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Westfield Community School – Mathematics

Scheme of Work for Year 7

Contents:

Long term plan - National Curriculum & National Numeracy Strategy (year 7)

Medium Term plan - Key Maths 71, 72 and 7ER text books split into 4 equal units

Short Term plan- Lesson by lesson planning, incorporating mental/oral starters, plenaries, tests &

additional worksheets etc.- Each unit is expected to last about 9 weeks, with 3 weeks for revision

and a summer examination. - Note that these plans are only suggestions and are not rigid- they were

designed for newer staff, to help pace staff & ensure coverage.

Please note this is working progress, so there are sure to be errors or pieces missing.

You are welcome to use as much of this as is useful. Any ideas/ thoughts are welcome, if not positively encouraged.

Year 7 Scheme of work 1999 - 2000


Attainment Target 1: Using & Applying Mathematics

2 Select the mathematics used in some classroom activities. Discuss work using mathematical language & begin to represent it using symbols & simple diagrams. Explain why an answer is correct.

3 Try different approaches & find ways of overcoming difficulties that arise when solving problems. Beginning to organise work & check results. Discuss mathematical work & begin to explain thinking. Use & interpret mathematical symbols & diagrams. Show understanding of a general statement by finding particular examples that match it.

4 Developing strategies for solving problems & are using these strategies both in working within maths & in applying maths to practical contexts.

Present information & results in a clear & organised way. Search for a solution by trying out ideas.

5 In order to carry through tasks & solve mathematical problems, identify & obtain necessary information. Check their results, considering whether these are sensible. Show understanding of situations by describing them mathematically using symbols, words & diagrams. Draw simple conclusions & give an explanation of reasoning.

6 Carry through substantial tasks & solve quite complex problems by independently breaking them down into smaller, more manageable tasks.

Interpret, discuss & synthesise information presented in a variety of mathematical forms. Writing explains & informs their use of diagrams. Beginning to give mathematical justifications.



Attainment Target 2: Number & Algebra

2 Count sets of objects reliably, & use mental recall of addition & subtraction facts to 10. Begin to understand the place value of each digit in a nos. & use this to order nos. up to 100. Choose the appropriate operation when solving addition & subtraction problems. Use the knowledge that subtraction is the inverse of addition. Use mental calculation strategies to solve nos. problems involving money & measures. Recognise sequences of nos., including odd & even nos.

3 Show understanding of place value in nos. up to 1000 & use this to make approximations. Begin to use decimal notation & to recognise negative nos., in contexts such as money & temperature. Use mental recall of addition & subtraction facts to 20 in solving problems involving larger nos. Add & subtract nos. with two digits mentally & nos. with three digits using written methods. Use mental recall of the 2, 3, 4, 5 & 10 multiplication tables & derive the associated division facts. Solve whole-nos. problems involving multiplication or division, including those that give rise to remainders. Use simple fractions that are several parts of a whole & recognise when two simple fractions are equivalent.

4 Use their understanding of place value to multiply & divide whole nos. by 10 or 100. In solving nos. problems, use a range of mental methods of computation with the four operations, including mental

recall of multiplication facts up to 10 × 10 & quick derivation of corresponding division facts. Use efficient written methods of addition & subtraction & of short multiplication & division. Add & subtract decimals to two places & order decimals to three places. In solving problems with or without a calculator, check the reasonableness of results by reference to knowledge of

the context or to the size of the nos. Recognise approximate proportions of a whole & use simple fractions & percentages to describe these. Recognise & describe nos. patterns, & relationships including multiple, factor & square. Begin to use simple formulae expressed in words. Use & interpret coordinates in the first quadrant.

5 Use understanding of place value to multiply & divide whole nos. & decimals by 10, 100 & 1000. Order, add & subtract negative nos. in context. Use all four operations with decimals to two places. Reduce a fraction to its simplest form by cancelling common factors & solve simple problems involving ratio &

direct proportion. Calculate fractional or percentage parts of quantities & measurements, using a calculator where appropriate. Understand & use an appropriate non-calculator method for solving problems that involve multiplying & dividing

any three-digit nos. by any two-digit nos. Check solutions by applying inverse operations or estimating using approximations. Construct, express in symbolic form, & use simple formulae involving one or two operations. Use brackets appropriately. Use & interpret coordinates in all four quadrants.

6 Order & approximate decimals when solving numerical problems & equations, using trial-&-improvement methods. Are aware of which nos. to consider as 100 per cent, or a whole, in problems involving comparisons, & use this to

evaluate one nos. as a fraction or percentage of another. Understand & use the equivalences between fractions, decimals & percentages, & calculate using ratios in

appropriate situations. Add & subtract fractions by writing them with a common denominator. When exploring nos. sequences, find & describe in words the rule for the next term or nth term of a sequence where

the rule is linear. Formulate & solve linear equations with whole-nos. coefficients. Represent mappings expressed algebraically, & use Cartesian coordinates for graphical representation interpreting

general features.



Attainment Target 3: Shape, Space & Measures

2 Use mathematical names for common 3-D & 2-D shapes & describe their properties, including nos. of sides & corners.

Distinguish between straight & turning movements, understand angle as a measurement of turn, & recognise right angles in turns.

Begin to use everyday non-standard & standard units to measure length & mass.3 Classify 3-D & 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D

shapes. Use non-standard units, standard metric units of length, capacity & mass, & standard units of time, in a range of

contexts4 Make 3-D mathematical models by linking given faces or edges, draw common 2-D shapes in different orientations

on grids. Reflect simple shapes in a mirror line. Choose & use appropriate units & instruments, interpreting, with appropriate accuracy, nos. on a range of measuring

instruments. Find perimeters of simple shapes & find areas by counting squares.

5 When constructing models & when drawing or using shapes, measure & draw angles to the nearest degree, & use language associated with angle.

Know the angle sum of a triangle & that of angles at a point. Identify all the symmetries of 2-D shapes. Know the rough metric equivalents of imperial units still in daily use & convert one metric unit to another. Make sensible estimates of a range of measures in relation to everyday situations. Understand & use the formula for the area of a rectangle.

6 Recognise & use common 2-D representations of 3-D objects. Know & use the properties of quadrilaterals in classifying different types of quadrilateral. Solve problems using angle & symmetry properties of polygons & angle properties of intersecting & parallel lines, &

explain these properties. Devise instructions for a computer to generate & transform shapes & paths. Understand & use appropriate formulae for finding circumferences & areas of circles, areas of plane rectilinear

figures & volumes of cuboids when solving problems. Enlarge shapes by a positive whole-nos. scale factor.



Attainment Target 4: Handling Data

2 Sort objects & classify them using more than one criterion. When information is gathered, record results in simple lists, tables & block graphs, in order to communicate findings.

3 Extract & interpret information presented in simple tables & lists. Construct bar charts & pictograms, where the symbol represents a group of units, to communicate information

gathered, & interpret information presented to them in these forms.4 Collect discrete data & record them using a frequency table.

Understand & use the mode & range to describe sets of data. Group data, where appropriate, in equal class intervals, represent collected data in frequency diagrams & interpret

such diagrams. Construct & interpret simple line graphs.

5 Understand & use the mean of discrete data. Compare two simple distributions, using the range & one of the mode, median or mean. Interpret graphs & diagrams, including pie charts, & draw conclusions. Understand & use the probability scale from 0 to 1. Find & justify probabilities, & approximations to these, by selecting & using methods based on equally likely

outcomes & experimental evidence, as appropriate. Understand that different outcomes may result from repeating an experiment.

6 Collect & record continuous data, choosing appropriate equal class intervals over a sensible range to create frequency tables.

Construct & interpret frequency diagrams. Construct pie charts. Draw conclusions from scatter diagrams, & have a basic understanding of correlation. When dealing with a combination of two experiments, identify all the outcomes, using diagrammatic, tabular or other

forms of communication. In solving problems, use knowledge that the total probability of all the mutually exclusive outcomes of an experiment

is 1.



National Numeracy Strategy Programme of Study – Year 7

Numbers & the Number SystemPlace value, ordering and rounding Understand and use decimal notation and place value. Compare and order decimals in different contexts. Order, add and subtract positive and negative numbers in

context. Round numbers, including to one and two decimal places. Make and justify estimates and approximations (of numbers and

calculations).

Properties of numbers Recognise square numbers to at least 12 x 12, the cubes of 1, 2, 3, 4,

5 and 10, and the corresponding roots. Recognise and use multiples, factors and primes (less than 100); use

tests of divisibility. Write numbers as products of primes, using index notation.

Fractions, decimals, percentages, ratio and proportion. Use the equivalence of fractions, decimals and percentages in

describing proportions and convert between them (e.g. to order fractions).

Find fractions and percentages of quantities. Understand the relationship between ratio and proportion and use

ratio and proportion to solve simple problems.

CalculationsNumber operations and the relationships between them. Consolidate understanding of the operations of multiplication and

division, their relationship to each other and to addition and subtraction, and of the principles (not the names) of the arithmetic laws.

Know and use the order of operations.

Mental methods and rapid recall of number facts. Consolidate the rapid recall of number facts, including multiplication

facts to 10 x 10, and quickly derive associated division facts. Consolidate and extend mental methods of calculation to

include decimals, fractions and percentages. (accompanied where appropriate by suitable jottings).

Written methods Consolidate efficient written methods of addition and subtraction of

whole numbers, and (extend to) decimals. Refine written methods of multiplication and division of whole

numbers to ensure efficiency, and extend to decimals with two places.

Calculator methods Plan and carry out calculations using the facilities on a calculator,

including the square-root and percentage keys, the memory and brackets.

Interpret the display on a calculator in different contexts (fractions, decimals, money, metric measures, time).

Checking results Judge whether an answer is reasonable and check results,

including using:– knowledge of number system;– rounding to approximate;– inverse operations;

AlgebraEquations and formulae Use letters or symbols to represent unknown numbers or

variables. Know that algebraic operations follow the same conventions and

order as arithmetic operations. Simplify linear algebraic expressions by collecting like terms; begin to

multiply a simple term over a bracket. Use formulae from mathematics and other subjects, substitute

numbers in simple formulae and, in simple cases, derive a formula. Construct and solve simple linear equations, selecting an appropriate

method.

Sequences and functions Generate and describe in words common integer sequences, and

sequences from practical contexts. Generate terms of a sequence, given a rule (e.g. finding one term

from the previous term, finding a term given its position in the sequence).

Describe the general term of a simple sequence in words, then using symbols.

Express simple functions in words, then using symbols.

Graphs Find co-ordinate pairs that satisfy a rule and plot these on a co-

ordinate grid. Recognise that a function such as y = 3x+7 corresponds to a straight-

line graph. Begin to plot the graphs of linear functions arising from real-life

problems; discuss and interpret a range of graphs arising from real situations.

Using & Applying Mathematics to Solve Problems Solve problems and puzzles in a variety of contexts, (number, algebra,

shape, space and measures). Choose and justify the use of an appropriate and efficient

method of solving a problem. Explain methods and reasoning, orally and in writing.Predict, generalise and suggest extensions by asking ‘What if…?’



Shape, Space & MeasuresLines and angles Use accurately the vocabulary and notation associated with lines

and angles. Recognise and use parallel lines and the sum of angles at a

point, on a straight line and in triangles.

Properties of shapes Visualise, describe and sketch 2-D shapes in different orientations. Use the geometric properties of triangles and quadrilaterals. Visualise and describe 3-D shapes from 2-D representations.

Transformations Understand and use the language and notation associated with

reflections, translations and rotations. Reflect 2-D shapes in given mirror lines, and recognise line

symmetry. Translate 2-D shapes. Rotate 2-D shapes about a given point, and recognise rotational

symmetry.

