Key Stage 3 Subject: Maths Foundation Year: Year 7 Year 8 Year 9 Topic/Module: Geometry

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1 Subject: Foundation Topic/Module: Geometry Time Geometry Metric Units Angles/Polygons Bearings Transformations watch Clips N21 N7 N7 N7 N7 N7, R2, G10, 46 G16, 122 G14 G13, G17, 45, 121 G23 G18, G4 48 G5 50 G6 G28, 148 Interpret simple bus, train timetables, TV guides and distance tables Convert between units of time Work out start, finish and journey/programme/recipe times Know, pick from a list or state suitable units of capacity and time; cm3, ml, litre, seconds, minutes, hours, days Draw and measure lines to the nearest mm Choose suitable units, to measure length, mass and capacity. Order metric measurements, can involve decimals and a mix of units. Convert between metric units of length, mass and capacity. Convert between units of area and convert between units of volume Convert between units of volume and capacity Use a protractor to measure and draw angles. Know the properties (angle, side, symmetry) of scalene, right angled, isosceles and equilateral triangles Identify and know properties (angle, side, symmetry) of quadrilaterals. Know and use basic angle facts; sum of angles on straight line & in a triangle, angles around a point, sum of angles in a quadrilateral, vertically opposite angles to find missing sides and angles. Be able to prove angles in a triangle add to 180 and angles in a quadrilateral add to 360 Calculate, find or use exterior angles to find other missing angles in simple diagrams. Understand and use alternate, corresponding and co interior angles. Measure and draw bearings. Reflect a shape on a squared grid and a horizontal, vertical or diagonal mirror line Reflect a shape on a coordinate grid given the equation of the line to reflect it over (line will be parallel to x or y axis or y=x or y= x). Translate a shape given instructions in sentence form. Translate a shape given a vector. Rotate shape about its centre, one of its vertices or pt given on squared or plain paper Enlarge a shape by a positive scale factor given a point on plain paper or squared grid or a coordinate on a set of axes.

2 Similarity R10, 144 Know what is means to say shapes are similar & know that similarity relates back to enlargement as the sides have changed in length but the angles stay the same. Work out missing lengths in similar 2D shapes. Know that a shape within a shape can be similar so the question doesn't have to mention similarity. Congruency Perimeter Area Circles G31, 12 G8, G20, 53,54 G24 G20, 55, 56 G20 G2, 116, 149 G22, 118 G22, Know what is means to say shapes are congruent and identify congruent shapes Know that congruency relates to rotation, reflection & translation as the shape is not changed in size just in a different orientation Find the perimeter of a rectangle not drawn to scale Calculate the perimeter of compound shapes made from rectangles or rectangles&triangles Given the perimeter of a shape find missing dimensions Calculate the area of rectangles and triangles Calculate the area of compound shapes made from rectangles or rectangles and triangles. Calculate the area of parallelograms and trapeziums. Given the area of shape find missing dimension Solve problems involving area. May involve algebra. Name the following parts of a circle; radius, diameter, circumference, chord, tangent, arc, sector, segment. Calculate the circumference of a circle given radius or diameter giving answer in terms of pi or as a rounded value. Calculate the area of a circle given radius or diameter giving answer in terms of pi or as a rounded value. Know circle questions can be non calculator as it can ask for an estimate of area/circumference using 3 as an approx for pi or say to leave answer in terms of pi. Calculate the radius or diameter when you know the circumference or area. Work out the length of an arc. May be asked to leave answer in terms of pi so can be on noncalculator papers too. Work out the area of a sector. May be asked to leave answer in terms of pi so can be on noncalculator papers too. Given an arc length or sector area find the radius/diameter or angle Assessment: End of unit assessment

