Chislehurst and Sidcup Grammar School Mathematics Department Year 9 Programme of Study

Transcription

1 Chislehurst and Sidcup Grammar School Mathematics Department Year 9 Programme of Study Timings Topics Autumn Term - 1 st half (7 weeks - 21 lessons) 1. Algebra 1: Expressions, Formulae, Equations and Inequalities (7) 2. Algebra 2: Brackets and Factorising (3) 3. Fraction (3) Module 1 Test Topic 1, 2, 3 Non-Calculator (2) Module 1 Problem Solving Task (1) 4. Straight Linear Graphs (3) : 2 lessons Autumn Term - 2 nd half (7 weeks - 21 lessons) 5. Simultaneous Equations (5) 6. Fractions, Decimals and Percentages (6) 7. Ratio and Proportion (3) Module 2 Test Topic 4, 5, 6, 7 - Calculator (2) Module 2 Problem Solving Task (1). Probability (4) : 2 lessons Spring Term - 1 st half (6 weeks - 1 lessons) 9. Pythagoras Theorem (4) 10. Trigonometry (5) Module 3 Test Topic, 9, 10 - Calculator (2) Module 3 Problem Solving Task (1) 11. Algebra 3: Bracket and Factorising (6) 12. Measures, Perimeter, Area and Volume (7) Spring Term - 2 nd half (6 weeks - 1 lessons) Summer Term - 1 st half (6 weeks - 1 lessons) Module 4 Test Topic 11, 12 Calculator (2) Module 4 Problem Solving Task (1) 13. Angles and Polygons (4) 14. Transformations of Shapes (4) 15. Statistics (6) 16. Indices and Standard Form (7) End of Year Exams Revision (4) : 1 lesson End of Year Examinations Up to and including topic Real Life Graphs and Curved Graphs (3) Summer Term - 2 nd half (5 weeks - 15 lessons) End of Year Problem Solving Task (1) 1. Construction and Loci (4) 19. Sequences (3) 20. Algebra and Number works (4) 21. Investigations

2 YEAR 9 - TOPIC 1 Algebra 1: Expressions, Formulae, Equations and Inequalities (7 lessons) Simplify algebraic expressions 6 P147 Ex A 1.1 Substitute numbers into formulae 6 P43 Ex 3A Substitute expression into a formula 7 P Ex 9C-D P196 Ex 9G Solve linear equations including brackets 6 P43 Ex 3A Understand the difference between equations, formulae and P116 Ex 5J 6 P43 Ex 3A identities 1.2 Solve equations involving square and cube roots 6/7 P149 Ex B 1.3 Solve equations involving fractions 7 P50 Ex 3D 1.4 Solve simple inequalities and represent the solution on a number line 7 P51 Ex 3E 1.5 Change the subject of a formula 7/ P 203 Ex 11E P Ex 9E-F YEAR 9 - TOPIC 2 Algebra 2: Brackets and Factorising (3 lessons) Expand linear expressions 6 P105 Ex 5A 2.1 Factorise linear expressions Expand double brackets of the form (x + a) (x + b) 7 P Ex 5C-H YEAR 9 - TOPIC 3 Fractions (3 lessons) 3.1 Review four rules for fractions 6/7 P1 Ex 2A Understand and calculate the reciprocal of a number 6/7 P34 Ex 2G P16 P39 Ex 1C 3.2 Converting factions and recurring decimals P13 Ex 7F P41 Ex 1E Module test after this topic Chislehurst and Sidcup Grammar School - Mathematics Department Page 2

3 YEAR 9 - TOPIC 4 Straight Linear Graphs (3 lessons) 4.1 Review drawing straight line graphs from their equations 6/7 P205 Ex 11F 4.2 Understand the meaning of m & c in the equation y = mx + c 4.3 Plot straight line graphs of the form y= mx + c or ax + by = c 6 7 YEAR 9 - TOPIC 5 Simultaneous Equations (5 lessons) 5.1 Solve a pair of simultaneous equations by eliminating one variable including multiplying one or both equation(s) 5.2 Solve a pair of simultaneous equations by plotting their graphs and recognise that the point of intersection is the solution 5.3 Form and solve simultaneous equations from worded questions Solve a pair of simultaneous equations by the method of substitution Solve simultaneous equations graphically where one is non linear 7 P 46 Ex 3B 7 P 56 Ex 3G P 4 Ex 3C P56 Extension work P Ex 10B-E P213 Ex 10G P Ex 10F YEAR 9 - TOPIC 6 Fractions, Decimals and Percentages (6 Lessons) Understand the effect of multiplying or dividing by numbers between 0 and Round to a number of significant figures and estimate the answer to calculations 7 P32 Ex 2F 7 P36 Ex 2H 6.2 Review calculations with decimals 7 P Review calculating percentages including percentage changes 6.4 Calculate an original amount given the final amount and the % increase or decrease 6.5 Understand the effect of a repeated percentage change and Solve problems that involve compound interest 6/7 P24 Ex 2C P21 Ex 2B P61-67 Ex 3B-D P6-73 Ex 3E-F P73-0 Ex 3G-I Chislehurst and Sidcup Grammar School - Mathematics Department Page 3

