YEAR 8: SUMMER TERM

Teaching objectives for the oral and mental activities

a) Order, add, subtract, multiply and divide integers.b) Multiply and divide decimals by 10, 100, 1000, 0.1, 0.01.c) Round numbers, including to one or two decimal places.d) Know and use squares, cubes, roots and index notation.e) Know or derive prime factorisation of numbers to 30.f) Convert between fractions, decimals and percentages.g) Find the outcome of a given percentage increase or

decrease.

h) Know complements of 0.1, 1, 10, 50, 100.i) Add and subtract several small numbers or several

multiples of 10, e.g. 250 + 120 – 190.j) Use jottings to support addition and subtraction of whole

numbers and decimals.k) Calculate using knowledge of multiplication and division

facts and place value, e.g. 432 0.01, 37 0.01, 0.04 8, 0.03 5.

l) Recall multiplication and division facts to 10 10.m) Use factors to multiply and divide mentally, e.g. 22

0.02, 420 15.n) Multiply by near 10s, e.g. 75 29, 8 –19.

o) Use partitioning to multiply, e.g. 13 1.4.p) Use approximations to estimate the answers to

calculations, e.g. 39 2.8.

q) Solve equations, e.g. n(n – 1) = 56, + = –46.

r) Visualise, describe and sketch 2-D shapes, 3-D shapes and simple loci.

s) Estimate and order acute, obtuse and reflex angles.

t) Use metric units (length, mass, capacity, area and volume) and units of time for calculations.

u) Use metric units for estimation (length, mass, capacity, area and volume).

v) Convert between m, cm and mm, km and m, kg and g, litres and ml, cm2 and mm2.

w) Discuss and interpret graphs.x) Calculate a mean using an assumed mean.

y) Apply mental skills to solve simple problems.

Number 4 (6 hours) Y8 Summer term

Calculations (82–87, 92–107, 110–111)

Measures (228–231)

COREFrom the Y8 teaching programme

A. Understand addition and subtraction of fractions and integers, and multiplication and division of integers; use the laws of arithmetic and inverse operations.

B. Use the order of operations, including brackets, with more complex calculations.C. Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages, squares and square roots,

cubes and cube roots; solve word problems mentally.

D. Make and justify estimates and approximations of calculations.

E. Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places.

F. Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.

G. Check a result by considering whether it is of the right order of magnitude and by working the problem backwards.

H. Use units of measurement to estimate, calculate and solve problems in everyday contexts.

Unit: Number 4 Year Group: 8

Number of 1 Hour Lessons: 6 Class/Set: Core Note Many of the objectives are consolidating or repeating objectives from ‘Number 3’ and work should be planned considering the progress made in ‘Number 3.

Oral and mental Main Teaching (2 lessons) Notes PlenaryObjective h, i and jUsing mini white boards or other means, ask for complements of numbers to 50 and 100extend to decimals

e.g. 1.2 complement to 10 (8.8) etc.

Explore how to mentally complete calculationse.g. framework section 4page 93 (last Y8 paragraph)page 97page 101extend into main teaching if necessary.

Objective d. jSquares and square rootsRevisit estimating √ of numbers < 200 and squaring numbers up to 100.(use calculator to check and revisit key pressing operations).

Objective A (integer) F (decimals)Model addition and subtractions of integers – extend to decimals using standard column procedures – highlight short cuts and estimations (relate to number line or ruler if needed).Practise in groups/pairs if needed with questions/problems in context if possible (Objective H)_____________________________________________

Use oral and mental objective k to revisit multiplication and division by 0.1, 0.01 etc. and multiples, extend to standard column procedures for multiplication and division of integers and decimals by integers and decimals to 2 decimal points (Objective F)Build on work done in ‘Number 3’.Set problems in context.Insist on estimates and approximation by rounding where possible.Build in objective G by modelling inverse operation to check results for some problems.

Extend to 3 lessons if necessary.

Vocabularyequivalentinverse

Much of this work will depend on progress in ‘Number 3’.

Generalise on procedures especially checking answers and inverse operations.

