Route Map (Start September 2012) Year 9

Transcription

1 Route Map (Start September 2012) Year 9 3 th 7 th Sept 10 th -14 th Sept 17 th 21 st Sept 24 th 28 th Sept 1 st -5 th Oct 8 th -12 th Oct 15 th 19 th Oct 22 nd -26 th Oct 29 th Oct-2 nd Nov 5 th -9 th Nov Holiday Algebra 1/2 8 lessons Number 1 12 lessons Algebra 3 8 lessons G&M 1 12 lessons 12 th -16 th Nov 19 th -23 rd Nov 26 th 30 th Nov 3 rd -7 th Dec 10 th -14 th Dec 17 th -21 st Dec 24 th -28 th Dec 31 st Dec-4 th Jan 7 th -11 th Jan 14 th -18 th Jan G&M 1 12 lessons Statistics 1 8 lessons G&M 2 8 lessons Holiday Holiday Exam week Finish exam 21 st - 25 th Jan 28 th Jan-1st Feb 4 th -8 th Feb 11 th -15 th Feb 18 th -22 th Feb 25 th Feb-1 st Mar 4 th - 8 th Mar 11 th -15 th Mar 18 th -22 nd Mar 25 th -29 th Mar Number 2 10/11 lessons Algebra 4 12 lessons Holiday Algebra 4 12 lessons Statistics 2 5/6 lessons G&M 3 8 lessons 1 st -5 th Apr 8 th -12 th Apr 15 th -19 th Apr 22 nd -26 th Apr 29 th Apr-3 rd May 6 th -10 th May 13 th -17 th May 20 th -24 th May 27 th - 31 st May 3 rd -7 th Jun Holiday Holiday Holiday Algebra 5 8 lessons Statistics 3 8 lessons G&M 4 8 lessons 10 th -14 th June 17 th -21 st Jun 24 th -28 th Jun 1 st 5 th Jul 8 th -12 th Jul 15 th -21 th Jul 22 rd -26 th Jul Holiday Solving Problems 8 lessons Statistics 4 8 lessons

2 Algebra 1/2 Foundation Generate & describe an integer sequence. Plot the graphs of linear functions. Core Generate terms of a sequence. Write an expression for the nth term of a sequence. Find the inverse of a linear function. Construct functions of real life problems. Extension Find the next term & nth term of a quadratic sequence. Deduce properties of the triangular and square number sequences. Know simple properties of quadratic functions. Integer Graphs Function Terms Sequence Expression Nth Term Triangular Numbers Square Numbers Properties Quadratic Linear

3 Algebra 3 Foundation Know the meanings of the words formula and function. Construct & solve linear equations with an unknown on both sides. Begin to use graphs & solve problems on direct proportion. Core Distinguish the different roles played by letters & symbols in equations, formulas and functions. Construct & solve linear equations with an unknown on both sides & a positive or negative solutions. Use a systematic approach to trial & improvement questions. Solve problems involving direct proportion. Formula Function Construct Equations Solve Symbols Equations Unknown Positive Negative Trial Improvement Direct Proportion

4 Algebra 3 Continued Extension Solve a pair of simultaneous equations by eliminating one variable. Use the graphical method to solve where there is only one solution, more than one solution or no solutions with quadratic graphs. Simultaneous Equations Variable Elimination Substitution Quadratic Graphical

5 Algebra 4 Foundation Recognise & use factors, multiples, primes, highest common factors & lowest common multiples. Use squares, positive & negative & their square roots. Recognise equations of the form y=mx + c. Core Use prime factor decomposition. Use index notation & simple index laws. Find the gradient & intercept of a straight line with the equation y=mx+c Construct functions based on real life problems. Interpret graphs arising from real life solutions. Factors Mulitples Primes Highest Common Factor Lowest Common Multiple Positive Negative y=mx+c Index Intercept Gradient Extension Know & use the generalised form of the index laws.

