Maths Y10 Curriculum (Foundation)

Dates Autumn term 1 Autumn term 2 Spring term 1 Spring term 2 Summer term 1 Summer term 2

Focus (i) Real Life Graphs (i) Ratio (i) Right Angled Triangles (i) Multiplicative (i) Constructions, Loci (i) Perimeter, Area and Reasoning and Bearings Volume (ii) Straight Line Graphs (ii) Proportion (ii) Probability (ii) Quadratic Equations (iii) Transformations and Graphs

Key By the end of the sub- By the end of the sub-unit, By the end of the unit, By the end of the unit, By the end of the sub- By the end of the unit, Knowledge unit, students should be students should be able students should be able students should be able unit, students should be students should be able and able to: to: to: to: able to: to: understanding (i) Use input/output (i)Understand and express (i)Understand, recall and (i)Understand and use (i)By the end of the sub- (i)Recall the definition of a Prior ; the division of a quantity use Pythagoras’ Theorem compound measures: unit, students should be circle and identify, name knowledge: Draw, label and scale into a number of parts as a in 2D, including leaving density; able to: and draw parts of a circle Maths topics axes; ratio; answers in surd form and pressure; Understand clockwise including tangent, chord already taught at KS2 listed Use axes and Write ratios in their being able to justify if a speed: and anticlockwise; and segment; at end of this coordinates to specify simplest form; triangle is right-angled or convert between metric Draw circles and arcs to a Recall and use formulae for document points in all four Write/interpret a ratio to not; speed measures; given radius or given the the circumference of a quadrants in 2D; describe a situation; Calculate the length of the read values in km/h and diameter; circle and the area Identify points with given Share a quantity in a given hypotenuse and of a mph from a speedometer; Measure and draw lines, enclosed by a circle coordinates and ratio including three-part shorter side in a right- calculate average speed, to the nearest mm; circumference of a circle = coordinates of a given ratios; angled triangle, including distance, time – in miles Measure and draw 2휋푟πr = 휋푑πd, area of a point in all four Solve a ratio problem in decimal lengths and a per hour as well as metric angles, to the nearest circle = 휋푟πr2; quadrants; context: range of units; measures; degree; Use 휋π ≈ 3.142 or use the Find the coordinates of use a ratio to find one Apply Pythagoras’ use kinematics formulae to Know and use compass 휋π button on a calculator; points identified by quantity when the other is Theorem with a triangle calculate speed, directions; Give an answer to a geometrical information known; drawn on a coordinate acceleration (with formula Draw sketches of 3D question involving the in 2D (all four use a ratio to compare a grid; provided and variables solids; circumference or area of a quadrants); scale model to a real-life Calculate the length of a defined in the question); Know the terms face, circle in terms of 휋π; Find the coordinates of object; line segment AB given change d/t in m/s to a edge and vertex; Find radius or diameter, the midpoint of a line use a ratio to convert pairs of points; formula in km/h, i.e. d/t × Identify and sketch planes given area or perimeter of segment; Read values between measures and Understand, use and recall (60 × 60)/1000 – with of symmetry of 3D solids; circles; from straight-line graphs currencies; the trigonometric ratios support; Make accurate drawings for real-life situations; sine, cosine and tan, and of triangles and other 2D Draw straight line graphs problems involving mixing, apply them to find angles Express a given number as shapes using a ruler and a Find the perimeters and for real-life situations, e.g. paint colours, cement and lengths in general a percentage of another protractor; areas of semicircles and including ready reckoner and drawn conclusions; triangles in 2D figures; number in more complex Construct diagrams of quarter-circles; graphs, conversion Compare ratios; Use the trigonometric situations; everyday 2D situations Calculate perimeters and graphs, fuel bills graphs, Write ratios in form 1 : 푚m ratios to solve 2D Calculate percentage involving rectangles, areas of composite shapes fixed charge and cost per or 푚m : 1; problems including angles profit or loss; triangles, perpendicular made from circles and unit; Write a ratio as a fraction; of elevation and Make calculations and parallel lines; parts of circles; Draw distance-time Write a ratio as a linear depression; involving repeated Understand and draw Calculate arc lengths, graphs and velocity-time function; Round answers to percentage change, not front and side elevations angles and areas of sectors graphs; Write lengths, areas and appropriate degree of using the formula; and plans of shapes made of circles; Work out time intervals volumes of two shapes as accuracy, either to a given Find the original amount from simple solids; Find the surface area and for graph scales; ratios in simplest form; number of significant given the final amount Given the front and side volume of a cylinder; Interpret distance-time Express a multiplicative figures or decimal places, after a percentage elevations and the plan of Find the surface area and graphs, and calculate: relationship between two or make a sensible increase or decrease; a solid, draw a sketch of volume of spheres, the speed of individual quantities as a ratio or a decision on rounding in Use compound interest; the 3D solid. pyramids, cones and sections, total distance fraction. context of question; Use a variety of measures composite solids; and total time; Know the exact values of in ratio and proportion (ii)By the end of the sub- Round answers to a given Interpret information (ii)By the end of the sin 휃θ and cos 휃θ for 휃θ = problems: unit, students should be degree of accuracy. presented in a range of sub-unit, students 0°, 30°, 45°, 60° and 90°; currency conversion; able to: linear and non-linear should be able to: know the exact value of rates of pay; graphs; tan 휃θ for 휃θ = 0°, 30°, 45° best value; Understand clockwise Interpret graphs with Understand and use and 60°. Set up, solve and interpret and anticlockwise; negative values on axes; proportion as equality of the answers in growth and Draw circles and arcs to a Find the gradient of a ratios; decay problems; given radius or given the straight line from real- Solve word problems Understand that 푋X is diameter; involving direct and life graphs; (ii)By the end of the sub- inversely proportional to Measure and draw lines, inverse proportion; Interpret gradient as the unit, students should be 푌Y is equivalent to 푋X is to the nearest mm; Work out which product able to: rate of change in is the better buy; proportional to 1푌1Y; Measure and draw distance-time and speed- Scale up recipes; Interpret equations that