STARTER:

MAIN ACTIVITY:

PLENARY:

Please refer to the enclosed grids, suggesting possible starter topics to be used in the first 5-10 minutes of each lesson.  These can provide an interactive start to the lesson when mental skills can be rehearsed, sharpened and developed and when vocabulary can be extended.  The document “10 minute starters – General Activites” provides a bank of useful ideas to dip into.  Items on display in the classroom can also help (number line, fact cards, puzzles, question cards, 1-100 square).  A set of vocabulary cards can be useful as a starter but also used with individuals in the main part.

Also dip into Mymaths “Games”, including Darts, Blockbusters, Weakest Link & Times it all out.

Use the content from the scheme with direct teaching input and pupil activities.

Summarise the lesson, distribute solutions and ask “What have you learned?”.  Is there some way that the pupils can be challenged with a question or activity that extends the ideas of the lesson?

Starters:

6. Fractions, decimals and percentages (calculations with and conversion between) WB/SH

7. Simplifying expressions (collection of like terms, removal of brackets, mult and div.) WB/SH Use powerpoint presentation “Simplifying Help” to go over all ideas

8. Negative numbers (this is the main cause of errors in later work, especially algebra) WB Also, www.mymaths.co.uk has substitution of negatives section useful as a starter

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Pythagoras’ theorem:

6. Using Pythagoras’ theorem (a²+b²=c² please) to find the lengths of missing sides in a right-angled triangle, including the hypotenuse: include questions where the answers can be left in “surd” form or which give surds as known lengths.

7. Learning of the main Pythagoras triples i.e. (3,4,5), (5, 12,13), (7,24,25), (8,15,17) and multiples of these.  Put in context e.g. which isosceles triangle has the biggest area … one with sides 5,5,6 or one with sides 5,5,8?

8. The converse of Pythagoras’ theorem: is a given triangle right-angled?

9. Applications of Pythagoras including finding the distance  between two coordinates (generalise to give Distance = √ [(x 2 -x 1 )² + (y 2 -y 1 )²]) and the length of a square given its diagonal.

Extension: pupils should deal with two stage problems and those in three dimensions, leaving intermediate answers as surds.

P189

P219

Rayner8 P189 Ex1, 2

“Wonky Squares” see MCA

Mymaths/ Games/ Millionaire

PPT – Pythagoras Visuals & Pythagoras Questions

Notice patterns in triples beginning with an odd shortest side i.e. 7,24,25 … the longer sides are consecutive and add to the square of the other side.

Converse

Hypotenuse

Surd

Triple

Techn: builders used triples to get corners at 90 ° in the past (X)

Distance travelled to disaster zones and cost of the project (C)

Starter:

6. Angles – all rules of angles (use rayner 8 P42 Ex1,2) SH

6. Probability – revision of simple ideas and sample space diagrams WB /RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Equations:

1. Use of starter/preceding homework to recap on one-sided and two sided equations such as:

          3(x-7) +3 = 15; 10x + 4 = 3x –2; 4(3-2x) = 7(2x +1)

Remember that one sided should be done by reading the algebra (I think of a number, …) and double-sided by firstly subtracting the smallest algebraic term off both sides to return to a one-sided equation.

2. Equations involving a single negative term e.g. 10 – 4x = 17 (link to above by imaging there is “0x” on the other side).

3. Equations involving fractions: recap on those requiring cross-multiplication (see end of year 7 scheme) and extend to ones where we need to multiply through by the denominator first e.g. 4/x + 10 = 5.

4. Solving problems involving equations

Extension idea: pupils make an equation crossword with integer solutions, involving all types of equations met to date.

P123-5

Rayner8 P129-134:

Framework maths Page 68-69

Board work

Rayner8 Ex7 P133-4

Framework maths Page 68-69

Framework maths Page 138-139

BBC website: “Equation Match” acts as nice recap; waldo site has equations, as does www.easymaths.com

No decimals – give answers as exact fractions.

Always subtract the smallest algebraic term from both sides so we arrive back at a one-sided equation that is easy to read as “I think of a number ..”

