sets r = recap level 3-5; c = core 6 (bold); e = extension ... · pdf filecalculate interior...

14
Sets 4 & 5 R = Recap level 3-5; C = Core level 6 (bold); E = Extension level 7 (italics) Teacher support material available here: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm Y10 & 11 Foundation GCSE SOW Date Topic Notes Examples Reference GCSE Rayner (Foundation) Resources Done 23 rd Jun – 23 rd Jul Change of timetable. 1. INDICES: STANDARD FORM R: Multiplication and division Factors C: Squares, cubes; square roots, and cube roots Prime factors E: Index notation E: Standard form Knowing tables up to 10 x 10 Positive integers only Positive integer powers only With and without calculator including negative indices What is 5 5? How many 6's in 48? Find the factors of 20. Find 3 2 , 2 3 , √25 ; √49 2 ; √64 3 Find HCF of 216 and 240 Simplify a 5 a 3 ; m 4 m 2 Evaluate 2.762 10 12 4.97 10 21 (cal.) Evaluate 2.8 10 4 7 10 6 (no cal.) Evaluate 2.8 10 4 7 10 6 (no cal.) P16-17 ( & P40-43 (powers & roots) P5-9 (HCF etc.) There is teacher support material for each unit, including teaching notes, mental tests, practice book answers, lesson plans, revision tests & activities. The teacher support material is available online Clip 44 Factors, Multiples and Primes Clip 95 Product of Prime Factors Clip 96 HCF & LCM Clip 99 Four rules of Negatives Clip 45 Evaluate Powers Clip 46 Squares, Cubes & Roots Clip 135 Standard Form Calculations NRICH activities: 23 rd Jul – 31 st Aug SUMMER HOLIDAYS 1 st September (Y10) 2. FORMULAE: ALGEBRAIC FRACTIONS R: Evaluate simple formulae Find with positive integers C: Construct & use simple formulae E: Substitution of any number into simple formulae With & without a calculator Find A = l b when l = 3, b = 5. Find the perimeter of this rectangle given n = 5 Given q 2, v 21, find the value of v 2 q 2 . P65-70 (formulae) P83-85 (substitution) NRICH activities October (Y10) 3. ANGLE GEOMETRY R: Drawing and measuring angles with a protractor Line and rotational symmetry of 2-D objects C: Angle properties of straight lines, points, triangles, quadrilaterals, parallel lines Up to 360 o Use standard convention for labelling sides & angles of polygons Find all the lines of symmetry of a square P108-109 (draw & measure angles) P129-131 (symmetry) P110-116 (angles) Clip 67 Alternate angles Clip 68 Angle sum of a Triangle Clip 69 Properties of Special Triangles Clip 70 Angles of Regular Polygons NRICH activities Clip 150 Circle theorems

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Page 1: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

Sets 4 & 5

R = Recap level 3-5; C = Core level 6 (bold); E = Extension level 7 (italics) Teacher support material available here: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Y10 & 11 Foundation GCSE SOW

Date Topic Notes Examples

Reference GCSE Rayner (Foundation) Resources

Done 23rd Jun – 23rd Jul Change of timetable.

1. INDICES: STANDARD

FORM

R: Multiplication and division Factors

C: Squares, cubes; square roots, and

cube roots

Prime factors

E: Index notation

E: Standard form

Knowing tables up to 10 x 10

Positive integers only

Positive integer powers only

With and without calculator

including negative indices

What is 5 5? How many 6's in 48?

Find the factors of 20.

Find 32 , 23, √25; √492

; √643

Find HCF of 216 and 240

Simplify a5 a3; m4 m2

Evaluate 2.762 1012 4.97 1021(cal.)

Evaluate 2.8 104 7 106 (no cal.)

Evaluate 2.8 104 7 106 (no cal.)

P16-17 ( & P40-43 (powers & roots) P5-9 (HCF etc.)

There is teacher support material for

each unit, including teaching notes, mental tests, practice book answers,

lesson plans, revision tests & activities.

The teacher support material is available online

Clip 44 Factors, Multiples and Primes

Clip 95 Product of Prime Factors

Clip 96 HCF & LCM

Clip 99 Four rules of Negatives

Clip 45 Evaluate Powers

Clip 46 Squares, Cubes & Roots

Clip 135 Standard Form Calculations

NRICH activities:

23rd Jul – 31st Aug

SUMMER HOLIDAYS

1st September (Y10)

2. FORMULAE: ALGEBRAIC

FRACTIONS

R: Evaluate simple formulae Find with positive integers

C: Construct & use simple formulae

E: Substitution of any number into simple

formulae

With & without a calculator

Find A = l b when l = 3, b = 5.

