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 FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• Square numbers and square roots (learn the first 15) and approximate square roots (e.g. √ 90) (Include applications e.g. could 2303 be a square number? NNS P55-8) : my maths/ number/ powers is good with e.g.

   tab 4 on “Squares & Cubes” being a loop game, tab 67 being “Beat the clock” and, under “Games” there is Squares and Cubes Match 1 & 2; PPT Learning squares & roots

• Cube numbers and cube roots (learn the first 6 and also 10 3 ; Rayner P87)) website games as for square numbers

• Mental indices, including 0 x , 1 y , powers of 2, 5 and 10. (See NNS Top of pages 90 & 91) : PPT presentation (yr 8 “Indices”)

• Complements (NNS P88, 89) : Whole class game (ask MC)

• Multiplying and dividing by 10, 100, 1000, … including decimals (NNS P38, 88; Rayner P148) : Mini whiteboards

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Rules and Expressions:

0. The rules of algebra (no multiplication sign, divisions written as fractions, products written with numbers first)

1. Using the rules of algebra in order to read and write expressions, including those involving simple indices and brackets (mention BODMAS at this stage in order to stress the difference between, say, 3x² and (3x)²).  Mini whiteboards are useful here.

Pupils should be encouraged to build up layers by reading the algebra i.e. I think of a number (x), multiply it by 3 (3x), add 7 (3x+7) and then multiply all of this by 4 (4(3x+7)).

Extension idea: pupils to try writing much more complicated expressions including, say, I think of a number, multiply it by 2 and subtract it from 10; the reciprocal of a number etc.

112-114,115

RaynerP58 Ex1&2

Framework Maths P69

Algebra Framework P1, 6, 8

Worksheets:

Translation

Using Letters 1&2

Words → Symbols

Symbols → Words

Algebra

B.o.d.m.a.s.

Brackets

Commutative

Expression

Index/Indices

Inverse

Squared

Symbol

Term

Use of symbols in science (X)

Substitution:

Substituting numbers into expressions: use linear expressions and those involving simple indices.  Extend from use of positive numbers into simple fractions and decimals.

Use BBC Website interactive “Late Delivery” to check substitution skills and to reinforce BODMAS.

Extension idea: write some expressions with a value of 20 if x=5, say.

138-9

Framework Maths P69

Algebra Framework P6

Worksheets:

Building

Spider

Racing Letters

Evaluate

Integer

Substitute

Variable

Use of formulae in science (X)

Equations:

Construction and solution of one-sided equations by reading the algebra layers and peeling them off in reverse e.g. 4(3x+7)=88 or 3x²+5=80.  To include squares, cubes & roots.

Move directly into a correct mathematical layout, avoiding flow-charts.  Solutions should be given as whole numbers or fractions.  From penultimate line of working, practice conversion of improper fractions to mixed numbers e.g. 8x=47 ⇒ x=47/8 ⇒ x=5⅞

Extension idea: try more difficult powers and roots e.g. x 4 -1=15

113; 122-5

Pyramids P9

Rayner7P153Ex2&3 (basic)

STP 7A

 Ex21B P392; Ex21G P402

Framework Maths P157

Algebra Framework P5, 15

Worksheets:

Think of a number

Waldo equations levels 1 & 2 and PPT One sided Equations

Construct

Convert

Equation

Improper Fraction

Mixed Number

Solve

Unknown

Balancing chemical equations (X)

Formulae: (N.B. See starter on “Subject of a Formula” e.g. px+q=r so x=??)

0. Distinguish between an expression, equation and formula

1. Substitute into formula (e.g. C=2a², find C when a=5) … clear working, please

2. Simple reverse examples, links to equation work (e.g. P=2a+3b, find a when P=28 and b=6)

3. Write simple formulae e.g. perimeter of a rectangle (more difficult for most able e.g. a formula for the midpoint of two numbers, extending to two coordinates)

P140-1 (Sub.)

P142-3 (Write)

Rayner7 P219 Ex3

STP 7A

P315 – 325

 (Select qus. as appropriate)

Algebra Framewok P15

Framework Maths: P77, 221

Derive

Formula(e)

Subject

Scientific formulae – try & use examples from other subjects (X)

STARTERS FOR THIS SECTION: Please cover the following during this handling data section (*’d means features in the scheme)

• Written methods of addition and subraction (3 digit numbers) (See PPT - Maximise/Minimise game or STP 7A Ch1; Rayner P14,19)

• Written methods of multiplication – demonstrate a variety of methods e.g. box method. (STP 7A Ch2; Rayner P14,182) – PPT Long Multiplication

• Written methods of division – demonstrate how to deal with any remainder as a fraction (STP 7A Ch2; Rayner P14,183)

• Mental Fractions e.g. an eigth of 480, 1½ x 18 (NNS P 98, 99) : try “fraction wheels” idea on an OHP

• Mental Percentages e.g. 10% of 350, 95% of 450, … (NNS P72, 73) (% Wheels) (Charts 6); Mymaths/ Number/ Percentages or a brainstorm in pairs e.g. do as many %’s of 240

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

N.B. Book library space for task one.  Show use of EXCEL on interactive whiteboard as a lesson starter or plenary (NB Focus is on EXCEL in year 7, but you may wish to show AUTOGRAPH also … this will be taught in year 8 upwards).

Show averages on EXCEL

Averages & Spread:

0. For a list of data (frequency tables later) find the mean, median and mode (measures of average) and the range (measure of spread): this will have been covered at primary level, so try some applied questions e.g. think of four numbers with a mean of 8; find four numbers such that mean<mode<median (see yr 8 “Averages” ppt presentation)

1. Appreciate why there are 3 types of average, discussing the dis/advantages of each one and which measure would be appropriate in a given instance.

2. Compare two simple distributions using the range and one of mean, median or mode e.g. footballer A has mean number of goals per match as 2.3 and range of 0; footballer B has mean 2.3 and range of 6.  Who would you want on your team? (see NNS p261)

Extension: e.g. find the mean of given algebraic expressions e.g. SAT 2000 P1 Q10 and also changes to average & spread in transformed data e.g. SAT 2002P2 Q9

24-25

256-9; 260-1 (nice ideas)

272-3

Rayner7P185 Ex1&2

STP 7A

Ex19B P359

Ex19D P362

Ex 19E P364 (1-9)

Ex19F P367

Ex19G P368

Practical 2 P371

Give a list of topics and say which is most appropriate average, if at all e.g. height, shoe size, house number

BBC Website “Train Race is nice for given skills.