3 Topic/Module: Number Number1 234 Four Operations Order of Operations Factors, Multiples, Primes Watch Clips N3, N4, N13, N14, 17 N16, N20, 75 N10, N11, 28 N30, 78 Add and subtract 3 digit numbers using column method Solve whole number problems involving only one operation with 2, 5 and 10 times table only e.g. 3 books costing 5 each N5 Multiply by 2,3,4,5 and 10 N17, 30 N15, 19 Multiply and divide by 10, 100, 1000, any power of 10 Multiply and divide numbers that are multiples of 10, for e.g.: 600 x 40 Multiply and divide numbers up to 3 digits by a single digit number Multiply 3 digit by 2 digit numbers using grid method N28 Multiply 3 digit by 2 digit numbers using column method N6 Divide by 2,3,4,5 and 10 Use short division with simple problems including dividing a decimal by an integer. Divide a 3 digit integer by a single or 2 digit integer. Use short division where the answer goes to further decimal places than the Q had Check answers using estimation Understand the relationships between number operations, including inverse operations Work out the answer to a calculation given the answer to a related calculation Understand and be able to apply the hierarchy of operations to calculations Work out multiples or find all the factors of any number. Find the HCF and LCM of simple numbers by listing factors/multiples. Know what makes a number prime, identify and recognise prime numbers. Find the prime factor decomposition of a number. Write it in index form.

4 Powers and roots Find 2 to the power of. Or say what power of 2 a value is, eg 32 N25, 29, 81 Know all square numbers to 15 2 N46, 81 Find all positive and negative square roots of square numbers. Estimate square roots N25, 29, 81 Know all cube numbers to Find cubes and cube roots. Solve word problems involving powers & roots Use of Calculator N44, 77 Know how to enter fractions & mixed numbers Know how to turn an answer into a decimal or mixed number Use bracket, negative, any power/root, memory buttons N27, 31 Round to the nearest 10, 100, 1000, whole number Rounding Bounds N27, 32 Round to decimal places. N38, 90 Round to significant figures Know not to round inappropriately during a question. Use ANS, memory button or values rounded less than what the final answer wants. Know that bounds questions don't have to mention bounds, they can be find max/min for example. Clue is they give rounded values. Find upper and lower bounds when a value has been rounded to nearest 5, 10, 50, and so on. Find bounds when a value has been rounded to nearest whole number or decimal places Find bounds when a value has been rounded to significant figures number of significant figures that is less than the number of digits (e.g.: Find the bounds of 270g which has been rounded to 2sf) Assessment: End of unit assessment

5 Topic/Module: Algebra ALGEBRA 234 Watch Clips Describe simple functions in words or symbols. Simple functions A3, 36 Expressions Vocab Expanding Brackets A4, A6, A7, 7, 33, 34, 35, 137 A2 A8, A18, 93, 134 Find inputs & outputs or missing operations of simple functions written in words or symbols using up to two operations. Simplify expressions by collecting like terms (terms are + and ) or by x. Use the index laws to simplify algebraic calculations, expressions and fractions Write simple expressions given a description in words or to represent function machines. Derive formulae with two part calculations e.g. the total cost of hiring a function room for a party is 50 deposit plus 5 per guest. Write a fomula for total cost, T, for n guests. Understand the difference between an expression, identity, equation and formulae. Understand meaning of variable and coefficient. Multiply an integer, or letter or both over a single bracket Expand and simplify expressions such as 10 ± 2(x + 3) Expand and simplify expressions with two brackets such as 8(x 2) ± 5(x + 7) Expand & simplify double brackets including ones such as (2x + 5)(3x 7) & (2x + 3) 2 Factorising Solving linear equations A9, 94 A12, A17, A19, 100, 135, 137 Factorise a linear and non linear expressions using a single bracket. Know that 'FULLY factorise means there is more than one common factor. Solve simple one step linear equations and check the solution is correct. Solve two step linear equations using function machines or balancing method. Answers can be fractional or negative. Solve linear equations that have brackets. Answers could be fractional or negative. Solve linear equations with x on both sides. Answers can be fractional or negative.

6 Solve linear inequalities Changing the subject Solving quadratic equations A20, 5, 138, 139 A13a, 101, 136 List the integer values that satisfy an inequality Show inequalities on a number line or vice versa, inc. double inequalities Form and solve linear inequalities in the same progression as equations above and represent the solution on a number line. Rearrange a simple equation/formula to change the subject Solve simple quadratic equations e.g. 2x 2 = 50 Assessment: End of unit assessment