Balance(d)

Equation

Integer

Inverse

Term

Solve

Cross-multiply

Denominator

Link to balancing equations in Chemistry (X)

Trial & Improvement:

Solving equations other than linear ones by the method of trial and improvement (always remember to work to one more decimal place than the answered is required to).  Include approximation of roots. (Will be revisited in context in yr9 so focus on technique here)

P133-5

Cases of quad and cubic e.g. x³+x=110 (pick from Rayner9 P53 Ex3)

Use of a spreadsheet

SEE ICT booklet

PPT Trial & Improvement

Trial & Improvement

Cubic

Quadratic

Starter:

1. Substitution (NNS P139, 141) WB

2. Variety of mental/written calculations (Rayner 2 P67-72, 79-80) WB

3. Pythagoras’ theorem

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C./

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Negative Numbers: use of starters to recap on non-calculator manipulation of negative numbers including squaring and cubing and their substitution into algebraic expressions and formulae.

Extension idea: look at negatives with a variety of powers and roots.  OR if n=-4, which expression will have the greatest value e.g. n², n-2, 2n, n/2, 2/n etc.

P49, 51

Rayner8 P20 Ex1-4, Rev. Ex & tests

Framework maths Page 58-59

Substitution spider or loop game; A3 write on wall;

Mymaths/ Algebra/ Formulae – Beat the clock

Positive

Negative

Integer

Science – variety of uses (X)

Indices and standard form:

6. Recap on index notation and evaluate numerical indices mentally and by use of calculator key: include fractions, decimals and negatives. (Ensure pupils know the squares from 1-15 and the cubes from 1-6, 10). E.g. what is the unit digit in 136³?

7. Extend number line to include zero, negative and fractional indices e.g. evaluate 17 0 , 4 -2 , 169 ½ . (Keep recapping on these during the year)

8. Rules of indices – multiplying, dividing and brackets for indices with the same base.

9. Writing and interpreting numbers in standard form and their input/interpretation using a calculator (EXP button)

Extension idea: pupils to cope with e.g. 64 -⅔ or to find missing indices in equations e.g. 8 x =32 … what is x?

P59, 115

P37 has prefixes

Rayner8 P29 Ex3 (easy)

Framework maths Page 58-61

Rayner9 P1-11 & other sources; MC2 P11

Framework maths Page 100-101

Introduce zero, negative and fractional indices with “Power Cables” – ask MCA.  Check on a calculator.

Make sure pupils know about negative square roots.

Mymaths/ Number/ Powers has Indices 1 (rules & match game with an algebraic plenary)

PPT – Standard Form What’s Up?; Indices – True/False & Zero/Neg/Frac Indices

Base

Index/Exponent

Standard Form

Use of scientific data e.g. distance between planets (X);

Use of world issues data e.g. debts (C)

Estimation and Rounding:

6. Recap on rounding to a given number of decimal places: you could use calculator questions here e.g. 3.762 7 (as always, write the full answer off the calculator before rounding).

7. Rounding numbers to a given number of significant figures (the number of significant figures in a number is all of the digits excluding zeros at the beginning or end).

8. Using numbers rounded to one significant figure to estimate the solution to a numerical problem e.g. (37²-16²x13)/0.53 … includes bodmas.

Extension idea: pupil to write quiz for class on estimation, for which they must have a good idea of the solutions.  This may include research e.g. Estimate the number of decibels at which concorde flies.  Estimate the angle at which a plane comes into land.

P45,111

Rayner8 P31Ex2-4, Game; MC1 P1,18,31

Rayner9 P85 Ex1

Framework maths Page 102-103

BBC website – “Rounding Off” – nice and visual!;

Mymaths/ Number/ Accuracy has lesson significant figs. And Number/Mental methods has Estimation

PPT-Rounding 1&2 and Estimation

Decimal Place

Estimate

Significant Figure

Upper/lower bound

Errors in science when doing experiments (X)

Use of world issues data e.g. debts, population (C)

Starter:

6. Indices – zero, negative and fractional and rules of. WB SH Or powerpoint presentation “Indices”

7. Solution of one and two sided equations, including brackets and fractions (NNS P123, 125) RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Scatter graphs & use of Autograph:

6. Construction of scatter diagrams (why are these used instead of e.g. a bar chart).

7. Understanding correlation and using a line of best fit, inserted by eye, on graphs where correlation is present.  Try and decide which variable should go on which axes e.g. Temp vs no. of ice creams – as temp rises, more ice creams are sold, but not the other way around.

8. Include a look at outliers on a scatter diagram – how are they shown?

Use mathematical challenge book 3 p20-21 for pupils to do their own investigation with scatter diagrams.

KEY POINTS: can you always put in a best fit? Is it always a line? Does it always go through the origin? What do points above/below line mean in given context etc.   Bear in mind this is the main area used on the GCSE cw and pupils understanding has been poor in the past.