Framework Maths: P55-7

PPT – Intro to averages

Average

Mean

Median

Mode

Modal Class

Range

Spread

Use of data from other subjects (X); e.g.P.E., Geography average temperature and temp. variation

Use data to explore the diversity of national and regional ethnicity & religion (C)

Handling data task one: see additional handouts.  Undertake learning resource centre task with emphasis being on comparing and interpretation and use of EXCEL.

Spreadsheet

Project includes cross-curricular data (X)

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Doubles and halves (NNS P88, 89) and recognising possible uses of this (e.g.x5) (NNS P96, 97) : Whole class game (see MC) or www.mymaths.co.uk “Darts”

• Adding/Subtracting 0.1, 0.01, 0.001 (NNS P36, 37, 92) (Number Stick).

• Shape visualisation problems (NNS P184, 185)

• Simple rearranging the subject of a formula * (Hard Equations 1 worksheet)

• Mental algebraic substitution (use later as a recap on the first few lessons) : Dice race game.

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Negative Numbers:

0. Interpreting, using and ordering negative numbers.

1. Addition and Subtraction of negative numbers (using a number line)

2. Multiplication and Division with negative numbers

3. Simple indices work with negative numbers e.g. (-4)².  Include negative square roots!  

4. Include average questions i.e. median to order, mean to add and divide.

Extension idea: Maths Challenge 2 Pg18-9 “True, False and Iffy Negative statements”.

48-50

51,57

Rayner7P189 Ex1, 2, 3 & 4

STP 7A

Ex17H-L P326

Framework Maths: P18-21

Link with algebra and try some substitutions

NNS uses pyramids and magic squares (see p48)

SAT 2000P1 Q2

GSP – see ACD

PPT – Negatives ordering

Positive

Negative

Integer

Science/ Geography: temperature scales (X)

Introduction to Decimals:

0. Place value in decimals and the link to fractions

1. Ordering decimals ( make use of inequality symbols )

2. Reading decimal scales

36

40

Rayner7 P27

Ex1,2 & 3

STP 7A

Ex5D P77

Ex5M P92

BBC Website “Builder Ted” is a good starter for ordering decimals or mymaths (number/ decimals/ ordering)

Tenths

Hundredths

Thousandths

Decimal Point

Ascending

Descending

<, >, ≤ , ≥

Compare with use of a comma in, say, France (X)

Decimal Places:

0. Rounding a decimal to a given number of decimal places (N.B. Reinforce here that, with calculator calculations, we write the full answer off the calculator before rounding.  Keep stressing from now on.)

Extension: find some fractions that are all, say, 0.6 to 1 decimal place.

42-45

Rayner7 P34 Ex2

STP 7A

Ex7K-7L P134

My maths (number/decimals/

Rounding off – includes Beat the Clock)

Decimal Place(s)

Approximate

≈

P.E. Ordering times in a 100m race (X)

STARTERS FOR THIS SECTION: Please cover the following during this shape section (*’d means features in the scheme)

• Mixed questions on all starter ideas to dateperhaps using 0-9 cards, number fans or powerpoint presentations on whiteboard (True/False, ABCD, Weakest link etc.)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

The Vocabulary of shape:

Please ensure that the pupils have a basic understanding of the following terms and the key properties of the shapes mentioned (e.g. trapezium has one pair of parallel sides)

1. Vocabulary of shapes and solids to include:

Congruent, Similar, Face, Edge, Vertex, Parallel, Perpendicular, Regular, Tessellate, Concave, Convex, Diagonal, Line, Plane, Polygon, Prism, Pyramid, Quadrilateral, Regular.

2. Naming of triangles/quadrilaterals/polygons & their key properties, including symmetry:

-Scalene, Isosceles, Equilateral, Right-Angled

-Square, Rectangle, Parallelogram, Rhombus, Trapezium, Kite, Arrowhead (NNS p34)

-Triangle, Quadrilateral, Pentagon, Hexagon, … , Dodecagon, … , Icosagon , …

3. Naming of solids and their key properties:

-Pyramids (square-based, triangular-based=tetrahedron, circular-based=cone, … )

-Prisms (square-based=cuboid/cube, circular-based=cylinder, … )

-Sphere

Extension idea; Maths Challenge 2 P3-4 “True, False and Iffy Shape Statements”.

WHY NOT TRY A BIRCHFIELD INTERACTIVE WORDSEARCH ON THIS TOPIC?

178-9

184-5 (visualising problems)

186-7

198-200

Using & Applying Exs P34,35

STP 7A

Ch11 P197 (Symm if needed)

Rayner7 P56Ex4

Framework maths P245

Rayner7P21 Ex1, 2

Try to examine knowledge of properties with some probing questions e.g. is it possible to have a right-angled equilateral triangle?; True or False – a square is a rectangle etc.

Birchfield - wordsearch

MCA has shape sheets in folder e.g. crossword

NNS P184-5 gives possible visualisation problems

As given in content section (insist on correct spellings and terminology at all times)

Artwork – what shapes have been used? (X)

Religion – Islamic patterns (C)

Angles:

1. The definition (Angle=turn), vocabulary and labelling of angles

2. Recap on estimating, measuring and drawing angles (esp. obtuse and reflex)

3. Using protractor skills to construct triangles (2 sides and an included angle given or 2 angles and the included side)

4. Using compass skills to construct triangles (3 sides known, inc. equilateral triangle): pose the question “When is it impossible to draw a triangle where the three sides are known?” (Maths Challenge 2 P28 “Extra4” poses this as a nice investigation).

Extension idea: research into congruent triangles; construction of polygons.

222-2

232

Rayner7 P139 Ex1-7

STP 7A

Ex 10D – Ex 10H P178;

Ex12D – Ex12G P220

Framework Maths P137; 237; 239

Mymaths / Shape/ Angles has Angler game, Measuring Angles

Acute/Obtuse/Reflex

Angle – a turn

Arc

Construct

Degree(s)

Protractor

Right Angle

Sketch

Straight

Geog – link to bearings & directions (X)

What angle would we fly on to get from e.g. London to e.g. Iraq – use current affairs to locate countries (c)

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• Reading and plotting coordinates in all four quadrants.  Finding the mid-point of two coordinates* (NNS P218-9 & STP 7A P308, 311, Rayner P52) Mymaths “Connect5” & “FlippyNeck” games

• Mental work with negative numbers (NNS P93) : mini boards

• Multiplying and dividing with multiples of 10 e.g. 200 x 3000, 90000 ÷ 30) (NNS P89) : mini boards

• Recap on previous algebraic work – one-sided equations (use waldo “Equations” levels 1 & 2)

• Recap on previous algebraic work – substitution (include decimals, negatives and fractions) “Substituting Negatives” in algebra section of Mymaths (Algebra/ Formula/ Beat the clock)

• Generate a sequence given a formula* (Charts 17) or linear sequences in Mymaths (includes printable wordsearch)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Sequences:

0. Define a sequence and generate further sequence terms.  Include familiarity with known sequences such as square, cube, triangular, rectangular &Fibonacci.