Deal with observed misconceptions. Explore equivalent calculations and

why they are equivalent. Model difficult questions. Pupils note down what is to be

learned. Model incorrect solutions observed

and discuss. Revisit oral and mental starters to

assess learning. Ask for paired solutions to questions

with explanations of methods – explore alternatives.

Oral and mental Main teaching (2 lessons) Notes PlenaryObjective fUse fractions target board to match equivalent fractions (extend to decimals and percentages), or using mini white boards invite students to give equivalents as teacher points to a point on a number line.e.g. 0.5 ½ 50%

Discuss how we convert.

Count up in fractions using a counting stick.

Chant together.1/5 of 1 is …...1/5 of 2 is …...1/5 of 3 is …..

(See multiplicative relationships Y8mini-pack)

Objectives A and C (fractions) incorporating (D, G and H)Model the process of adding simple fractions (eg 1/4 + 3/8) revisit why 1/4 = 2/8 etc.Paired work solving problems.Extend to questions with improper fractions answerse.g. 3/4 = 3/8 = 6/8 + 3/8 = 9/8Discuss conversion of improper fractions to mixed numbers.Further paired work – develop to include subtraction.Develop to worded questions or questions in context or extend to 1/2 + 1/3 etc.

Game ideaRoll dice 4 times to create a ‘sum’e.g. 1, 5, 3, 6 would give1/5 + 3/6 pupils calculate answer and check with calculator.(See fraction game for extended activity)*Extend to ÷ and x as time allows for whole class or groups.

Much of the ground work will have been covered in ‘Number 2’.The work here can consolidate, revisit or extend that work.

VocabularyNumeratorDenominatorEquivalentMixed NumbersLowest termsCancelProper/improperFactorMultiple

*Calculators with fraction key needed.

Generalise processes. Produce flow chart on what we do

when faced with an addition of fractions problem. (See fraction flow chart example)*

Model solution to problems e.g. 1/10 + 1/15 using 30 and then 150 as common denominators.

Why is 3 x 1/5 the same as 1/5 of 3? How do we change an improper

fraction to a mixed number (vice versa?)?

Explore links between fraction decimals and percentages.

Extend to 2½ x 2½ link to partitioning(2 + ½) (2 + ½) etc.

Oral and Mental Main Teaching (1 lesson) Notes PlenaryObjective gWhich is bigger½ or 60%¾ or 70%0.7 or 60% etcjustify answersextend to ordering several quantities.

Objective HWhat fraction is 25 cm of a metre?What fraction is 3” of a foot etc. (Mini-white board responses) or choose from fraction on blackboard/OHT.

Objective a and Objective B‘Countdown’ using the digits 3, 7, 2 and 8 and any operations, can you make 25?

(3 x 7) + (8 ÷ 2)Use each digit only once.Discuss brackets’ use and alternative solutions.

Objective C (or d from mental)Revisit rounding particularly to nearest whole number – nearest 10, 100 etc.Discuss estimates to get a good approximatione.g. 467 x 24 400 x 25 or 500 x 20

(see framework section 4 page 103)Include 127 x 31 19

Tasks/activities based on the aboveOpportunity to link back to calculations where pupils estimate and then complete calculation.Opportunity to extend to worded questions.

VocabularyBest estimateRoundApproximately

Calculators needed.

Generalise Consolidate Revisit difficult questions. Use in context How does the Head

of Maths estimate how many packs of exercise books to order each year?How many report slips will the school order this year etc.

When do we need to over estimate or always round up etc.

Revisit starters not used.

Oral and Mental Main Teaching (1 lesson) Notes PlenaryRepeat ‘count down’ activity stressing the use of brackets

Objective BHow many different answers are possible putting brackets into this expression.

3 x 5 + 3 – 2 x 7 + 1(See page 87 of framework)

Work in pairs, discuss feedback.Discuss BODMAS – establish that addition can be done before multiplication by using brackets e.g. 6 x (2 + 3)Task – how would you calculate 100 ? (Mental) 4 x 5 How would you use a calculator to complete this calculation? (brackets, memory, reciprocal key)How do we do it without special keys?Establish 10 ÷ 4 ÷ 5 NOT 10 ÷ 4 then x 5. Consolidate – practise with and without special keys.Extend to 46 x 32 41 x 11 link to approximation if time . Model and extend to questions involving roots and powers as on (page 87).