Extension Idea: can the very best pupils find the equation of their line of best fit and use this algebraic relationship for predictions?

Autograph Functions: demonstration of using Autograph to construct a scatter diagram and also to find its correlation (-1 to +1) and the meaning of this value.

P267, 271

Rayner8 P137 Ex1,2; p145 shows use of ICT

Framework maths Page 154-155

MC3 P20-1

BBC website: “Data Picking” – which is the correct scatter graph? ; www.mymaths.co.uk

PPT Correlation

Pupils can use excel data and use autograph package

Correlation indicates a statistical relationship which may not mean anything in practice

Correlation

Line of Best Fit

Data e.g. from Geog.; Pupils should be able to create an efficient scale with equal intervals (X)

Handling Data task one: F01 is needed.  Pupils use task to practice use of autograph.

See separate info

Hypothesis

Real-life Graphs: interpreting a range of real-life graphs, including distance-time and speed-time graphs.

Extension idea: pupils to write a paragraph about a journey and then construct both a distance-time and speed-time graph for this.

P173-7 has nice ideas

Rayner8 P123

Ex1; P183 Ex4

Framework maths Page 188-189

www.mymaths.co.uk has some great real life graphs which are plotted in real time

Accelerate

Conversion

Distance

Velocity

Context from a variety of subjects(X)

Show how adverts can use graphs to mislead (C)

Starters:

1. Shapes of graphs – horizontal, vertical, diagonal, parabolic, cubic. WB/RE Or powerpoint presentation “Graph shapes”

6. Decimal calculations e.g. 0.2 x 0.3   1 ÷ 0.02    If 38 2 is 1444, what is the value of 3.8 2

7. Simplifying expressions using the three rules of indices WB

8. Averages e.g. mean of 4, 8, 8 and 10 etc WB

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Simplifying Expressions:

Throughout this section use starters and homeworks to recap on simplifying algebraic expressions  by collecting like terms, multiplication and division, including fractions and negatives e.g. simplify:

               3x – 7y + 8x –3y;  3x + 8x² - 4x;  4ab + 7ba

               10x x 4y x 3z;  3p x 4p x 6p

               9ab²/3b;  (6x + 15)/3

Extension idea: an expression simplifies to 3a²b + 6ab … what was the original expression?

P117

Rayner8 P37 Ex1,3 + Board work

Framework maths Page 62-63

Use A3 write on arithmagons, walls etc.

PPT – Simplifying & Simplifying Help

Collect

Like terms

Product

Simplify

Brackets:

6. Recap on expanding linear brackets including those with a negative outside e.g. 3(x – 6) – 7(2x – 8)

7. Expanding double brackets e.g. (x + 4)(x +3); (y – 7)²; (2y + 1)(3y – 2) and trying to put in a context e.g. write an expression for the area of a rectangle with sides of x+5 and x-10

8. Use the skill of expanding double brackets to solve simple equations in which the x² term drops away e.g. (x + 4)(x + 7) = (x + 6)(x – 2) … link to pythag.

Extension idea: include some proof work e.g. prove that the difference between the nth term of 2,8,18, 32, … and 0,3,8,15, … is n²+1

P113-117; 119

Rayner8 P127 Ex1,2

Framework maths Page 64-65

Rayner9 P20 Ex1

Rayner9 P20 Ex2

Mymaths/ Algebra/ Use of symbols has single (tab1-4) and double (tab5-9) with “Beat the clock”

Applications of negatives e.g. find the difference between 8x-17 and 3x-9.

Sheet available SAM

Bracket

Expand

Factor

F.O.I.L.

Starters:

6. Rounding – decimal places and significant figures WB

6. Measures e.g. roughly how many pints in a gallon, pound in a kilogram RE

7. Algebra simplification WB/SH

8. Ratio e.g. if the ratio of men to women is 2:3 and there are 12 men, how many women are there? WB

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Starter : quick test on proof that angles in a triangle add up to 180 ° and those in a quadrilateral sum to 360 ° - done in year 7 (??), give notice of test.

