Foundation. Scheme of Work. Year 9. September 2016 to July 2017

Transcription

1 Foundation Scheme of Work Year 9 September 06 to July 07

2 Assessments Students will be assessed by completing two tests (topic) each Half Term. These are to be recorded on Go Schools. There will not be fixed dates for these. Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan

3 NUMBER Understand and order integers: Write numbers in words and writing numbers from words: Add and subtract integers: Recall all multiplication facts to 0 0, and use them to derive quickly the corresponding division facts: Round to any numbers of significant figures. Rounding to decimal places Multiply or divide any number by powers of 0: Multiply and divide integers: Add, subtract, multiply and divide negative numbers: Round whole numbers to the nearest: 0, 00, 000, : Recognise even and odd numbers Identify factors, multiples and prime numbers Find the prime factor decomposition of positive integers Find the common factors and common multiples of two or three numbers Find the Lowest common multiple (LCM) and Highest common factor (HCF) of two numbers Recall integer squares up to 5 5 and the corresponding square root Recall the cubes of,,, 5 and 0 Find squares and cubes Find square roots and cube roots / / /0 6 /68a/68b /79/

4 ANGLES Measure and draw lines, to the nearest mm Measure and draw angles, to the nearest degree 6 Estimate sizes of angles Recall and use properties of angles: at a point angles at a point on a straight line, including right angles vertically opposite angles Find the size of missing angles at a point or at a point on a straight line Distinguish between acute, obtuse, reflex and right angles Name angles Give reasons for calculations Use geometric language appropriately Identify points, lines and angles Use two letter notation for a line and three letter notation for an angle Distinguish between scalene, equilateral, isosceles and right-angled triangles Understand and use the angle properties of triangles Find a missing angle in a triangle, using the angle sum of a triangle is 80º Use the side/angle properties of isosceles and equilateral triangles Understand and use the angle sum of triangles /

5 COLLECTING AND RECORDING DATA Design and use data-collection sheets for grouped, discrete and continuous data Collect data using various methods Sort, classify and tabulate data and discrete or continuous quantitative data Group discrete and continuous data into class intervals of equal width Extract data from lists and tables Design and use two-way tables for discrete and grouped data Use information provided to complete a two way table AVERAGES AND RANGE Calculate the Mean, Mode and Median from a set of data Calculate the Range from a set of data 6 6 PERCENTAGES Calculate the Percentage of a quantity (Calculator and non-calculator) 86/87 ASSESSMENTS /

6 ALGEBRA Indices Laws Introduction to indices Working with indices Index notation Multiply and divide with variables and numbers using index laws Use notation and symbols correctly Write an expression Simplify algebraic expressions in one or more like terms, by adding and subtracting Understand the difference between the word equation, formula, and expression and identity Multiply a single algebraic term over a bracket Substitution Multiply a single algebraic term over a bracket(two brackets) and simplify Expand double brackets Factorise algebraic expressions by taking out common factors 9 8 /5 7 7,5,5 9,a/b 95 a b 9 ALGEBRA Be able to write simple equations Solve Equations with one operation Solve Equations with two operations Solve equations with letters on both sides 5 5 5

7 DECIMALS 9 and ROUNDING Manipulating Decimals /Use inverse operations (use one calculation to find the answer to another): Check calculations by rounding, eg 9 0 0: Check answers by reverse calculation, eg if 9 = 07 then 07 9 = Understand place value, identifying the values of the digits: Write decimals in ascending order of size: Write decimals to a given number of decimal places / significant figures: Estimating answers Add and subtract decimals: Multiply and divide decimal numbers by integers and decimal numbers: Know that, eg = 5 5 / / /9 0/90 9 7/8 66/67 STANDARD FORM All applications 8

8 TWO DIMENSIONAL SHAPE Recognise triangles and quadrilaterals and their properties Identify shapes which are congruent Identify shapes which are similar, including all circles or all regular polygons with equal number of sides(extra RESOURCES NEEDED) Identify and name parts of a circle Draw a circle when given its radius of diameter Recognise reflection symmetry of -D shapes Identify and draw lines of symmetry on a shape Recognise rotation symmetry of -D shapes Identify the order of rotational symmetry of a -D shape Draw or complete diagrams with a given number of lines of symmetry Draw or complete diagrams with a given order of rotational symmetry Use congruence criteria for triangles. SSS SAS ASA RHS Make accurate drawing of triangles and other -D shapes using a ruler and a protractor Use straight edge and a pair of compasses to do standard constructions such as Construct a triangle Construct an equilateral triangle Understand, from the experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not Construct the perpendicular bisector of a given line Construct the perpendicular from a point to a line Construct the bisector of a given angle Construct angles of 60º, 90º, 0º, 5º Draw parallel lines Construct diagrams of everyday -D situations involving rectangles, triangles, perpendicular and parallel lines / 9 0/ a/b 5