7 Subject: Middle Topic/Module: Geometry Time Geometry Metric Units watch Clips N7 Work out start, finish and journey/programme /recipe times N7, R2, 112 Convert between metric units of length, mass and capacity. Convert between units of area and convert between units of volume 112 Convert between units of volume and capacity G16, 122 Know properties (angle, side, symmetry)of scalene, right angled, isosceles &equilateral triangles Angles/Polygons G14 G13, G17, 45, 121 G23 G19, 123 Identify and know properties (angle, side, symmetry) of quadrilaterals. Know and use basic angle facts; sum of angles on straight line & in a triangle, angles around a point, sum of angles in a quadrilateral, vertically opposite angles to find missing sides and angles. Be able to prove angles in a triangle add to 180 and angles in a quadrilateral add to 360 Calculate, find or use exterior angles to find other missing angles in simple diagrams. Know and use 180(n 2) for total interior angles Bearings Geometric proofs Transformations G19, G18, G28, Know/use that total exterior angles add to 360 Know and use that an interior + its exterior angle adds to 180 Given an exterior, or an interior, or total interior work out the number of sides Solve missing angle problems involving polygons and other angle facts. May involve algebra Understand and use alternate, corresponding and cointerior angles. Solve missing angle problems involving parallel lines and other angle facts. May involve algebra Measure and draw bearings. Use angle facts to work out bearings in diagrams not drawn to scale. Use angle facts and properties of shapes to write geometric proofs. Reflect a shape on a coordinate grid given the equation of the line to reflect it over (line will be parallel to x or y axis or y=x or y= x). Translate a shape given a vector. Rotate a shape through a coordinate Enlarge a shape by a positive scale factor given a point on plain paper or squared grid or a coordinate on a set of axes. Enlarge a shape by a fractional scale factor given a point on plain or squared paper or a coordinate on a set of axes Describe a transformation fully. (Translation, reflection, rotation or enlargement)

8 Topic/Module: Number Number1 345 Order of Operations Watch Clips N28 Four Operations N16, N20, 75 N30, 78 Multiply 3 digit by 2 digit numbers using grid method Multiply 3 digit by 2 digit numbers using column method Divide a 3 digit integer by a single or 2 digit integer. Use short division where the answer goes to further decimal places than the Q had Check answers using estimation Work out the answer to a calculation given the answer to a related calculation Understand and be able to apply the hierarchy of operations to calculations Find the prime factor decomposition of a number. Write it in index form. Factors, Multiples, Primes Powers and roots N31, 79, 80 Know that questions requiring you to find either the HCF or LCM as commonly put into a real life context and no mention of HCF/LCM Find 2 to the power of. Or say what power of 2 a value is, eg 32 N25, 29, 81 Know all square numbers to 15 2 N46, 81 Find the HCF and LCM of numbers using the prime factor decomposition (using a Venn diagram too) Find all positive and negative square roots of square numbers. Estimate square roots N25, 29, 81 Know all cube numbers to Find cubes & cube roots. Solve word problems involving powers and roots Use of Calculator Rounding N44, 77 Know how to enter fractions & mixed numbers Know how to turn an answer into a decimal or mixed number Use bracket, negative, any power/root, memory buttons N27, 32 Round to decimal places. N38, 90 Round to significant figures. Know not to round inappropriately during a question. Use ANS, memory button or values rounded less than what final answer wants

9 Bounds Know that bounds questions don't have to mention bounds, they can be find max/min for example. Clue is they give rounded values. Find upper and lower bounds when a value has been rounded to nearest 5, 10, 50, and so on. Find bounds when a value has been rounded to nearest whole number or decimal places Find bounds when a value has been rounded to significant figures number of significant figures that is less than the number of digits (e.g.: Find the bounds of 270g which has been rounded to 2sf) Do all of the above but writing bounds as limits of accuracy instead. Calculate the lower and upper bound of perimeters, areas and volumes. 206 Perform all four operations with Bounds Assessment: End of unit assessment