Add in Exterior angle of a triangle (proof)

P183

Rayner8 P46 Ex3

(Ex1,2 P42)

 Framework maths Page 18-19

MC has proof books available for use

Exterior

Interior

Quadrilateral

Shape visualisation :

Visualise quadrilaterals from given properties (pupils must know these so a sheet of notes may help afterwards: see Rayner9 P30) and common (regular) polygons and solids (e.g. tetrahedron).  Include angle, side and symmetry properties.  Also discuss other key shape words e.g. tessellation, congruent, similar, parallel, perpendicular, vertex, …

Extension ideas: open-ended questions e.g. is it possible to tessellate a pentagon? A hexagon? …

P 185, 187

Rayner8 P185-7 (some ideas);

MC2 P4

Guess the shape appearing from behind a board; Yes/No Game;

True/False statements

SAM has property cards

Mini Whiteboard

Edge

Parallel

Perpendicular

Polygon

Regular

Vertex

Islamic Patterns in Art (X/C)

Area:

6. Recap on the area of a square, rectangle and triangle, including units.

7. Prove and use the area formulae for parallelogram and trapezium (you may wish to give kite also).  Include questions with inconsistent units, solutions where area units must be converted and also reverse examples.

Circles:

6. Recap on names associated with a circle (circumference, radius, diameter, centre, arc, segment, sector, chord, and tangent)

7. Circumference of a circle (define π to be the number of times that the diameter of a circle can fit into its circumference) and perimeters of simple associated shapes e.g. semicircles.

8. Area of a circle: go on to include questions involving quarter circles, semi-circles etc.

Extension idea: work out the area of a circle from its circumference, find a shape with perimeter of 100cm, which encloses the largest area.

P235-7

Problems P19

P235-7

Rayner8 P16 Ex1,2

Rayner8 P51 Ex1-4

Framework maths Page 78-79

Mymaths/ Shape/ Area has trapezium & parallelogram visual aids

Mymaths/ Shape/ Cirlces – tab 8 only

MCA has a variety of circles and string to introduce π by an investigation

Area

Surface

As given

π

Area of different continents (C)

Starter:

6. % multiplying factors. %’s without a calculator  e.g. a books price increases from £5 to £6, what % increase is this? If 40% of a number is 12, what is the number? WB

7. Shape vocabulary and properties WB/RE

8. Pythag theorem including recall of triples WB

9. Multiplying and dividing by multiples of 10 WB

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Fractions:

Recap on all calculations met in year 7, namely ordering, addition/subtraction, multiplication/division, fraction of a quantity and fractional increase/decrease.  

Extension idea: “Egyptian fractions” – see MC.

P67, 69

Rayner8 P 8 Ex1-5; MC1 P11-13

Framework maths Page 50-53

The NNS has lovely examples to apply skill, rather than just practising repeatedly

www.mymaths.co.uk has pairs game

Denominator

Improper

Mixed Number

Numerator

Musical notes (X)

Calculations with percentages (* met in year 7):

6. Percentage of a quantity – calculator and non-calculator methods(More emphasis needed here – students found difficult last year): reinforce key issues e.g. 10% rise followed by 20% rise is not a 30% rise

7. Percentage Increase/Decrease – some pupils could not cope with the decimal method in year 7 and this now must be mastered (e.g. Increase by 15% is x1.15; Decrease by 15% is x0.85; Finding 15% is x0.15)  Include compound interest questions (explain how this is different than simple interest) and decimal multipliers to find this quickly.

8. Percentage Change – find the percentage change using the formula:

% Change = Actual Inc/Decrease     x      100%

                                                               Original Value

6. Reverse Percentage questions – link to work on decimal multipliers e.g. a television costs £240 in a 10% sale.  What did it cost full price?

Extension idea: which is best - £300 invested in a 2% simple interest account or £300 invested in a 0.5% compound interest account?

P71, 73, 77

Problems P3

Rayner8 P212 Ex1,2; supplement with other sources e.g. Rayner9 P132Ex1,2 (leave3)

Framework maths Page 50-53

0-9 cards or number fans in mental work

www.mymaths.co.uk has compound work

PPT – Decimal Multipliers & Reverse Percentages

Initial

Interest

Original

Percentage

Profit/Loss

VAT and interest rates (W); What % of your salary do you get to keep? (W)

What % of money donated to charity goes to good causes (C)

Polling issues – what % swing in the vote would take labour from power? (W/C)

Starter:

6. Numerical calculations, e.g. if 36 x 62 is 2232, what is 36 x 31, complete the calculation: 3.4 x ? = 6.8 x 3.5 WB

7. Recap on known squares and cubes WB

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

N.B. Book LRC for handling data task two (see below)

Highlight use of Autograph as you teach the content below

Groupings and group boundaries: discuss why we group and also why we might group equally or unequally.  Look at different types of groupings e.g. 0-10, 10-20, … versus 0-9, 10-19, … and discuss their upper and lower bounds.  A good practice would be to recap on histograms and to have pupils labelling the horizontal axes with correct upper & lower bounds.