Co-ordinates Consolidate use of the conventions and notation for

2-D co-ordinates in all four quadrants. Find co-ordinates of points determined by geometric information.

Construction Consolidate measuring and drawing:

– lines to the nearest millimetre– angles to the nearest degree, and extend to reflex angles.

Construct triangles and other 2-D shapes, using a ruler and protractor.

Measures Use names and abbreviations of metric and imperial units for

estimation, measurement, calculation and problem solving in contexts involving length, area, mass, capacity and time.

Convert from one metric unit to another (e.g. grams to kilograms).

Know rough metric equivalents of imperial measures in common use (feet, miles, pounds, ounces, pints, gallons).

Read and interpret scales on a range of measuring instruments.

Calculate the perimeter and area of compound shapes made up of rectangles.

Calculate the surface area of cuboids and compound shapes made from cuboids.

Handling DataSpecifying a problem, planning and collecting data Respond to a given problem and predict and hypothesise about

possible answers. Identify which data need to be collected and how. Collect data from surveys, experiments and secondary sources, and

record in a frequency table, grouped where appropriate in equal class intervals.

Processing data Calculate statistics from data, using ICT as appropriate:

– find the mode of a small data set;– calculate the mean of a set of discrete data, using a calculator for a large number of items;– find the median of a small number of items;– find and use the range of a set of values.

Representing data and interpreting and discussing results Construct graphs and diagrams to represent data (e.g. bar-line graph,

frequency diagram for a discrete variable). Use ICT to produce graphs and charts, and identify which are most

useful in the context of the problem. Interpret diagrams and graphs (including pie charts), and draw

inferences based on the shape of graphs and simple statistics for a single distribution.

Compare two simple distributions using the range and one of the measures of average.

Probability Use vocabulary and ideas of probability, drawing on experience. Recognise that probability is a way of measuring chance or likelihood:

know that probabilities lie between 0 and 1, and calculate probabilities based on equally likely outcomes in simple contexts.

Identify all possible outcomes of an experiment. Collect experimental data and record in a frequency table, and

estimate probabilities based on the data. Compare experimental and theoretical probabilities in simple contexts.

All of this work has been covered!


Westfield Community School – MathematicsYear 7 : Unit 1

Topic Time NC Descriptors Resources Notes Key Words1 Graphs1 Statistics: about our school

2 Pie charts

3 Tallying in groups

4 Location

5 Scatter graphs

1

1

1

1

1

H3

H5

H3H4

N4

H6

Construct bar charts & pictograms, where the symbol represents a group of units, to communicate information gathered, & interpret information presented to them in these forms

Interpret .., including pie charts, & draw conclusions

Group data, where appropriate, in equal class intervals, represent collected data in frequency diagrams & interpret such diagrams

Use & interpret co-ordinates in the first quadrant

Draw conclusions from scattergraphs, & have a basic understanding of correlation

Extension: 7ER Ch1 p7-9

Extension: 7 ER Ch1 p2-6


Library activity- need to book library. Compare lengths of words in different types of books. CAME worksheet ‘Lengths of words’

Some co-ordinate pictures stuff?71:WS required – p15?

Investigate correlations of the human body. E.g height 3 circumference of the head

StatisticsDataBar chartRepresentsPictogramKey

Pie chartAngle

TallyGrouped data

Co-ordinatesX axisY axis

Scatter graphsCorrelation

Test Yourself 1 Pupils mark and fill in pupil assessment booklet. WS: Graphs, with key words

2 Symmetry1 Lines of symmetry

2 Symmetry in everyday life

3 Turnings

1

1

1

S4

S4

S5

Reflect simple shapes in a mirror line

Use language associated with angles




Bring in pictures that show symmetry from the real life

Line of symmetryMirror line

VerticalHorizontal

TurnClockwiseAnticlockwisePoints of the compass



4 Rotational symmetry 1 S5 Know all symmetries of 2D shapes Find pictures in real life that show rotational symmetry from real life

Rotational symmetryOrder of rotational symmetryCentre of rotation

Test Yourself 1 Pupils mark and fill in pupil assessment booklet. Play hangman with key words

3 Number Patterns1 Factors, multiples & primes

2 Patterns in number

3 Rules & robots

2

1

1

N2

N4

N4

N4?

Recognise sequences of nos, including odd & even nosRecognise & describe nos patterns, & relationships including multiple, factor

Recognise & describe nos patterns, & relationships including multiple, factor & square


Extension; 7ER Ch3 p33-38

*Highest common factor*Prime factorWS required- p54/55?

EXCEL program :’Spot the pattern and find the rule’

Counting numbersOdd numbersEven numbersMultipleFactorPrime

Square nosTriangle nos

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.Word search with key words

4 Arithmetic and the calculator1 Rounding up and rounding down

2 Mental arithmetic

3 Estimation

1

1

2

N3

N3

N4

N3N4

Show understanding of place value in nos up to 1000, & use this to make approximations

Use mental recall of the 2,3,4,5 & 10 tables, & derive the associated factsUse… mental recall of facts up to 10 10 & quick derivation of corresponding facts

In solving problems with or without a calculator, check the reasonableness of

WS required – p73/74?

Rounding

Estimate



4 Priority of operations 1 N4?

results by reference to knowledge of the context or to the size of the nos

Extension: 7ER Ch 4 p40-44 Snap cards availableMini investigation: Using 1, 2, 3, and 4 find all the numbers 1 - 30

BODMASBracketsPower

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.Mental work 10

mins every lesson

N3

N4

N5

N6

S2S3

S5

Show understanding of place value in nos up to 1000 & use this to make approximationsUse mental recall of +/- facts to 20+/- nos. with 2 digits mentallyUse mental recall of the 2,3,4,5 & 10 tables & derive the associated factsUse their understanding of place value to & whole nos. by 10 or 100Use a range of mental methods of computation with the four operations, including mental recall of facts up to 10 10 & quick derivation of corresponding division facts+/- decimals to 2 decimal placesUse understanding of place value to / whole nos. & decimals by 10, 100 & 1000Calculate fractional or percentage parts of quantities & measurementsUnderstand & use the equivalences between fractions, decimals & percentagesBegin to use standard units to measure length & massClassify 2D shapes in various ways using mathematical properties such as reflective symmetry for 2D shapesUse standard metric units of length, capacity & massUse language associated with angleConvert one metric unit to another

See mental starters on short term planning for exact coverage

Activities 4 Choose from above ideas or make up some of your own (but share!)AT1 task 1Gnome Homes

3

Revision and unit test 3 Use ‘Questions’ section for revision



Year 7 : Unit 2Topic Time NC Descriptors Resources Notes Key Words

5 Shape & construction1 Names of polygons

2 More about polygons

3 Using compasses

4 Tessellations & congruence

2

1

1

1

S2

S6

S2S5

S5

S5?

Use mathematical names for common 2D shapes, & describe their properties, including nos of sides & cornersKnow & use the properties of quadrilaterals in classifying different types of quadrilateral

Identify all the symmetries of 2D shapes

.. constructing shapes..

Extension: 7ER Ch 5 p53-54

Extension: 7ER Ch 5 p50-52& p55-58 (though these pages could be used as an activity and used with the whole class)

Equilateral, isosceles, scaleneRectangle, square, rhombus, parallelogram, trapezium, kite, arrowheadWS required – p94/97/98?

TriangleQuadrilateralParallelPolygon

VertexVerticesDiagonalRegularConvexConcave

CircumferenceArcSemicircleDiameterRadiusChordCircle

TessellationCongruent

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.6 Decimals: what’s the point?1 Place value in whole numbers

2 The decimal point

1

1

N3

N4

(N7

N3

Show understanding of place value in nos up to 1000 Use their understanding of place value to whole nos. by 10 &100Solve problems involving calculating with powers – 72 only)

Begin to use decimal notationUse understanding of place value to /

Extension: 7ER Ch 6 p60-63 71:WS required – p123

WS required p125 (p127 72)

DigitThousand HundredTenUnit

Decimal point



3 Working with decimals

4 Problems involving decimals

2

2

N5

N4

N5

N6

whole nos & decimals by 10, 100 & 1000

Add & subtract decimals to 2 dp & order decimals to 3dpUse all 3 operations with decimals to 2dp

Order & approximate decimals when solving numerical problems


TenthsHundredthThousandth

Round

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.7 3D work: the extra dimension1 Identifying solids

2 Using isometric paper

3 Nets of cubes & cuboids

4 More about nets & solids

1

1

hwk

1

S6

S6

S4

S4S6

Recognise & use 2-D representations of 3-D objects

Make 3-D mathematical models by linking given faces or edges



Leave out exercise 7:2 – see AT1 task – can do now or later!

Can do ‘Hexominoes’ as extra AT1/ activity – RD has a lot of cut out shapes etc.

Can do some of the ‘Extra things to do’ p160 as activities

2-D3-DPrismCubeCuboidPyramidTetrahedronPolyhedron

Isometric

NetEdge FaceVertex

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.8 Probability1 Probability scales

2 How the theory works

3 Experiments & games

1

1

2

H5

H5

H5

Understand & use the probability scale from 1 to 0

Find & justify probabilities, by selecting & using methods based on equally likely outcomes

Find & justify probabilities, &

Extension: 7ER Ch 7 p93

Extension: 7ER Ch 7 p94-96 Can use experiments in the book, or

ProbabilityRandom

Theoretical probability

Experimental



4 When the theory doesn’t help

1 H5

approximations to these, by selecting & using methods based on equally likely outcomes & experimental evidence, as appropriate


RD has a probability circus that she has created, if you wish to borrow it

probability

Relative frequency

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.Mental work 10

mins every lesson

N3

N4

N5

N6

S2S3S5

H4H5

Show understanding of place value in nos up to 1000 & use this to make approximations+/- nos. with 2 digits mentallyUse their understanding of place value to & whole nos. by 10 or 100Use a range of mental methods of computation with the four operations, including mental recall of facts up to 10 10 & quick derivation of corresponding division facts+/- decimals to 2 decimal placesUse understanding of place value to / whole nos. & decimals by 10, 100 & 1000Calculate fractional or percentage parts of quantities & measurementsOrder, add & subtract negative nos. in contextUnderstand & use the equivalences between fractions, decimals & percentagesAdd & subtract fractions by writing them with a common denominatorBegin to use standard units to measure length & massUse standard metric units of length, capacity & massUse language associated with angleConvert one metric unit to anotherIdentify all symmetries of 2-D shapesInterpret simple line graphsUnderstand & use the mean of discrete data


Activities 3 Choose from above ideas or make up some of your own (but share!)AT1 task 2Eulers’s Formula

3 Link to chapter 7 exercise 7:2

Revision and unit test 3 Use ‘Questions’ as revision



Year 7 : Unit 3

Topic Time NC Descriptors Resources Notes Key Words9 Algebra: writing letters1 Writing simple formulas

2 Two-stage formulas

3 How to make people understand

4 Collecting terms

5 Substituting in formulas

1

1

1

1

1

N5

N6

N6

N5

N5

Construct, express in symbolic form, & use simple formulae involving 1 or 2 operations

When exploring nos sequences, find & describe in words the rule for the next term or nth term of a sequence where the rule is linear

Use simple formulae

Emphasise AT1 usage

Excel program:’algebra’

AlgebraFormula

Terms

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.10 Angles1 Introducing angles

2 Calculating with angles

3 Angles in triangles

4 Constructions

1

2

1

1

S5

S5S6

S5

S5

Measure & draw angles to the nearest degree, & use language associated with angle

Know the angle sum at a pointSolve problems using angle ..properties of intersecting lines

Know the angle sum of a triangle

When constructing models & when drawing or using shapes, measure & draw angles to the nearest degree

Right angleDegreeAcuteObtuseReflex

Opposite angle

Isosceles Equilateral

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.