BODMAS or BIDMAS

VocabularyReciprocalIndex numberPower

Generalise – note down key findings for students to learn.

Why can’t 16 = 16 ? 4 x 4 What might someone have done to

get this answer:(16 ÷ 4 then x 4)

Revisit different keys to use on a calculator to solve the above.

Read out some worded questions leading to expressions like: 42 etc6 x 3

Check pupils’ responses. Do calculations.

Space Shapes and Measures 3 (4 hours)Y8 Summer Term

Geometrical reasoning: lines, angles and shapes (190–191)

Transformations (202–215)

Ratio and proportion (78–81)

COREFrom the Y8 teaching programme

A. Know that if two 2-D shapes are congruent, corresponding sides and angles are equal.

B. Transform 2-D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT; identify all the symmetries of 2-D shapes.

C. Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor; explore enlargement using ICT.

D. Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation.

Unit: Space shape and measures 3

Year Group: 8

Number of 1 Hour Lessons: 5 Class/Set: Core

Oral and mental Main Teaching (2-3 lessons) Notes PlenaryObjective rRevisit names of shapes and properties. (perhaps use OHT of SSM2 asking about angles shapes- labelling etc.)Establish the meaning of congruence.Talk about transformations to produce a patterns (worksheet OHT SSM5) Relate to wall paper perhaps and designers’ ideas or methods of producing patterns. Begin to discuss how we describe transformations. Discuss what changes and what stays the same.

Objective A and BRevisit last activities with quick sharp questions. Perhaps use an OHT of SSM3 to ask about congruence and translations.

Objective AActivities to establish congruence and rules for establishing congruence. Perhaps use worksheet like SSM2 or SSM3 to decide through measuring whether shapes are congruent. Can we prove congruence? How can we prove a diagonal of a square can produce two congruent triangles –extend to a parallelogram and rhombus.Objective BFocus on translations. Introduce vector notation to describe translations. Clarify corresponding (sides angles vertices etc.)

Objective BDiscuss and model reflections – initially in horizontal and vertical lines - then use coordinate plane. Establish rules and conventions. Highlight object and image distance from line of reflection symmetry. How does it relate to lines of symmetry within shapes? Move to reflection in non-vertical/horizontal lines.

VocabularySimilarCongruent EnlargementCorresponding TransformationTranslationVectorOrientation

ReflectionSymmetryObjectImage

Revisit vocabulary used- encourage use and sentence description of transformations.

Discuss other transformations yet to be covered.

Relate to ICT and drawing packages – how to they allow us to transform a shape? – Model using simple word package if facilities are available.

Check understanding of vector notation.

How else could we describe a translation (bearings)?

Re-establish –what is different – what stays the same after a transformation.

Model difficult reflections- discuss strategies.

Extend to 3D reflections using isometric paper.

Establish rules and strategies and conventions.

.

Oral and mental Main Teaching (2-3 lessons) Notes PlenaryObjectives A and BModel before and after transformations and ask students to describe accurately the transformations.

Objectives C and DShow two pictures where one is an enlargement of the other. (SSM4) Discuss why one is an enlargement. How do we describe an enlargement? Introduce or revisit ratio of corresponding side length. Ask for equivalent ratios. Ask students to calculate corresponding lengths of a shape given a ratio for enlargement.

Objectives BModel some rotations.Establish we need a direction, angle and centre of rotation to describe rotations. Practise exercises on rotations and combining transformations

Objectives C and DModel enlargement introducing centre of enlargement and scale factor. Practice exercises needed.Extend to centres of enlargement at a vertex of a shape and within a shape. Explore how to find a centre of enlargement.

Consolidation work can be done using worksheet SSM1 and the questions on SSM1q. (This could be incorporated into the problem solving unit.

VocabularyRotationCentre of rotationCombineOrigin

Centre of enlargementEnlargementEquality of ratiosScale factorProjected lines

Revisit rules for describing rotations

Establish –what is different – what stays the same after a transformation.

Relate to rotation symmetry of shapes.