1. Focus on linear sequences – finding a formula for the nth term by the method of first differences (e.g. 3, 7, 11, 15, 19, … ⇒ t(n)=4n-1 or 20, 18, 16, 14, 12, … ⇒ t(n)=22-2n )

Extension idea: Maths Challenge 2 P37-8 “Rules for number sequences”

Framework maths covers this section e.g. P3,5,121

8; 144-7

149, 151, 156-7

Rayner7 P1 Ex1&2

STP 7A

       Ex4L P59

Ex4Q P61

Invest.1 P63

Boardwork for linear sequences

Rayner7 P213 Ex1&2

Algebra Framework P4, 9

Corner 2Corner MCA NNS P28

Waldo website “Sequences” is good interactive linear practice

Mymaths – Algebra/ Sequences

PPT Linear sequences intro

Consecutive

Rule

Pattern

Sequence

Term

Difference

Linear

Nth Term

Fibonacci in every day life e.g. pineapples!(X)

Other sequences: (N.B. Starter: generating a sequence given the nth term formula)

0. The nth term of simple quadratic sequences by the method of second differences

1. The nth term of simple fractional sequences e.g. 1/3, 1/7, 1/11, 1/15, 1/19, … )

2. The nth term of simple “shifted” sequences e.g. 9, 16, 25, 36, 49, … ⇒ T n =(n+2)²

Extension idea: investigate the limit of certain sequences e.g. T(n) = n/(3n-1)

Briefly make use of mapping notation P160

Framwork Maths P225

Mymaths/ Algebra/ Sequences -  “Quadratic sequences”

Function

Input/Output

Mapping

Quadratic

NB: Good time to do ICT task activity (see booklet) entitled “Omnigraph 2”

Graphs: (Starter: plotting and reading coordinates in all four quadrants, inc. midpoint)

0. Define an algebraic graph – an infinite number of coordinates which have something in common

1. Recognising horizontal and vertical line graphs

2. Suggesting an equation (or mapping) from a list of ordered pairs (link to sequence work): BBC Website “Planet Hop” is a good interactive site to practise reading/writing coordinates and deciding on the equation of a line.  Link sequence

NB Try & show Autograph on interactive board – pupils can go away and use it.  Perhaps you could get them to investigate graph shapes for a hw, say.

218-9

164-5; 166

Rayner7 P158 Ex1,2

STP 7A P345 (brief)

Framework Maths: p127-9

Algebra Framework P2 & 3

Autograph

Worksheet:

Four in a Line

Axis/Axes

Coordinate

Equation

Graph

Horizontal/Vertical

Midpoint

Origin

Quadrant

Really ensure pupils can plot a good scale with equal intervals & transfer this skill to other subjects (X)

Appreciate that equations of the form y=3x+7 give rise to straight line graphs and to plot straight line graphs (Focus on explicit examples e.g. y=5x-4, but include simple implicit ones e.g. x+y=7, often best tackled by considering what happens when x=0 and y=0)

As above

Rayner7 P162Ex3

As above

Diagonal

Linear

0. Simple quadratic graphs: plot y=x² and be familiar with “parabola”

1. Appreciate the shapes of various graphs given by their equations i.e. horizontal, vertical, diagonal and parabolic – use graph shape cards (MC)

171

Boardwork

Algebra F.work P14

Use Autograph for shapes of graphs

Curve

Parabola

Quadratic

Path of a projectile in Physics (X)

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Adding and subtracting decimals (written methods) (Rayner P31) Mymaths/ Number/ Decimals

• Multiplying with decimals (decimal x integer) (NNS P88, 89, 104, 105) (Rayner P146) – use my maths/ number/ decimals/ multiplication – has “Beat the clock” game at end

• Multiplying with decimals (decimal x decimal) (Rayner P149) website as above

• Dividing with decimals (decimal ÷ integer e.g.989.3 ÷ 4) (NNS P106-7) (Rayner P147)

• Dividing with decimals (decimal ÷ integer e.g. 0.2 ÷ 4 or decimal ÷ decimal e.g. 0.9 ÷ 0.03) (NNS P88, 89)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Fractions:

0. Define proper, improper, mixed fractions and numerator and denominator

1. Converting between mixed numbers and improper fractions

2. Equivalent fractions and cancelling fractions (with and without calculator)

3. Appreciation that a/b means a ÷ b (as in algebra)

4. Ordering fractions (by making the denominators equivalent)

5. Fractions on the calculator i.e. show use of fraction button ( cancelling, +, -, conversion to decimals, …)

Extension idea: e.g. find a fraction which is greater than one quarter but less than three tenths? Generalise to a fraction which lies between two fractions that I am thinking of, but I am not going to  tell you what they are.

60-65

This puts questions in “nice” contexts e.g. Find a three-digit fraction equivalent to 1.5.

Rayner7P46 Ex1,2

STP 7A

Ex5B P73

Ex5C P75

Ex5L P90

Ex6F P106

Ex6G P107

Maths Challenge 2 Pg 21 “Fractions with a Calculator”.

Framework Maths P42; 47

Mymaths – number/ fractions/ equivalent

Proper/Improper

Mixed Number

Numerator

Denominator

Equivalent Fraction

Simplest Form

Cancel

Convert

All subjects – make use of cross-curricular data (X)

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

Calculating with fractions:

0. Calculating a fraction of a quantity (with and without a calculator) e.g.⅝ of £40

1. Addition and Subtraction of fractions (check solutions on calculator)

2. Multiplication and division of fractions (check on calculator, cancel before multiplying)

Extension idea: extend calculations to fractions involving algebra; Egyptian fractions (see SAT 2002 P1 (level 6-8) Qu9)

66-68

Rayner7 P48Ex3

STP 7A

Ex5K P87 Q1-12

Rayner7P50 Ex4

STP 7A

Ex6B-6E P97

Ex6H-6I P108

N/A

Pupils should become familiar with the term reciprocal in this work, being able to answer e.g. What is the reciprocal of 2½?