P253, 255

Get pupils to take varying data sets and show they can group, using un/equal classes as approp.

Group

Lower bound

Upper bound

Un/equal group

Continuous

Use data from other subjects (X) and world issues (C)

Averages:

Extend earlier work to finding mean from a grouped frequency table, including algebraic examples.  Focus on interpretation of results, trying to compare with other data.

Also mention modal class and why it’s difficult to find the median.

P257

Board work

Collect own grouped data and find the mean, interpreting the result.

PPT – Grouping&Finding an average; Averages recap

Class boundary

Midpoint

Handling data task two: learning resource centre task to practice above.  This will include researching own information and using Autograph functions appropriately.

See additional information

Working in new groups and using ICT to present (W)

Starter:

6. Substitution, with emphasis on negative numbers WB

7. Speed e.g. if a bird flies 30km/hr, how far will it fly in one minute. If a man cycles 20 km in 20 mins, what speed is he cycling at? WB

8. Race game RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Coordinates : recap on plotting in all four quadrants.  The Midpoint of two coordinates.

Extension: pupils to have a look at coordinates in three dimensions.

Framework Maths Book 9 P93

Midpoint

Straight line graphs :

Recap on recognising and plotting diagonal, horizontal and vertical lines from year 7.

Generalise straight lines graphs as y=mx+c and use I.T. to investigate the effect of changing m and c.  Hence, write down the gradient, direction and y-axis intercept on line equations, including those needing simple rearrangement (not met yet).  Don’t worry about a great understanding of gradient at this stage.  Try and use Autograph on whiteboard to familiarise students – you may wish to set an activity on this, even as a homework.

P165; try graphical calculator problems p13;167

Rayner8 P177 Ex 1,2; Rayner9 P154 Ex1

Framework maths Page 86-93

Autograph or Waldo “Straight line Graphs”. Activity SSM14 Heinemann ICT

BBC website: “Planet Hop” is nice reminder.

PPT- Y=mx+c true or false & Graph Aerobics

Coefficient

Gradient

Graphs

Intercept

Link to graph work in science (X)

Curved Graphs:

Knowing what shape a graph will be from its equation (linear, parabola/quadratic, S-Shaped/cubic).  Plotting curves from a given equation.

Extension idea: pupils to investigate simple transformations of quadratic and cubic functions using I.T.

Rayner8 P182 Ex3; Rayner9 P156 Ex2

Framework maths Page 94-95

Waldo “Functions 1” allows shapes of cubics and quadratics to be seen

Autograph

Cubic

Function

Quadratic

Parabola

Starter:

1. Indices – zero, negative and fractional and rules of. WB SH

2. Solution of one and two sided equations, including brackets and fractions (NNS P123, 125) RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Conversion between fractions, decimals and percentages:

Recap on conversion with and without a calculator, including learning of key conversions (ask MC).

Extend to include an investigation into why some fractions have recurring decimal equivalents.

P65,99,109

Rayner8 P146 Ex1-5; Rayner9 P27 Ex4

BBC website – “Saloon Snap”;

PPT -Fraction Family

Convert

Decimal Places

Exact

Finite

Recurring

Calculations with decimals:

Check that pupils can perform the four rules with decimals: this is to include e.g. 0.03 x 0.0007 or 0.9 ÷ 0.03

Further mental strategies with decimals e.g. x and ÷ by 0.1, 0.01, …

P39,97

Rayner8 P69 Ex3-7

Framework maths Page 50-53

NNS has nice statements e.g. Multiplying by 0.01 is the same as dividing by 100?

Starter:

1. Fractions, decimals and percentages (calculations with and conversion between) WB/SH

2. Simplifying expressions (collection of like terms, removal of brackets, mult and div.) WB/SH

3. Negative numbers WB

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Bearings:

Finding three-figure bearings and reverse bearings ( ± 180 ° from original bearing): include some work on scale drawings here.

Extension idea: pupils to investigate the relationship between bearings and reverse bearings using year 7 angle work.  Why is it ±180º?; Design a treasure map with distances and bearings to follow.