Perhaps visit the conjecture that two reflection equal a rotation of 180o

-when is this true? What happens to coordinate

under transformations – can we find rules?

How can we check A4 is an enlargement of anA5 piece of paper?

Move around a piece of A4 and A5 paper. Guess where the centre of enlargement is (use smaller pieces on an OHP).

Revisit rules and ratios. Relate to shadows cast by the sun

and similarity.

Algebra 5 (8 hours) Y8 Summer term.Equations and formulae (116–137)

Sequences, functions and graphs (164–177)

Solving problems (6–13, 28–29)

COREFrom the Y8 teaching programme

A. Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.B. Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets)

using appropriate methods (e.g. inverse operations, transforming both sides in the same way).

C. Begin to use graphs and set up equations to solve simple problems involving direct proportion.D. Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT.E. Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs

arising from real situations.F. Solve more demanding problems and investigate in a range of contexts: algebra.G. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for

algebraic manipulation.

Unit: Algebra 5 Year Group: 8

Number of 1 Hour Lessons: 8 Class/Set: Core

This unit revisits and builds upon Algebra 4. Core groups will need to address any items not covered in Algebra 4 here. Extend work with equation and expressions particularly with inclusion of fractions and negatives if Algebra 4 is secure. Objectives E, F and G are the targets for groups secure in Algebra 4.Oral and mental Main Teaching (2/3 lessons) Notes PlenaryObjective A and objective a(Using mini white boards)Put 1, 2, 4, 8, on the blackboard.Ask students to make other numbers using the above and the four operations.e.g. 21 = (2 x 8) + 4 + 1share results. Code each number e.g.a = 1, b = 2, c = 4, d = 8Repeat the activity but ask for expressions to make the target numbers.

Objective AOffer expression –ask for simplificationse.g. 2 (x + z) 3x + 2x + 1Check misconceptions and generalise.

Objective ARevisit bracketsi.e. 3 x 24 = 3(20 + 4) = 3 x 20 + 3 x 4because this is the same as 20 x 3 + 4 x 3we have 20 lots of 3 and 4 lots of 3 to give 24 lots of 3 i.e.24 x 3 = 3 x 24Explore.Extend to algebra 3(a + b) 3(a + 2b) a(a + 2b) etc.Practice questions needed.

Activities (choose and develop from the activities worksheets)Magic squaresFollow on cardsAddition squaresTiles (or Tactiles available from Tarquin Publications)Number walls ( also in framework page 117)

In these two lessons – try activities which encourage the use of collecting like terms in interesting ways.

VocabularyDistributiveCollectLike termsSimplify

Address generalisations. Deal with misconceptions. How can we check

2(a + b) = 2a + 2b(substitution/model)

How many a’s in ab?(answer b) – explore.

How many a’s in 2a2? Extend to factorisation.

If this is x

and this is y

What is this?

(Ans x –y) What would 2(x – y) look like?

4(x – y)? Is it the same as 4x – 4y?

Model.

Oral and mental Main Teaching (2/3 lessons) Notes PlenaryMissing numbers

2 x = 47

÷ 3 = 6

2 + 5 = 21

etc. Pupils feedback how they solved the problem.

Missing numbers but this time writing as in algebra.

3a – 2 = 17 etc.a = 21 (expect 3 as an7 answer)

Fences (if x is the width of a fence

25What does this give in algebra?

3x + 7 = 25 etc.Solve

7 2 3x – 2 = 7 3x = 9 x = 3

Objective BNeed to build on ‘algebra 4’ towards the stage where students can solve:

4(n + 3) = 6(n – 1)

At each stage try and build in worded questions since the objective is to construct and solve linear equation.Encourage checks by substitution.

VocabularyExpressionSimplifyEquationSolveSolutionVariable

Generalise on successful strategies – model questions and solutions (Objective G)

Model building/constructing equations from worded problems.

a + b = 10Can we solve this equation?

What about3(x + 2) = 3x – 1 Does this have a solution?

3(x + 2) = 15=>x + 2 = 5 Why?=>x = 3 Why?Is this a good method?What has happened?Do we always have to multiply out brackets?

x x 7 x

x x x

Oral and mental Main Teaching (2/3 lessons) Notes PlenaryObjective wRevisit starters from ‘Algebra 3’.