Westfield Community School – Mathematics11 Extending the number line1 Introducing negative numbers

2 Co-ordinates in all four quadrants

3 Graphs of number patterns

2

2

2

N5

N5

H4

Order, add & subtract negative nos. in context

Use & interpret co-ordinates in all 4 quadrants

Construct & interpret simple line graphs

Connect 4 or battleships?

NegativePositive

OriginQuadrant

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.12 Units of length & scale drawing1 An introduction to units of length

2 Scale drawings

3 Finding lengths

4 Imperial to metric conversion

1

1

1

2

S5

S6

S6

S5

Know the .. imperial units still in daily use & convert one metric unit to another

Know the rough metric equivalents of imperial units still in use & convert one metric unit to another

Millimetre, centimetre, metre, kilometre

Find packaging in the kitchen etc that has imperial units (if any still exists?)

InchFeetYard

Scale

Divisions

Mental work 10 mins every lesson

N3

N4

N5

N6S4S5

S6H5

+/- nos. with 2 digits mentallyUse mental recall of the 2,3,4,5 & 10 tables & derive the associated factsRecognise & describe nos patterns, & relationships including multiple, factor & squareUse understanding of place value to / whole nos. & decimals by 10, 100 & 1000Order, add & subtract negative nos in contextAdd & subtract fractions by writing them with a common denominatorFind simple perimeters of simple shapes & find areas by counting squaresKnow the angle sum of a triangle & that of angles at a pointUnderstand & use the formula for the area of a rectangleKnow & use the properties of quadrilaterals in classifying different types of quadrilateralUnderstand & use the probability scale from 0 to 1Find & justify probabilities, & approximations to these, by selecting & using methods based on equally likely outcomes


Test Yourself 1 Pupils mark and fill in pupil assessment booklet.Activities 4 Choose from above ideas or make up some of your own (but share!)Revision and unit test 3 Use ‘Questions’ as revision



Year 7 : Unit 4Topic Time NC Descriptors Resources Notes Key Words

13 Algebra: into the unknown1 Inverse operations

2 Equations

3 Trial & improvements

1

2

1

N5

N6

N6

Check solutions by applying inverse operations

..Solve linear equations with whole nos coefficients

..Approximate decimals when solving numerical problems & equations, using trial & improvement methods

Emphasise can be used for checking answers to any question

Encourage good setting out

Common NCT topic!

InverseFunction machine

EquationSubject

Trial & improvement

Test Yourself 1 Pupils mark and fill in pupil assessment booklet14 Area and perimeter1 Irregular shapes

2 Area of rectangles

3 Perimeters of shapes

4 Areas of triangles and parallelograms

5 Compound shapes

1

1

1

1

1

S4

S5

S4

S6

S6

Find perimeters of simple shapes & find area by counting squares

Understand & use the formula for the area of a rectangle

Understand & use appropriate formulae for finding areas of plane rectilinear figures

Investigation to find the formula for the area of a triangle – or practical methods to prove the formulae work!

PerimeterArea

Units

HeightBase

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.


Westfield Community School – Mathematics15 Fractions and percentages1 Introducing fractions

2 Working with fractions

3 Fractions, decimals & percentages

4 Ordering fractions

1

2

2

1

N5

N5

N6

N6

N5

Reduce a fraction t its simplest form by cancelling common factorsCalculate fractional parts of quantities & measurementsAdd & subtract fractions by writing them with a common denominator

Understand the equivalences between fractions, decimals & percentages

NumeratorDenominator

Improper fractionMixed numberEquivalent fraction

PercentageRecurring decimal

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.16 Statistics: what does it all mean?1 The mean

2 Other types of average

3 The range

4 Misleading statistics

2

2

1

1

H5

H7

H4

H5

H7

H4

H7

Understand & use the mean of discrete dataEstimate the mean.. of sets of grouped data

Understand & use the mode, median & range to describe sets of dataCompare 2 simple distributions, using the range & one of mean, median or modeDetemine the modal class & estimate the mean, median & range of sets of data of grouped data, selecting the most statistic appropriate to the line of enquiry

Maybe a good internet activity in here somewhere?

Mean

ModeMedian

Range

Test Yourself 1 Pupils mark and fill in pupil assessment booklet.Mental work 10 mins

every lesson

N4 Add & subtract decimals to 2dp & order decimals to 3dpRecognise approximate proportions of a whole & use simple fractions & percentages to describe these



Westfield Community School – MathematicsN5N6

S5

S6

H5

H6

Check solutions by estimating using approximationsUnderstand & use equivalences between fractions, decimals & percentages, & calculate using ratios in appropriate situationsKnow the angle sum of a triangle & that of angles at a pointKnow the rough metric equivalents of imperial units still in daily use & convert one metric unit to anotherKnow & use the properties of quadrilaterals in classifying different types of quadrilateralCompare 2 distributions, using the range & one of the mode, median or meanIn solving problems, use the knowledge that the total probability of all mutually exclusive outcomes of an experiment is 1

AT1Crosses

3

Activities 2 Choose from above ideas or make up some of your own (but share!)Revision and unit test 3 Use ‘Questions’ as revision


Westfield Community School – Mathematics7: Unit 1: Chapter 1: Graphs

Lesson 1 Lesson 2 Lesson 3 Activity 1

Men

tal Using the number cards, practise some

basic tables and the reverse (division) questions

Countdown: 100, 8, 5, 1, 3, 7Target: 336Can you find more than 1 way of reaching the target?

A dice with 10, 100 & 1000 and a bag of numbers- multiply the two numbers together

NN

S

For sets of discrete data, construct frequency tables

Construct graphs & diagrams to represent data, on paper

Interpret diagrams & graphs

Interpret diagrams & graphs (including pie charts)

Construct frequency tables, grouped where appropriate in equal class intervals

Construct graphs & diagrams to represent data on paper

Construct frequency tables, grouped where appropriate in equal class intervals

Interpret diagrams & graphs and draw simple conclusions based on the shape of the graphs

Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs & charts, using ICT as appropriate

Mai

n th

eme

Introduce idea of surveys collecting data. Explain bar charts & pictograms are ways of displaying that data.Go through bar charts – gaps between the bars (discrete data), label axis & give titlesGo through pictograms – remember to give a key and title

71: Do p2 –6 exercise 1:1Extension: p21 Q1 & 2

72: Do p2 –6 exercise 1:1Extension: p21 Q2

Extension: 7ER chapter 1 p7 – 9 exercise 1:2 Stem & leaf diagrams

Introduce idea of pie charts and the angle represents number of itemsGo through basic fractions: ¼ ½ ¾ 1/8 of a circle

71: Do p7 - 9 exercise 1:3Extension: p21 Q3

72: Do p7 & 8 exercise 1:3Extension: p21 Q3 - 5

Extension: 7ER chapter 1 p2 – 6 exercise 1:1 Pie charts

Explain bar charts for grouped data – no gaps between the bars (continuous data), labelling axis and titles.Go through tallying and setting up tally charts

71: Do p10 & 11 exercise 1:4 Q1 & 2Extension: p21 Q4

72: Do p10 – 12 exercise 1:4 Q 1 – 3Extension:

Extension: 7ER chapter 1 p10 – 14exercise 1:3 Two-way tables

*In the library (book in advance!)

Find two books, one reading (fiction) book and one text (non-fiction) book.Count the number of letters in each word in the first 50 words of each book. Record your data in a tally chart (one tally chart for each book)Draw two bar charts, one for each set of data. What differences do you notice between the two charts? What conclusions can you draw?

Now put the books back in the correct place.

Extension: Type up findings, using Word for the report and EXCEL for the graphs and table

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71: Do p6 exercise 1:272: Do p6 exercise 1:2

71: Do p13 exercise 1:4 Q3 & 4 (not g)72: Do p12 & 13 exercise 1:4 Q 4 – 6 (not g)

Plen

ary Have some pictograms & bar charts

drawn, but with mistakes. e.g incorrect scale, no title – How many mistakes can you find in these examples?

With a pre-drawn pie chart, ask pupils to work out number of items for different starting numbers.What other fractions could you work out easily?

Have a tally table and bar chart drawn that have mistakes. What are the problems? If you were the teacher, what would you say to the pupil?


Westfield Community School – MathematicsLesson 4 Lesson 5 Activity 2 Lesson 6

Men

tal *Have a set of 2D shapes, test

pupils on properties such as symmetry, and names of the shapes (including spelling)

Start with ½ = 20How many other equivalences can you find?e.g. ¼ = 10, 1 = 40, 1/10 = 4

Checklist for chapter 1:

NN

S

Use conventions & notation for 2D co-ordinates..; find co-ordinates of points determined by geometric information

Interpret diagrams & graphs, & draw simple conclusions based on the shape of graphs

Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs & charts, using ICT as appropriate

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Recap co-ordinates. How many different ways can they think of to remember across, then up?

71: Do p15 exercise 1:5 Q2 & 3Extension:

72: Do p15 exercise 1:5 Q2 & 3Extension:

Extension:

Introduce idea of correlation and scatter graphs.Other interesting correlations, about the human body (arm span & height, wrist to elbow & foot length, 3 head size & height etc.)Can do as a class exercise, as both levels have the same exercise

71: Do p16 & 17 exercise 1:6Extension: p21 Q5 & 6

72: Do p16 & 17 exercise 1:6Extension: p22 Q6

Extension: pick one of the above correlations and repeat the exercise

Using collected information or prepared information, get pupils to put information onto a spreadsheet on EXCEL and display the graph. Pupils can also plot line of best fit and compare different data.

Write up report using Word, and import tables and graphs from EXCEL into the word document

71: Do p24 ‘Test Yourself’ section72: Do p24 ‘Test Yourself’ section

Mark and correct answers

Fill in pupil assessment booklet

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*For display purposes? Co-ordinates pictures worksheet

Learn key words- spellings, definitionsAnd/or finish report

Plen

ary Play Connect 4, but using a set

of axis. Girls versus boys (or tables)

Match the scatter graphs with the statements. Have prepared statements and graphs, pupils have to match the pairs, explaining their thinking behind their matched pairs.

Test pupils on key words – spellings and definitions

*Use 72 p22 Q7


Key Words:StatisticsDataBar chartRepresentsPictogramKeyPie chartAngleTallyGrouped dataCo-ordinatesX axisY axisScatter graphsCorrelation

Westfield Community School – MathematicsYear 7: Chapter 1: Graphs

Rearrange the letters to make words that you have learnt about this chapter.Now match them to the pictures below.

TASITCTSIS IEP THRCA GCTSAPTHERARTAAD GNLAE RLCTONIRAEOABR HRCAT YLTLA EYKPERTERESNS PORGUDE TDAA CPOAIMRTGRIONCOTDAE X – SAXI Y – XASI

Title: …………………………………….

Frequency

0 up to 10


Pupil’s choice

frequency

A B C

…………..

…………

(x , y) ………………….

5

4

3

2

1

………………………………

…………

…………………………………..

…………………………….

It shows a ……………………………..

……………………………………….

A

B

C

……… …………..….. 2 people

………………………………

…………..

Westfield Community School – Mathematics10 up to 20

20 up to 30


Westfield Community School – Mathematics7: Unit 1: Chapter 2: Symmetry

Lesson 1 Lesson 2 Lesson 3 Lesson 4

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Using the number cards:addition and subtraction, with numbers of 2 figures

*Compliments:Up to 10 I say 6, they say 4Up to 100 I say 45, they say 55Up to 1000 I say 998, they say 2

Place value questions – how do you say this number, 4291?What value does the 2 have in this number, 52491?Etc.