6 Algebra 4 Continued. Extension Continued Investigate parallel lines and perpendicular lines and the gradients of these lines. Plot simple quadratic and cubic graphs. Parallel Perpendicular Gradients Cubis Quadratic

7 Algebra 5 Foundation Simplify an algebraic expression by collecting like terms. Multiply a single term over a bracket. Plot the graphs of linear functions. Core Factorise an expression by taking out a common factor. Use formulae from maths and other subjects. Substitute into expressions and formula. Change the subject of a formula. Generate points of functions in the form of ay+bx=0 Solve increasingly demanding problems across the topic of algebra. Algebraic Expressions Collecting Multiply Bracket Linear Functions Expression Factorise Subjects Substitute Formula

8 Algebra 5 Continued Extension Square a linear expression. Expand the product of two linear expressions & simplify where possible. Solve linear inequalities with one variable. Begin to solve inequalities with two variables. Derive more complex formulas. Change the subject of these equations and formulas. Square Linear Product Expressions Simplify Solve Inequalities Formulas Subject Equations

9 Number 1 Foundation Order decimals Add & subtract fractions by writing them with a common denominator. Calculate fractions of quantities Multiply & divide fractions by fractions & whole numbers. Interpret percentage Reduce a ratio to its simplest form. Divide a quantity into two or more parts. Use unitary method to solve problems on ratio & proportion. Round any given number to a power of 10 or a given number of decimal places. Decimals Add Subtract Fraction Quantity Percentage Ratio Simplest form Unitary Method Rounding Power Core Use efficient methods to add, subtract, multiply & divide fractions.

10 Number 1 Continued Core Continued Compare fractions, decimals & percentages. Solve questions on percentage change. Use proportional reasoning. Understand the effects by multiplying by 0 and 1. Understand the effect of powers. Use known facts to calculate unknown facts. Make & justify estimations and approximations. Extension Understand & use proportionality. Recognise & use reciprocals. Round to a given number of significant figures. Fraction Decimal Percentage Proportional Mulitplying Powers Estimations Approximations Reciprocal Proportionality Significant Figures

11 Number 2 Foundation Multiply & divide integers by 0.1 and 0.01 Consolidate standard column methods. Solve complex problems by breaking them down into smaller tasks. Core Extend knowledge of integer powers of 10. Use rounding to make estimates. Know a recurring decimal is an exact fraction. Use standard column procedures Check results using appropriate methods. Use a calculator efficiently. Enter numbers in a calculator given a context e.g. Time or money Multiply Divide Integers Powers Rounding Estimates Calculator Efficiently Monday Standard Form Extension Write numbers in standard form

12 Number 2 Continued Extension Continued Understand upper & lower bounds Round to a given number of decimal places or significant figures. Use algebraic methods to convert a recurring decimal to a fraction. Enter numbers in standard form into a calculator. Upper & Lower Bounds Rounding Decimal Places Significant Figures Algebraic Recurring Fractions Decimal

13 Geometry & Measure 1 Foundation Identify alternate & corresponding angles. Understand the proofs of angles in a triangle & quadrilateral. The exterior angle of a triangle is equal to the sum of the opposite interior angles. Solve geometrical problems using special triangles & quadrilaterals. Use mathematical equipment to construct triangles. Use mathematical equipment to construct a perpendicular of a line and an angle bisector. Core Explain how to calculate the sum of the interior angles of a polygon. Solve problems using parallel line properties Know the parts of a circle. Alternate Corresponding Proof Triangle Angle Opposite Interior Exterior Construct Perpendicular Bisector Polygon Sum Circle Parallel

14 Geometry & Measure 1 Continued Core Continued Find the locus of points Extension Understand & apply Pythagoras s theorem. Know that the tangent of a circle meets the radius at a perpendicular. Extend our knowledge of constructions. Find the locus of more complex rules. Locus Pythagoras Tangent Circle Radius Perpendicular

15 Geometry & Measure 2 Foundation Given coordinate find the midpoint of a line segment. Know rough metric and imperial conversions. Use formulas for the areas of triangles, parallelograms & trapeziums. Calculate the areas of compound shapes. Know the formulas for finding the surface area & volume of cuboids and shapes made from cuboids. Core Convert between area measurements & volume measurements. Know & use the formula for the area & circumference of a circle. Calculate the surface area & volumes of prisms. Coordinate Metric Imperial Formula Rectangle Triangle Parallelogram Trapezium Cuboids Cubes Surface Area Volume Measurements. Circumference Area Prisms Convert

16 Geometry & Measure 2 Continued Extension Use properties of similar triangles. Recognise measurements given to the nearest unit may be inaccurate. Understand & use measures of speed. Know the formulas for finding the length of arcs & areas of sectors. Calculate the lengths, areas & volumes in prisms including cylinders. Similar Triangular Speed Sectors Length Arc Cylinders Volume Prism