Objective sDiscuss cm mand a conversion graph extend to imperial metric and discuss.Why is ºC ºF different?

Objective C, D, E, FA different approach would be to present x and y tables with missing valves e.g.

Find the relationship (y is double x)Make the equation y = 2x and plot the graph.Generalise about graph line of x = 2 y = 3 etc.i.e. lines parallel to axes.Re-establish y = mx + c with gradient intercept idea.Extend to problems of distance/time and direct proportion (see framework page 137)Link to muliplicative relationships.

Much of this builds on ‘Algebra 3’ or can be used to complete ‘Algebra 3’ if not all the areas were covered.

ICT Graph package or Excel could be used.

Revisit human graphs (Algebra 3) Model change from gallons to litres

ORFrancs to Euros etc. and how graphs could help.

Establish direct proportion in a straight line (y = mx) and how it differs from y = mx + c.

Explore where functions intersect The line y = xe.g. y = 3x – 2 intersects at (1,1). Note that in a function this is a special point since input = output.

x 3 5 2 1

y 6 10 7 2 99

Notice order of numbers.

Shape, space and measures 4 (9 hours) Y8 Summer term

Geometrical reasoning: lines, angles and shapes (198–201) Transformations (216–217)Coordinates (218–219)Construction and loci (220–227)Mensuration (232–233, 238–241)

A. Know and use geometric properties of cuboids and shapes made from cuboids; begin to use plans and elevations.

B. Make simple scale drawings.

C. Given the coordinates of points A and B, find the mid-point of the line segment AB.

D. Use straight edge and compasses to construct: a triangle given three sides (sss) – use iCT to explore this construction.

E. Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle.

F. Use bearings to specify direction.

G. Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids.

Unit: Shape, Space and measures 4 Year Group: 8

Number of 1 Hour Lessons: 9 Class/Set: Core

Oral and mental Main Teaching (1 or 2 lessons) Notes PlenaryObjective rDraw each shape on the board.

Say that each one is a plan view of a 3D shape.Invite pupils to describe the 3D shape.Establish alternatives and that a plan view is not sufficient.

Objective AChoose one of the starter shapes or another shape and establish what other elevations will look like to picture the shape.

E.g. Plan Side

Front

Discuss dotted lines for hidden lines.Paired work building shapes from cubes and drawing 3D sketches (isometric paper) and plans/elevations.

OR

Set question on using plans/elevation to produce 3D or vice versa.

Search the net for Soma Cubes for some good diagrams.

Key VocabularyElevationPlan viewIsometric

Revisit key language. Use examples from lesson to discuss. Use a task similar to the starter

activity. Model using isometric paper to

construct a confusing shape made from cubes.

Show some 3D shapes and ask which views give the most information.

(Page 199) some interesting questions to assess understanding.

Oral and mental Main Teaching (2 lessons) Notes PlenaryObjective rTry some visualisation activities (See sheet – ‘Imagine’)Teacher reads out visualisation and pupils try and guess the every day object.

OR

Extend the work on plans and elevations e.g. give plan new and 2 elevations and ask pupils to describe or sketch the 3D shape.

Objective GRevise area of rectangle.Extend to surface area of a cube/cuboid.Try and link to formulae and brackets to generalise.

2lw + 2lh + 2hw = 2(lw + lh + hw)Questions on finding surface area of cubes, cuboids – extend to shapes made from cuboids.Link to cost of painting a room given coverage of paint and cost per litre. (See page 239 onwards)Volume of cube, cuboids and shapes made from cuboids.Demonstrate and set tasks.Extend to: capacity of shapes in litres; one shape filling another.

U.A.M.I have 60cm of stiff wire. I make a cuboid with the wire (frame).If it was solid what could be its maximum volume/surface area?Will factors/prime factors help? (Objective e)

Key VocabularyVolumeSurface Area

What is area? What is volume? Why do we use the word capacity? What is the link between volume and

litres? (Relate to c.c. and car engine’s size)

Model some solutions. Model doing formula perhaps. Can nets help in finding Surface

Area? How can we calculate surface area of

the walls of a room? Can we find a formula to help decorators?

