Foundation. Scheme of Work. Year 10 September 2016-July 2017

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1 Foundation Scheme of Work Year 10 September 016-July 017

2 Foundation Tier Students will be assessed by completing two tests (topic) each Half Term.

3 PERCENTAGES Use percentages in real-life situations VAT value of profit or loss simple interest Compound Interest Percentage Change Reverse Percentages Interpret Growth and Decay Find a percentage of a quantity in order to increase or decrease Write one number as a percentage of another number / 0,8 86/ Use percentages to solve problems /89

4 Foundation Tier THREE DIMENSIONAL SHAPES Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone Know the terms face, edge and vertex Use isometric grids (now projections) Draw nets and show how they fold to make a -D solid Understand and draw front and side elevations and plans of shapes made from simple solids Given the front and side elevations and the plan of a solid, draw a sketch of the -D solid Find volumes of shapes by counting cubes Recall and use formulae for the volume of cubes and cuboids Calculate the volumes of prisms and shapes made from cubes and cuboids Volumes of other prisms Find the volume of a cylinder Find the surface area of cubes, cuboids, cylinders and triangular prisms 11a/11b Convert between units of area Convert between units of volume Perform calculations with density, mas, volume and pressure 1 1

5 Foundation Tier EQUATIONS AND INEQUALITIES Set up simple equations Rearrange simple equations Solve simple equations Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation Solve linear equations which include brackets, those that have negative signs occurring anywhere in the equation, and those with a negative solution Solve linear equations in one unknown, with integer or fractional coefficients Use linear equations to solve word problems a 100 1a/b 1a/b 17 Solve linear inequalities Represent the solution set on a number line Use the correct notation to show inclusive and exclusive inequalities Solve real life problems on areas and volumes, eg the length of a rectangular room is m longer than the width. If the area is 0 m², find the width. 17 Introduction to Bounds Find upper and lower bounds up to two decimal places 1 Calculate upper and lower bounds of rectangles Use inequality notation to specify error intervals due to rounding 1

6 Foundation Tier GRAPHS 1 Solve problems involving money conversions, e.g. s to Euros etc. Draw graphs representing real examples like filling a bath/containers Interpret and draw linear graphs, including conversion graphs, fuel bills etc. Solve problems relating to mobile phone bills with fixed charge and price per unit Interpret non-linear graphs like the number of cans in a vending machine at times throughout the day Interpret gradients from real life graphs e.g. for height of bath water vs time, the gradient is the rate of filling Draw distance time graphs Interpret distance time graphs and solve problems Substitute values of x into a quadratic function to find the corresponding values of y Draw graphs of quadratic functions Use quadratic graphs to solve approximate solution of a quadratic equation from the graph of the corresponding quadratic function Sketch Quadratic, cubic and reciprocal functions. Assessments 1/

7 Foundation Tier TRANSFORMAT IONS Identify and Understand the four types of Transformations Recognise that all corresponding angles in similar shapes are equal in size Describe and transform -D shapes using single translations Understand that translations are specified by a distance and direction using a vector Describe and transform D shapes using single rotations Understand that rotations are specified by a center and an angle Find the center of rotation / 0/17 9 Rotate a shape about the origin or any other point Describe and transform D shapes using single reflections Identify the equation of a line of symmetry 8 Describe and transform D shapes using enlargements of a positive and fractional scale factor Understand that an enlargement is specified by a center and scale factor Find the center of an enlargement Identify the scale factor of an enlargement as the ratio of the lengths of two corresponding sides Describe and transform D shapes using transformation combinations RATIO AND PROPORTION Understand what is meant by ratio Write a ratio in its simplest form; and find an equivalent ratio Solve a ratio problem in context, eg recipes Share a quantity in a given ratio Understand and use examples in direct proportion Write a ratio in the form 1:n Write a ratio as a linear function

8 PROBABILITY Foundation Tier Distinguish between events which are: impossible, unlikely, even, likely and certain to occur Mark events and/or probabilities on a scale of 0 to 1 Write probabilities in words fractions, decimals, and percentages Add simple probabilities Identify different mutually exclusive outcomes and know that the sum of all outcomes is 1 Use 1 - p as the probability of an event not occurring List all outcomes for two successive events systematically Use and draw Sample Space Diagrams Find the probability of an event happening using relative frequency Compare relative frequencies from samples of different sizes Complete Two Way Tables and find probabilities from them Estimate the number of times an event will occur given the probability and the number of trials Draw, complete and understand Frequency Trees Use simple Tree Diagrams to find probability of an event happening Use harder Tree diagrams ( and or rule) Draw Venn diagrams Use and understand notation of Venn diagrams Understand sampling populations Stratified sampling 1 / / a 17b 1 176

9 Assessments / Foundation Tier PYTHAGORAS THEOREM Use Pythagoras theorem to find the hypotenuse Use Pythagoras theorem to find a shorter side Use Pythagoras theorem to find if a triangle is right angled Use Pythagoras theorem to find the length of a line segment from a coordinate grid Apply Pythagoras theorem to practical situations 10a,b,c FORMULAE Use formulae from mathematics and other subjects expressed initially in words and then using letters and symbols Substitute numbers into expressions Substitute numbers into a formula 9 9 Change the subject of a formula Find the solution to a problem by writing an equation and solving it FACTORISING Simple factorisation one number or letter outside bracket Simple factorisation with two coefficients Factorise quadratics including the difference of two squares Solve quadratic equations by factorizing Roots and turning points of quadratics 101,

10 Assessments /6 Foundation Tier PROPORTION Use direct and inverse proportion graphically and algebraically 199 Simultaneous equations Simultaneous equations ( real life,algebraic and graphical) Solving simultaneous equations Setting up simultaneous equations(real life) Use graphs to solve simultaneous equations GRAPHS Find the equation of a line through two points or through one point with given gradient 19 Assessments 7/8

11 TRIGONOMETRY Foundation Tier Use the sin, cos and tan trigonometric ratios for right-angled triangles Know the exact values of sin, cos and tan at key angles (0, 0,, 60, 90 degrees) AVERAGES Find the mean, mode, median and range from data in tables 10 CIRCLES Using formula find the area of a circle (and inverse) Using formula find the circumference of a circle (and inverse) Find area and perimeter of half and quarter circles Find the area and perimeter of a sector of a circle Find the arc length of a sector of a circle ANGLES Revision of all angle facts (parallel lines, interior/exterior angles in polygons) 10,1 BEARINGS Understand that bearings are clockwise, written as a three figure number and measured from North Draw and accurately measure bearings Use and interpret maps and scale drawings Construct accurate scale drawings 1

12 Assessments 9/10 Foundation Tier D SHAPES Identify shapes which are Similar or Congruent Prove and understand that two triangles are congruent Recognise similar shapes and find missing sides Use scale factors to find missing sides D SHAPES Find the volume and surface area of a sphere and hemisphere Find the volume of pyramids Find the volume and surface area of a cone Find the volume of a frustrum W/C 19 TH JUNE 017 YEAR 10 EXAMS (TWO PAPERS)

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