P233

Rayenr8 P222 Ex1,2

A-Z Walsall: plan or follow a journey

using scales and bearings(PJW);

Mymaths/ Shape/ Bearings – includes snooker game

ActivitySSM15 Heinemann ICT

ACD has treasure map

Bearing

Reverse bearing

Geog e.g. work on world map (X)

Bearings between UK and certain countries featured in the news currently (C)

Locus:

Required constructions are midpoint and perpendicular bisector of a line, angle bisector, perpendicular from a point to a line, perpendicular from a point on a line.  Applications, including those in context (e.g. construct the locus of a girl’s path as she runs around a room with her arm always touching the wall) and geometric ones (e.g. construct the locus of all points always 5cm from a given point).

Extension idea: pupils to work with intersecting loci questions.

P221-7

Rayner8P47 Ex1-3

Framework maths Page 220-223

Mymaths/ Shape/ Construction and Loci are good: has constructions to show pupils

Starter:

6. General revision – pass the parcel tape game

7. Averages (thinking problems) PP

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Histograms and frequency polygons: recap on histograms and when they are most appropriately used, referring back to work on groupings.  Extend to look at frequency polygons, especially how they can be use to compare data easily.

P 261, 263

Rayner 9 P68 Ex3

Try and devise a task where pupils must collect their own data and use of autograph package (SATS )

PPT – Bars & Histograms

Discrete

Continuous

Histogram

(Frequency) polygon

Try and use data from other subjects (X) and world issues e.g. age groups of population in varying countries (C)

Homework task: recap on all graph types to date plus some misconceptions that may arise.  Pupils should know the most appropriate graph type for varying discrete and continuous data sets and be able to construct pie, stem & leaf, bar charts and histograms.

See homework sheet (MCA)

Look at misleading graphs in the media (C)

Starter:

6. Simplifying expressions SH

7. Race game RE

8. Expanding brackets SH

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Sequences:

6. Recap on finding a formula for the nth term of a linear and a quadratic sequence by the method of differences.  Pupils to appreciate that the coefficient of x² is half the value of the second difference (own investigation)

7. Extend to include the nth tem of fractional sequences and those involving powers and factors.

8. Knowledge of known sequences: a full numerical and diagrammatic appreciation of the square and triangular numbers (see MC for a help sheet).  Pupils to know Fibonacci also (comes in on Maths Challenges & team challenge

Extension idea: pupils could try harder quadratic sequences with a more operations e.g. 9, 15, 23, 33, 45, …

P151

P27; 146-7; 155-9

Rayner8 P169 Ex3

Framework maths Page 10-13

Framework Maths 9 P7

Texts are weak: supplement material

Waldo website: “Sequences” revises linear ones

MCA has sheet.

Link to Chinese Square roots.

Linear

Quadratic

Term

Triangular

Square

Discuss fibonaci and golden ratio in all subject areas (X)

Sequence by Structure:

General problems (see MC for a mixed sheet).

The jigsaw problem (extend from squares into rectangles and prove algebraically that all pieces have been accounted for).

The skeleton tower problem (see MC for an OHP).

Some diagrams in ex3 P176; MC2 P38

Framework maths Page 176-179

See SAM for envelopes and ideas

PPT – Sequences by Structure

Describe

Explain

Justify

Starter:

6. Correlation and scatter diagrams SH

6. Mixed revision SH

7. Percentages (thinking) RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C. Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Ratio and Proportion:

6. Simplifying ratios, including to the form 1:n (use the golden ratio of the human body).

7. Using ratios to find unknown quantities.

8. Sharing in a given ratio.

9. Increasing / decreasing in a given ratio e.g. adapting a recipe

10. Working with problems involving proportion.

Extension idea: algebraic ratio e.g. the ratio of pigs to cows on a farm is x:y³.  If there are3x²y 6 cows, how many animals are there in total?

P79, 81

Problems P4-5 are good e.g. unit conversion, adapting a recipe etc.

Rayner8 P157 Ex1-3

Framework maths Page 112-113

Framework maths Page 54-55and page 186-187

MyMaths/ Number/ Ratio has all methods and Beat the clock

World Recipe sheets (see MCA): choose a meal and adapt for a certain number of people; Activity NA9 in Heinemann ICT

Ratio

Proportion

Map Scales in Geog. (X)

Ratio of working hours to leisure time across Europe (W)

Two Way Tables:

Constructing and reading information in two way tables and using this information to appreciate the difference between, say, proportion and percentage e.g. What proportion/percentage of year 8’s are blond girls?

P255

See SAM for sheet

Can they collect data from another subject area?

