Scheme of Work Maths Stage 8

7/31/2019 Scheme of Work Maths Stage 8

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V1 1Y08 Mathematics Stage 8 1

Scheme of Work Stage 8 Mathematics

Overview

Term 1 Term 2 Term 3

1A Number and Calculation 2A Number and Calculation 3A Number and Calculation

1B Algebra and Geometry 2B Algebra and Geometry 3B Algebra and Geometry

1C Handling Data and Measures 2C Handling Data and Measures 3C Handling Data and Measures


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FrameworkCodes

Learning Objective Activities Resources Comments

8Nc3 Recall simple equivalent fractions,decimals and percentages.

FDP snap with equivalent fractions.matching pairs exercises.

FDP cards/dominoes

8Nc7 Recall relationships between units ofmeasurement.

Select and use the correct type of unitsto solve problems.


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Unit 1B: Algebra and Geometry

FrameworkCodes


8Ae1 Know that letters play different rolesin equations, formulae and functions;know the meanings of formulaandfunction.

Develop function machines and writetheir output as a formula.

8Ae2 Know that algebraic operations,including brackets, follow the sameorder as arithmetic operations; use

index notation for small positiveinteger powers.

Differentiated exercises. ReviewBIdmas/Bodmas

8Ae3 Construct linear expressions. Using a collection of cards build andsimplify expressions - paired work.

Algebra term cards with 3x,2x,+3 etc

8Ae4 Simplify or transform linearexpressions with integer coefficientscollect like terms; multiply a singleterm over a bracket.

Differentiated exercises.

8As1 Generate terms of a linear sequenceusing term-to-term and position to-term rules; find term-to-term andposition-to-term rules of sequences,

including spatial patterns.

Find next xx terms of a given sequence.work out 9th term using t-t rules and p-trules.Create spatial patterns that fit a given

sequence.

Matchsticks or similar andgenerated patterns

8As3 Express simple functions algebraicallyand represent them in mappings.

From a set of points (str. line graph)develop an algebraic expression.

8Gs1 Know that if two 2D shapes arecongruent, corresponding sides andangles are equal.

Given a selection of shape find thosecongruent.

Define correspondingand congruent.


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8Gs2 Classify quadrilaterals according totheir properties, including diagonalproperties.

Venn diagram exercises Practicalsorting.

Cut out shapes and largecircles

8Gs3 Know that the longest side of a right-angled triangle is called thehypotenuse.

8Gs4 Identify alternate angles andcorresponding angles.

8Gp1 Find the midpoint of the line segmentAB, given the coordinates of points Aand B.

Given A (x1,y1) and B (x2,y2) know anduse mp = ( x1+x2, y1+y2)

2 2


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Unit 1C: Handling Data and Measures

FrameworkCodes


8Gp4 Interpret and make simple scaledrawings.

Make a scale drawing of yourclassroom.

Blocks/model building to draw

8Ml1 Choose suitable units ofmeasurement to estimate, measure,calculate and solve problems in arange of contexts, including units ofmass, length, area, volume or

capacity.

Find a missing dimension given otherand volume e.g. a cuboid is 2cm wideand 7cm high its volume is 42cm

3hoe

long is it?

More complex problemcan be created bymixing units e.g. m andcm

8Dc1 Identify and collect data to answer aquestion; select the method ofcollection, sample size and degree ofaccuracy needed for measurements.

Carry out a meaningful survey in smallgroups Make a starting hypothesis.

8Dc2 Know the difference between discreteand continuous data.

8Dc3 Construct and use: frequency tables with given equal

class intervals to gather

continuous data two-way tables to record discrete

data

Display the data from your surveyselecting the most appropriate formatand showing you know the difference

between discrete and continuous data.

8Dp1 Calculate statistics for sets of discreteand continuous data; recognise whento use the range, mean, median andmode and, for grouped data, themodal class.

Sets of sample data can begenerated in Excel of found onthe internet


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8Di1 Interpret tables, graphs and diagramsfor discrete and continuous data, anddraw conclusions, relating statistics

and findings to the original question.

Analyse the results of your surveycheck the validity of your hypothesis.

8Db1 Know that if the probability of anevent occurring is p, then theprobability of it not occurring is 1 p.

Differentiated exercises.

8Db2 Find probabilities based on equallylikely outcomes in practical contexts.

Rolling dice or spinning spinnersMixing D4,D6,D8 and D10s producesgood results.

Packs of polydice Dx is an x sided diewith equally likelyoutcomes No 1-x


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Unit 2A: Number and Calculation

FrameworkCodes


8Ni2 Identify and use multiples, factors,common factors, highest commonfactors, lowest common multiples andprimes; write a umber in terms of itsprime factors, e.g. 500 = 22 53.