4 YEAR 9 - TOPIC 7 Ratio and Proportion (3 lessons) Simplify ratios 5 P1 Compare ratios by writing them in the form 1:m or m: Solve problems involving ratios Solve direct and inverse proportion problems 7 P 26 Ex 2D P3-95 Ex 4B-H 7.3 Use direct proportion problems graphically 6 P 53 Ex 3F YEAR 9 - TOPIC Probability (4 lessons) Understand probability vocabulary and be able to explain P44-45 Ex 2A 6/7 P160 Ex 9A different probability statements.1 Understand independent, mutually exclusive and P45-50 Ex 2B-E exhaustive events and calculate probabilities using these 6 P161 Ex 9B definitions.2 Use relative frequency to estimate probabilities 6/7 P167 Ex 9D.3 Use tree diagrams to calculate probabilities P164 Ex 9C P52-5 Ex 2F-G YEAR 9 - TOPIC 9 Pythagoras Theorem (4 lessons) Understand and use Pythagoras' theorem to find any given side of a right angled triangle 7 P 60 Ex 4A Recognise Pythagorean triples: 3, 4,5 triangles, 5, 12, 13 triangles etc and their multiples should be discussed 7 P64 Extension work 9.1 Apply Pythagoras' theorem to solve a range of problems including finding lengths in isosceles triangles 7/ P 62 Ex 4B 9.2 Given the coordinates of points A and B find the length of AB 7 P 62 Ex 4B 9.3 Use Pythagoras Theorem to find missing lengths and angles in circles P 70 Ex 4E 9.4 Justify Pythagoras Theorem using algebra P76 Extension work Chislehurst and Sidcup Grammar School - Mathematics Department Page 4

5 YEAR 9 - TOPIC 10 Trigonometry (5 lessons) 10.1 Recognise all three trigonometry ratios (sine, cosine, P11 Ex 10B tangent) in a right angled triangle P14 Ex 10C 10.2 Use a calculator to find the sine, cosine and tangent of an angle P1 Ex 10B-10C 10.3 Know (without using calculator) the value of sin, cos and tan of special angles 30 0, 45 0, and Find a side give one other side and an angle P11 Ex 10B-10C P Ex16A-E 10.5 Find an angle given its sine, cosine or tangent P11 Ex 10B-10C P Ex16G 10.6 Solve worded problems using trigonometry, including bearings P17 Ex 10D Know how to draw and recognise trigonometry graphs Module test after this topic YEAR 9 - TOPIC 11 Algebra 3: Brackets and Factorising (6 Lessons) Multiply out single brackets and collect like terms 5/6 P195 Ex 11A Factorise into single brackets 7 P197 Ex 11B P Ex 7A 11.1 Multiply out two brackets in the form (a+b)(c+d) 7 P199 Ex 11C 11.2 Factorise quadratic expressions of the form x 2 + bx + c including the difference of two squares 11.3 Factorise quadratic expressions where coefficient of x 2 is >1 Simplify algebraic expressions which involve quadratic factorisations P202 Ex 11D P202 Extension work P105Ex 5b P Ex7B-G P Ex 7H-M Chislehurst and Sidcup Grammar School - Mathematics Department Page 5

6 YEAR 9 - TOPIC 12 Measure, Perimeter, Area and Volume (7 lessons) Convert between metric units for lengths, area and volume 5/6 P 113 Ex 6B 12.1 Solve problems involving compound measures, e.g. speed and density Review surface area and volume of prisms (and cylinders) 6/7 P 119 Ex 6E 6/7 P116 Ex 6D P116 Ext work 12.3 Calculate arc length and area of a sector P 115 Ex 6C P274 Ex 13B P Ex13D-E P Ex13C 12.4 Calculate volume and surface area of a cone, sphere and pyramid 12.5 Dimension Analysis 7 P F Module test after this topic YEAR 9 TOPIC 13 Angles and Polygons (5 lessons) Review angles on parallel lines: alternate, corresponding, vertically opposite, supplementary & interior Review sum of angles in a triangle and identify scalene, isosceles and equilateral triangles Continue to use the conventions for labelling lines, angles and shapes Know the names of polygons up to 10 sides 6 Know that the exterior angles of any polygon add to 360 o 6 Find the sum of the interior angles of any polygon by splitting the shape into triangles and multiplying by Understand how to use angle facts to find unknown angles in various diagrams involving polygons Prove simple facts geometrically Know that tangent to a circle is perpendicular to the radius at the point of contact Chislehurst and Sidcup Grammar School - Mathematics Department Page 6

