Scheme of Work Maths Stage 7

7/31/2019 Scheme of Work Maths Stage 7

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V1 1Y08 Mathematics Stage 7 1

Scheme of Work Stage 7 Mathematics

Overview

Term 1 Term 2 Term 3

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

1B Algebra and Measures 2B Algebra and Measures 3B Measures

1C Handling Data and Geometry 2C Handling Data and Geometry 3C Handling Data and Geometry


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Unit 1A: Number and Calculation

FrameworkCodes

Learning Objective Activities Resources Comments

7Nc1 Consolidate the rapid recall ofnumber facts, including positiveinteger compliments to 100,multiplication facts to 10 x 10 andassociated division facts.

Revise multiplication tables from 1 to 10,and addition and subtraction facts fornumbers between 0 and 20.Look for patterns that make mentalcalculations easier, for example whathappens when 9 is added to a two digitnumber, or that 5 + 7 is the same as 6 + 6.Ask questions such as which pairs ofnumbers will add together to make 17?

Follow me cardsNumber cardsMultiplication Tables

Many aspects of thisunit may well befamiliar or even priorknowledge for somepupils. How will youfind out which? SeeAssessment sectionof Teacher Guide andsample lesson plans.

7Np1 Interpret decimal notation and placevalue; multiply and divide wholenumbers and decimals by 10, 100or 1000.

Use a number line with place valueheadings and moveable cards with singledigits on them to discuss place value.Investigate how the digits move in relationto the decimal point when multiplied ordivided by the powers of ten.

Ensure that the class understands thatmultiplying by 10, 100 and 1000 makes thenumber bigger while dividing by these

numbers makes the number smaller.Progress to paper and pencil methods.

Search for place value athttp://teachers.guardian.co.uk/resources.aspx

7Np2 Order decimal includingmeasurements, changing these tothe same units.

Give each pupil a decimal number then getthem to line up in order of size.Select 4 decimal cards for individuals toorder explaining strategy to a partner.

Decimal cards
http://teachers.guardian.co.uk/resources.aspxhttp://teachers.guardian.co.uk/resources.aspxhttp://teachers.guardian.co.uk/resources.aspxhttp://teachers.guardian.co.uk/resources.aspx


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FrameworkCodes


7Nf3 Compare two fractions by usingdiagrams, or by using a calculatorto convert the fractions to decimals,e.g. 3 and 13

5 20

7Ni1 Recognise negative numbers aspositions on a number line, andorder, add and subtract positive andnegative numbers in context.

Wall size number line. Give each pupil a+/- number then get them to line up in orderof size.Select 4 negative number cards forindividuals to order explaining strategy to apartner.

Negative number cards


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Unit 1B: Algebra and Measures

FrameworkCodes


7Ml1 Choose suitable units of measurement toestimate, measure, calculate and solve problemsin everyday contexts.

Spot the incorrect unit match list of itemsand units.

Unit cards

7Ae1 Use letters to represent unknown numbers orvariables; know the meanings of the words term,expressionand equation.

Producing a written form for the I think of anumbergame. Identify terms equations.For a whole class activity practise usingmathematical vocabulary by picking outterms, expressions, variables and equationsfrom various examples.Show that expressions can only besimplified (or evaluated) but that equationsin one variable can be solved. Discussequations in two variables. Show that termscan contain brackets.

7Ae2 Know that algebraic operations follow the sameorder as arithmetic operations.

Replace numbers with letters in familiarsituations.

2 x a + b = 2a +b2a

2= 2 x a x a

7Ae3 Construct simple algebraic expressions by usingletters to represent numbers.

Start by using words as the variables whensimplifying algebraic expressions. Forexample, a shopping basket contains 6apples and 2 bananas and 2 apples. Thisleads to 6a+2b+2a.

Use think of a number games to constructsimple equations. Find out what formulaeare being used in students other subjectsand make use of them. Use currencyconversion formulae.


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FrameworkCodes


7Ae4 Simplify linear expressions e.g. collect like terms;multiply a constant over a bracket.

Paired work to justify actions to partner andact as a check on results.

http://www.transum.org/Money/currency.asp

7As1 Generate terms of an integer sequence and finda term given its position in the sequence; findsimple term-to-term rules.