Use factor trees for LCM and HCF 3circle Venn diagrams for sorting factorsand multiples.

8Nf4 Add and subtract fractions and mixed

numbers; calculate fractions ofquantities (fraction answers); multiplyand divide an integer by a fraction.

Differentiated exercises. Fraction cards used to

generate random questions

8Nf5 Calculate and solve problemsinvolving percentages of quantitiesand percentage increases ordecreases; express one givennumber as a fraction or percentage ofanother.

Can be a hard problem to calculateoriginal price given a percentage loss.needs lots of practice.

Sale literature from any shopsflyers etc.

8Nf6 Use equivalent fractions, decimalsand percentages to compare differentquantities.

Finding the best value from different

suppliers.

8Nc2 Recall squares to 20 20, cubes to 5 5 5, and corresponding roots.

10 quick mental questions.

8Nc5 Use known facts and place value tomultiply and divide simple decimals,e.g. 0.07 9, 2.4 3.

Look for patterns in multiplication tables12 x 10, 12 x 1 , 12 x 0.1 etc.


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8Nc6 Use known facts and place value tocalculate simple fractions andpercentages of quantities.

As above what do you know? Whatdoes it tell you?

8Nc8 Solve simple word problems includingdirect proportion problems.

Can you find the Mathematics in all thewords?

Reading can be aproblem star t simple

8Nc11 Consolidate adding and subtractingintegers and decimals, includingnumbers with differing numbers ofdecimal places.

Head to head challenges with twostudents best of three questions wins.

8Nc12 Divide integers and decimals by asingle-digit number, continuing thedivision to a specified number ofdecimal places, e.g. 68 7.

Pencil and paper methods of longdivision - check with a calculator.

Calculators


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8Ae5 Derive and use simple formulae,e.g. to convert degrees Celsius (C)to degrees Fahrenheit (F).

Plot given pairs of temperatures anddraw lines through data points -develop a formula.

8Ae6 Substitute positive and negativeintegers into formulae, linearexpressions and expressionsinvolving small powers, e.g. 3x2 + 4or 2x3, including examples that leadto an equation to solve.

Check your formula from above withdifferent values, plot them. Do they lieon a straight line?Generate some real life situations thatlead to nice formulas.

8As4 Construct tables of values and useall four quadrants to plot the graphsof linear functions, where yis givenexplicitly in terms of x; recognisethat equations of the form y= mx+ccorrespond to straight-line graphs.

Draw graphs relating to the above workmoving towards an understanding ofy=mx+c being always a straight line.

8Gs7 Draw simple nets of solids, e.g.cuboid, regular tetrahedron, squarebased pyramid, triangular prism.

Use ruler and compasses to constructthe net of each solid, colour and makethem into a mobile, which onesbalance-why?

8Gs8 Identify all the symmetries of 2Dshapes.

Work by families i.e. all triangles thenquadrilaterals etc.

Tracing paper or similar Line symmetry androtational


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8Gs9 Use a straight edge and compassesto construct: the midpoint and perpendicular

bisector of a line segment the bisector of an angle

Needs quite a lot of practice to securethese skills.

Will need to bedemonstrated carefully

8Gp2 Transform 2D shapes by rotation,reflection and translation, andsimple combinations of thesetransformations.

Ties in with symmetries above prepareactivity sheets or slides depending onthe technology available.

Cad package or even wordcan be used to insert andtransform shapes


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Unit 2C: Data Handling and Measures

FrameworkCodes


8Ml2 Know that distances in the USA, theUK and some other countries aremeasured in miles, and that onekilometre is about 5/8 of a mile.

8Ma2 Derive and use formulae for thearea of a triangle, parallelogram and

trapezium; calculate areas ofcompound 2D shapes, and lengths,surface areas and volumes ofcuboids.

Work in teams to derive the formulasfrom the formula for the area of a

rectangle. within teams pairs work oncompound shapes, then swap withother teams to find the areas.

Basic plastic shapes that canbe used to build up compound

shapes.

8Ma3 Use simple nets of solids to workout their surface areas.

Carefully create nets from solid boxes. Boxes and scissors Collect cardboardboxes

8Dp2 Draw, and interpret: frequency diagrams for

discrete and continuousdata

pie charts simple line graphs for time

series stem-and-leaf diagrams

Investigate volumes and surface areasof boxes-plot the results.

Brainstorm ideas to generate other

types of graphs.

Use the internet to researchdata

8Di2 Compare two distributions, usingthe range and one or more of themode, median and mean.

Analyse the graphs and data fromabove.


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8Db3 Find and list systematically allpossible mutually exclusiveoutcomes for single events and for

two successive events.