angles, to the nearest time graphs, graphs of describe direct and inverse degree; Convert between Distinguish between containers filling and currencies; proportion. Know and use compass events which are emptying, and unit price Find amounts for 3 directions; impossible, unlikely, even graphs. people when amount for Draw sketches of 3D 1 given; chance, likely, and certain solids; to occur; (ii)By the end of the sub- Solve proportion Know the terms face, unit, students should be problems using the edge and vertex; able to: unitary method; Identify and sketch planes Mark events and/or Identify congruent Recognise when values of symmetry of 3D solids; probabilities on a shapes by eye; are in direct proportion probability scale of 0 to 1; Understand clockwise by reference to the graph Write probabilities in Make accurate drawings and anticlockwise; form; words or fractions, of triangles and other 2D Understand that Understand inverse decimals and percentages; shapes using a ruler and a rotations are specified by proportion: as 푥x Find the probability of an protractor; a centre, an angle and a increases, 푦y decreases event happening using Construct diagrams of direction of rotation; (inverse graphs done in theoretical probability; everyday 2D situations Find the centre of later unit); Use theoretical models to involving rectangles, rotation, angle and Understand direct include outcomes using triangles, perpendicular direction of rotation and proportion ⟶⟶ dice, spinners, coins; and parallel lines; describe rotations; relationship 푦y = 푘푥kx List all outcomes for single Understand and draw Describe a rotation fully events systematically; front and side elevations using the angle, direction Work out probabilities and plans of shapes made of turn, and centre; from frequency tables, from simple solids; Rotate a shape about the Work out probabilities Given the front and side origin or any other point from two way tables; elevations and the plan of on a coordinate grid; Record outcomes of a solid, draw a sketch of Draw the position of a probability experiments in the 3D solid. shape after rotation tables; about a centre (not on a Add simple probabilities; (ii)By the end of the sub- coordinate grid; Identify different mutually unit, students should be Identify correct rotations exclusive outcomes and able to: from a choice of know that the sum of the diagrams; probabilities of all Understand congruence, Understand that outcomes is 1; as two shapes that are translations are specified Using 1 − 푝p as the the same size and shape; by a distance and probability of an event not Visually identify shapes direction using a vector; occurring where 푝p is the which are congruent; Translate a given shape probability of the event Use straight edge and a by a vector; occurring; pair of compasses to do Describe and transform Find a missing probability standard constructions: 2D shapes using single from a list or understand, from the translations on a including algebraic terms; experience of coordinate grid; constructing them, that Use column vectors to triangles satisfying SSS, describe translations SAS, ASA and RHS are Understand that (iii)By the end of the sub- unique, but SSA triangles distances and angles are unit, students should be are not; preserved under able to: rotations and translations, so that any Find the probability of an construct the figure is congruent under event happening using perpendicular bisector of either of these relative frequency; a given line; transformations; Estimate the number of construct the times an event will occur, perpendicular from a (iii)By the end of the given the probability and point to a line; sub-unit, students the number of trials – for construct the bisector of should be able to: both experimental and a given angle; Understand that theoretical probabilities; construct angles of 90°, reflections are specified List all outcomes for 45°; by a mirror line; combined events Draw and construct Identify correct systematically; diagrams from given reflections from a choice Use and draw sample instructions, including the of diagrams; space diagrams; following: Identify the equation of Work out probabilities a region bounded by a a line of symmetry; from Venn diagrams to circle and an intersecting Transform 2D shapes represent real-life line; using single reflections situations and also a given distance from a (including those not on ‘abstract’ sets of point and a given coordinate grids) with numbers/values; distance from a line; vertical, horizontal and Use union and equal distances from two diagonal mirror lines; intersection notation; points or two line Describe reflections on a Compare experimental segments; coordinate grid; data and theoretical regions may be defined Scale a shape on a grid probabilities; by ‘nearer to’ or ‘greater (without a centre Compare relative than’; specified); frequencies from samples Find and describe regions Understand that an of different sizes; satisfying a combination enlargement is specified Find the probability of of loci; by a centre and a scale successive events, such as Use constructions to factor; several throws of a single solve loci problems (2D Enlarge a given shape dice; only); using (0, 0) as the centre Use tree diagrams to Use and interpret of enlargement, and calculate the probability of and scale drawings; enlarge shapes with a two independent events; Estimate lengths using a centre other than (0, 0); Use tree diagrams to scale ; Find the centre of calculate the probability of Make an accurate scale enlargement by drawing; two dependent events. drawing from a diagram; Describe and transform Use three-figure bearings 2D shapes using to specify direction; enlargements by: Mark on a diagram the a positive integer scale position of point 퐵B given factor; its bearing from point 퐴A; a fractional scale factor; Give a bearing between Identify the scale factor the points on a map or of an enlargement of a scaled plan; shape as the ratio of the Given the bearing of a lengths of two point 퐴A from point 퐵B, corresponding sides, work out the bearing of simple integer scale 퐵B from 퐴A; factors, or simple Use accurate drawing to fractions; solve bearings problems; Understand that Solve locus problems distances and angles are including bearings. preserved under reflections, so that any (iii)By the end of the sub- figure is congruent under unit, students should be this transformation; able to: Understand that similar shapes are enlargements Define a ‘quadratic’ of each other and angles expression; are preserved – define Multiply together two similar in this unit. algebraic expressions with brackets; Square a linear expression, e.g. (푥x + 1)2; Factorise quadratic expressions of the form 푥x2 + 푏푥bx + 푐c; Factorise a quadratic expression 푥x2 − 푎a2 using the difference of two squares; Solve quadratic equations by factorising; Find the roots of a quadratic function algebraically.