What comes next? games What's my rule? http://math.rice.edu/~lanius//Lessons/Patterns/rect.html

7As2 Generate sequences from spatial patterns anddescribe the general term in simple cases.

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Unit 1C: Handling data and Geometry

FrameworkCodes


7Gs1 Identify, describe, visualise and draw2D shapes in different orientations.

Discuss experimental error andaccuracy and emphasise the need foraccuracy (for example, use a sharppencil).

Name shapes atwww.mymaths.co.ukhttp://www.mathsnet.net/shape/ks3index.html

7Gs2 Use the notation and labellingconventions for points, lines, anglesand shapes.

Decide on the number of points neededto identify different lines angle andshapes - maximum/minimum

7Gs3 Name and identify side, angle andsymmetry properties of specialquadrilaterals and triangles, andregular polygons with 5, 6 and 8sides.

Sorting by symmetry, angles Learn thenames of common shapes for a bingoquiz.

7Gs4 Estimate the size of acute, obtuseand reflex angles to the nearest 10degrees.

Discuss acute, obtuse and reflex anglesand the need to check which scale onthe protractor to use.

Measuring angles athttp://www.mymaths.co.uk/

7Dc1 Decide which date would be relevantto an inquiry and collect andorganise the data.

Decide on a sound reason forconducting your survey, then considerthe data you need to collect.

7Dc2 Design and use a data collectionsheet or questionnaire for a simplesurvey.

Carry out the survey giving thought towhere and how. Consider the possiblebias in different situations andquestions.
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8/18V1 1Y08 Mathematics Stage 7 8

FrameworkCodes


7Db1 Use the language of probability todescribe and interpret resultsinvolving likelihood and chance.

Analyse the results for each group andthen put the data for compatible groupstogether to produce more reliableresults.

Impossible unlikelyevens likely certain

7Db2 Understand and use the probabilityscale from 0 to 1.

Class discussion of the probability ofcertain events Convert words tonumbers via their position on theprobability line Impossible =0 etcSort events into probability order givena numerical value.

Can be represented byfractions or decimals

7Db3 Find probabilities based on equallylikely outcomes in simple contexts.

Carry out an experiment [rolling dice orspinners] to produce relativefrequencies - use to predictprobabilities. Have another group checkby repeating the experiment. List alloutcomes from a selection event.


9/18



Unit 2A:

FrameworkCodes


7Mt2 Know the relationships betweenunits of time; understand and usethe 12-hour and 24-hour clocksystems; interpreting timetables;calculate time intervals.

Set a clock time ask what time it wouldbe in 45 min, or 97 min

Digital and analogue clocks

7Ni2 Recognise multiples, factors,common factors, primes(all less

than 100) making use of simpletests of divisibility; find the lowestcommon multiple in simple cases;use the "sieve" for generatingprimes developed by Eratosthenes.

Factor race teams compete to completethe factor list of a given number.

Use factor trees to find common factorsand LCM.

100 square grid colouredpencils or crayons

7Ni3 Recognise squares of wholenumbers to at least 20 x 20 and thecorresponding square roots; use thenotation 7

2and 49.

Square root bingoMatching pairs 7 and 49 etc.

Square root bingo cardsMatching pairs on "Mymaths"

7Nf4 Add and subtract two simplefractions e.g. 1 + 9, 11 - 5

8 8 12 8

Find fractions of quantities (wholenumber answers); multiply a fractionby an integer.

Quick fire questions 1/2 of 32 etc.Matching the answers to the questions.

Fraction Dominoes May need to findcommon denominators

7Nf5 Understand percentages as thenumber of parts in every 100; usefractions and percentages todescribe parts of shapes, quantitiesand measures.

Divide graph paper squares intodifferent % e.g. 30% red 70% blue oreven 25% red, 30% green, 45% b lueetc.


10/18V1 1Y08 Mathematics Stage 7 10

FrameworkCodes


7Nc5 Calculate simple fractions andpercentages of quantities, e.g. onequarter of 64, 20% of 50kg.

Compare, which is bigger 20% of 50kgor 15% of 70kg etc.

7Nc6 Use the laws of arithmetic andinverse operations to simplifycalculations with whole numbersand decimals.