*How what’s to make a million?2 dice- one with 10, 100 & 1000, and one with 1-6 on. Roll both, multiply answers together. Keep adding scores until the million is reached. Play boys vs girls – first to reach the million

NN

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Understand & use the language & notation associated with reflections

Recognise & visualise the symmetry of a 2D shape: reflection in given mirror lines, and line symmetry

Understand & use the language & notation associated with reflections

Recognise & visualise the symmetry of a 2D shape: reflection in given mirror lines, and line symmetry

Understand & use the language & notation associated with.. rotations

Recognise & visualise the transformation & symmetry of a 2D shape: rotation about a given point, & rotation symmetry

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Go through lines of symmetry and idea of reflecting at right angles into the mirror line

71: Do p26 –28 exercise 2:1 & 2:2Extension: p45 Q1 & 2

72: Do p26 –28 exercise 2:1 & 2:2Extension: p46 Q 1

Extension: 7ER chapter 2 p16 – 19exercise 2:1 Reflection

Recap symmetry. Introduce ideas of horizontal and vertical lines.

71: Do p31 & 32 exercise 2:4Extension: p46 Q3 & 4

72: Do p34 - 36 exercise 2:5Extension: p46 Q2, 4 & 5

Extension: 7ER chapter 2 p20 – 22exercise 2:2 Reflection

Discuss ‘turns’, using language such as clockwise/ anticlockwise and fractions of turns.Introduce points of the compass.

71: Do p35 – 37 exercise 2:6Extension:

72: Do p37 – 39 exercise 2:6Extension:

Extension: 7ER chapter 2 p23 & 24exercise 2:4 Rotation

Introduce the idea of rotational symmetry. Explain language ‘order of rotational symmetry’ and ‘centre of rotation’.

71: Do p38 – 41 exercise 2:7Extension: p46 Q 5 & 6

72: Do p40 – 43 exercise2:7Extension: p46 Q3

Extension: 7ER chapter 2 p23 & 24exercise 2:4 Rotation

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71: Do p29 – 30 exercise 2:372: Do p31 exercise 2:3 Q2 & 3

Go through magazines etc. and find pictures that show symmetry from real lifeAnd/or learn key words – definitions and spellings

Plen

ary *Copy 72 p29 exercise 2:3 Q1 onto an

OHP sheet. Work through with class, encouraging and following up discussion

.

*With set of 2D shapes, get pupils to find lines of symmetry, specify vertical or horizontal lines of symmetry

All class stand up- give instructions and class follow them. E.g turn clockwise by ¼, turn anti-clockwise by ¾ etc.

*Using the pictures brought in by the pupils, find their order of rotational symmetry (or used prepared pictures)

Lesson 5Year 7 Scheme of work 1999 - 2000

Westfield Community School – MathematicsM

enta

l Checklist for chapter 2:N

NS

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71: Do p48 ‘Test Yourself’ section72: Do p49 & 50 ‘Test Yourself’ section



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Finish any incomplete exercises, and do any corrections from this chapter.

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Test pupils on key words – spellings and definitions

Use ‘maths language’ hangman

7: Unit 1: Chapter 3: Number PatternsYear 7 Scheme of work 1999 - 2000

Key Words:Line of symmetryMirror lineVerticalHorizontalTurnClockwiseAnti-clockwisePoints of a compassRotational symmetryOrder of rotational symmetryCentre of rotation

Westfield Community School – MathematicsLesson 1 Lesson 2 Lesson 3 Lesson 4

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tal

What else can you say? 50% = 120, ½ = 120 etc.Use other starters such as 25% = 12…

Fizz – BuzzFizz for multiples of 2, and buzz for multiples of 5.

A dice with 10, 100 & 1000 and a bag of numbers- divide the number by the dice score

Have some pictures of everyday objects (pre-measured). Quiz: how long do you think these objects are? Make sure you use the appropriate units.

NN

S

Recognise & use multiples, factors Recognise & use multiples, factors (divisors), common factor, highest common factor & lowest common multiple in simple cases, & primes (less than 100)

Recognise the first few triangular numbers, squares of numbers to at least 12 12 and the corresponding roots

Express simple functions at first in words, then using symbols

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Go through odd, even, counting numbers, factors, divisors and multiples.

71: Do p50 - 53 exercises 3:1 & 3:2Extension:

72: Do p52 – 55 exercises 3:1 & 3:2Extension:

Extension: 7ER chapter 3 p28 – 30exercises 3:1 & 3:2

Introduce prime numbers.Introduce highest common factor, & prime factor, though only in 72 book. Also common factor & lowest common multiple

71: Do p53 – 55 exercises 3:3 & 3:4 Extension: p66 Q5 - 7

72: Do p55 –57 exercises 3:3 – 3:5Extension: p68 Q2

Extension: 7ER chapter 3 p30 –32exercises 3:3 – 3:5

Introduce square and triangular numbersAlso square roots

71: Do p56 –57 exercises 3:5 & 3:6 Extension: p57 & 58 ‘Patterns from tables’

72: Do p58 – 60 exercises 3:6 & 3:7Extension: p60 & 61 ‘Patterns from tables’

Extension: 7ER chapter 3 p33 – 38exercises 3:6 – 3:9

Go through use of number machines

71: Do p59 –61 exercises 3:7 & 3:8 Extension:


Extension:

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Finish exercises, including extension questions, if time.And/or learn key words – definitions and spellings

71: Do p61 & 62 exercise 3:9 72: Do p64 & 65 exercise 3:10

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ary

Class competition: pick a number between 1 and 50. Work out the factors, add the factors together – that is your score – who has the highest score? Do with multiples of particular numbers etc.

Pick a number – what are the factors? What are the prime factors?Pick two numbers – what are the common factors, lowest common multiple & highest common factor?

Flash cards, with numbers on – what can you tell me about this number?e.g. 9 is a square number, it is a multiple of 3, its factors are 1, 3 & 9, it is odd! Etc.

*Number machine on the desk – Input number is… and out put number is..What was the function?

Activity 3 Lesson 5


100% = 240


enta

l Checklist for chapter 3:N

NS

Express simple functions at first in words, then in symbols

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ICT: EXCEL Spot the pattern and find the rule




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Plen

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Test key words – spellings and definitions


Key Words:Counting numberOdd numberEven numberMultipleFactorDivisorsPrime numberPrime factorSquare numberTriangular numberCommon factorHighest common factorLowest common multipleSquare root


Year 7: Chapter 3: Number PatternsI A C O M M O N F A C T O RT H I R T Y S I X W S Z A OS O S R O T C A F B Q L C TE P Q O T V O M E L U K O CH T N S H D U E S G A O T AG S T I D L N V N Q R W W FI E S V T D T A A O E R P EH W Y I E M I R P L A T I MC O P D H R N E V E L G O IS L P U T M G E T F H U E RE V I F Y T N E W T Z J A P

Find the missing words in the sentences below, then find the words in the grid above.

1. Numbers that end in 2, 4, 6, 8 and 0 are called numbers.

2. Numbers that end in 1, 3, 5, 7and 9 are called numbers.

3. 1,2, 3, 4 are called c numbers.

4. The of 12 are 1, 2, 3, 4, 6 and 12.

5. 1, 3, 6, 10 are numbers

6. 1, 4, 9, 16 are numbers.

7. 12 and 18 have / s 1, 2, 3 and 6.

8. A number has 2 factors; one and itself.

9. The / s of 14 are 2 and 7.

10. The square of 36 is 6.

11. 4, 8, 12, 40, 484 are all s of 4.

12. 1, 3 and 5 are all d of 15.

13. The common multiple of 8 and 6 is 24.

14. The common factor of 24 and 36 is 12.

15. is not a prime number, as it only has one factor!


Westfield Community School – Mathematics7: Unit 1: Chapter 4: Arithmetic and the Calculator


Men

tal

Start with 25% = 9, what other facts can you find?e.g 50% = 18, 10% = 3.6 etc.Could even include ½ = 18!

Using the number cards, give pupils +/ questions, with numbers of two digits.Include some questions involving decimals, with 2dp.

*With a set of number cards 1 – 100. Give a starting number e.g. 16, pupil pulls out a card and gives a method of reaching from 16 to their number. Next pupil pulls out a card and gives method of reaching their number from last number.

*With a set of 2D shapes, discuss the angles – estimating the sizes and using language such as acute, obtuse etc.

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S

Round large positive numbers to the nearest 10, 100 or 1000

Consolidate the rapid recall of number facts, including.. facts to 10 10, & quickly derive associated facts


Make & justify estimates & approximations of calculations


Make & justify estimates & approximations of calculations

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Introduce rounding to the nearest 10, 100 and to the nearest 1000.

71: Do p70 – 72 exercises 4:1 – 4:3Extension: p89 Q1

72: Do p72 –73 exercises 4:1 – 4:3Extension: p74 exercise 4:4

Extension: 7ER chapter 3 p28 – 30exercises 3:1 & 3:2

Go through times tables and reinforce that division is reversed tables

71: Do p73 – 74 exercises 4:4 – 4:6Extension: p89 Q2 & 3

72: Do p77 – 78 exercises 4:7 – 4:9Extension:

Extension:

Introduce idea of rounding to get approximate answers. Emphasise good checking practice.


72: Do p79 – 83 exercises 4:10 & 4:11Extension: p91 Q1 - 5

Extension:

Recap briefly work from last lesson


72: Do p83 exercise 4:12Extension:

Extension:

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71: Do p382 – 383 Help Yourself Section 1 exercises 1 - 372: Do p74 – 76 exercises 4:5 & 4:6

71: Do p79 exercise 4:972: Do p396 – 397 Help Yourself Section 1 & 2 exercises 1 - 3


Westfield Community School – MathematicsPl

enar

yPut some numbers on the board. Pupils throw a dice with 10, 100 & 1000 on. Pick a numbers and round to number on the dice.

Put some answers on the board, what could the / questions have been?

Pick questions from ‘real life’ e.g. shopping bills etc.– pupils have to estimate the answers and explain how they estimated.

Similar to last lesson, however pupils decide the questions for other pupils

Lesson 5 Activity 4 Lesson 6

Men

tal Start with a length 5 metres, what else

could we write instead?(Aiming for metric conversions, however for more able, could include imperial!)

Checklist for chapter 4

NN

S

Know & use the order of operations, including brackets

Carry out calculations with more than one step using brackets and the memory

Know & use the order of operations, including brackets

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Introduce BODMAS. Explain about brackets and powers.

71: Do p85 – 86 exercises 4:13 & 4:14Extension: p90 Q7 - 9


Extension: 7ER chapter 4 p40 - 43exercises 4:1 – 4:3

*Snap cards – play snap as per normal in pairs, however cards have a sum on which requires working out first.Two levels, in different coloursOnce pairs played, winners move on etc.

71: Do p92 ‘Test Yourself’ section72: Do p94 Test Yourself’ section



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Learn key words – spellings, definitions and alternative words (sum, product etc.)And/ or using the numbers 1, 2, 3, 4, can you make all the numbers upto 30? (using each number once –can make more difficult – must use all four numbers)

71: Do p84 exercise 4:1272: Do p84 – 86 exercises 4:13 & 4:14


Key words:RoundingEstimateBODMASBracketsPowerSum?Product?Quotient?Difference?


enar

yPut some questions on the board such as 3 + 4 5 = 35What order should the functions be done to make the answer? Put the brackets in.If there where no brackets, what would the answer be?

Test pupils on key words, spellings & definitions. Include alternative words such as sum, product etc. *Use some match cards.