Framework maths: P45; 49; 191

Mymaths – number/fractions/ addition&subtraction

PPT – Add&take fractions

“of” means multiply

“per” means divide

Percentages:

Understanding the definition of a percentage and why they are in regular use

72-3

Percentage

Calculating with percentages:

0. Calculating a percentage of a quantity:

-without a calculator (e.g. 10%, 95%, 1%, …) (see previous starter)

-with a calculator: read 43% of 95 as 43 ÷ 100 x 95

70-73

Using & Applying P2

Rayner7P69Ex2&3

STP 7A

Ex5k P88 Q13 →

Mymaths/ Number/ Percentages (mental)

Understand VAT and Interest rates; also tax levels – how much money do you actually take home? (W)

STARTERS FOR THIS SECTION: Please cover the following during this shape section (*’d means features in the scheme)

• Know main fraction and percentage equivalences (NNS P98, 99) use Mymaths “Fraction Pairs” game (two different levels)

• Extend above to include decimals (NNS P98, 99 (see strategies))

• Solid Visualisation (NNS P198, 199)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Perimeter and Area:

1. Recap on Perimeter and find this for regular and compound shapes

2. Definition of area and rectangle and triangle formula; apply to compound shapes

3. Changing the units of area e.g. how many cm² are in a m²?

In this section, try to encourage an algebraic layout and include some reverse examples e.g. the perimeter of a square is 44cm – what is its length? Its area? Rayner1 Ex4 P105

Extension idea: Maths Challenge 2 Pg 14 “Extra 1”.

234-5

Using & Applying Examples 18-19, 34, 35

( lovely! )

Rayner7

P41 Ex4

P37Ex1,2,3

STP 7A

Ex14C – Ex14F P263

Rayner7P43Inves

P44 Ex5

Framework Maths P30-33 has further exercises; Waldo is good for triangles since the side that is the base can be altered; Mymaths/ Shape/ Area has rectanglesand triangles

Area

Base

Dimensions

Length

Perimeter

Surface

Width

Technology(X)

Area of developed versus developing countries (C)

Nets: (MAC has good “pull-up” visual aids)

Represent solids in two-dimensional form using isometric paper and then construct their nets using the compass and angle skills gained in SSM1 e.g. cube, cuboid, regular tetrahedron, …

Extension idea: net of a cylinder (algebraically or with string)

222-3

Rayner7P25Ex3

STP 7A

Ex20C, 20D P374

 Practicals 3&4 P232

Mymaths – Data/ Graphs/  Templates has iso paper

Framework Maths P241

Isometric

Net (often called a “development” in tech.)

Technology Construction (X)

Elevations front, plan and side elevations of a solid

Use Mymaths/ Shape/ 3D shapes/ Elevations for this topic

Technology 9X)

STARTERS FOR THIS SECTION: Please cover the following during this handling data section (*’d means features in the scheme)

• Mixed questions on all starter ideas to dateperhaps using 0-9 cards, number fans or powerpoint presentations (True-False, Weakest link, ABCD etc.)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Probability:

0. Basic Ideas ⇒ definition and associated vocabulary; use of scale from 0 → 1, probability of an event happening (p) using equally likely outcomes; probability of an event not happening (1-p) N.B. Do not accept “zero”, “nil”, “0/1” or a ratio as an answer

1. Experimental Probability – collect data from a simple experiment and use to estimate probability; understand that the more times the experiment is carried out the more accurate this probability will be.

Extension idea: use Maths Challenge 1 P28-9 for some statements to discuss.

22-23

276-80;282-5

Rayner7P199 Ex1-5

STP 7A

Ex13A p236

Ex13C P238

Ex13D P239

Practical P243

Use BBC Website interactive “Fish Tank” to look at equally likely probabilities and equivalent fractions.

Framework Maths: P61-5; 211-215

My maths/ Games “Higher/lower”

Biased

Certain/Uncertain

Equally Likely

Event

Fair/Unfair

Impossible

Likely/Unlikely

Outcome

Probability

Random

Success

Trial

Weather in Geography (X); Certainty in Religion (C)

Try some applied and SAT style questions – the level 6 SAT questions have been poorly answered in the past e.g. We have teachers, pupils and support staff at school: is the probability that I pick a teachers’ name off the school database equal to ⅓?

SAT questions(6-8):

2000 P1 Q3

2000 P2 Q10

2001 P1 Q10

2002 P1 Q 11

2002 P2 Q11

2003 P1 Q8

Listing Outcomes:

Use of lists and tables to list the outcomes of more than 1 event e.g. rolling 2 dice

281

STP 7A

Ex13B P236

Horse Race: if two dice are rolled and the horse with the total moves, which horse is most likely to win?

Mymaths/ Data/ Probability/ Listing outcomes

Outcomes

Sample Space

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• Factors and highest common factors (include applied problems e.g. what is the smallest number with exactly 3 factors? True or false – all even numbers have at least four factors.  Find the number below 100

which has the most factors.

• Multiples and lowest common multiples (include applied problems e.g. can an odd number be a multiple of 4? True or false – a prime number cannot be a multiple.)

• Definition of a prime and learning those under 30.

• Mixed decimal calculations

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Simplifying algebraic expressions:

0. Collecting like terms e.g. 3a + 2u + 5a – 8u OR 3x – 4y + 5x + 6x² OR 10abc + 3cba + 4bca

1. Multiplication and division e.g. 3y x 2w OR 4z x 5z x 2z OR 15w/3

In this section try some reverse examples (e.g. give some expressions equivalent to 2a + 3b) and revisit brackets (multiply out pairs and go on to collect like terms) and one-sided equations (e.g. 3x – x + 4x = 19)

Include context questions e.g. area of rectangle with width 3x and length 5x?

Extension idea: write as many expressions as you can that simplify to, say, 3x² + 5x

P7 Rectangle Example

115; 116-7

(nice ideas)

Rayner7P61 Ex3-5

STP 7A

Ex21H P405

Ex21j P406

(need extending); Invest.1 P338&413

Boardwork for x/ ÷

Algebra Framework P7

Mymaths – Algebra/ Use of symbols/ simplifying 1(+-) and 2 (x÷)

Framework Maths P73-75

PPT – Collecting Like terms & Simplifying Algebra Mix

Equivalent

Like terms

Product

Quotient

Simplify

Brackets:

Removing single brackets: appreciate numerically that 3(2+6) = 3x2 + 3x6 and then use algebraically.  Keep reinforcing that, if the algebra is read, it is easy e.g. 4(3x+7): I think of a number, multiply it by 3 add 7 and then MULTIPLY IT ALL by 4.  It would be worth, at this point, making the analogy to DIVIDE ALL e.g. (4x+16)/2 = 2x+8

116

Framework maths P161

Algebra Framework P8

Mymaths – Algebra/ Use of symbols/ Brackets (tabs1-4)

PPT- Simplifying expressions & expanding brackets

Expand

Simplify

Further Substitution:

Revisit substitution, but extend to negative numbers (e.g. a=3 and b=(-8), evaluate 2a – 3b).  Negative numbers should be written in brackets since –7² ≠ (-7)² (link to BODMAS).  Work should include simple indices e.g. what happens when you square, cube, … a negative?  Calculators should be used to check solutions in order to see the +/- button in correct use.