Get students to compare methods ofperforming a calculation, Can morethan 1 method get the correct answer?How, why, when?

7Nc11 Know when to round up or downafter division, when context requiresa whole number answer.

Questions on filling boxes, or seats onbuses.

The actual divisioncould require acalculator.

7Ml3 Read the scales on a range of

analogue and digital measuringinstruments.

Paired work, peer checking on the

answers, hands on work not justdiagrams.

A variety of measuring devices

7Ma1 Know the abbreviations for andrelationships between squaremetres (m2) centimetres (cm2) andmillimeters (mm2).

Sort into families Kilometres Kilogramsetc.


11/18



Unit 2B: Algebra and Measure

FrameworkCodes


7Ae5 Derive and use simple formulae e.g. tochange hours to minutes.

Create formulas using excel toconvert from one set of units toanother.

7Ae6 Substitute positive integers into simplelinear expressions/formulae.

Use Excel to generate values ofdifferent formulae.

7As3 Represent simple functions using

words, symbols and mappings.7As4 Generate coordinate pairs that satisfy a

linear equation, where y is givenexplicitly in terms of x, plot thecorresponding graphs; recognisestraight-line graphs parallel to the x- ory- axis.

Draw up tables of values for afunction and describe patterns foundin the tables.

Grid sheets with pre-drawnhorizontal and vertical lines

7Ma2 Derive and use formulae for the areaand perimeter of a rectangle; calculatethe perimeter and area of compoundshapes made from rectangles.

Divide compound shapes intorectangles finding the area of eachand the total area.

7Ml2 Know and use abbreviations for and

relationships between metric units;Kilo-centi-milli-; converting between;Kilometres Km, metres m, centimetrescm, millimetres mm;Tonnes t, kilograms km, and grams gLitres l, and millilitres ml.

Practice use of < > with different units

and conversions.

Units dominoes


12/18



Unit 2C: Handling Data and Geometry

FrameworkCodes


7Gs5 Start to recognise the angularconnections between parallel lines,perpendicular lines and transversals.

Colour angles which are the samewithin diagrams.

Acetate sheet for rotatablediagrams or use computers todraw and rotate diagrams.

7Gs6 Calculate the sum of angles at apoint, on a straight line and in atriangle, and prove that verticallyopposite angles are equal; deriveand use the property that the anglesum of a quadrilateral is 360.

Draw a triangle and mark its angles.Then tear it into three parts eachcontaining an angle and stick the threeangles together showing a straight linealso sum of angles = 180 Similarly anyquad = 2 triangles.

7Gs9 Recognise line and rotationsymmetry in two-dimensional shapesand patterns; draw lines of symmetryand complete patterns with two linesof symmetry; identify the order ofrotational symmetry.

Sheets of pre-drawn patterns orstudents generate computer patternsthat they can swap and compare witheach other.

7Dp1 Find the mode (or modal class forgrouped data), median and range.

Select a data set from those given tomatch a set of given criteria i.e. mode is7 range is 6.

Data sheets of randomnumbers.

7Dp2 Calculate the mean including from asimple frequency table.

Differentiated exercises.


13/18


FrameworkCodes


7Dp3 Draw and interpret bar line graphsand bar charts, frequency diagramsfor grouped discrete data, simple pie

charts, pictograms.

Use date from previous lessons to bedisplayed on various charts. Discusswhich chart is best for different types of

data.

7Db4 Identify all the possible mutuallyexclusive outcomes of a singleevent.

Rolling dice or spinning spinners togenerate data sets use different diceD4 D6 D8 etc for variety.

7Db5 Use experimental data to estimateprobabilities.

7Db6 Compare experimental andtheoretical probabilities in simplecontexts.

Compare results from different groupsthem to produce better sets of results.

Computer generatedfrequency graphs to showconvergence to a result.


14/18



Unit 3A: Number and Calculation

FrameworkCodes


7Nc7 Use the order of operations,including brackets, to work outsimple calculations.

Speed competitions to calculate thecorrect answer and/or insert brackets toachieve the correct answer.

Excel spreadsheets togenerate questions

7Nc8 Add and subtract integers anddecimals, including numbers withdifferent numbers of decimal places.