Find the perimeter of this rectangle given n = 5

Given q – 2, v 21, find the value of √v2 q2.

P65-70 (formulae) P83-85 (substitution)

NRICH activities

October (Y10)

3. ANGLE GEOMETRY

R: Drawing and measuring angles with a

protractor

Line and rotational symmetry of 2-D

objects

C: Angle properties of straight lines,

points, triangles, quadrilaterals,

parallel lines

Up to 360o

Use standard convention for

labelling sides & angles of

polygons

Find all the lines of symmetry of a square

P108-109 (draw & measure angles) P129-131 (symmetry) P110-116 (angles)

Clip 67 Alternate angles

Clip 68 Angle sum of a Triangle

Clip 69 Properties of Special Triangles

Clip 70 Angles of Regular Polygons NRICH activities

Clip 150 Circle theorems

Page 2: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

E: Angle symmetry & properties of polygons

Symmetry properties of 3-D shapes

Compass bearings

C: Basic Circle Theorems

Angle in a semi-circle

Radius is perpendicular to the tangent

Radius is perpendicular bisector of

chord

E: Angles in the same segment are equal

Angle at the centre is twice the angle

at the circumference. Opposite angles of a cyclic-

quadrilateral add up to 180 .

Include line and rotational symmetry. Easier to calculate

the exterior angle 1st

Include plane, axis and point

Symmetry

8 compass points and 3 figure

bearings

Calculate interior angle of a regular octagon/decagon

Describe fully the symmetries of this shape.

Scale drawings of 2-stage journeys

Calculate angles: BDA, BOD, BAD & DBO

Higher Rayners Ex23-25 p337-343 (circle theorems)

28TH Oct – 1st Nov

OCTOBER HALF TERM

November (Y10)

4. PYTHAGORAS THEOREM &

TRIGONOMETRY

R: Classification of triangles

Area of squares

C: Pythagoras Theorem

Isosceles, equilateral, scalene,

right-angled

Whole numbers only 2D only

Find the area of a square of side 4 cm.

Find x

P356 (Pythagoras)

NRICH activities:

Clip XX Pythagoras

Page 3: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

E: Trigonometry (sin, cos, tan)

Know the exact values of sin, cos and tan

at key angles

Angles of elevation and

depression

Bearings

2-D with right-angled triangles

only SOH – CAH - TOA

Ship goes from A to B on a bearing 040for 20 km. How far north has it travelled?

What are sin, cos and tan (0, 30, 45, 60, 90 degrees)?

Higher Rayner: Ex6-7 p294 (finding the length) Ex8 p297 (finding angles)

Clip 147 Trigonometry

December (Y10)

5. PROBABILITY

R: Basic probability; practical

probability Probability scale

C: Simple probability

Complimentary events

Listing combined outcomes of two

events

E: Relative frequency experimental

probability and expected results

Appropriate methods of determining

probabilities

Probability of 2 events

Multiplication law for independent

events

E: Conditional probability; dependent

events

E: Sets & Venn Diagrams Enumerate sets and combinations of sets

systematically, using tables, grids, Venn

diagrams and tree diagrams." "Calculate and interpret conditional

probabilities through representation

Using coins, dice, cards, etc.

Likely and unlikely events

pi 1; p p1

Use tree diagrams/ possibility

space diagram to find all possible outcomes

Using symmetry/experiment

Tree diagrams (Tree diagrams

could be introduced first)

By listing, tabulation or tree

diagrams

Sampling with replacement

Using Venn diagrams

If you toss a coin 100 times, how many heads would you expect?

pheads on fair coin1

2

If prain tomorrow2

3, what is pdry tomorrow?

Complete a possibility space diagram for the sum on two dice.

What is the probability of scoring a total of 7?

Do an experiment to find probability of drawing pin landing point up.

If p(rain) =2

3, then we would expect

2

3× 30 = 20 sunny days out of 30.

Probabilities from a deck of cards: pace4

52 =

1

31 (NB: not all children familiar

with cards – cultural/religious reasons)

There are 5 green, 3 red and 2 white balls in a bag. What is the probability of

obtaining: (a) a green ball (b) a red ball (c) a non-white ball?