STP 7A

Ex17M P336

Algebra Framework P11

Worksheet:

Substitution

Science formulae (X)

STARTERS FOR THIS SECTION: Please cover the following during this shape section (*’d means features in the scheme)

• Recap on mental % work and extend to increases and decreases

• Recap on sequences to date (Charts 18) use Waldo “Sequences” to work out linear nth terms mentally

• Perimeter and area problems e.g. If the area of a square is 169cm 2 , what is the area of a rectangle with the same perimeter? (NNS P18-19)

• Interpreting sketch graphs (NNS P173, 175)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

Surface Area:

Find the surface area of simple solids e.g. cubes and cuboids (extend to various prisms and pyramids if coping). Link to algebra e.g. write a formula for the surface area of a cube and a cuboid.

238, 240

Framework Maths: P37

Link to nets work in order to visualise all faces; Mymaths/ Shape/ Area has nice connection between nets and surface area

Surface Area

Edge

Face

Vertex

Cost of a project in Tech (X/W)

Volume:

0. Volume of a cuboid and solids made from cuboids and equivalence to capacity

1. Changing the units of volume e.g. how many cm³ are in a m³?

Extension idea: given the surface area of a solid, what is its volume?  Or: a cuboid has faces with areas 24cm², 32cm² and 48cm² - what is its volume?

239, 241

STP 7A

Ex20E – Ex20G P379

Mymaths/ Shape/ Volume/Cuboids

PPT – Volume of Cuboids

Capacity

Cross-section

Volume

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Strategies for multiplication (NNS P96, 97; Rayner P73) – see PPT – Long Multiplication

• Strategies for division (NNS P 96, 97)

• Multiplying and dividing by 0.1 and 0.01 (NNS P39, 89)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

Cross-

Curric.

Multiplication and Division with large numbers (may have been done as a starter):

e.g. ensure that pupils can evaluate, say, 2,000 x 30,000 or (4,000)² or 9,000,000/30,000

Such calculations can be checked on the calculator in order to appreciate how the calculator displays large and small solutions.  Enter numbers such as 8,000,000,000 using EXP button.

N.B. 10 9 =US billion, 10 12 = UK billion, but 10 9 is increasingly common in the UK

38

Boardwork

Use activity at bottom of P38 NNS as starter

Million

Billion

Trillion

Use real data e.g. on world issues (C)

Decimal Calculations (may have been done as a starter):

Check that the following calculations can be performed by written or mental methods:

0. Addition and Subtraction of decimals

1. Multiplication and Division of decimals by multiples of 10 e.g. 2.345 x 10, 000

2. Multiplication of a decimal by an integer and a decimal by a decimal

3. Division of a decimal by an integer and a decimal by a decimal: deal with remainders by adding more zeros in the following decimal places

N.B. May be useful to try estimation first (Rayner1 P35)

38

STP 7A

Ex 2H P29

Ex6J-6L P112

Ex7B-7E P121

Ex7J P130

Ex7M-7N P138

Rayner7P31, 146-9

Pupils can convert decimals to fractions and use earlier methods in some cases e.g. 0.3 ÷ 0.09

Mymaths – number/decimals is good: Beat the clock

Sum

Product

Difference

Quotient

Effective Use of Calculator Facilities:

0. Recap on BODMAS (Brackets, powers Of, Division or Multiplication, Addition of Subtraction) in order to ascertain the order of operations in complex calculations.  

1. Recognise that the calculator also works with BODMAS (e.g. 5+2x3 is 11, not 21) and use the following calculator facilities: brackets, memory, x y , square & cube root, fraction, +/-

86-87

108

Rayner7P96 Ex1-5

STP 7A

Ex2J P32

Algebra Framework P8 (points 1&2)

Charts 15

Framework Maths: P103

Mymaths/ algebra/ formulae - Bodmas

BODMAS

Brackets

Power

Index/Indices

Use of calc needed in many cc areas (X)

STARTERS FOR THIS SECTION: Please cover the following during this handling data section (*’d means features in the scheme)

• Mixed questions on all starter ideas to date, perhaps using 0-9 cards, number fans or powerpoint presentations (Weakest link, ABCD, True-False etc.)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Averages from a frequency table:

Calculate the mean, median and mode from a frequency table. (At this stage the median may be quite challenging and pupils should be encouraged to write out data in a list if stuck)

Extension idea: pupils to try examples involving algebra (i.e. fraction equations).

256

STP 7A

Ex19C P361

Ex19E P364 Q10 →

Mixed Ex. P369

Mymaths/ Data/ Averages/ Grouped data is good (not grouped, despite the title!)

Average

Frequency table

Spread

Use real life data e.g. compare average salary, age of death etc. in varying countries (C)

Handling data task 2: F01 needed.

Song words task (see handout) – focus on interpreting findings and using EXCEL functions.

See handout

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• Revisit one-sided equations, including those with negative and fractional solutions and where, initially, like-terms must be collected.

• Recap on addition and subtraction of fractions and extend to some simple algebraic examples

• Mental Proportion problems (use NNS P78)

• Mixed decimal calculations

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Equations with unknown on both sides: (Starter: revisit one-sided equations, including those with negative or fractional answers and where like-terms have to be collected initially)

Solving equations with unknowns on both sides by balancing (do NOT use change side/change sign).  Stress that we aim to change the two-sided equation into a one-sided one, which we can read and peel off the layers in reverse (as before).  (N.B. this can be done in one step by S ubtracting the S mallest algebraic term from both sides).  The following are examples of equations that should be studied:

3x + 5 = 7x + 8;  6x – 8 = 10x + 4;  7x + 6 = 4 – 3x;  6 – 2x = 9 – 5x;  7(x+3) = 11(x-8)

This topic is a further opportunity to work with fractional and negative numbers and to check solutions on the calculator (where necessary) using the fraction and negative keys.