Year 7: Chapter 4: Arithmetic & the calculator

1 2 3 4

5 6

7 8 9 10

11 12

13 14

15 16 17

18 19 20 21

22 23 24

25 26 27

28 29

Across Down1 Product of 5 and 8 1 3174 + 1462

2 Round 42,386 to the nearest hundred 2 (895 – 432) 10

5 8 multiplied by 7 3 8872 3927

6 2 + 7 9 4 4 to the power of 4

7 Sum 17 and 19 9 Product of 6, 12 and 100

8 Difference of 7312 and 3571 10 2 to the power of 8

11 1 005 005 times 5 11 Add 234 with 287

13 20 + 8 9 12 Share 4576 by 8

14 Subtract 83 from 162 13 Round 896 to the nearest 10

15 9² + 20 15 9583 divided by 7

16 Find the sum total of 136, 148 and 198 17 Estimate an answer to 23 39

18 Add together 8, 10 and 12 19 (270 + 350) 3 4

22 Divide 232 by 4 20 8 to the power of 3

23 Round 11 547 to the nearest thousand 21 3 4 5

25 Take away 196 from 292 24 Sum 73, 85 and 96

27 Find the product of 1005 and 5 26 7 times 3 squared

28 (5 + 6) 6²

29 3996 to the nearest 10


Westfield Community School – Mathematics7: Unit 1: AT1, revision and test


Men

tal

Jumps (median sheet)Copy onto OHP

538

714

267

Target: 37

Counting up in:½, ¼, 0.2, 3 etc

Round the world (median sheet)

NN

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Use 2D representations to visualise 3D shapes

See previous references to NNS Multiply …integers…. by 10 Choose and justify the use of an

appropriate and efficient method of solving a problem

See previous references to NNS

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Gnome Homes investigation (see teacher notes)Go through drawing 3D shapes in 2D on triangular dotty paper

Draw as many 4 ‘roomed’ houses in 3D as you can

Go through chapter 1 & 2 work.

71: Do p19 – 20 Ch 1Questions Q5 & 6 Do p42 –44 Ch 2 Questions

72: Do p20 Ch 1 Questions Q5 & 6 Do p44 – 45 Ch 2 Questions

Extension: Use Extension questions

Gnome Homes continued.

Painting of ‘faces’

Which is the cheapest house to paint and which is the most expensive?

Go through chapter 3 & 4

71: Do p63 -64 Ch 3 Questions Do p87 – 88 Ch 4 Questions

72: Do p66 – 67 Ch 3 Questions Do p89 – 90 Ch 4 Questions

Extension:Use Extension questions


How many different ways can you make the target?Median sheet- Trails

Westfield Community School – MathematicsH

wk

Colour the houses in 3 colours, to enhance the 3D effectAnd/or71: Do p18 – 19 Questions chapter 1 Q 1-472: Do p19 – 20 Questions chapter 1 Q 1-4

Complete any unfinished questions from revision work and any ‘painting prices from Gnome Homes.

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Make up some shapes using multi-link, can pupils draw them? (Copy dotty paper onto OHP? For group use??

Divide the board into 2 parts – what can you remember about the 2 chapters? What are the important facts you need to learn?

Go through investigation – this is what you should have, this is where you should be up to… Ask pupils questions on by 10

Divide the board into 2 parts – what can you remember about the 2 chapters? What are the important facts you need to learn?

Lesson 5 Lesson 6

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*Have a set of 2D shapes, test pupils on properties such as symmetry, and names of the shapes (including spelling)

NN

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Explain methods & reasoning , orally an in writing.

Predict, generalise and suggest extensions by asking “What if ..?”

Testing of: Recognise & use multiples, factors (divisors), common factor & primes (less than

100) Recognise the first few triangular numbers, squares of numbers to at least 12 12 Round large positive numbers to the nearest 10 or 100 (1000 for 72) Know & use the order of operations, including brackets Recognise & visualise the symmetry of a 2D shape: reflection in given mirror lines Recognise & visualise the transformation & symmetry of a 2D shape: rotation

symmetry For sets of discrete data, construct frequency tables Construct diagrams to represent data, on paper (pie chart for 72)

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Gnome Homes continued

Rent for houses.

Overall cost of each house

Test 7: Unit 1 (different test for different books, but a lot of overlap)

Non-calculator section only.



wk

71: Complete any unfinished questions from chapter 3 & 472: Complete any unfinished questions from chapter 3 & 4

Plen

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Any problems with first four chapters – discuss and help with any questions from pupils.



Gnome Homes.

The gnomes that live in Gnome-land make their houses out of 4 cubes.The villagers do not have house numbers, so have a method of recognising their own houses. Each house is of a completely different shape, therefore each gnome can find their own home, even after a night out on the town!

. Design and draw as many possible Gnome Homes as possible.

. If each gnome has to have a different shape, how many gnomes can you have in the village ?

The Mayor of Gnomeville decides to pay the village a special visit, so the gnomes decide to paint their houses in celebration. Each square face costs £10 to paint and so each of the gnomes have to work out how much their residences will cost in total.

. How much does each of your Gnome Homes cost to paint ?

. Who has the cheapest house ?

. Who has the most expensive house ?

When the Mayor arrives, he announces that he is putting a tax onto the gnomes' houses. Each gnome has to pay a ground rent of £20 for each square which covers the ground.

. How much does each of your gnomes have to pay ?

. Who has the cheapest / most expensive ground rent ?

. If you take both the painting and the ground rent into account, which of the gnomes has to pay the most / least ?

Extension:Introduce some further rules of your own and find the cheapest or most expensive property



Teacher's Notes - Gnome Homes

Equipment needed for the task:

triangular dotty paper, multi-link cubes ( please return after use! )

NB: This is a teacher led investigation and therefore copies of this worksheet are NOT available.

Objective of the task:

To check pupils' ability to draw cuboids and therefore highlight any pupils with spatial awareness problems.NB: Some pupils may need to practise drawing one cube first before progressing onto this task.

Other ideas that can be introduced:

Reflection/ rotation/ congruency - I would suggest that you do not allow reflections, rotations and use the idea of congruency.Allowing windows/ doors in the buildings.

Answers:

Attached are copies of all the possible houses. These only include ones that actually balance and reflections have also not been included.If you use different rules to those suggested in the starter, you will need to modify the answers!!



Year 71: Unit 1 Test: Non-Calculator

1. Using the numbers in the following list, answer the questions below:

1, 3, 4, 6, 8, 9, 11, 15, 16, 19, 20, 22, 24, 25

a) Give three even numbers. (N2)

b) Which are the multiples of 5? (N4)

c) Which are the factors of 48? (N4)

d) Give three square numbers. (N4)

e) Which are the prime numbers? (N4)

f) Which are the triangular numbers? (N4)

2. Round these numbers to the nearest 10

a) 43 b) 59 c) 15 (N3)


a) 849 b) 617 c) 399 (N3)

4. Work out:

a) 4 + 12 3 b) 10 2 4 c) (5 + 3) 6 (N )

5. Copy and complete these diagrams:

a) b) (S4)



6. Using the shapes in the following list, answer the questions below:

a) Which of these shapes have one line of symmetry? (S5)

b) Which of these shapes have rotational symmetry of order 5? (S5)

c) Which of these shapes have two lines of symmetry? (S5)

d) Which shape has no rotational symmetry? (S5)e) Copy this shape and draw on the lines of symmetry? (S5)

7. Here are some results from a recent test:

12 15 19 21 14 8 3 25 1 9 14 1823 26 19 13 11 9 17 28 6 15 29 24

a) Copy and complete the tally table: (H4)

Marks Tally Total1-56-1011-1516-2021-2526-30

b) Draw a bar chart from your tally chart (H3)

c) Draw a pictogram from your tally chart (H3)Use to represent 2 people


Now go back and check your workings



1. Using the numbers in the following list, answer the questions below:

1, 3, 4, 6, 8, 9, 11, 15, 16, 19, 20, 22, 24, 25

a) Which are the multiples of 5? (N4)

b) Which are the factors of 48? (N4)

c) Give three square numbers. (N4)

d) Which are the prime numbers? (N4)

e) Which are the triangular numbers? (N4)


a) 43 b) 59 c) 15 (N3)


a) 849 b) 617 c) 399 (N3)


a) 2356 b) 9847 c) 547 (N4)

5. Work out:

a) 24 + 18 3 b) 20 2 4 c) (25 + 43) 6 (N5)

6. Copy and complete these diagrams:

a) b) (S4)



7. Using the shapes in the following list, answer the questions below:

a) Which of these shapes have one line of symmetry? (S5)

b) Which of these shapes have rotational symmetry of order 5? (S5)

c) Which of these shapes have two lines of symmetry? (S5)

d) Which shape has no rotational symmetry? (S5)

e) Copy this shape and draw on the lines of symmetry? (S5)

8. Here are some results from a recent test:

12 15 19 21 14 8 3 25 1 9 14 1823 26 19 13 11 9 17 28 6 15 29 24

a) Copy and complete the tally table: (H4)

Marks Tally Total1-56-1011-1516-2021-2526-30

b) Draw a bar chart from your tally chart (H3)

9. Draw a pie chart of 9B favourite colours. (H5)

Favourite Colours of 9B

Red 16Green 8Yellow 4Blue 4TOTAL 32


Now go back and check your workings

Westfield Community School – Mathematics7: Unit 2: Chapter 5: Shapes & construction


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Using the number cards, add & subtract two digit numbers

Starting with 10% = 8, how many other facts can you work outWork in small groups with large sheet of paper.Display sheets and discuss

Complements of 10, 100, 20,50,1

I say 25, pupil says 75 for compliment of 100!

Telling the time questions.What is this time?12 hour and 24 hour?TimetablesDifference in timeFind finishing time, if starting time given and length and visa versa

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Use correctly the vocabulary for shapes

Begin to identify and use angle, side & symmetry properties of triangles & quadrilaterals


Use conventions & notation for 2D co-ordinates


Construct a triangle

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Discuss different types of triangles and quadrilaterals

71: Do p 94-98 Exercises 5:1 & 5:2Extension: p114 Q1 & 2 72: Do p96-100 Exercises 5:1 & 5:2Extension: p118 Q1 & 2

Extension: 7ER chapter 5 p53 – 54Exercise 5:2

Discuss parallel/ diagonals/ lines of symmetry/ rotational symmetry of quadrilaterals

All: Worksheet on ‘Triangles & quadrilaterals’

Extension:

Introduce vocabulary vertex/ edge/ face and regular shapes

71: Do p 100-104 Exercises 5:4 & 5:5Extension:

72: Do p102- 106 Exercises 5:4 & 5:5Extension:

Extension:

Introduce vocabulary relating to circles and go through using compasses, including drawing triangles given the lengths of the sides

71: Do p106 –109 Exercises 5:7 – 5:9 Extension: p114 – 115 Q 3 – 5 72: Do p108- 112 Exercises 5:7 – 5:9Extension:

Extension: Drawing triangles given 2 angles and one length

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71: Do p98 - 99 Exercise 5:3 72: Do p100 -101 Exercise 5:3

And make your own person/ picture/ object and make a table with descriptions, number of sides and name of the polygon

71: Do p104 Exercise 5:6 and finish exercises 5:4 & 5:5 72: Do p107 Exercise 5:7 and finish exercises 5:4 & 5:5

And learn vocabulary of triangles and quadrilaterals



enar

y Show pupils a variety of 2D shapes, get them to name it and discuss its properties.

Same as day before, but discuss additional properties such as rotational symmetry and number of diagonals

Hold up a variety of 3D shapes, pupils point out edges, vertices and faces. How many of each do the shapes have?

