digit negative integers Round decimals to the nearest whole number (integer) Round decimals to a given number of decimal places 5 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - - Multiply 2-, 3- and 4-digit numbers by a 2-digit number Divide 2-, 3- and 4-digit numbers by a single digit number without remainders and 3- and 4-digit numbers by a 2digit number without remainders Solve questions in context (e.g. money) involving addition and subtraction Show that: Square roots can be positive and negative Cube roots of a positive number are always positive Negative numbers cannot be square rooted, but can be cube rooted Add the powers to multiply numbers written in index form Subtract the powers to divide numbers written in index form Write any number written in index form ‘longhand’, and vice versa Identify all common multiples (up to a limit) for two numbers Find the LCM of two numbers by listing systematically List all factors of a number systematically Recall all prime numbers up to 100 Find the prime factor decomposition of positive integers and write answers as an ordered list (e.g. 2 x 2 x 3 x 5) Find a specific term in a sequence using the term-to-term rule Write the term-to-term ‘rule’ for a sequence of diagrams Compare two fractions by using a common denominator Order fractions by using a common denominator Change a decimal into a fraction (and vice versa) Convert fractions into recurring decimals Find a percentage of a quantity/measurement in context (without a calculator) Algebra - Multiply a single term over a bracket, Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - Simplify an expression by cancelling Simplify more complex expressions by collecting ‘families’ Substitute numbers into worded formulae Use letters to represent variables in a formula Substitute positive and negative numbers into expressions involving two letters only (e.g. y = 4x – 1, find y when x = 2) Use function machines to find coordinates Find the input of one-and two-stage function machine using inverse operations Write down the single inequality shown on a number line Data Handling and Probability - Complete a two-way table Design a data collection sheet for grouped data All skills listed in band 6 section (below) plus: 5 Support Numbers - Write down the value of any digit in an integer number Write the symbol < or > between two positive integer numbers Write a list of positive integer numbers in order of size Add 2- and 3-digit integers with no carrying Subtract 2- and 3-digit integers with no carrying Use multiplication facts to derive corresponding division facts Multiply and divide any integer or decimal by a power of 10 Multiply 2- and 3-digit numbers by a single digit number Add/subtract an integer and a decimal or two decimals Use index notation for squares and cubes and recognise the square root sign 4 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - Recall the cube numbers up to 5 x 5 x 5 and corresponding cube roots List multiples of a number systematically Recall all prime numbers up to 50 Write the term-to-term ‘rule’ of a sequence in words Find the next few terms in a sequence using the term-to -term rule Simplify a fraction Find equivalent fractions Carry out simple fraction-to-decimal conversions (and vice versa) Find a percentage of a number (without a calculator) Express a number as a percentage of another number Algebra - Simplify and expression by multiplying Simplify an expression by collecting ‘families’, Define and identify an ‘expression’, ‘term’ and ‘formula’ Show a single inequality on a number line (e.g. x < 4) Solve simple linear equations (e.g. x+2=4) Shapes - Plot coordinates in all four quadrants Recognise right-angled, equilateral, isosceles and scalene triangles Estimate the sizes of angles Recognise and accurately draw examples of acute, obtuse, reflex and right angles Data Handling and Probability List possible combinations of colours, foods, types of object, menu options etc., Identify key points on a timetable Work out the time taken for a journey from a timetable Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - 6 Support + Design a data collection sheet for discrete data Numbers Algebra Shapes - Add/subtract integers Round integers to the: 10,100,1000 Recall all multiplication facts up to 12 x 12 Write down the value of any digit in a decimal number Write the symbol < or > between two decimal numbers Write a list of decimal numbers in order of size Recall all square numbers up to 12 x 12 and corresponding square roots List all three-digit numbers that can be made from three given integers Recall all prime numbers up to 20 Write a fraction shown by the shaded part of a diagram Shade a diagram to show a given fraction Identify ‘families’ (i.e. like terms) Interpret algebraic notation, e.g. ab in place of a × b 3y in place of y + y + y and 3 × y a² in place of a × a a5 in place of a × a × a × a × a a/b in place of a ÷ b Identify an ‘expression’, ‘term’ and ‘formula’ Read scales on axes Below 4 Department: Mathematics Head of Department: Mr B Przystawski Email: [email protected] - Plot coordinates in positive quadrants Recognise the symbol for right– on each line) Identify two lines that are perpendicular on a diagram Describe angles as a measure of turning in clockwise/anticlockwise directions Data Handling and Probability Change a 12-hour clock time to 24-hour clock time and vice versa Find a later/earlier time by adding a number of hours /minutes to 12- and 24-hour times