Extension idea: include fractional or decimal coefficients

123-5

STP 7A

Ex21j P407

Ex21k P408Q1-60 (extend to brackets)

Framework maths P159, 163

Algebra Framework P5, 15, 17

Worksheets:

Equation Snakes

Equation Steps

NB Demonstrate “Balancing” first (ask MC)

Waldo “Equations” level 4 or my maths – Algebra/ Equations/ Solving equations (tab4 on)

Balance(d)

Commutative

Linear Equation

Simplify

Solve

Unknown

Balancing chemical equations in science (X)

Construction of equations in order to solve problems:

Reinforce the power of algebraic technique over simple guess work in order to solve problems efficiently.  More difficult contexts can be used for the most able.

Rayner7P156 Ex4,5(oneside)

STP 7A

Ex21k P410 Q61 →

BBC Website “Equation Match” is a good interactive test of above skills first

Construct

Logic/ problem solving in all subjects (X)

STARTERS FOR THIS SECTION: Please cover the following during this shape section (*’d means features in the scheme)

• Mixed percentage and fraction calculations

• Recap on known fraction, decimal and percentage conversions use Mymaths/ Games/ Matching pairs game (two levels) “Fractions”

• Midway values e.g. name a fraction/decimal between two others, or the number midway between -45 and 103, for example.

• Calculations with time: check knowledge of am/pm and 24 hour clock.  Applied questions e.g. how many seconds do you sleep for in a week? (Charts 74 & 75)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Metric and Imperial Units of measurement of length, capacity and mass:

Converting between metric units and between imperial units and knowing the rough metric equivalents of imperial measures in daily use.

Extension idea: Maths Challenge 1 P38  “Extra 6” suggests some old-fashioned units to investigate

Problems 20-21

228-9

Rayner7P101 Ex1-3

Ch8 P144 (Select)

Ex9A P158

Ex9B P160

Ex9C P162

Ex20H P387

Mymaths(number/  conversion/metric units)

BBC Weigh In

NNSp21-recipes

PPT – Conversion of units

Capacity

Conversion

Length

Mass

MFL – exchange rates (note use of comma) (X)

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Yes/No game with quadrilaterals, polygons and other shapes.

• Thinking about the shapes of graphs: consider a graph as a mapping from x → y and use this to think of the shapes of x 2 and x 3 graphs (recap on horizontal, vertical and diagonal also)

• Use known number facts to discover others e.g. if 15 2 =225, then what is 15x16?  If 23x45=1035, then what is 2.3x0.45?

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Equivalence of fractions, decimals and percentages:

0. Be able to convert from any one form to another (Include examples where a mixed list has to be ordered and, hence, converted to one type e.g. ⅝, 60%, 0.71)

The above work should include calculator conversions (making use of fraction button where appropriate), known mental conversions (e.g. ¼, ½, ¾, ⅓, ⅔, … ) and new facts from old (e.g. if ¼=0.25=25% then ⅛=0.125=12.5%)

1. Appreciate that recurring decimals are fractions, know key recurring decimals in fractional form and convert from a fraction to a recurring decimal by written division e.g. 1 ÷ 7

64-65

70

74-75

45

Rayner7P208 Ex1-4

STP 7A

Ex 5E – Ex5J P79

Ex7G-7H P128

Framework Maths: P51; 145; 193

Mymaths – number/decimals/ fractions,decimals, percentages – includes match game

PPT – Conversion fracdec%

NNS applied questions e.g. which is nearer to 1 – five sixths or six fifths?

Equivalent

Recurring

Bring in % in VAT, bills, tax levels (W)

Further Fraction calculations:

Recap on fraction of a quantity and extend to fractional increase and decrease (with & without a calculator).  The more able should be able to move on to doing this in one step e.g. to increase £60 by one fifth, rather than firstly finding one fifth of £60 and then adding it on, we can find six fifths of £60

N/A

Further Percentage calculations:

1. Finding one number as a percentage of another (weak area in SATs 2004)

2. Recap on percentage of a quantity and extend to percentage increase and decrease (with & without a calculator).  The most able should be able to move on to doing this in one step and, if possible, to recognise the decimal equivalence of such calculations.

77

Framework Maths P147, 149

PPT Percentage Calculations

Decimal multiplier

What % of a £1 donation goes to charity – compare different charities (C)

STARTERS FOR THIS SECTION: Please cover the following during this handling data section (*’d means features in the scheme)

• Mixed questions on all starter ideas to date, perhaps using 0-9 cards, number fans or powerpoint presentations (Weakest link, True-False, ABCD etc.)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

Collecting and Displaying Data:

Pupils should understand the difference between discrete and continuous data.  They should be able to collect data in (grouped) tally charts and in observation sheets and be able to construct the following (chosen appropriately):

     -Bar Charts (or vertical line graphs) and histograms (label with group boundaries)

     -Pie Charts

     -Stem and Leaf Diagrams

     -Pictograms

NB The references given are often very straightforward.  Select appropriately.  Focus on WHY we might group and also stem and leaf diagrams not seen before.  Stress difference between bar and histogram but only use equal class histograms at this stage.

252-3

262-5

Rayner7P108 Ex1-3

STP 7A

Ex3B – Ex3G P39 →

Ex22B – Ex22D P416 →

Make the data relevant

Framework Maths P95

Mymaths/ Data/ Charts/ Stem & Leaf

PPT – Pie Charts

Class interval

Continuous

Data

Discrete

Frequency

Grouped data

Qualitative

Quantitative

Statistics

Tally

Data from other subjects e.g. pie chart of class religions (C), Bar chart to compare population age figures (C)

Interpreting Charts and Diagrams:

Pupils should be able to interpret data presented in graphical form and read information from line graphs after correctly assessing the scale

Pupils should be able to complete and use information given in two-way tables and construct one for their own information (link this to % work)

255

268-71

Rayner7P227Ex3

STP 7A

Ex18A P340

(Old RaynerP99)

Framework Maths: P59; 97

Two-way Table

Geography etc.  … need to analyse info given (X)

Recognise how graphs can be used in advertising etc. to make spurious claims (C)

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme).  Revision ideas this half-term in the run-up to the exams.

• Revision of percentages and fractions (Non-calculator and calculator techniques)

• Revision of decimals (mental and written methods, ordering and rounding, counting on)

• Revision of primes, squares, cubes, roots, factors, multiples, divisibility etc.

• Revision of negative numbers (Charts 12)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Generating nth term formula by considering the structure of a problem:

The aim of this section is to generate formulae for patterns/sequences by considering the structure of a problem.  This can be a big jump for year 7 and it is worth, at this stage, using the difference method to obtain a formula first and then to explain in terms of structure (if stuck).  Results tables should begin with the simplest of cases and build up to include about 5 cases.  Hence, begin by recapping on the difference methods (starter?).