Roll two different dice or two spinnerslist all the outcomes.Carry out experiments to sample the

number of unknown counters in a bag.Suggest how m any of each type ofcounter are in the bag, given knowntotal.

Dice, spinners and counters.


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Unit 3A: Number and Calculation

FrameworkCodes


8Ni3 Calculate squares, positive andnegative square roots, cubes and

cube roots; use the notation 49

and364 3 and index notation for

positive integer powers.

Do quick quiz to test learned facts andmore complex problems to develop

understanding that 30 lies between 5and 6.

Scientific calculators would bevery useful.

Use known roots only

8Nf7 Simplify ratios, including thoseexpressed in different units; divide aquantity into more than two parts ina given ratio.

Develop from previous method ofdivision into two part ratio.Give the ratio and the value of one part- find the other values.

8Nf8 Use the unitary method to solvesimple problems involving ratio anddirect proportion.

There are some quicker shorts cuts thatstudents can find and use such asdividing by 2, 3 or some simple value.

Demonstrate unitarymethod

8Nc4 Use known facts and place value tomultiply and divide simple fractions.

Differentiated exercises needed. Where do you canceldown - does it matter?

8Nc9 Use the laws of arithmetic andinverse operations to simplifycalculations with integers andfractions.

Differentiated exercises neededencourage students to make up theirown examples.


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8Nc10 Use the order of operations,including brackets, with morecomplex calculations.

Differentiated exercises neededencourage students to make up theirown examples.

8Nc13 Multiply and divide integers anddecimals by decimals such as 0.6 or0.06, understanding where to placethe decimal point by consideringequivalent calculations, e.g. 4.37 0.3 = (4.37 3) 10, 92.4 0.06 =(92.4 100) 6.

Work in pairs or small groups todevelop and share successful methodsfor these problems.

Remember to look forpatterns in sets ofresults


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8Ae7 Construct and solve linear equationswith integer coefficients (unknown oneither or both sides, without or withbrackets).

Algebraic dimensions of rectangles leadto linear expressions of perimeter. Givea value to then be solved.

Algebraic calculators

8As2 Use a linear expression to describethe nth term of a simple arithmeticsequence, justifying its form by

referring to the activity or practicalcontext from which it was generated.

Explain why the number of matchsticksin figure 6 is ____Generalise the position to term rule.

Graphics calculators

8Gs5 Understand a proof that-the angle sum of a triangle is 180and that of a quadrilateral is 360-the exterior angle of a triangle isequal to the sum of the two interioropposite angles

Explain why the proof works. Showunderstanding it is true in all cases.

8Gs6 Solve geometrical problems usingproperties of angles, of parallel andintersecting lines, and of triangles andspecial quadrilaterals, explainingreasoning with diagrams and text.

Explain reasoning in logical stepsshowing how one step leads to another.


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Unit 3C: Handling Data and Measures

FrameworkCodes


8Gs10 Use a ruler and compasses toconstruct circles and arcs a triangle, given three sides (SSS) a triangle, given a right angle, hypotenuse and one side (RHS)

Review last units skills with ruler andcompasses. Give lots of examplescovering all types.Create patterns with intersecting circlesand colour them. Can you do the samewith Triangle types?

Rulers, compasses plainpaper if possible

8Gp3 Understand and use the language andnotation associated with enlargement;enlarge 2D shapes, given a centre ofenlargement and a positive integerscale factor.

Take care when preparing diagrams toallow working/answer space. Use 4quadrant axes to extend the use ofpositive scale factor.

Use word to create andenlarge shapes so studentscan find centres ofenlargement and decimalscale factors.

8Mt1 Draw and interpret graphs in real lifecontexts involving more than onecomponent, e.g. travel graphs withmore than one person.

Use graphs of two people starting fromthe same town at different times/speedDescribe journeys in word for studentsto graph.

8Ma1 Know the definition of a circle and thenames of its parts; know and use

formulae for the circumference andarea of a circle.

Link with construction of circle above.also link type of units to the differentformulas for length and area.

The area and circumference songworks well. "The circumference is

Pi times diameter" to the tune of"Here we sit like birds in thewilderness".

Much of this must begiven for students tolearn


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8Di3 Compare proportions in two pie chartsthat represent different totals.

Following on from the circle work circlegraphs.

8Db4 Compare estimated experimentalprobabilities with theoreticalprobabilities, recognising that: when experiments are repeated

different outcomes may result increasing the number of times an

experiment is repeated generallyleads to better estimates ofprobability

Group exercise rolling dice 200 times ,collect result and combine data fromgroups to create large sample set -show how estimate changes as moredata is added to the set.

Use a spreadsheet to graphlarge quantities of data toshow convergence towards alimit.

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Scheme of Work Maths Stage 8