Find the probability of obtaining a head on a coin and a 6 on a dice.

Examples of what pupils should know and be able to do for Venn

Diagrams:

Enumerate sets and unions /intersections of sets systematically, using tables, grids and Venn Diagrams. Very simple Venn diagrams previously KS2 content.

P422 (probability) MEP Examples P430 (sample space)

Unit 5 Teachers Notes MEP Textbook NRICH activities Sociable Cards Non-transitive Dice At Least One… Interactive Spinners What Does Random Look Like? Odds and Evens* In a Box

Clip 90 List Of Outcomes (Grade D)

Clip 132 Experimental Probabilities

(Grade C)

Clip 154 Tree Diagrams (Grade B)

Sumbook Foundation p56-59

Resources for Venn Diagrams

Page 4: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

using expected frequencies with two-way

tables, tree diagrams and Venn diagrams Investigate – Venn Diagrams:

ξ = {numbers from 1- 15}; A = {odd numbers}; B = {multiples of 3} and C = {square numbers}

(a) Draw a Venn diagram to show sets A, B & C. You’ll need 3 circles

(b) Which elements go in the overlap of

A & B

A & C

B & C

A, B & C

(c) Try and come up with three different sets where not all of the

circles overlap. How many different Venn diagrams with three

circles that overlap in different ways can you find?

Example:

X is the set of students who enjoy science fiction Y is the set of students who enjoy comedy films The Venn diagrams shows the number of students in each set, work out:

(i) P(X ∩ Y) (ii) P(X U Y)

20th Dec – 3rd Jan

CHRISTMAS HOLIDAYS

5th January (Y10)

6. NUMBER SYSTEM

R: Everyday examples of , , , Extend place value to decimals

Number system

Money

+, –, , whole numbers including long

multiplication and division

Multiplying and dividing by powers of 10

C: Rounding off

Including 1

10;

1

100; etc

Coins; changing between pence

and pounds; notation, e.g.

£1.27 not £1.27p

Without the use of a calculator

Decimal places and significant figures

Cost of 15 pens at 8p each

Next number in sequence 0.2, 0.4, 0.6, ...

Change 127 p to £s.

127 23, 465 15

25.62 100, 216.2 10, 14 0.2

1

7 to 2 d.p.; 39.96 to 3 s.f.

P206 (number system) P255 (rounding)

NRICH activities

Page 5: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

+, –, , decimals

E: Estimating answers

Use of brackets on a calculator

E: Irrational / rational numbers

Surds

Alt. use ( ) button on calculator

if available

9.7 3.86; £3.36 7; £114.81 3 29.4 + 61.2

14.8 ≈

30 + 60

15 ≈ 6

2.5 × 14.3

7.8 + 2.95≈ 3.32558 (𝑡𝑜 5. 𝑑. 𝑝)

Give examples of irrational numbers between 5 and 6. Discuss the 2 Set-squares (side lengths: 1,1,√2 and 1, √3, 2)

Show that (i) 0.0̇9̇ (ii) 0.16̇ are rational.

P257 (estimation) Higher Rayners: Ex3 p357 (surds)

Clip 101 Estimating (grade C)

Clip 157 Surds (A)

16th – 21st Feb

FEBRUARY HALF TERM

23rd February (Y10)

7. MENSURATION

R: Making 3-D shapes given nets

Using measuring instruments

and appropriate units

Appropriate degree of accuracy

Reading and interpreting scales

Area

C: Constructing nets of cuboids,

prisms, tetrahedrons

Appropriate degree of accuracy

Conversion of units

Volume/capacity problems

Draw and measure angles accurately

100 cm = 1 m, etc.

Rounding sensibly for the range of measures used and the

context

Estimating areas

Nets can be used (see below)

for surface areas and volumes.

Rounding sensibly for the

range of measures used and the

context

Familiarity with mm, cm, m, km, g, kg, tonne; inches, feet,

yards, miles, oz, lb, stones, litres, gallons

Include compound measures

such as density.

Draw a net of a cuboid 5 cm by 3 cm by 2 cm.

How many mm in 2.763 m?

Weighing a parcel to decide the postage

Find the area of the shaded shape

Which of these is the net of a cuboid?

A gallon is about 41

2 litres. How many litres will an 8 gallon petrol tank hold?