Please refer to the worksheet for this section: a useful introduction is the diagrammatic sequence of squares of dots, trying to derive as many formulae as possible to link the number of dots (D) with the length of the square (L) (See sheet called “Hollow Squares”.  “Diagram Thinking” is an alternative).  Move on to further problems from those given.

Extension idea: each task can be taken as far as possible.  Can pupils develop more than one formula for certain tasks and prove, algebraically, that they are the same?

26-33

154-5; 157 (nice ideas)

Framework Maths: P7, 123, 227

Algebra Framework P9-10

Worksheet (enclosed)

Worksheets:

Diagram Thinking

Hollow Squares

PPT – Sequences by structure

Generate

Nth term

Justify

Explain

e.g. justify the formula connecting no. of hydrogens and carbons (science) (X)

Solving Problems using an algebraic approach:

Pupils to appreciate that generalisation into algebra is the most effective means of solving.

Framework maths P229

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Revision of perimeter, area, surface area and volume

• Revision of angles and rules of angles

• Revision of handling data i.e. probability, averages and spread.

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

NB Good time to do ICT activity (see booklet) entitled “Using the internet”

Tests of Divisibility:

Recognise when a number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10.Apply e.g. what would the divisibility test be for 15?  Use Maths Challenge 2 P1-2.

Extension idea: Maths Challenge 3 P13 “Divisibility Rules”; Can you find a test for 7?

52, 53

Rayner7P18

STP 7A

Ex4G P55

In whole section, NNS has nice problems (see P52 → )

Divisible

Digital Root

Factors:

Find the factors of any number by pairing and explain why a square number has an odd number of factors.  Hence, when finding factors, we only need to search up to the square root.

Find Highest Common Factors (H.C.F.) and define prime factors

52

Rayn.7P83Ex1,3

STP 7A

Ex4B P50

Ex4I P56

BBC Website – “Grid Game” is good, interactive starter on all no. facts

Factor – “guzzinta”

H.C.F.

Product

Prime Factor

Multiples:

Finding the multiples of a number and the Lowest Common Multiple (L.C.M.) of more than one number

54

Rayn.7P84Ex2,3

STP 7A

Ex4C P50

Ex4J P57

Spreadsheets to generate multiples

Framework Maths P118

Multiple

L.C.M.

Primes:

0. Define a prime number as a number with only two factors

1. Testing for a prime number (search for prime factors up to square root)

Extension idea: for all of the above, pupils to investigate (true/false) statements e.g. 24 is the number below 100 with the most factors; A multiple cannot be prime etc. ALSO USE MATHS CHALLENGE 1 p14-16; MATHS CHALLENGE 2 P5 “EXTRA 1”.

Rayner7P88Ex5-7

STP 7A

Ex 4D P51

Sieve of Eratosthenes

MC has grid game to test above properites.

Prime

Try mixed NNS examples e.g. Find two primes with a sum of 45; Use the digits 6,7,8 to make the largest multiple of 6; Find the smallest number >50 with the same many factors as 50; Find a number that remains prime when its digits are reversed. Etc.

NNS as above

Framwork Maths P119, 183

Indices and Roots:

Check that all pupils know at least the first 15 square numbers and their corresponding roots and that they can square negatives, decimals (e.g.0.3²) and fractions (e.g. (⅜)²) and approximate square roots e.g. √ 98 and further square roots e.g. √ 36000000.

Check that all pupils know at least the first six cube numbers (and 10³) and their corresponding roots and that they can cube simple negatives

Use index notation and evaluate mentally and on calculator, including powers of 0, ,1, 2 & 10

Extension idea: investigate, say, when(-2) n is positive

56-58

e.g. What digit does 81² end in?

Rayner7 Ex3P94

STP 7A

Ex4E P53

Ex4F P54

Power

Index/Indices

Square root

Cube root

Prime Factor Decomposition:

Express positive integers as a product of prime factors, using factor trees if required.  Include applications e.g. if the product of my age and that of my younger sister is 700, how old could we be?  Try and use in calculation e.g. √ 576 (see NNS reference)

Extension idea e.g. use factor decomposition to work out square roots.

53

Rayner7Ex1P84

STP 7A

Ex4H P56

PPT – Factor trees

Factorise

Product

Prime factor

Use “real life” numbers e.g. £32,125 is the average salary in country X – decompose this number (C)

STARTERS FOR THIS SECTION: Please cover the following during this handling data section (*’d means features in the scheme)

• Revision of writing expressions and substitution (revise negative numbers here)

• Revision of equations

• Revision of brackets and collecting like terms

• Revision of graphs (equation, shape, plotting etc.)

• Revision of sequences

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Effect of outliers, missing data and anomalies: Stress the meaning of each term and look at their impact e.g. what happens to mean if one of your ages is recorded as 21 instead of 12?

Use Autograph to promote discussion

Anomaly

Outlier

Look at effect of outliers in advertising e.g. average salary is £32,000 in our company (W/C)

A mini statistics project (Aim/Collect/Display/Analyse/Conclude)- see data handling task 3:

Initially revise all Handling data skills to date and then undertake task 3.  Details in handout.  F01 needed.  The focus in again on interpretation, use of EXCEL and choosing graphs and calculations appropriately.

See handout

Promote skills of enquiry (c) and working in new teams (W); Use of ICT in reporting and presenting (W)

STARTERS FOR THIS SECTION: Please cover the following during this shape section (*’d means features in the scheme)

• Mixed questions on all starter ideas to dateperhaps using 0-9 cards or number fans

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Rules of Angles:

0. Sum of angles at a point; Sum of angles on a line; Vertically Opposite angles

1. Angles in a triangle and Exterior angles of a triangle

2. Angles in a quadrilateral

3. Alternate, Corresponding and Interior angles

4. Proof  that the sum of angles in a triangle is 180 °

NB The work should be used to reinforce the use and solution of equations e.g. x+55+89=180.  Emphasis must be placed on correct terminology – although “Z” angles is a useful way of identifying their position, they must be referred to as alternate angles now.

Extension idea: pupils extend work to angles in polygons (own research?).