Have some lengths of triangle edges – pupils come up to the board and draw them


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In pairs: each pupil writes 10 questions (and answers) around the theme of factors, multiples and primes.Swap questions, first pair to finish!


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Recognise and visualise the transformation and symmetry of a 2D shape

Recognise and visualise the transformation and symmetry of a 2D shape

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Discuss tessellations and introduce the word congruent. For some pupils could introduce the word similar

71: Do p110-112 Exercises 5:10 & 5:11Extension: p115 Q6 & 7 72: Do p113-115 Exercises 5:10 & 5:11Extension: p118 Q3

Extension: 7ER chapter 5 p50-52Exercise 5:1

Using the Extra Resource 7 book p55 – 58Design Esher pictures, using notes from the book




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Key Words:TriangleQuadrilateralParallelPolygonEquilateralIsoscelesScaleneRectangleSquareRhombusParallelogramTrapeziumKiteArrowheadVertex/ verticesDiagonalRegularConvexConcaveCircumferenceArcSemicircleDiameterRadiusChordCircleTessellationCongruent


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yShow pupils some tiles (in maths cupboard) – ask will this tessellate? Why?

Test pupils on key words, definitions & spellings.

7: Unit 2: Chapter 6: Decimals: what’s the point?Lesson 1 Lesson 2 Lesson 3 Lesson 4

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10 questionsPupils can ask 10 questions that require yes or no answers only, and have to identify the 2D shape.

Class counting:Using negative numbers, starting number 20, then repeatedly subtract 4.Make harder by using a decimal number, or starting with a larger numberetc.

0.50.90.2

0.70.60.1

0.30.80.4

Target = 2.4 or 0.24 or 0.024

Using the number cards:Recap times tables upto 10 10 amd derivation of corresponding facts

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Understand place value; & integers & decimals by 10, 100 & 1000 and explain the effect

Understand decimal notation & place value; & integers & decimals by 10, 100 & 1000 and explain the effect

Compare and order decimals in different contexts; know that when comparing measurements they must be in the same units

Use standard column procedures to +/ whole numbers and decimals with upto 2 dp

Consolidate understanding of the operations to / of +ve whole nos and decimals

/…; extend to / decimals with 1 or 2 dp by single digit whole nos



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eGo through place value and effects of multiplying by 10, 100 & 1000 (NB: move numbers – not the decimal point)

71: Do p120-123 Exercises 6:1 – 6:3Extension: 72 p141 Q1 & 2 72: Do p122 – 125 Exercises 6:1 – 6:3Extension: p141 Q1 & 2

NB: can do exercises 6:1 & 6:2 orallyDo not need worksheet – pupils can copy out table

Extension: 7ER chapter 6 p60-62 exercises 6:1 & 6:2

Go through place value after the decimal point and discuss effects of multiplying and dividing by 10, 100 & 1000, with both decimals and whole numbers (NB: move the numbers – not the decimal point)

71: Do p125- 126 Exercises 6:4 & 6:5Extension: 72: Do p127 - 128 Exercises 6:4 & 6:5Extension:

Worksheet needed for 6:4 in both books

Extension: 7ER chapter 6 p63 exercise 6:3

Discuss ordering decimals (and explain units must be the same) and how to set out questions for addition and subtraction.

71: Do p128- 130 Exercises 6:7 – 6:9Extension: p139 Q3- 5 72: Do p131- 134 Exercises 6:8 & 6:10Extension: p141 Q3 & 4

Extension: 7ER chapter 6 p6467 exercises 6:4 –6:6

Go through how to set out and do multiplication and division of decimals

71: Do p131 Exercises 6:10 – 6:11Extension: p139-140 Q6 & 7 72: Do p134 Exercises 6:11 & 6:12Extension: p142 Q5

Extension: 7ER chapter 6 p68-69 exercises 6:7 & 6:8

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71: Do p127 Exercises 6:6 And learn the place values upto millions and down to thousandths 72: Do 128 – 129 Exercise 6:6 & 6:7

71: Do p386- 387 Help yourself Exercises 8 - 10 72: p4--- 401 Help yourself Exercises 8 – 10 And if time p142 Q6

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ary Have some numbers written on the board,

such as 34000. Ask what is the number and if this was the answer to a multiplication question, what was the question?

Same as yesterday, but numbers less than 1.

Have some +/- questions and their answers written up, with mistakes. Spot the mistakes.

Same as yesterday but with / questions and answers.

Lesson 5 Lesson 6 Lesson 7

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Start with 50cm written on the board.What does this mean to you?How many everyday items can you think of that are approximately that length, height etc.What other ways can you say 50cm? In metres, km, inches, feet????

Using the number cards:Do some simple fractions addition and subtraction questions


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Round.. decimals to the nearest whole nos or 1 dp

Enter numbers and interpret the display in different contexts (decimals, money, metric measures)

Round.. decimals to the nearest whole nos or 1 dp

Enter numbers and interpret the display in different contexts (decimals, money, metric measures)



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eGo through rounding decimals correct to 1,2 and 3 dp

71: Do p133-134 Exercises 6:6:12 – 6:14Extension: p140 Q8 72: Do p135 Exercise 6:13Extension:

Extension: 7ER chapter 6 p70-71 exercise 6:9 & 6:10

Recap all operations of decimals and how to set out workings

71: Do p134- 136 Exercises 6:15Extension: p140 Q 9-12 72: Do p137-138 Exercises 6:14Extension:





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71: p390 - 391Help yourself Exercises 15-17 72: p404 – 405 Help yourself Exercises 15-17

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Have some calculator displaying answers in pounds, what are the answers corrected to the nearest penny

Have some worded questions – what type of mathematical function would you have to do to solve this problem?

Test pupils on key words, definitions & spellings.Fill in the gaps type sheet?

7: Unit 2: Chapter 7: 3D work: the extra dimensionLesson 1 Lesson 2 Activity 2 Lesson 3

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I like.. (median sheet)With the quadrilaterals sheet.

Calculator Nim (median sheet) Countdown:25, 5, 8, 2, 1, 6Target: 226

How many different ways can you find the target, using the numbers above, no more than once each?

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Use 2D representations to visualise 3D shapes

Use 2D representations to visualise 3D shapes and deduce some of their properties

Use 2D representations to visualise 3D shapes and deduce some of their properties

Use ruler & protractor to construct simple nets of 3-D shapes, e.g cuboid, regular tetrahedron, square-based pyramid, triangular prism


Key words:DigitThousandHundredTenUnitDecimal pointTenthHundredthThousandthRound


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eDiscuss what 3D shapes are, and how we can draw them in 2D

71: Do p145-150 Exercises 7:1 & 7:3Extension: p163 Q 1-4 72: Do p146-152 Exercises 7:1 & 7:3Extension: p166 Q1-3

Extension: 7ER chapter 7 p84-86

Introduce the pupils to isometric paper and explain what isometric means.Go through drawing on isometric paper.

71: Do p152-154 Exercises 7:4 & 7:5Extension: p164 Q 5-8 72: Do p154-156 Exercises 7:4 & 7:5 Extension: p167-168 Q5-8

Extension: 7ER chapter 7 p74-77 exercises7:1 &7:2

Pentominos and hexominos-Can you draw all of them?

Is there a pattern – look at one square/ 2 squares- dominos/ 3 squares- trominos/ 4 squares??

Which of the pentominos make open boxes? Which of the hexominos make boxes?

Which of the shapes tessellate?Also some puzzles- see RD pack

Recap what nets are.

71: Do p158-160 Exercises 7:7 & 7:8Extension: p160 ‘Extra things to do’ 72: Do p160-163 Exercises 7:7 & 7:8 Extension: p163 ‘Extra things to do’

Extension: 7ER chapter 7 p78-83 exercises 7:3- 7:6

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71: Do p155-157 Exercise 7:6 72: Do p157-159 Exercise 7:6

And learn key words: spellings and definitions

Continue the pentominos and hexominos activity. Extend with ideas shown on previous lesson.

And/ or choose 5 3D shapes, draw them in 2D and draw their nets, cut them out and make them

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On OHP, have some 2D representations of 3D shapes. Pupils have to work out what shapes the drawings represent.

Some shapes drawn in 2D on isometric paper, pupils have to make the shapes with multilink.

Have some nets draw and cut out, hold them up, pupils guess what shapes they would make when put together.

Lesson 7

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NN

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Test pupils on key words, definitions & spellings.Hangman?

7: Unit 2: Chapter 8: ProbabilityLesson 1 Lesson 2 Lesson 3 Lesson 4

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Have some line graphs on an OHP. Discuss what the line represents and what is happening.

Give pupils a list of numbers, find the means (Could roll dice, or pick out numbers from a bag)

Extend to medians and modes etc.

0.0024 is the answer.If the question only involves multiplying or dividing, what could the questions have been?

Using the number cards:Adding and subtracting negative number questions


Key words:2-dimensional3-dimensionalprismcubecuboidpyramidtetrahedronpolyhedronisometricnetedgefacevertex

Westfield Community School – MathematicsN

NS

Use vocabulary and ideas of probability, drawing on experience

Understand & use the probability scale from 0 to 1

Understand & use the probability scale from 0 to 1; find & justify probabilities based on equally likely outcomes in simple contexts

Collect data from a simple experiment & record in a frequency table

Understand & use the probability scale from 0 to 1; find & justify probabilities based on equally likely outcomes in simple contexts

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Discuss words relating probability, and place words onto a probability scale, include 0 to 1 on scale

71: Do p168-169 Exercise 8:1Extension: p186 Q1 72: Do p172-173 Exercise 8:1 Extension:

Extension: 7ER chapter 8 p93 Exercise 8:3

Go through equally likely probabilities.

71: Do p170-173 Exercise 8:2 & 8:3Extension: p186 Q2 & 3 72: Do p174-177 Exercise 8:2 & 8:3 Extension: p190 Q2 & 3

Needs one suit of cards for each pair of pupils for exercise 8:3

Extension: 7ER chapter 8 p94-95 Exercises 8:4 & 8:5

Class is split into pairs. 3 stations around the classroom with game 1, 2 and 3 set up. Pairs rotate around the stations spending approx. 10 minutes on each.At end, collate answers and discuss outcomes of the games.

Recap briefly theoretical probability.

71: Do p178-180 Exercise 8:5Extension: p187 Q 4 72: Do p183-184 Exercise 8:5Extension: p190 Q4 & 5

Extension: 7ER chapter 8 p96 Exercise 8:6

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71: Do p177-179 Exercise 8:4 72: Do p173-175 Exercise 8:4

And learn words relating to probability

Worksheet on probability – 72 pupils have to do the extension questions too!

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Draw a large probability scale on the board, pupils discuss probabilities and label them on the scale

Quick fire probability questions Match the probability questions with the answers


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Show pupils different 2D shapes and discuss their angles, using the correct language.Can extend to discussing symmetries, parallel sides, diagonals etc.




NS

Estimate probabilities based on data from a frequency table

Collect data from a simple experiment & record in a frequency table; estimate probabilities based on this data

Compare experimental & theoretical probabilities in simple contexts

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Go through examples of probabilities that can not be worked out exactly e.g. drawing pin landing point upwards etc.Introduce idea of experimental probability.

71: Do p181-183 Exercise 8:6Extension: p187 Q 5-7 72: Do p172-173 Exercise 8:1 Extension: p190 Q6

Extension: 7ER chapter 8 p88-91 Exercise 8:1 & 8:2

Probability circus

Several stations of mixed probability experiments for pupils to work on in groups of 4-ish

Discuss results after collating them




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Write up the results from the experiments.And design an experiment of your own – what results would you expect?