7 YEAR 9 - TOPIC 14 Transformations of Shapes (4 lessons) Review all transformations; reflections, rotations, translations P Ex 14B-E 5/6 Worksheet and enlargements P Ex14G-H 14.1 Carry out fractional and negative enlargements on plane P Ex 14B 7 P 176 ex 10A shapes on a coordinate axis 14.2 Describe all four transformations 7 P Ex 14B-E P Ex14G-H 14.3 Carry out and describe the result of combined P Ex 14F transformations P30 Ex 14J YEAR 9 - TOPIC 15 Statistics (6 lessons) 15.1 Interpret graphs, diagrams and tables and write comments about the data given 7 P 90 Ex 5C & 5D 15.2 Know how to work out the IQR for discrete data. Understand the meaning and advantages of the IQR Draw and interpret Cumulative Frequency Diagrams P 95 Ex 5E P Ex D 15.4 Use a Cumulative Frequency Diagram to find the median and interquartile range 15.5 Draw box plots from a given set of data or Cumulative Frequency Diagram Calculate an estimate of the mean and modal class from frequency table or grouped data Compare two sets of data given their CF graphs or box plots 15.7 Carry out their own investigation using their own data and the techniques they have learned P 95 Ex 5E 7 7 P 97 Ex 5F 7 P 100 Ex 5G P Ex E-H P162 Ex B Chislehurst and Sidcup Grammar School - Mathematics Department Page 7

8 YEAR 9 - TOPIC 16 Indices and Standard Form (7 lessons) Understand and use index notation for positive and negative integer powers 5/ Know and use the rules of indices, with negative and fractional indices (-a or 1/a) 7/ 16.2 Simplify algebraic expressions involving indices including negative indices, e.g. 7/ P147 Ex A 16.3 Convert between ordinary numbers and numbers in standard form and vice versa 7 P127 Ex 7A 16.4 Add and subtract numbers in Standard Form P42-43 Ex 1F 16.5 Multiply and divide numbers in standard form (with and without a calculator) P Ex 7B-C P42-43 Ex 1F End of Year Exams after this topic YEAR 9 - TOPIC 17 Real Life Graphs and Curved Graphs (4 lessons) 17.1 Draw and interpret real life graphs 7 P9 Ex 1D 17.2 Generate points and plot graphs of quadratic and cubic functions both manually and using a calculator or computer 17.3 Know how to draw reciprocal graphs (and exponential graphs) 7/ P151 Ex C-D P249 Ex 12C P253 Ex 12D 17.4 Recognise different straight lines and curves P254 Ex 12E Chislehurst and Sidcup Grammar School - Mathematics Department Page

9 YEAR 9 - TOPIC 1 Constructions and Loci (4 Lessons) 1.1 Construct a perpendicular bisector and an angle P Ex 1D 6 bisector 1.2 Construct the locus of points which are equidistant from P32-36 Ex 1B a fixed point (the circle) 7 P Ex 1D 1.3 Construct the locus of points which are equidistant from P32-36 Ex 1B two given points (the perpendicular bisector of two points) Construct the locus of points which are equidistant from P32-36 Ex 1B two fixed lines (the bisector of the angle) Solve problems involving intersecting loci in two P396 Ex 1E 7 dimensions, including regions Solve problems involving loci in three dimensions P39 Ex 1F YEAR 9 - TOPIC 19 Sequences (3 lessons) Understand a formula can be used to generate a sequence 5/6 P 2 Ex 1A 19.1 Find a formula for the n th term of a linear sequence 5/6 P 2 Ex 1A P19 Ex 9I 19.2 Understand a formula can be used to generate a P19 Ex 9I 7 P 4 Ex 1B quadratic sequence 19.3 Find a formula for the n th term of a simple quadratic P19 Ex 9I 7 P 4 Ex 1B sequence 19.4 Investigate the limits of different sequences 7 P 11 Ex 1E P19 Ex 9I YEAR 9 - TOPIC 20 Algebra and Number Works ( lessons) 20.1 Review all basic Number and Algebra works, especially 6/7 - Substitution / Order of Operations - Fractions - Simplifying algebraic expressions - Expansion of double brackets - Factorisation including quadratic expressions 20.2 Convert recurring decimals to fractions and vice versa Simplifying Surds Calculations with Surds Expansion of three brackets or more Co-ordinate Geometry E Chislehurst and Sidcup Grammar School - Mathematics Department Page 9

10 YEAR 9 - TOPIC 21 Using and applying Mathematics: Investigations (2 Lessons) Level Represent problems and synthesise information in algebraic, geometric or graphical form Solve substantial problems by breaking them into simpler tasks Present a concise and reasoned argument, using symbols, diagrams, graphs and related explanatory text Suggest extensions to problems Chislehurst and Sidcup Grammar School - Mathematics Department Page 10