PPT –Two way

Two-way table

Used to access info in all subjects (X) and from current affairs (C)

Starter:

6. Nth term of linear and quadratic sequences SH

7. Shapes of graphs RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Surface Area:

Finding the surface area of a variety of solids, including cylinders.  Pupils should represent the solids using nets and try and derive algebraic formulae of their own.

Extension idea: pupils to research cones and other pyramids or the sphere.

P239

Framework maths Page 82-83

Wooden solids in F12

“Pull Up” nets (MCA)

Mymaths/ Shape/ 3Dshapes

Net

Surface Area

Link to developments in Tech. (X)

Volume:

Finding the volume of prisms, representing such solids on isometric paper and from different views (work to include cube, cuboid, triangular prism and cylinder)

Extension: you can make two different cylinders by folding an A4 sheet either horizontally or vertically: which cylinder has the largest volume?

P239-41

Rayner8 P218 Ex1,2;  P228 Ex1-4

Framework maths Page 80-81 and page 212-213

Drawing a hexagon first on the isometric paper is the best way to see a cube develop.

Mymaths/ Shape/ volume looks at cylinders & prisms

Capacity

Cross-section

Isometric

Prism

Pyramid

Volume

Starter:

6. Area and circumference of circles including reverse examples WB

7. Area of quadrilaterals SH

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Hypotheses:

Pupils to understand the term “hypothesis” and to practice constructing ever more complex hypotheses on a subject of interest to them.

e.g. Simple: newer houses are more expensive than older ones

       Complex: the price of a house is affected by its age, location and no. of bedrooms

P251, 253

Framework maths Page 228-229

Start simple & try and build to a more complex hypothesis with many variables as required in year 10 (MCA PowerPoint)

Hypothesis

Can pupils make hypothesis based on other subjects? (X) plan a project to look at school based issues e.g. the canteen and healthy eating (C)

Handling data task three: the Long Jump task – this is a project to mimic the whole handling data cycle.  Again the emphasis is on the most appropriate graph at each stage, using computers where necessary and making pertinent conclusions based on evidence.

The hall might be useful to do the “jumping” in!; Autograph

Starter:

6. General mixed revision starters in run-up to exams

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Formulae:

1. Recap on expression versus equation versus formulae.

2. Using and writing formulae – substitution of numbers into formulae (negative numbers must be written in brackets), including where inverses are needed (e.g. the approximate area of a circle is given by A=22r²/7 – use the formula to find the area of a circle with radius 3cm and the diameter of a circle with area of 58cm²) and writing formula e.g. write a formula for the perimeter of a 9 by 9 square with a smaller square cut from its corner).  Pupils should bring formulae from all subjects. & include mental formulae work with negatives and decimals.

3. Simple changing the subject of a formula – only include ones that can be “read” at this stage but do use squares and roots e.g. p = qx² - r: rearrange to make “x” the subject.

Extension idea: negative and fractional terms for the best pupils.

P139-143

Rayner8 P102 Ex1-4 (more negatives needed)

Framework maths Page 142-145

E.g. Write a formula for the surface area of a cuboid

PPT – Rearranging formulae

www.easymaths.com has practice

Equation

Expression

Formula

Rearrange

Rule

Subject

Substitute

Formulae in science (X)

Algebraic fractions:

Extend earlier numerical work with fractions to those involving algebra e.g. add 3/x and 6/y.

Extension idea: link back to fractions in equation work.

P63

Framework maths Page 136-137

PPT- Algebraic fractions

Starter:

6. Pythagoras – mixed problems (Board work or SH)

7. Recap on algebraic equivalence of odd and even numbers, extend to proof RE

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Calculator facilities:

Pupils should be able to carry out calculations on the calculator involving negatives, brackets, powers, roots, reciprocals, memory.  Use this as an opportunity to re-visit rounding decimal places and significant figures.

P87, 109

Rayner8 P88

Ex 1-6 (select)

Use of OHP calculator may help in lesson

BODMAS

Memory

Reciprocal

Proof and Counter Examples:

Recap on ideas of proof and introducing the idea of a counter-example e.g. all numbers have an even number of factors, all the angles in an isosceles triangle must be acute.

Proving simple statements e.g. the sum of 3 consecutive integers is always a multiple of three; the difference between a multiple of seven and the equivalent multiple of five is always an even number.

Extension idea: pupils to write their own proof statements.