Speed competitions to calculate thecorrect answer.

Number cards decimal andInteger.

7Nc9 Multiply and divide decimals withone and/or two places by singledigit numbers, e.g. 13.7 x 8, 4.35 5.

Differentiated exercisese.g. ? x 3.1 = 12.4

7Nc10 Know that in any division where thedividend is not a multiple of thedivisor; there will be a remainder,e.g. 157 25 = 6 remainder 7. Theremainder can be expressed as afraction of the divisor e.g. 157 25= 6 7

25

Division of bead or counter into groupsuse of an abacus.

Match pairs of fractions 6 and 1 15 5

Fraction cards pairing properand improper fractions

7Nf6 Calculate simple percentages ofquantities (whole number answers)and express a smaller quantity as afraction or percentage of a largerone.

Speed competitions to calculate thecorrect answer. Compare two givenparts, which is larger?

Practise the use of < >and similar notation

7Nf7 Use percentages to represent andcompare different quantities.

Speed competitions to calculate thecorrect answer.


15/18


FrameworkCodes


7Nf8 Use ratio notation, simplify ratiosand divide a quantity into two partsin a given ratio.

More complex problem two studentsshare $x in ratio 5:7 smallest share is$15 how much is the larger share?

7Nf9 Recognise the relationship betweenratio and proportion.

7Nf10 Use direct proportion in context;solve simple problems involvingratio and direct proportion.

Differentiated exercises use real orplastic money to share out in a givenratio.

Plastic or toy money


16/18



Unit 3B: Measure

FrameworkCodes


7Nf3 Compare two fractions by usingdiagrams, or by using a calculator toconvert the fractions to decimals,e.g. 3 and 13

5 20

Compare two or more fractions - placein order of size.

Fraction dominoes with mixeddiagrams and fractions.

7Ma3 Derive and use formula for thevolume of a cuboid; calculate

volumes of cuboids.

Given a fixed number of 1cm3 cubes,what is the cuboid with the largest

volume you can build?

Building cubes

7Ma4 Calculate the area of cubes andcuboids from their nets.

Measure nets and then construct theminto solids and check results.

Empty cardboard boxes

7Mt1 Draw and interpret graphs in real lifecontext involving more than onestage e.g. travel graphs.

Plot distance from home graphs invarious contexts including graph formore than one person.

Travel graphs on Mymaths


17/18



Unit 3C: Handling Data and Geometry

FrameworkCodes


7Dc3 Construct and use frequency tablesto gather discrete data, groupedwhere appropriate in equal classintervals.

Carry out a survey that will produce thedesired results, offer option in pre-selected intervals.

7Di1 Draw conclusions based on theshape of graphs and simplestatistics.

Test a hypothesis which generated theabove survey.

7Di2 Compare two simple distributionsusing the range and the mode,median or mean.

Complete the survey with two differentclasses or groups and compare theresults.

7Gp1 Read and plot coordinates of pointsdetermined by geometricalinformation in all four quadrants.

Battle ships in four quadrants.Treasure Hunt to find a selectedcoordinate from "closer" or "furtheraway" responses.

7Gp2 Transform two-dimensional shapesby: reflection in a given line,

rotation about a given point, translation.Know that shapes remain congruentafter these transformations.

Pre drawn shapes on a coordinate grid. Transformation GolfMymaths.


18/18


FrameworkCodes


7Gs7 Solve simple geometrical problemsby using side and angle properties toidentify equal lengths or calculate

unknown angles, and explainreasoning.

Differentiated exercises withincreasingly more complex diagram.Moving towards two step problems.

7Gs8 Recognise and describe commonsolids and some of their properties,e.g. the number of faces, edges andvertices.

20 questions with a solids name as theanswer.

7Gs10 Use a ruler, setsquare and protractorto:Measure and draw straight lines tothe nearest millimetre.Measure and draw acute, obtuse and

reflex angles to the nearest degree.Draw parallel and perpendicularlines.Construct a triangle given two sidesand the included angle (SAS).Construct squares and rectangles.Construct regular polygons, given aside and internal angle.

Pre-drawn sheets to practicemeasuring.Differentiated exercises to practiceconstructions of polygons.

Scheme of Work Maths Stage 7

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