9 ASSESSMENTS / ANGLES Understand and use the angle properties of quadrilaterals Use the fact that angle sum of a quadrilateral is 60º Give reasons for angle calculations. Use geometrical language appropriately to name and recognise regular polygons. 0 Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles Know that the sum of the exterior angles of any polygon is 60 Calculate the size of each exterior/interior angle of a regular polygon Recall and use properties of perpendicular lines Mark perpendicular lines on a diagram Mark parallel lines on a diagram Understand and use the angle properties of parallel lines Find missing angles using properties of corresponding and alternate angles Understand the proof that the angle sum of a triangle is 80 Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices 0 0 Understand tessellations of regular and irregular polygons Tessellate combinations of polygons Explain why some shapes tessellate and why other shapes do not

10 FRACTIONS Visualise a fraction diagrammatically Understand a fraction as part of a whole Write a fraction in its simplest form and recognise equivalent fractions Compare the sizes of fractions using a common denominator 5/6 70 Write an improper fraction as a mixed number and vice versa Multiplying Fractions Find fractions of amounts Dividing Fractions Add and subtract fractions by using a common denominator Convert between fractions and decimals Reciprocals a/b 8 76 ALGEBRA Use index notation to write numbers Find the value of numbers using indices Use indices rules to simplify expressions Use brackets and the hierarchy of operations (BIDMAS): ASSESSMENTS 5/6

11 CALCULATOR SKILLS Convert between fractions and decimals and recognise recurring decimals. Understand reciprocals Calculate answers with powers and routes Calculate answers with complex calculations MEASURE Interpret scales on a range of measuring instruments. Indicate given values on a scale Read transport timetables and plan journeys Calculate the difference in times Convert between hour and hour clock times 6b Know that measurements using real numbers depend upon the choice of unit Convert units within one system Convert metric units to metric units (Metric equivalents should be known) Use the relationship between distance, speed and time to solve problems Use the relationship of density, mass, volume and pressure to solve problems Introduction to bounds Standard errors 5 55

12 PROCESSING, REPRESENTING AND INTERPRETING DATA Draw: o Pictograms o Composite bar charts o Comparative and dual bar charts o Vertical Line Charts o Histograms with equal class intervals o Frequency diagrams for grouped discrete data o Line graphs o Time Series Graph o Scatter Graphs Interpret: o composite bar charts o comparative and dual bar charts o scatter graphs o Time Series Graph From pictograms, bar charts, line graphs and histograms with equal class intervals etc. o read off frequency values o calculate total population o find greatest and least values Recognise simple patterns and characteristic relationships in bar charts, line graphs etc. Use dual or comparative bar charts to compare distributions Represent data in a pie chart o Interpret data in a pie chart o Understand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie charts From pie charts o find the total frequency o find the size of each category 8

13 SEQUENCES Generate a term to term sequence and recognise the rule Find the missing numbers in a number pattern or sequence Generate a sequence from the n th term Find the n th term of a number sequence Find whether a number is part of a given sequence Continue a sequence derived from diagrams Use a calculator to produce a sequence of numbers Recognise and use sequences of triangular, square and cube numbers Recognise Fibonacci type sequences Recognise quadratic sequences and geometric sequences, ASSESSMENTS 7/8 PERIMETER AND AREA OF D SHAPE Find the perimeter of rectangles, triangles and compound shapes Find the area of a : o Rectangle o Triangle o Parallelogram o Trapezium Calculate areas of compound shapes made from triangles and rectangles Solve a range of problems involving areas including cost of carpet type questions

14 GRAPHS Use axes and coordinates to specify points in all four quadrants in -D: Identify points with given coordinates: 8 8 Find the coordinates of the midpoint of a line segment. Draw and name horizontal and vertical lines on graphs. Recognise that equations of the form y = mx + c correspond to straightline graphs. Plot and draw graphs of straight lines of the form y = mx + c using a table of values Plot and draw straight line graphs of the form y = mx + c without a table of values Use y=mx +c to identify parallel lines Find the gradient of a straight line from a graph Find the equation of a line through two points or through one point with given gradient ASSESSMENTS 9/0

15 TRANSFORMATIONS 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 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 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 /5 50/

16 PROBABILITY Distinguish between events which are: impossible, unlikely, even, likely and certain to occur Mark events and/or probabilities on a scale of 0 to 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 Use - 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 Draw Venn diagrams Use and understand notation of Venn diagrams / / a 7b A Complete GCSE Paper (Old Style) Two papers.