P122 (nets) P399 (converting units) P140 (area) P399 (converting units)

NRICH activities

Clip 124 metric units

Clip 71 & 72 Circles

Clip 73 Area of compound shapes

Clip 120 & 121 surface area

Clip 122 & 177 Volume

Clip 126 compound measures

Page 6: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

Area and perimeter of squares,

rectangles, Triangles; Volumes of

cubes and cuboids

Area/ circumference of circles

Volumes of triangular prisms and

cylinders

E: 2-D representations of 3-D objects

Difference between discrete &

continuous measures

Areas of parallelograms, trapezia, kites, rhombuses and composite shapes

Volumes of prisms and composite

Solids. Surface area of simple solids: cubes, cuboids, cylinders

Length of circular arc, areas of sectors and segments of a circle

Volume/capacity problems

Simple upper and lower bounds

These must be known 'by

heart'

A r2 , C D

V = Area of cross-section

length

V r2h

Use of isometric paper

To include estimation of

measures

Area of cross-section length

of prism

Include compound measures

such as density & pressure

Find the volume of this given base = 3cm, height =4cm & length = 12cm Estimate the volume in a can of coke.

Given the plan and side elevation, draw a 3D isometric diagram of the object.

Illustrate current postal rates; shoe sizes

Find the area of this kite.

Calculate the shaded area given a = 5

Use Pressure, P = Force ÷ Area and density = mass ÷ volume

h 8 m 7.5 h < 8.5

P328 (circles)

28th March – 12th April

EASTER HOLIDAYS

13th April (Y11)

8. DATA HANDLING

R: Two-way tables including timetables

and mileage charts

Interpreting and constructing

pictograms and bar charts

12 hour and 24 hour clock

Discrete data only

16.27 4.27 pm

If a train arrives at a station at 13:26 and the connection leaves at 14:12, how long do you have to wait?

Unit 8 MEP P374 (2 way tables)

Unit 8 Teachers notes

Unit 8 MEP Text

Clip 85 Two-Way Tables Grade D

Clip 86 Pie Charts (Grade D)

Clip 88 Frequency Diagrams (Grade D)

Page 7: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

C: Interpreting and constructing pie

charts and line graphs

Questionnaires and surveys

C: Frequency graphs

Calculation of angles (total

frequency a factor or multiple

of 360)

Fairness & bias

For grouped data; equal

intervals. Include frequency

polygons and Histograms

2160 trees are planted. How many are oak?

P185 (pie charts) P381 (questionnaires)

Clip 89 Stem-and-Leaf Diagrams

(Grade D)

Clip 84 Questionnaires and Data

Collection (Grade D)

Clip 134 Designing a good

Questionnaire (Grade C)

9. DATA ANALYSIS

R: Mean, mode, median, range for discrete data

C: Mean for discrete data and tally

charts

E: Problems involving the mean

Mean, median, modal class for grouped data

Including discrete and

continuous data

Find mean, mode, median and range for these golf scores at a particular hole: 2, 4, 5, 4, 3, 5, 4, 4, 3, 5, 4

Find the mean number of goals on these games.

No of goals 0 1 2 3 4 5 6+ Frequency 2 4 5 3 0 1 0

The mean of 6 numbers is 12.3. When an extra number is added, the mean changes

to 11.9. What is the extra number?

Unit 9 MEP P173 (averages) P191 (tally charts)

Unit 9 Teachers notes NRICH activities M, M and M Searching for Mean(ing) Litov's Mean Value Theorem

Clip 133 Averages From a Table (Grade

C)

May END OF YEAR 10 EXAMS This will be used to help set for Y11

23rd May – 30th Jun

MAY HALF TERM

1st June

10. EQUATIONS

R: Negative numbers (number lines) in

context

Ordering directed numbers

+, –, , directed numbers

C: Simplifying expressions

Manipulating and solving

Simple linear equations

Linear equations

E: Trial and improvement methods

Expansion of brackets

Factorisation of functions

Temperature problems

Use a number line

One fraction and/or one bracket

Algebraic solutions

Common terms, difference of

two squares

6o 4o

?

-8, -5, …, …, …, 7, … ; order: -7, -7.7, -7.5, -8, -7.79, 7 smallest to biggest

5 4 ? 54 ? (-5) (-7) =?

2a 3b a 2b ?

Expand 2 a 6?