Explore shortcuts in calculations.2 x 6.5 x 5 for instance (objective l)

Explore surface area and volume using fractions and decimals.

Explore ‘twice as big’ for area and volume – what problems does this create?

What about 10% increase in area or volume? (Objective g).

Oral and mental Extended Main Teaching (1 lessons or maybe 2 lessons) Notes PlenaryObjectives E, u, v.Quick fire questions on how many cm in a metre – change 2.3cm to mm etc. (Mini white board responses).What is the area/volume of….?Show me 10 cmShow me 1 metreShow me 50 cm.

Using paper or co-ord. grid in plastic sleeves to make mini- white boards (see sheet).Ask pupils to plot at points given pairs of co-ordinates shouted out by teacher.After each pair ask pupils to join each pair with a straight line and find mid-point.Record results.Look for a pattern/rule e.g. for (x, y) (x1, y1)midpoint (x + x1, y + y1) 2 2 Ask pupils to write a sentence to describe the rule. Check it works.

Objective BRevisit ideas from muliplicative relationships on ratio and scale.Explore making scale drawings of objects and discuss suitable scales.(Kitchen planning catalogues are a useful resource).Build towards students making a scale drawing of a plan view of their bedroom as a homework task.

Vocabulary (some from Y7)Axes Axis Co-ordinates

Mid-pointEnlargeReduce.

Explore why mid-point rule worked for pairs of co-ordinates – check they can remember the rule.

Who uses scale drawings? How and why? Is a plan view always best? Are maps really to scale (No since

roads would be too wide).(How wide would a road be if it was scaled up from a map?)

Link to geography ICT. How are scales/plans used?

Oral and mental Main Teaching (1 lesson could extend to 2 with) Notes PlenaryObjective rImagining loci.Teacher describes situations e.g. tip of aeroplane propeller – ‘plane is still’ – ‘plane moves in straight line’ etc.Stone thrown in different situations.Part of a child’s body on a playground swing (consider feet and head!!)A goat tethered to a stick in a field etc.Pupils model on paper or mini-white boards.(See page 225 for more loci ideas)

Objective D and EDemonstrate using a 2 metre piece of string – the different triangles your can make with a perimeter of 2 metres.Activity (Pairs)Pupils with a 30cm drinking straw or 30cm piece of string experiment to find how many triangles can be made.Tabulate results.Take feedback – what triangles cannot be made? (e.g. 16cm, 7cm, 7cm) Why not?Ask pairs to make a triangle 12cmm 9cm, 9cm. Model, with a straw or string, the movement of the two 9cm sides until they intersect. (Highlight – loci)Extend to how this could help us to construct this triangle in books using pair of compasses and ruler.TaskExercises on constructing triangles and quadrilaterals (S.S.S.).

Extend to 2 lessons if needed. Questions needed involving sketching loci.Link to constructions work from earlier unit.

If a dynamic geometry package is available model loci and construction. Could use logo to produce shapes.

VocabularyPerimeterLocusLociIntersect(S.S.S.)CongruentLocus in a plane.

Revisit why, given a perimeter, some triangles cannot be made.

Ask pupils to demonstrate constructions.

How many different triangles with lengths 10, 12, 18 can we make?

What other 3 measurement would enable us to construct a triangle (if we had a protractor).

What is a circle? (Define as a locus) What about a sphere?

Oral and mental Main Teaching (2 lessons ) Notes PlenaryObjectives s and yRevisit acute, obtuse & reflex angles.Show me –Guess the size etc.Working out missing angles particularly in triangles and using parallel lines, corresponding and alternate or interior (allied) angles.

Navigating a person from A to B in a classroom (or even around school using imagination) using directions, distance and bearings.(Could use a shape to navigate around an OHT of a map).

Objective F Introduce – model bearings, revision of protractor use.Stress 3 figures and clockwise from North.Encourage drawing in all the North lines.Draw attention to North lines being parallel.Encourage look and say activities. The bearing of A from B is ….! etc.

Paired activityProduce a worksheet with points A, B, C, D, E ……H. Pupils have to draw in and label bearings to get from A to H via other points.Feedback and discuss.