Some statements p33 – nice one involving mult. grid

MC1 P24 ; MC2 P23; MC3 P2 GCSE Rayner and Rayner7 P197 for counterexamples)

You may find some ideas in Proof Books (see MC)

See SAM for envelopes

PPT – Counter Examples and Proof

Consecutive

Can we prove if God exists? (C)

Starter:

1. Fractions, decimals and percentages (calculations with and conversion between) WB/SH

2. Simplifying expressions (collection of like terms, removal of brackets, mult and div.) WB/SH

3. Recap on proof for sum of interior angles in a triangle and quadrilateral

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Transformations:

Pupils should be able to carry out and to describe:

6. a reflection in a given mirror line (link to graph work)

7. a rotation with a given centre, direction and size

8. a translation with a given column vector

9. an enlargement with a given centre and scale factor (positive and fractional only at this stage)

10. a combination of the above transformations.

Extension idea: what is the connection between the scale factor when enlarging shape A to shape B and enlarging shape B to shape A?

P203-213

Rayner8 P162 Ex1-4; P96 Ex1,2; P116 Ex1-3

Framework maths Page 120-129

www.mymaths.co.uk (ref/rot) or Autograph

BBC website: “Bathroom Tiles” is nice.

Waldo maths: “Enlargement” is a great visual.

PPT – Enlargment & Ratio

Enlargement

Reflection

Rotation

Scale factor

Translation

Enlarging solids and investigation into area and volume change

Extension idea: represent your findings algebraically

Framework maths Page 130-131

(Brief at this stage – will revisit in y9)

Why do elephants have big ears? (science)

Starter:

6. Mixed revision via pass the parcel tape game

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Probability :

Recap on year 7 ideas of probability scale, equally likely outcomes and sample space diagrams to observe outcomes from two events.

Extension ideas: use maths challenge statements.

P276-285

Problems P23

Rayner8 P203 Ex1-4; MC1 P29

Framework maths Page 30-41

Horse race game – see MCA

PPT – Prob recap & space (1&2)

Event

Outcome

Probability

Sample Space

Link to risk in RS (X/C)

Tree diagrams:

Extend sample space diagrams into tree diagrams for simplest cases at present.  Use “x” for “AND” probabilities and “+” for “OR” probabilities: derive this from simple questions from sample space diagrams.

Extension ideas: construct a tree diagram to show what you might do over the bank holiday weekend and the chance of each event.

Board work

See SAM for worksheets

Waldo “Combining Probability” allows simple use of x and + to be seen.

Tree diagram

AND – x

OR - +

Starter:

1.  Mixed Transformations SH

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

Brackets and common factors:

1. Recap on removal of single and double brackets by a starter.

2. Introduce single bracket factorisation only (i.e. common factors): you could start with 12x+24 on the board … where did it come from?

Extension idea: write as many factorised expressions as possible for 18x+54.

See SAM for worksheets

Framework maths Page 66-67

PPT –Factorisation &

Why Do we factorise?

Mymaths/ Algebra/ Use of symbols

Common factor

Factorise

Algebra review: mixed questions on substitution, formulae, rearranging, writing and solving equations, algebraic fractions, simplifying expressions (like terms and x/ ÷ ), graphs etc.

N.B. A focus on key “exam” style words would be useful e.g. simplify, solve, evaluate, factorise, substitute etc.

Set up a circus of algebra problems in the class for pupils to move around.

Exam style words

Starter:

1. General revision to ensure you group is prepared for year 9 – brackets, indices, triples, factorisation, solving, graph shapes etc.

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework Maths

Other Ideas/

Resources

Vocabulary

X/W/C

Compound Measures:

Knowledge and use of formulae for speed, density and pressure: units must be consistent before formulae can be used.  Do “thinking” examples first not relying on formula (See SAT mental)

P229, 233

Framework maths 9 P95

Rayner9 P160 Ex1,2

Mymaths/ Shape/ Measures - Speed

Density

Pressure

Speed

Obvious use in science (X); Look at population densities in the developed and developing world (X/C)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

Rayn/M.C.

Framework

Other Ideas/

Resources

Vocabulary

X/W/C

True, false and iffy number statements.

Puzzles

MC1 P8

MC1 P39

Counterexample

Mixed calculations involving percentage, ratio, fractions, decimals, standard form and indices.

MC3 P10

CONTENT:

(Key Objectives Listed in bold)

NNS

Resources

Key Texts

Other Ideas/

Resources

Vocabulary

X/W/C

How many ways can a family of varying sizes be arranged for a photo?  Extend to families including identical twins, triplets, … or both.

Get pupils out as resources

Factorial

Recap on work: averages, graphs, and probability.