17 Geometry & Measure 3 Foundation Identify symmetries in 2d shapes. Understand & use the language of enlargement. Make simple scale drawings. Consolidate the understanding between ratio & proportion. Reduce a ratio into its simplest form. Core Understand congruence. Transform 2d shapes by a combination of reflections, rotation & translations. Know that translations, reflections & rotations preserve length. Identify reflection in 3d shapes. Enlarge 2d shapes with a centre of enlargement & a whole number scale factor. Identify scale factor. Use & interpret maps & scale drawings. Symmetries Enlargement Scale Ratio Proportion Simplest Form Congruence Translations Reflections Rotations 2d 3d Centre Scale Factor Interpret Maps

18 Geometry & Measure 3 Continued Core Continued Use proportional reasoning to solve a problem. Extension Distinguish between practical demonstration & proof. Know that if 2d shapes are similar sides and angles will be the same. Enlarge a shape by fractional scale factor. Begin to use sine, cosine & tangent in right angled triangles. Proportional Proof 2d 3d Similar Sine Cosine Tangent Right Angled Triangle

19 Geometry & Measure 4 Foundation Solve problems involving special triangles & quadrilaterals. Know & use geometric problems of cuboids. Make simple scale drawings. Know & use the formula for the volume of a cuboid. Calculate the volume & surface areas of shapes made from cuboids. Core Solve problems using properties of angles in parallel lines. Visualise 2d representations of 3d shapes including plans & elevations. Use & interpret maps & scale drawings. Calculate the surface area &volume of prisms. Give solutions to a reasonable degree of accuracy. Isosceles Equilateral Triangle Quadrilateral Volume Surface Area Cubiods Scale Parallel Lines Alternate Corresponding Scale Plans Elevations Surface Area Prisms Accuracy

20 Geometry & Measure 4 Continued Extension Understand & apply Pythagoras theorem. Calculate lengths, areas & volumes in prisms. Begin to use sine, cosine & tangent in right angled triangles. Recognise the accuracy needed of measurements. Pythagoras Length Area Volume Prisms Sine Cosine Tangent Measurements

21 Statistics 1 Foundation Decided which data to collect to answer a question. Collect data using a suitable method. Calculate averages where appropriate, mode, median, mean & range. Construct bar charts, pie charts, frequency diagrams etc using paper & ICT. Interpret graphs and data. Compare two distributions using the averages. Core Suggest problems to explore using statistics. Discuss primary & secondary sources. Design a survey or experiment. Construct tables for large data sets including equal & appropriate class intervals. Create & use a time series. Data Collection Median Mean Range Mode Bar Charts Pie Charts Interpret Primary Secondary Statistics Survey Class Intervals Time Series

22 Statistics 1 Continued Core Continued Have a better understanding of correlation. Interpret graphs & draw conclusions. Compare two or more distributions. Extension Identify possible sources of bias. Find the median and quartiles for large data sets. Construct on paper & ICT suitable lines of best fits & frequency polygons. Analyse data to find patterns and exceptions. Draw conclusions. Correlation Graphs Conclusions Distributions Bias Median Quartiles Polygons Frequency

23 Statistics 2 Foundation Know the probability of an event occurring is p Know the probability of an event not occurring is 1-p. Record all possible mutually exclusive events for an experiment. Know that the increasing number of times an experiment is performed, the more accurate the outcome. Core Use the vocabulary of probability. Know that the total sum of the probabilities is 1. Estimate probabilities from experimental data. Use appropriate methods to add, subtract, multiply & divide fractions. Probability Mutually Exclusive Experiment Accurate Sum Data Multiply Divide Fractions Frequency Extension Understand relative frequency.

24 Statistics 3 Foundation Decide which data to collect to answer a question. Plan how to collect data. Calculate averages including,mode, median, mean & range. Interpret graphs, tables & charts. Construct stem & leaf diagrams. Core Discuss primary & secondary data. Gather data from primary & secondary sources. Interpret Graphs & diagrams. Compare two or more distributions. Solve problems by breaking them down into smaller more manageable tasks. Data Mode Median Mean Range Tables Charts Stem & Leaf Primary Secondary Graphs Distributions Bias Extension Identify sources of bias.

25 Statistics 3 Continued Extension Continued Identify what extra information might be needed. Find the median & quartiles for large data sets. Construct on paper & using ICT frequency polygons. Understand line of best fit. Analyse data to find patterns. Median Quartiles Frequency Polygon Inter-quartile Range Line of best fit

26 Statistics 4 Recap of all probability work covered throughout the year. Amend any misconceptions that might occur. Can extend students where necessary.