Paired activityReturn journeys measuring return bearings from B to A etc.Make links – move to calculating return bearings.Extend to scale drawings and worded questions.

VocabularyAcuteObtuseReflexParallelTransversalAlternateCorrespondingInteriorBearingClockwiseCompass directionsThree-figure-bearing____________________The next unit is on problem solving and this unit may extend into it.

Revisit starter using bearings. Model difficult problems. Discuss generalisation and strategies. If distances are scaled, why aren’t

bearings/angles? How has our angle work helped? Who will use bearings? Address misconceptions.

Handling data 3 (7 hours) Y8 Summer Term

Handling data (248–275) Probability( 284–285) Solving problems (28–29)

COREFrom the Y8 teaching programme

A. Discuss a problem that can be addressed by statistical methods and identify related questions to explore.B. Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources.

C. Plan how to collect the data, including sample size;D. construct frequency tables with given equal class intervals for sets of continuous data.

E. Collect data using a suitable method, such as observation, controlled experiment, including data logging using ICT, or questionnaire.

F. Calculate statistics, including with a calculator; calculate a mean using an assumed mean; know when it is appropriate to use the modal class for grouped data.

G. Construct, on paper and using ICT:- bar charts and frequency diagrams for continuous data;- simple line graphs for time series;

- identify which are most useful in the context of the problem.H. Interpret tables, graphs and diagrams for continuous data and draw inferences that relate to the problem being discussed; relate

summarised data to the questions being explored.I. Compare two distributions using the range and one or more of the mode, median and mean.

J. Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is presented.

K. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using graphical representation, and also resources, including ICT.

Unit: Data Handling 3 Year Group: 8

Number of 1 Hour Lessons: 7 Class/Set: Core

Oral and mental Main Teaching (2 lessons) Notes PlenaryObjective wDisplay a graph and invite comments about interpreting the chart.(See example) H. D. A.Begin by covering up the title, key and all other labels. Reveal a few at a time- asking questions about what the chart might show.

Revisit with other charts (perhaps HDC stem and leaf or less familiar charts) (pages 263 or 357), H.D.D. Discuss two way table (see example)(Page 255) H.D.E.

Objectives A, B, C.Paired activity – discuss and then share how the information on the starter chart might have been collected.Discuss with whole class types of data collection – questionnaire, observation, interview, data base, experiment.Pose situations where data is needed for collection and ask groups to decide on which way the data could be collected.(See page 249 for possible situations.) Take feedback.Discuss accuracy needed and discrete/continuous data.Discuss sample size!

Objective E Data CollectionProvide an acetate sheet of pupils’ names and an OHT pen for each group and ask them to collect data.E.g. Height, arm span, hair colour, shoe size, time to get to school, birth month, number of filling, brothers/sisters etc.Display each acetate and discuss the data and any emerging observations/conjectures– recording system – accuracy.

VocabularySamplePrimary sourceSecondary sourceData logData baseDiscreteContinuousTwo way tables.

Year 7 Vocabulary (revisit)SurveyQuestionnaireExperimentDataStatisticsGrouped dataClass intervalTallyTableFrequencyData collection sheetStem and leaf

Revisit key vocabulary. Model with help of students how to

produce a data collection sheet. Model questions that would/would

not work in a questionnaire “How do people give misleading pictures using charts?”

Explore continuous/discrete data and assess understanding.

How could we make predictions about Y8 pupils using our data – what are the problems?

Would our group be a good sample for all our Y8’s, East Riding’s Y8’s, the country’s Y8’s?

What types of charts best display our data? (Is HDB compared to HDA ok?)

Which recording sheet is best? What statements can we make using

our data? Ask pupils to discuss difficulties in

collecting data.

Much of this will be revisited in Year 9. Sowing seeds and touching on ideas may be the main aim of this unit.

Oral and mental Main Teaching (1 or 2 lessons) Notes PlenaryObjective. w OHTs of bar chart (H.D.A) and frequency diagram for discrete and continuous data (H.D.G.)Discuss differences.Revisit range and mean.

OHT of stem and leaf diagram. (HDC)Discuss.Ask questions – respond with mini white boards.