10 Topic/Module: Algebra ALGEBRA 345 Watch Clips Simplify expressions by collecting like terms (terms are + and ) or by x. Expressions A4, A6, A7, 7, 33, 34, 35, 137 Use the index laws to simplify algebraic calculations, expressions and fractions Derive expressions or formulae with two part calculations e.g. the total cost of hiring a function room for a party is 50 deposit plus 5 per guest. Write a fomula for total cost, T, for n guests. Vocab Expanding Brackets A2 A8, A18, 93, 134 Understand the difference between an expression, identity, equation and formulae. Know meaning of variable and coefficient Multiply an integer, or letter or both over a single bracket Expand and simplify expressions such as 10 ± 2(x + 3) Expand and simplify expressions with two brackets such as 8(x 2) ± 5(x + 7) Expand and simplify double brackets including ones such as (2x + 5)(3x 7) and (2x + 3) 2 Factorising Solving linear equations A9, 94, 157 A12, A17, A19, 100, 135, 137 Factorise a linear and non linear expressions using a single bracket. Know that 'FULLY factorise means there is more than one common factor. Factorise quadratic expressions into double brackets where a=1 including the difference of two squares (may have fractional coefficients) Solve two step linear equations using function machines or balancing method. Answers can be fractional or negative. Solve linear equations that have brackets. Answers could be fractional or negative. Solve linear equations with x on both sides. Answers can be fractional or negative. Construct and solve linear equations. Qurestions can involve real life scenarios (such as peoples ages) or geometry. Solve fractional linear equations that have x in the numerator

11 List the integer values that satisfy an inequality Solve linear inequalities Changing the subject Trial and improvement A20, 5, 138, 139 A13a, 101, 136 A16 Show inequalities on a number line or vice versa, inc. double inequalities Form and solve linear inequalities in the same progression as equations above and represent the solution on a number line. Solve double linear inequalities (e.g.: 7 < 2x + 1 < 11) and represent the solution on a number line. Know the effect of multiplying/dividing both sides of an inequality by a negative number. Rearrange a simple equation/formula to change the subject Change the subject of more complex formulae including powers Not really appearing in the way it used to now. Use it to show that a solution must lie between two values only in equations with x 2 or x 3 Solving quadratic equations Simultaneous equations 157, 158 A24, A26, 140, 162 Solve simple quadratic equations e.g. 2x 2 = 50 Solve quadratic equations by factorising where a=1 inc. difference of two squares. Know equation must equal zero before solving Form a quadratic equation to then solve. Solve a pair of simultaneous equations using elimination when both given in the form ax + by = c. Form and solve simultaneous equations Solve simultaneous equations by drawing graphs and finding the point/s of intersection Assessment: End of unit assessment

12 Subject: Higher Topic/Module: Geometry Geometry Metric Units watch Clips 112 Convert between units of area and convert between units of volume Convert between units of volume and capacity Angles/Polygons Bearings Geometric proofs Transformations G23 G19, 123 G19, G18, G28, G34, Be able to prove angles in a triangle add to 180 and angles in a quadrilateral add to 360 Know and use 180(n 2) to calculate interior angles of a polygon Know/use total exterior angles add to 360 Know and use that an interior + its exterior angle adds to 180 Given an exterior, or an interior, or total interior work out the number of sides Solve missing angle problems involving polygons and other angle facts. May involve algebra Understand and use alternate, corresponding and co interior angles. Solve missing angle problems involving parallel lines and other angle facts. May involve algebra Use angle facts to work out bearings in diagrams not drawn to scale. Use angle facts and properties of shapes to write geometric proofs. Reflect a shape on a coordinate grid given the equation of the line to reflect it over (line will be parallel to x or y axis or y=x or y= x). Translate a shape given a vector. Rotate a shape through a given coordinate on a set of axes. Enlarge a shape by a positive scale factor given a point on plain or squared paper or a coordinate on a set of axes. Enlarge a shape by a fractional scale factor given a point on plain paper or a squared grid or a coordinate on a set of axes Describe a transformation fully. (Translation, reflection, rotation or enlargement) Enlarge a shape by a negative scale factor given a point or a coordinate. Or backwards. Describe fully a single transformation that is equivalent to a combination of two other transformations.

13 Similarity Congruency Area Circles R10, G20, 55, 56 G20 G22, 118 G22, 117 G Know what is means to say shapes are similar & know that similarity relates back to enlargement as the sides have changed in length but the angles stay the same. Work out missing lengths in similar 2D shapes. Know that a shape within a shape can be similar. Work out either the LSF, ASF or VSF to then find a missing length, area or volume. Know that congruency relates to rotation, reflection and translation as the shape is not changed in size just in a different orientation Prove if triangles are congruent if one of the following is met: SSS,SAS,ASA,RHS Use congruence to solve problems in triangles. Calculate the area of parallelograms and trapeziums. Given area of a shape find missing dimension Solve problems involving area. May involve algebra. Calculate the circumference of a circle given radius or diameter giving answer in terms of pi or as a rounded value. Calculate the area of a circle given radius or diameter giving answer in terms of pi or as a rounded value. Know circle questions can be on a non calculator paper as it can ask for an estimate area or circumference using 3 as an approx for pi or say to leave answer in terms of pi. Calculate the radius or diameter when you know the circumference or area. Solve problems involving parts of circles, for example find perimeter of a semi circle, find area of path between concentric circles. Work out the length of an arc. May be asked to leave answer in terms of pi so can be on noncalculator papers too. Work out the area of a sector. May be asked to leave answer in terms of pi so can be on noncalculator papers too. Given an arc length or sector area find the radius/diameter or angle Solve problems involving arcs and sectors. Calculate area of a segment of a ¼ of a circle Assessment: End of unit assessment