Solve x 3 7; x 5 10; 3x 15

Solve 2x 3 7; 3x 4 x 18

Solve for x to 2 d.p. x3 7x 6 20 using trial & Improvement

Multiply out 2r 3s2r 5s)

Factorise (i) x2 1 (ii) x2 x

P65 (simplifying) P71 (equations)

NRICH activities

Clip 105 Solving Equations

Clip 106 Forming Equations

Clip 140 Solving Quadratic Eqs by

Factorising

Clip 141 Difference of Two Squares

Clip 142 Simultaneous Linear Equations

Page 8: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

Solve quadratic equations by factorising

E: Simultaneous linear equations

Algebraic solutions inc.

deriving from real-life

situations

Solve (i) x2 1 (ii) x2 x

Solve: x 4y 7 and x + 2y = 16; Solve 2x y 5 and x 4y 7

11. FRACTIONS and

PERCENTAGES

R: Conversion between fractions,

decimals and percentages

Finding simple fractions and

percentages of quantities

C: Expressing quantities as a

percentage or a fraction

Finding fractions and percentages

of quantities

E: Percentage and fractional changes

Manipulating fractions

E: Compound interest

Appreciation and depreciation

Reverse percentage problems

Know common equivalents

1

4;

1

2;

3

4;

1

3 ;

2

3 ; 10%

Discount, VAT, commission

, , , with or without a

calculator

0.5 = 1

2= 50%

1

4 of 20, 10% of £50, 20% of 10 kg

30 out of 50; 17 out of 20 =

3

8 of 72 ? 13% of £97 =

20% VAT on hotel bill of £200?

1

2 +

1

3 ;

3

8 ×

1

3 ;

1

2 ÷

1

8

A car costs £5,000. It depreciates at a rate of 5% per annum. What is its value after 3

years?

The price of a television is £79.90 including 17.5% VAT. What would have been the price with no VAT?

P210 (converting from FDP) P394 (fraction of an amount)

NRICH activities

Clip 47 Equivalent Fractions

Clip 48 Simplification of Fractions

Clip 49 Ordering Fractions

Clip 55 Find a Fraction of an Amount

Clip 56 & 57 arithmetic with Fractions

Clip 58 Changing Fractions to Decimals

Clip 139 Four Rules of Fractions

Clip 51 & 52 % of Amount

Clip 53 & 54 Change to a %

Clip 92 Overview of %

Clip 93 & 136 Increase/dec. by a %

Clip 137 Compound Interest

Clip 138 Reverse %

Jun 24th

START OF NEW TIMETABLE START OF YEAR 11

Year 10 become Year 11

June

12. NUMBER PATTERNS and

SEQUENCES

R: Simple number patterns

C: Recognise and continue number

patterns

E: Find the formula for the nth term of a

linear sequence.

Odd / even / multiple Explain the pattern in words If numbers ascend in 3’s, that’s the 3 x table = 3n.

1, 3, 5, 7, ..., ... ; 3, 6, 9, 12. ..., ...

Fibonacci – 1, 1, 2, 3, 5, ..., ... ; 1, 4, 7, 10, ..., ...

For sequence, the number of sides is 4, 7, 10,

...,.... How many sides in the 100th pattern?

Find the n th term for the sequence 8, 11, 14, 17, ..., ..., ...

P84 (number patterns) P90 (nth term)

NRICH activities

Clip 65 Generate a Sequence from Nth

term

Clip 112 Finding the nth term

Page 9: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

Recognise & use sequences of triangular,

square, cube, Fibonacci, quadratic & geometric sequences

Then find the number before the 1st term (=5), so, nth term is 3n+5

List (i) 12 – 162 (ii) 13 – 53 (iii) the 1st 10 triangular numbers

Continue the sequence: 1, 1, 2, 3 …

Continue the sequence: 1, 2, 4…

13. GRAPHS

R: Coordinates

C: Coordinates

Plotting straight lines and curves given

values

C: Equation of straight line

E: Graphs in context, including

conversion and travel graphs (s – t and v – t) and an understanding of speed as a

compound unit

Scatter graphs and lines of best fit

Draw & recognise Graphs of common

functions

Graphical solution of simultaneous

equations

First quadrant only

4 quadrants; directed numbers

Use y = mx + c to identify parallel lines

Draw and interpret

Gradient and area under graph

a for polygon graphs only

Quadratic, cubic, reciprocal and exponential equations

Plot the points (3,2, (4,0) and (0,1).

Identify coordinates of points in the xy-plane.