Plen

ary Discuss ways of working out the

probabilities of these things: probability of a matchbox landing on its side? etc


7: Unit 2: AT1, revision and testLesson 1 Lesson 2 Lesson 3 Lesson 4


Key words:ProbabilityRandomTheoretical probabilityExperimental probabilityRelative frequency


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lUsing the number cards, ask fraction questions – adding and subtracting – start with common denominator and then different but easy to work out eg quarters and eights etc

Start with 10% = 8 as a starting fact, what other facts can you write down? Work in tables or pairs with large sheet of paper. Don’t forget decimals of fractions too!

With large 1 – 100 grid, play connect 4 with a difference. Pupils pick where they want to put their cross – must give a sum that has that number as the answer. E.g want to cross out 24 so say 6 4. Can make questions complicated e.g. / by 10, 100 & 1000, decimals, % etc.Can make it connect 5 etc..

Cards with everyday products on: Estimate the size of the packaging, what is the weight?What units are best to use?What other units could we say that is equal to?

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See previous references to NNS Use ruler & protractor to construct simple nets of 3-D shapes, e.g cuboid, regular tetrahedron, square-based pyramid, triangular prism

Solve problems and puzzles in a variety of contexts

Predict, generalise and suggest extensions by asking “What if…?”

See previous references to NNS

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71: Do p113 Ch 5 Questions Do p137 – 138 Ch 2 Questions


Extension:

Euler’s Relation (see teacher’s notes and link to chapter 7 exercise 7:2)

Draw nets for some 3D shapes, then make them.

Keep for next lesson.

Using the shapes made by the pupils and plastic 3D shapes, count the faces, vertices and edges.

Put the numbers into a table and look for a connection between the three variables.

Go through chapter 7 & 8

71: Do p161 - 162 Ch 7 Questions Do p184 – 185 Ch 8 Questions

72: Do p 164 - 165 Ch 7 Questions Do p188 – 189 Ch 8 Questions

Extension:

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71: Finish Chapters 5 & 6 Questions72: Finish Chapters 5 & 6 Questions

Write up investigation so far: diagrams, method, table of results, patterns, rules

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Divide board into two sections – what facts can you add to each side about chapters 5 & 6.

Have some 3D shapes – what are their names? What are the shapes of the sides? What are their properties? E.g do they have symmetry – line or rotational?

What do the words face, vertex or edge mean? Can you think of other words that mean the same thing?

Divide board into two sections – what facts can you add to each side about chapters 7 & 8.

Lesson 5 Lesson 6



enta

l Using the number cards:Questions that involve adding and dividing decimals, with 1 or 2 dp.

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Predict, generalise and suggest extensions by asking “What if…?”

Testing of: Begin to identify and use angle, side & symmetry properties of triangles

& quadrilaterals Recognise and visualise the symmetry of a 2D shape Understand place value; & integers & decimals by 10, 100 & 1000 Use standard column procedures to +/ whole numbers and decimals with

upto 2 dp Consolidate understanding of the operations to / of +ve whole nos

and decimals Understand & use the probability scale from 0 to 1; find & justify

probabilities based on equally likely outcomes in simple contexts Estimate probabilities based on data from a frequency table Use ruler & protractor to construct simple nets of 3-D shapes, e.g cuboid

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Using the computer room:

Complete the write up for Euler’s Relation investigation by testing your rule on other 3D shapes. Can you write your rule in more than 1 way?

Do all 3D shapes fit the rule or are there any exceptions?

What can you find out about Euler on the internet? Is your rule correct?


Non-calculator section only

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71: Finish chapters 7 & 8 Questions 72: Finish chapters 7 & 8 Questions

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on the internet.




1. I have three sides and three angles which are all equal.

a) What am I? b) What is also true about me?

2. I have four sides and two pairs of parallel sides.


3. I have four equal sides, but my angles are not 90º.

a) What am I? b) How many pairs of parallel sides do I have?

4. I have six equal sides.

a) What am I? b) How many vertices do I have?

5. How many lines of symmetry do the following shapes have?

a) b) c) d)

6. Write down the following number in figures:

a) nine thousand and six

b) three million, five hundred and six thousand two hundred and one

7. Write these numbers in words:

a) 6127 b) 1030652

8. Work out these sums:

a) 64 10 b) 3.6 100 c) 760 10 d) 84 1000

9. Put these in order of size, starting with the smallest first: 2.45, 3.06, 2.3, 3.1

10. Work these out:

a) £3.24 5 b) £8.06 46p


Westfield Community School – Mathematicsc) £12 + £1.46 d) £8.96 4



11.

The counters above are placed into a bag. If I pull out one counter from the bag, what is the probability that it will be:

a) grey b) pink c) white d) white or grey

12. In a bag, there are 5 red counters, 6 blue counters and 10 green counters. What is the probability that the first counter I pull out will be:

a) blue b) red c) green or blue d) white

13. In a box of chocolates, there are 8 toffees, 12 strawberry creams and 4 nougats.If I choose a chocolate from the box, what is the probability that I will choose:

a) nougat b) toffee c) strawberry cream

Make sure you cancel down the fractions as far as possible for this question!!

14. If I throw a drawing pin 100 times, and the pin lands with the point in the air 68 times.

a) How many times does the pin land with the point pointing downwards?

b) What is the experimental probability of the drawing pin landing point downwards?

c) What is the experimental probability of the drawing pin landing point upwards?

d) If I throw the drawing pin 200 times, how many times would you expect the pin to land point upwards?

15. Draw a net for a cuboid, which has a length of 4cm, a width of 3cm and a height of 2cm.

Now go back and check your work until time is up!




1. I have three sides and three angles which are all equal.


2. I have four sides and two pairs of parallel sides.


3. I have four equal sides, but my angles are not 90º.

a) What am I? b) How many pairs of parallel sides do I have?

4. I have six equal sides.

a) What am I? b) How many vertices do I have?

5. How many lines of symmetry do the following shapes have?

a) b) c) d)

6. Write down the following number in figures:

a) nine thousand and six

b) three million, five hundred and six thousand two hundred and one

7. Write these numbers in words:

a) 6 127 b) 1 030 652

8. Work out these sums:

a) 6 10² b) 3 105 c) 8.4 1000 d) 47 1000

9. Put these in order of size, starting with the smallest first: 2.452, 3.16, 2.3, 3.1, 2.45

10. Work these out:

a) £3.24 9 b) 24 6.92Year 7 Scheme of work 1999 - 2000

Westfield Community School – Mathematicsc) 12 + 3.67 d) £8.95 4


Westfield Community School – Mathematics11. Round the following numbers to the number of decimal places in the brackets:

a) 4.793486 (to 3 dp) b) 23.990123 ( to 1 dp)

12.

The counters above are placed into a bag. If I pull out one counter from the bag, what is the probability that it will be:

a) grey b) pink c) white d) white or grey

13. In a bag, there are 5 red counters, 6 blue counters and 10 green counters. What is the probability that the first counter I pull out will be:

a) blue b) red c) green or blue d) not green

14. In a box of chocolates, there are 8 toffees, 12 strawberry creams and 4 nougats.If I choose a chocolate from the box, what is the probability that I will choose:

a) nougat b) toffee c) not nougat

Make sure you cancel down the fractions as far as possible for this question!!

15. If I throw a drawing pin 100 times, and the pin lands with the point in the air 68 times.

a) What is the experimental probability of the drawing pin landing point downwards?

b) What is the experimental probability of the drawing pin landing point upwards?

c) If I throw the drawing pin 600 times, how many times would you expect the pin to land point upwards?

16. Draw a net for a cuboid, which has a length of 4cm, a width of 3cm and a height of 2cm.

17. Use your compasses to draw a triangle, which has side lengths of 7cm, 5cm and 6cm.

Now go back and check your work until time is up!


Westfield Community School – Mathematics7: Unit 3: Chapter 9: Algebra: writing letters


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On OHP, have some shapes drawn with length of sides, some angles etc.Go through perimeters, areas for rectangles and missing angles inside the triangles.Pupils make up some questions for their neighbour and swap. Return to writer for marking – discuss results and corrections.

Using the 1 – 100 grid, two teams playing against each other trying to get 6 crosses in a row. However number they choose must fit category that teacher gives each time. E.g a multiple of 4, an even number, a prime number etc.

Quadrilateral match cards:Match the names, with the shape, with the description of its properties (e.g parallel sides, and symmetries)Which table can do it the quickest?Discuss answers as whole class.

The answer is ½, what could the question have been?Using adding and subtracting, find two fractions that will make this answer.Can you find factions that have different denominators? More than 2 fractions?

NN

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Use letters or symbols to represent unknown nos or variables

In simple cases, derive a formula Know that algebraic operations follow the same conventions & order as arithmetic operations

In simple cases, derive a formula

Simplify linear algebraic expressions by collecting like terms

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Go through what algebra is and how letters are variables. Explain ab means a b etc.

71: Do p192 – 194 Exercises 9:1 & 9:2Extension: p 211 Q1

72: Do p 194 – 196 Exercises 9:1 & 9:2Extension:

Do exercise 9:1 orally with both groups

Extension:

Go through how to use patterns to find rules e.g if pattern goes up in 4s, then first part of the rule is to 4Use exercise 9:4 as example

71: Do p197 –198 Exercises 9:5 & 9:6Extension: P211 Q3 & 4

72: Do p199 –200 Exercises 9:5 & 9:6Extension:

Extension: 7ER chapter 9 P104 – 106 Exercises 9:4 & 9:5

Recap lesson 1 ab means a b

71: Do p200 –202 Exercise 9:7 & 9:8Extension: p 211 Q2

72: Do p202 –203 Exercise 9:7 & 9:8Extension:

Do exercise 9:7 orally (vary slightly – use harder ones for 72 pupils)

Extension: 7ER chapter 13 p142 - 145 Exercise 13:1

Go through collecting terms (adding and subtracting only)

71: Do p205 –206 Exercise 9:10 & 9:11Extension: p211 Q4

72: Do p206 –207 Exercise 9:10 & 9:11Extension: p215 Q2

Do exercise 9:10 orally (the same for both groups)

Extension: 7ER chapter 9 p98 - 100 Exercise 9:1

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71: Finish Exercise 9:2 and do p195 Exercise 9:3

72: Finish Exercise 9:2 and do p197 Exercise 9:3

71: Finish Exercise 9:8

72: Finish Exercise 9:8

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Round the room – how else can I say 5a? c b? How could I write this phrase in algebra? Etc.

Have some number patterns on the board – find the rule. Can you imagine what diagrams these could come from?

Given b = 4a + 5 which bit of the formula would you do first?If a = 10, what would b be equal to?

Have answers to some ‘collecting term’ questions on the board. Split class into teams – call out question – first team to cross out the correct answer wins a point. Members in the teams take turns to run!


Westfield Community School – MathematicsActivity 1 Lesson 5 Lesson 6

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Worksheets required and OHP of square paper (non-permanent pens to be used please)Have some non-regular shapes – estimate the area of these shapes: first without the square OHP on top, then using the OHP squares. Work in pairs, share your answers with the table. Get whole class together, who thinks they have the best answer – why?


NN

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Simplify linear algebraic expressions by collecting like terms; begin to multiply a simple term over a bracket

Substitute nos in simple formulae

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Excel: Simplifying expressionsWith powerpoint presentation

Extension: within program goes onto multiplying out brackets and simplifying answers

Go through substituting numbers into algebra, recap letters are variables!(Idea that a is a pigeonhole where we can put any nos into works quite well)

71: Do p207 –208 Exercises 9:12 & 9:13Extension: p211 - 212 Q5, 6 & 7

72: Do p208 –209 Exercises 9:12 & 9:13Extension: p215 - 216 Q3, 4 & 5

Do exercise 9:12 orally (the same for both groups)

Extension: p 102 – 103 Exercise 9:3




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For all: 7ER p101 Chapter 9 Exercise 9:2

71:

72: Do exercises 9:14 & 9:15

Plen

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take it turns to roll a dice and substitute their number into one of the formulas and give the answer to the class



Key words:AlgebraFormulaTerm

Westfield Community School – Mathematics7: Unit 3: Chapter 10: Angles

Lesson 1 Activity 2 Lesson 2 Lesson 3

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Have some pictures of bags of counters: what is the probability of …? Can you cancel down the fraction?Which probability is more likely?