Objective G, D, KEither using data collected from last lesson (most appropriate since it is real data) or other data.Model construction of bar chart and frequency diagram (with grouped data).Discuss ‘< x <’ terminology and different groupings in a frequency table. (Use ICT if possible).Extend to simple line diagram for time series._____________________________________________Ask pupils to form a hypothesis e.g. Boys spend more time exercising than girls!Set extended home work (paired if necessary).1. Hypothesis2. Data collection sheet3. Grouped frequency table4. Frequency diagram5. Interpret findings

VocabularyRangeMeanHypothesisDistributionContinuous dataDiscrete data

What are the key points to label on a chart?

How do we decide which chart is the best for our data? (Relate back to unit H.D.2)

Revisit discrete/continuous data definitions.

When is it inappropriate to use a line graph? (Compare H.D.A. and H.D.B.)

Why is ICT useful in constructing charts?

Are there any problems with using ICT?

Are there any rules for grouping data? Advice?

How do we label grouped data? Revisit <, >, ≤, ≥ etc.

Objective JPupils will perhaps feedback in later lessons orally

Oral and mental Main Teaching (2 lessons) Notes PlenaryObjective x– starterWhat is the mean of:a. 3, 4, 5b. 6, 7, 8c. 99, 100, 101Explore process of how to quickly state the mean.

What is the mean of:a. 2, 4 and 9 => 5b. 12, 14 and 19 => 15c. 102, 104, 109 => 105Predictions – generalise.

Objective FSet question relating to starter using an assumed mean. If pupils can cope – model and extend to positive and negative difference (Page 257).

Revise – mode and median (Objective I)Model finding mode, median and mean from grouped frequency tables.(Clarify if necessary by expanding the table to model possible raw data.)

When confident use range, mean, mode, median to compare two sets of data.

Sets of data needed to compare.

VocabularyAssumed meanModeModal class

Record methods of calculating mean, median, mode & range for grouped data.

Record method for using an assumed mean for a simple set of data.

Why does the assumed mean method work?

Using mean, mode, median & range for two sets of data ask pupils to draw conclusions.

Duracel batteries last longer – model process of proving/disproving this.

Know when to use mean, mode, median or range (See page 257).

Oral and mental Main Teaching (Remaining time) Notes PlenaryRevisit key vocabulary.Questions on averages/range.Reviewing interpreting graphs.Discuss recently published newspaper graph.Definitions – ask for definition of:DiscreteContinuousFrequency

Ask for sentences including key vocabulary etc.Revisit assumed mean calculations etc.Population Pyramid for Brazil (H.D.F.) - discuss.

Objective LPupils could feedback on their surveys. Giving a short presentation.Further work could be supplied as needed.Mixed challenging questions could be set (See page 25).ICT could be explored further to plot graphs and calculate means.

Much will be revisited in Year 9 and extended.

Summarise all work covered and key ideas.

How can we display data, group data, conduct a survey, interpret results, compare two sets of data?

Solving problems (6 hours) Y8 Summer term

Solving problems (2–35)Ratio and proportion (78–81)COREFrom the Y8 teaching programme

A. Solve more demanding problems and investigate in a range of contexts: number and measures.

B. Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic or graphical form, using correct notation.

C. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation.

D. Use logical argument to establish the truth of a statement; give solutions to an appropriate degree of accuracy in the context of the problem.

E. Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples.

F. Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.

Unit: Solving Problems Year Group: 8

Number of 1 Hour Lessons: 6 Class/Set: Core Oral and mental Main Teaching Notes PlenaryAs appropriate to strengthen or assess previously covered concepts

OR

brainstorming approaches to solving some problems from the framework.

The last unit may encroach into this one.Page 2 – 35 give lots of problems that could be given to groups of students to solve (available on disk in school or by downloading the framework).Cut and paste groups of questions together to tackle in specific lessons as appropriate.The emphasis is on using and applying the knowledge gained in solving problems and developing thinking and reasoning skills.SAT papers may be another useful source.Particularly look again at the ideas in multiplicative relationships.

This unit does not have to be the last unit it could be done earlier.

Model problem solving techniques and generalise on approaches.

Produce flowcharts or help sheets (with help of students on problem solving).