Plot graph for values x –3 –2 –1 0 1 2 3 y 9 4 1 0 1 4 9

Find equation of straight line joining points (1, 2) and (4, 11).

Find equation of straight line going through points (1, 3) and gradient 4. Which lines are parallel? y = 3x = 1, 2y = 6x – 8, -3x + y = 7 etc.

Calculate the speed for each part of the journey

Name the type of correlations illustrated below

Solve graphically: (i) y = x + 5 and y = 7 – x (ii) x + y = 4and 2x + y = 10

P104 (coordinates) P289 (straight line graphs) P301 (curves) Higher Rayners: Ex21 p126 Ex23 p129 Q1-4 (straight line graphs) Ex 24 p131 (y = mx + c) Ex23 p129 Q5-8 (gradients)

NRICH activities

Clip 113 Drawing straight line graphs

Clip 116 Drawing Quadratic Graphs

Clip 114 Finding the Equation of a

straight line

Clip 143 Understanding y=mx+c

Clip 117 Real-life Graphs

Clip 87 Scatter Graphs (Grade D)

Clip 145 Graphs of Cubes & Reciprocal

Functions

July

SUMMER HOLIDAYS

Year 11

Page 10: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

September (Y11)

14. LOCI & TRANSFORMATIONS:

CONGRUENCE and SIMILARITY

R: Line and rotational symmetry

Drawing shapes to correct size

C: Scale drawings

Construction using protractor

and compasses

Simple enlargements and

reflections

E: Constructions of loci

Enlargements

Reflections

Rotations

Translation

Similarity – similar triangle & shapes

Notation 1 : 200, etc.

Triangle and other shapes

Positive integers scale factors

About point(s) and line(s)

Positive integers and simple

fractions for scale factor

Reflect lines in oblique lines

Describe the mirror line using simple equations

Rotation about any point 90o , 180o in a given direction

Finding the centre of rotation

by inspection.

Using vector notation Internal line ratio (BE:CD = 3:5) Draw 2 separate triangles and

find scale factor/multiplier (= 5

3)

Find rotational symmetry of a ; ; pentagon, isosceles triangle

Make scale drawing of garden or playground

Construct a triangle ABC, AB = 10cm, AC = 7cm and BC = 6.5cm using compasses

Construct the locus of points equidistant from both lines

Enlarge diagram by scale factor 1

3 , centre A (inside triangle)

Find the Equations of the mirror lines and reflect the shape in the

line y = 0, y = -3, y = x

Draw image after translation (−32

)

Calculate (i) x and y (ii) ratio of areas

ABE and BCDE

P129 (symmetry) P346 (scale drawings) P119 – 125 (constructions) P352 (loci) P127 & p318 (enlargements) P311 (reflection0 P314 (rotation) P325 (translations) Higher Rayner: Ex29-30 p227 (lengths & similarity)

NRICH activities Decoding, Combining, and simplifying transformations (3 lessons needed)

Clip 127 bisecting a line

Clip 128 perpendicular to a line

Clip 129 bisecting an angle

Clip 130 Loci

Clip 74-77 Transformation

Clip 149 Similar Shapes

Clip 179 Congruent Triangles ICT lesson Combining Transformations: Play ‘TranStar’ http://www.mangahigh.com/en_gb/games/

Page 11: Sets R = Recap level 3-5; C = Core 6 (bold); E = Extension ... · PDF fileCalculate interior angle of a regular octagon/decagon Describe fully the symmetries of this shape. ... height

Congruence – conditions for triangles

Use the criteria to prove

congruence: SSS SAS AAS

RHS

Prove that ▲ABX & ▲CDX are congruent

Higher Rayner: Ex6 p169 (congruence)

(Y11)

OCTOBER HALF TERM

November (Y11)

15. VARIATION: RATIO &

PROPORTION

R: Simple ratios

Equivalent ratios and fractions

C: Unitary ratios; direct and inverse

variation

Map scales / ratios

Proportional division

E: Direct and inverse variation

E: Functional representation

Graphical representation

Recipes Mixed units

Mathswatch Clip 159 leads into this topic in a very easy way

y x , y x2 , y x3 ,

y 1

𝑥; y

1

𝑥2

If the teacher/pupil ratio is 1:20, and there are 15 teachers, how many pupils are

there? 5:15 1:3

If 5 books cost £15, what is the cost of 8 books? If 8 people take 3 days to paint some railings, how long would 6 people take?

e.g. 1:20 00; 1 cm to 2 km If the map scale is 1:250 000, what is the actual distance between two churches 3 cm

apart on

the map?