(iv)By the end of the sub- unit, students should be able to:

Generate points and graphs of simple quadratic functions, then more general quadratic functions; Identify the line of symmetry of a quadratic graph; Find approximate solutions to quadratic equations using a graph; Interpret graphs of quadratic functions from real-life problems; Identify and interpret roots, intercepts and turning points of quadratic graphs.

Key Skills (i)Students should be (i)Students should know (i)Students should be (i)Students should be (i)Students should be (i)Students should know able to plot the four operations of able to rearrange simple able to interpret scales able to measure and the formula for Prior coordinates and read number. formulae and equations, on a range of measuring draw lines. calculating the area of a knowledge: scales as preparation for instruments. rectangle. (ii)Students should have rearranging .(Ii)Students should be Maths topics (ii)Students should be a basic understanding of trigonometric formulae. Students should be able able to square negative Students should know already taught able to substitute into a fractions as being ‘parts to find a percentage of numbers. how to use the four at KS3 listed at formula. of a whole’. an amount and relate end of this (iii)Students should (ii)Students should percentages to Students should be operations on a document recall basic shapes. recall basic angle facts. decimals. able to substitute into calculator.

formulae. Students should be Students should Students should be able able to plot points in all understand when to to rearrange equations (ii!)Students should be four quadrants. leave an answer in surd and use these to solve able to plot points on a

form. problems. coordinate grid. Students should have an understanding of Students can plot Students should know Students should be the concept of rotation. coordinates in all four speed = distance/time, able to expand single quadrants and draw density = mass/volume. brackets and collect Students should be axes. ‘like’ terms. able to draw and recognise lines parallel (iii)Students should to axes and 푦y = 푥x, know how to add and 푦y = −푥−x. multiply fractions and decimals. Students will have encountered the terms Students should have clockwise and experience of anticlockwise expressing one number previously. as a fraction of another number.

Assessment GEM tasks only End-of-term assessment GEM tasks only End-of-term assessment GEM tasks only End-of-year assessment Title (marked by the teacher (marked by the teacher (marked by the teacher with feedback to with feedback to with feedback to students) students) students)

Ongoing GEM task at the end of GEM task at the end of GEM task at the end of GEM task at the end of GEM task at the end of End-of-year assessment assessment every two week period. every two week period. every two week period. every two week period. every two week period. Students green pen Students green pen mark. Students green pen Students green pen mark. Students green pen mark. Teacher provides Teacher provides mark. Teacher provides Teacher provides mark. Teacher provides feedback (addressing feedback (addressing feedback (addressing feedback (addressing feedback (addressing misconceptions). misconceptions). misconceptions). misconceptions). misconceptions).

End of topic assessment End of topic assessment End of topic assessment End of topic assessment End of topic assessment

Homework Hegarty Maths Hegarty Maths Hegarty Maths Hegarty Maths Hegarty Maths Hegarty Maths

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