181-3

Using & Applying P16-17

Rayner7 P128 Ex1-5

STP 7A

Ex10K –Ex10M P190;

Ex12C P216 & Ex12L P227

Ex12H P225

Ch 15 P275 (Parallel)

Sheet on proving angles in a triangle (see MCA)

Waldo Maths site “Angles-the X rule”, “Angles & parallel lines” & “Angles in Triangles” are nice visual lessons; Mymaths/ Shape/ Angles has “Angles in parallel lines”

PPT Angles in Parallel Lines Quiz

Intersect

Parallel

Point

Straight

Sum

Transversal

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• See fraction starter below.

• Short algebra tasks – see algebra 5 content (use any unused ideas) ( ≈ 4lessons)

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Proof by algebraic techniques:

Introduce the idea of proof and prove some simple statements algebraically e.g. the sum of 3 consecutive integers is always a multiple of 3; the sum of an even and an odd number is always odd.  Use Maths Challenge Book 1 P24-6 & Book 2 P23-5 for some guidance.

32-35

N/A

(Intro. P197 Rayner)

Compare an algebraic and a geometric proof e.g. sum of odd and even is odd.

PPT - Proof

Proof

Can we prove that God exists? (C)

Equations:

Recap on all work to date and extend to simple cases involving fractions (focus on “cross-multiplication” at this stage): begin by investigating relationships within equivalent fractions  i.e. (Use as a starter)

, an understanding of which is required for much later work, including similar figures, trigonometry, etc.  More detailed work will be done on fractional equations in year 8.

Framework Maths P219

BBC Website “Equation Match” is a good interactive review of previous work on equations.

Cross-multiply

0. Simplifying expressions: recap on multiplication, division, collecting like terms and expanding brackets.

1. Extend bracket work to have a look at negatives e.g. 3(x+2) – 5(x-8).  Try and include other situations in which negatives appear and which regular mistakes are made e.g. If P=3x+7 and Q=2x-9, find P-Q.

Framework Maths P223

A3 write on sheets – Arithmagons etc.

Expand

Simplify

0. Recap on graph work (horizontal, vertical, diagonal, parabolic, plotting, etc.)

1. Use the graphical calculators (or personal plotting) to look at:

          -Parallel lines y=x+1, y=x+2, …

          -Lines of varying steepness y=x, y=2x, y=3x, …(P12 NNS)

0. Have a look at drawing and interpreting some real life graphs at this stage e.g. if you have 11 housepoints and you get 4 a week from now on, draw a graph to represent this information.  Can you establish its equation?

167

137; 172-7

Framework Maths P231

Algebra Framework P14

Autograph & constant controller or

Waldo Site “Straight line graphs” is a look at varying m & c.

Gradient

Intercept

Steepness

MFL: Conversion Graphs (X)

STARTERS FOR THIS SECTION: Please cover the following during this handling section (*’d means features in the scheme)

• Select other starters as required (i.e. ones skipped earlier in year, ones that need repeating or a  focus on key failings in summer examination).

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

Travel graphs:

Key points (i.e. horizontal lines, steeper lines, lines with a negative slope) and a basic understanding of speed (e.g. travelling 20km in 15 minutes is equivalent to 80km/hr.  Is this fast?).  Try to encourage “speed” questions by thinking, not by the formula S=D/T

173

Rayner7 P222 Ex1&2

Get pupils to draw the travel graphs for the journeys that you make across the front of the room

Accelerate

Decelerate

Motion

Speed

Physics (X)

Plot a distance-time graph to a disaster zone (C)

Other Real life graphs:

Examples to include conversion graphs and depth of water in various containers, say.

Extension idea: pupils to draw a depth/time and a volume/time graph for various containers.

172-177

STP 7A

Ex18B P343

Framework maths P233

Mymaths/ Algebra/ Graphs/ Real life – tab1-3 is speed, 6-8 are filling containers

MFL: currency; Science Exp.(X)

STARTERS FOR THIS SECTION: Please cover the following during this number section (*’d means features in the scheme)

• Ratio calculations e.g. sharing in a given ratio (see examples P80, 81 NNS)

• Select other starters as required (i.e. ones skipped earlier in year, ones that need repeating or a  focus on key failings in summer examination).

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

Proportion:

Simple direct and indirect proportion e.g. if 8 coffees cost £3.28, how much would 13 cost? If 4 men take 9 days to dig a hole, how long would it take 7 men? Use the cost or value of 1 item as an intermediate line of working.

79

Rayner7 P136 Ex2 (add in indirect examples)

Use recipes from different cultures.

Framwork maths P151

Proportion

Direct/Indirect

Inversely

What proportion of babies die before their 2 nd birthday? (C); What proportion of your salary do you keep? (W)

Introduction to Ratio:

1. Understand the idea of a ratio and use ratio notation, cancelling to simplest form and using equivalent ratios.

2. Understand the relationship between ratio and the fraction family e.g.

The ratio of black:white is 1:4 – the proportion of black is 20% or 0.2 or 1/5

78

Rayner7P137 Ex3

Framework Maths P153

Obtain the ratio of the height of your belly button to your full height in the form 1:n.  Do you fit the Golden Ratio?

Ratio

Cancel

Simplest form

Equivalent

Golden Ratio e.g. in Art (X)

Ratio Calculations: to include sharing in a given ratio (link to fraction work)

e.g. If the ratio of pigs:cows on a farm is 2:3 and there are 24 cows, how many pigs are there?

      If the ratio of girls:boys in a class is 4:7 and there are 33 pupils in total, how many boys are there?  

4-5 (Mix of examples)

80-81

As above

Extend to algebra if able.

Food Tech: recipes (X); What is the ratio to time spent working and on leisure in the UK? (W)

STARTERS FOR THIS SECTION: Please cover the following during this algebra section (*’d means features in the scheme)

• Mixed questions on all starter ideas to dateperhaps using 0-9 cards or number fans

CONTENT:

(Key Objectives Listed in bold)

NNS

Reference

Key Texts

STP/Rayn

Other Ideas/

Resources

Vocabulary

X/W/C

NB Good time to do ICT activity (see booklet) entitled “Omnigraph”

Symmetry: ensure that pupils understand rotational and reflection symmetry, especially when applied to quadrilaterals and polygons.

Extension idea: Maths Challenge 1 P17: “Exploring Holes”; P19 -20“Symmetry Plus”; Maths Challenge 2 P33 “Extra 5”.

Rayner7 P174 Ex4; P177 Ex2,3

Pupils to construct a rangoli patterm for display

Reflection

Rotation

Order

Artwork (x)

Mixed Work: Undertake mixed examples on the following, where needed:

Angles and the rules of angles

Perimeter and Area

Surface Area and Volume (make sure the two are not confused)

Conversion of metric and imperial units

As before

Using & Applying Examples P14-21

As before

As before