Share £30 in the ratio 2:3.

For the following data, is y proportional to x? x 3 4 5 6

y 8 10 12 14

If y is proportional to the square of x and y 9 when x 4, find the positive value of

x for which y 25.

P234 (ratio) P238 (maps) P242 (proportion) Higher Rayners: Ex12-13 p263-267 P267-269 (common curves to discuss)

NRICH activities Ratio problem 23 from UKMT

Clip 159 Direct & Inverse Proportion

November (Y11)

MOCK EXAMINATIONS

1ST Round of MOCKS

December (Y11)

16. INEQUALITIES

R: Simple inequalities using a number line

C: Solution of inequalities on a number

line

E: Solution of linear inequalities and

simple quadratic inequalities

Notation: or , < or >,

● or ○

Mark on a number line x 5, x 2

List whole numbers n which satisfy 4 n 2 List whole numbers n which satisfy

Solve for x: (a) 5x 2 x 16 (b) x2 25

P283 (inequalities)

NRICH activities

Clip 108 Inequalities

Clip 109 Solving Inequalities

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January (Y11)

17. VECTORS

C: Vectors and scalars

Sum and difference of vectors

Resultant vectors

Components

Multiplication of a vector by a

scalar

Applications of vector methods to 2-

dimensional geometry

Vector notation

(𝑎𝑏), 𝐴𝐵⃗⃗⃗⃗ ⃗ or a

A plane is flying at 80 m/s on a heading of 030However, a wind of 15 m/s is

blowing from the west. Determine the actual velocity (speed and bearing) of the

plane.

𝑂𝐴⃗⃗⃗⃗ ⃗ = a and 𝐴𝐵⃗⃗⃗⃗ ⃗ = b

Write down, in terms of a and b,

(i) 𝑂𝐵⃗⃗ ⃗⃗ ⃗, (ii) 𝑂𝐶⃗⃗⃗⃗ ⃗, (iii) 𝐴𝐶⃗⃗⃗⃗ ⃗, (iv) 𝐶𝐵⃗⃗⃗⃗ ⃗

Rayners Higher: Ex15 p317 (addition & scalar multiplication)

See Heinemann Mechanics 1 Chapter 1_LiveText for examples

Clip 180 Vecors

December (Y11)

CHRISTMAS HOLIDAYS

January (Y11)

REVISION

Linear (A) Past paper booklets to be prepared in-house. Revision Workbooks to be ordered (payment to be collected beforehand) Intervention to be organised by teachers.

Review the entire SOW again from the beginning of Year 10!

P454 – 466 (revision)

Foundation Revision Workbooks (to buy in from Pearson)

February

FEBRUARY HALF TERM

March of Y11 2ND MOCK

2 papers in the hall This decides which students need intervention

March – May (Y11)

REVISION & INTERVENTION

With emphasis on p49, p260 & p405

Review the entire SOW again! Use the Test yourself exercises at the end of each chapter

P454 – 466 (revision)

Foundation Revision Workbooks (to buy in from Pearson)

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NOTES FOR THE TEACHER

There is teacher support material for each unit, including teaching notes, mental tests, practice book answers, lesson plans, revision tests, overhead slides and additional activities. The teacher support material is only

available online.

Resources: Teacher support material for each unit, inc. teaching notes, mental tests, answers, lesson plans, revision tests and additional

activities is available online on the MEP website: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Homework: a variety of tasks can be set ranging from short Q&A to extended pieces of investigation work. When you set homework – you

MUST mark it and record it. You could also ask students to make summary notes of each topic to lay foundations for independent study.

Fronter has been loaded with a wealth of homework practice which students should be directed to by you.

Lesson planning & Expectations: You are expected to have extremely high expectations of all you students at all times – refer to the

diagram

Closing the Gap: Know your students, Plan effectively, Enthuse & Inspire, Engage & Guide, Feedback appropriately & Evaluate together

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FORMULAE SHEET

Perimeter, area, surface area and volume formulae

Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone:

Curved surface area of a cone = rl

Surface area of a sphere = 4 r 2

Volume of a sphere = 3

4 r 3

Volume of a cone = 3

1 r 2h

Kinematics formulae

Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken:

v = u + at s = ut + 21 at2 v2 = u2 + 2as