14 Topic/Module: Number Number1 456 Watch Clips Order of Operations 92 Work out the answer to a calculation given the answer to a related calculation Factors, Multiples, Primes Bounds N31, 79, Find the HCF and LCM of numbers using the prime factor decomposition (using a Venn diagram too) Know that questions requiring you to find either the HCF or LCM as commonly put into a real life context and no mention of HCF/LCM Know that bounds questions don't have to mention bounds, they can be find max/min for example. Clue is they give rounded values. Find upper and lower bounds when a value has been rounded to nearest 5, 10, 50, and so on. Find bounds when a value has been rounded to nearest whole number or decimal places Find bounds when a value has been rounded to significant figures number of significant figures that is less than the number of digits (e.g.: Find the bounds of 270g which has been rounded to 2sf) Do all of the above but writing bounds as limits of accuracy instead. Calculate the lower and upper bound of perimeters, areas and volumes. 206 Perform all four operations with Bounds When asked to use bounds to estimate a value for a letter in an equation then find both LB and UB and find a value they both round to. Calculate the lower and upper bounds with questions involving compound measures or standard form. Assessment: End of unit assessment

15 Topic/Module: Algebra ALGEBRA 456 Expressions Vocab Expanding Brackets Factorising Solving linear equations Solve linear inequalities Changing the subject Watch Clips 33, 34, 35, 137 A2 A8, A18, 93, 134, 178 A9, 94, 157 A12, A17, A19, 100, 135, 137 A20, 5, 138, 139 A13a, 101, 136 Use the index laws to simplify algebraic calculations, expressions and fractions Understand the difference between an expression, identity, equation and formulae. Know the meaning of variable and coefficient Expand and simplify expressions with two brackets such as 8(x 2) ± 5(x + 7) Expand and simplify double brackets including ones such as (2x + 5)(3x 7) and (2x + 3) 2 Expand and simply three expressions e.g. x(x+2)(x 3) or (2x 5)(x+3) 2 Factorise a linear and non linear expressions using a single bracket. Know that 'FULLY factorise means there is more than one common factor. Factorise quadratic expressions into double brackets where a=1 including the difference of two squares (may have fractional coefficients) Solve linear equations that have brackets. Answers could be fractional or negative. Solve linear equations with x on both sides. Answers can be fractional or negative. Construct and solve linear equations. Qurestions can involve real life scenarios (such as peoples ages) or geometry. Solve fractional linear equations that have x in the numerator Form and solve linear inequalities in the same progression as equations above and represent the solution on a number line. Solve double linear inequalities e.g.: 7 < 2x + 1 < 11 & show solution on number line. Know the effect of multiplying/dividing both sides of an inequality by a negative number. Rearrange a simple equation/formula to change the subject Change the subject of more complex formulae including powers Change the subject of more complex formulae where the subject appears twice

16 Trial and improvement Iteration Solving quadratic equations Simultaneous equations , 158 A24, A26, 140, 162 Not really appearing in the way it used to now. Use it to show that a solution must lie between two values only in equations with x 2 or x 3 Find approximate solutions to equations using iteration. Be able to also use a calculators ANS button to perform iteration. Solve simple quadratic equations e.g. 2x 2 = 50 Solve quadratic equations by factorising where a=1 or the difference of two squares. Know equation must equal 0 before can solve. Form a quadratic equation to then solve. Solve a pair of sim equations using elimination when both given in the form ax + by = c. Form and solve simultaneous equations Solve simultaneous equations by drawing graphs and finding the point/s of intersection Assessment: End of unit assessment