Using the number cards: Adding and subtracting negative numbersPut 4 on board: how many sums can you write that have the answer 4

Countdown:50, 8, 4, 5, 2, 7Target= 435How many different ways can you find the target?

In pairs or tablesStart with 25 100 = 2500How many other related sums can you find? E.g. 2500 100 = 25, 2.5 1000 = 25, 25 10 = 2.5 etc.

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Use accurately the vocabulary and notation with lines and angles

Recognise and use the sum of angles at a point, on a straight line

Recognise and use the sum of angles at a point, on a straight line

Recognise and use parallel lines and the sum of angles at a point, on a straight line

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Go through fractional turns and directions.Whole class stand up – give instructions turn ¼ turn clockwise.Then go through angles in a right angle, on a straight line and about a point. Introduce names of angles e.g acute etc.

71: Do p216 – 219 Exercises 10:1 & 10:2Extension:72: Do p220 – 223 Exercises 10:1 & 10:2Extension: p 242 Q1Can do all orally and practically since the same for both books

Extension: p110 – 112 Chapter 10 Exercise 10:2

One plain sheets of paper, pupils put a dot, draw 3 lines coming from the dot in different directions. Measure the angles, what do you notice?Draw more lines coming from your dot? Does your theory still work?Same idea, but with a straight line only? Can you guess what the answer is going to be before you do it?Same idea, but draw crosses. Measure the angles – what do you notice?

Recap rules found from day before.Rules for angles on a straight line, around a point and opposite angles

71: Do p222-224 Exercises 10:5 & 10:6Extension: p 235 Q1 & 2

72: Do p227 – 229 Exercises 10:5 & 10:6Extension:

Extension:

Recap briefly rules found from day before.Rules for angles on a straight line, around a point and opposite anglesExtend to parallel lines: alternate angles

71: Do p226-227 Exercises 10:8 & 10:9Extension:

72: Do p231 – 233 Exercises 10:8 & 10:9Extension:


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71: Do p119 –221 Exercises 10:3 & 10:472: Do p223 – 226 Exercises 10:3 & 10:4

Design a poster which will help you remember some/ all of the angles facts you have learnt so far in this chapter.

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Find objects around the room – to face them how far and in what direction would you have to turn?Do the objects have angles? If so, what type of angle are they?

Discuss pupils results. What conclusions can we go away with?

Pupils take in turns to list rules they remember so far from the chapter and give an example to show how they work

Have an OHP of diagrams with questions on them. Discuss answers.




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lHave some quadrilateral shapes. What are they? How do you spell that? How many sides, vertices & faces? How many lines of symmetry? Rotational symmetry? How many diagonals? Does it tessellate?

Class in teams: using the 1 – 100 grid.Ask tables questions and reversed (e.g division), first team to cross out the correct answer wins a point. Who has most points at the end?

Checklist for chapter 10:N

NS

Recognise and use the sum of the angles in triangles

Consolidate measuring & drawing: - lines to the nearest mm - angles to the nearest degree , and extend to reflex angles Construct triangles using a ruler and

a protractor

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Use exercise 10:10 to introduce angles in a triangle, either as demonstration or whole class.

71: Do p229 - 230 Exercises 10:11 & 10:12Extension: p 235 Q3, 4 & 5

72: Do p235 - 236 Exercises 10:11 & 10:12Extension: p 242 Q2, 3 & 4


Go through homework and check understanding.Go through how to construct triangles where 3 lengths are given.

All: corrections from the homework, then questions from the board on drawing triangles where 3 side lengths are given.

72: Extension: p238 Exercise 10:13 Q 7 - 10




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71: Do p231 – 232 Exercise 10:1372: Do p237 – 238 Exercise 10:13 Q1 - 6

All: Worksheet: ‘Parallel lines’Using opposite angles and alternate anglesExtension section for 72 pupils

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Here are some triangles – what are the missing angles?How can you check your answr is correct?

Get pupils up to the board to draw some triangles, discussing the best approaches.

Test pupils on key words, spellings and definitionsWorksheet ‘Angles’: match the mixed up words with the diagrams

7: Unit 3: Chapter 11: Extending the number lineYear 7 Scheme of work 1999 - 2000

Key Words:Right angleDegreeAcuteObtuseReflexOpposite anglesIsosceles triangleEquilateral triangle

Westfield Community School – MathematicsLesson 1 Activity 3 Lesson 2 Lesson 4

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Higher or lower:In pairs pupils have cards with 0 –9 on. Face down in a row with the first card showing only. Will the nest card be higher or lower? What is the probability of it being higher/lower?

Questions on perimeter and areas of rectangles. For more able, reverse the questions: if an equilateral triangle has a perimeter of 27cm, what is the length of the side?

With dice: throw both dice to create a 2 figure number and then throw again to create another one. Add them together.Repeat but subtract the numbers.

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Order positive and negative numbers in context

Order, add & subtract positive and negative numbers in context

Find co-ordinate pairs and plot these on a co-ordinate grid


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Discuss negative numbers and where pupils might have come across the before.Show pupils a number line.

71: Do p240 – 243 Exercises 11:1 & 11:2Extension: p255 Q1 & 4

72: Do p246 – 249 Exercises 11:1 & 11:2Extension: p262 Q1

Extension:

Take class to a corridor. Put numbers from 8 to 8 in a line on the floor. Demonstrate how to walk the line for simple sums such as 4 + 2 and 8 2, so pupils see direction to move in for adding and subtracting sums. For a positive number, you walk forwards, for a negative number you walk backwards.Now try some more sums with pupils walking the line – can you work out where the pupil will end up before they get there.Later on, shut your eyes, work out the sum, is this the answer you’ve got?Get pupils to make up questions and walk line etc.

Recap co-ordinates in the first quadrant. Recap (x , y) and their directions.Go onto 4 quadrants – get pupils drawing co-ordinates onto axis. Do lots of class practise!

71: Do p247 – 248 Exercise 11:4 Q1 - 4Extension: p255-256 Q2, 3, 5 & 6

72: Do p253 – 254 Exercise 11:4 Q1 - 4Extension: p264 Q4 & 5

Extension:

Recap co-ordinates in four quadrants.

71: Do p248 – 249 Exercise 11:4 Q5 - 8Extension: p256 Q7

72: Do p254 – 255 Exercise 11:4 Q5 - 7 Extension: p262 Q2

Extension:

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71: Do p244 – 245 Exercise 11:3 72: Do p250 – 251 Exercise 11:4


Plen

ary Have examples of temperatures from

papers etc Discuss what places are the coldest/ hottest

On an OHP have some shapes drawn onto axis. What are the co-ordinates of the corners of the square? Parallelogram? etc

On OHP, have a shape drawn with a mirror line. Plot the image of the shape and name the co-ordinates of the corners of the shape.

Activity 4 Lesson 5 Lesson 6 Lesson 7



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lNumbers on the board: e.g 24: what times tables does this come up in? What are its factors? Factor pairs?Is it prime?Extend to what fractional times tables it could come in for more able.

1710

836

259

Trails: target number is 48

Checklist for chapter 11:N

NS


Find co-ordinate pairs that satisfy a ruleand plot these on a co-ordinate grid

Find co-ordinate pairs that satisfy a ruleand plot these on a co-ordinate grid

Recognise that a function such as y = 3x + 7 corresponds to a straight line graph

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Choice of two games:Battleships or connect 4.

Difference instead of putting crosses/ ships in the squares, you place them on the co-ordinates.

For battleships, use co-ordinates instead of A1 etc.For connect 4, must say co-ordinate before you draw it on.

Could have a ‘class championship’ or round robin idea.

Go through labelling axis and how to plot co-ordinates on graph paper.Since pupils will be drawing graphs, emphasise graph paper should be used, with a sensible size axis.

71: Do p250 – 251 Exercise 11:5Extension: p256 Q8

72: Do p256 - 257 Exercise 11:5 Extension: p263 Q3

Extension: 7ER Chapter 11 p118 –123 Exercise 11:1

Recap work from yesterday. Discuss how we could perhaps name the lines so that everyone would be able to know which line we had drawn. Go through straight line graphs are in the format of y = mx + c

71: Do p252 Exercise 11:6Extension:

72: Do p258 – 259 Exercise 11:6Extension:

Extension: 7ER Chapter 11 p124 –125 Exercise 11:2




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71: Finish exercise 11:5 72: Finish exercise 11:5 And/or 7ER Chapter 11 p118 –123 Exercise 11:1

Design a picture on 4 quadrants – write down the points you have to plot and join together to copy your picture.And/orWorksheet with co-ordinate pictures?


Key Words:PositiveNegativeOriginQuadrant


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y Have a graph drawn and its rule. What do you notice about the graph and how it relates to the rule?Discuss ‘steepness’ linking to what the pattern went up in.

Same idea as yesterday, but extend into more detail of gradient – graphs with same pattern have the same gradient etc.

Test pupils on key words, spellings and definitions

7: Unit 3: Chapter 12: Units of length and scale drawingLesson 1 Lesson 2 Lesson 3 Lesson 4

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Have a selection of fractions on the board/OHP. Pupils have to pick two and say whether they are equal, greater than or less than. Could reverse idea, teacher asks for two fractions that are equal etc.

Good old fashion mental test on / 10,100 1000 with whole numbers and decimals!

Throw a dice at pupil, whatever number is upright, multiply it by….So teacher throws to pupil and says times by 8 etc. Faster with 2 dice and two pupils at a time!

Ask some probability questions based on equally likely events.E.g 6 counters in a bag, two are red, three are green and one is blue. What is the probability of …?

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Use names & abbreviations of metric & imperial units for estimation & measurement in contexts involving length



Convert one metric unit to another Know rough metric equivalents of

imperial measures in common use (feet, miles, pounds, ounces, pints, gallons)

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Discuss units – what ones have pupils come across before? Introduce imperial and conversions. Go through metric and its conversions.

71: Do p260 – 262 Exercise 12:1 & 12:2Extension: p279 Q 1, 3, & 4

72: Do p258 – 259 Exercise 12:1 & 12:2Extension: p 287 Q1

Extension:

Explain scale drawing and discuss where pupils might have previously seen scales/ or in which subject.

71: Do p266 - 268 Exercise 12:4Extension: p 270 Q5

72: Do p274 – 276 Exercise 12:4Extension: p287 Q2 & 3

Extension:

Recap scales and how to use them.


72: Do p277 – 280 Exercises 12:5 & 12:6Extension: p 287 -288 Q4 & 5

Extension:

Recap imperial and metric units. Discuss why we need to be able to convert between one system and another.

71: Do p272 – 273 Exercise 12:7Extension: P280 Q9

72: Do p281 – 282 Exercise 12:7Extension: p 288 Q6

Can do Q1 & 2 orally with the whole class as it is the same for both groups

Extension:

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71: Finish exercise 12:472: Finish exercise12:4

Finish any unfinished exercises/ correctionsAnd/orDraw a scale drawing of a room in your house. Include the furniture and do not forget to use a sensible scale (1cm: 1m?)



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y Quick around the room questioning: how long do you think a car would be in metres, centimetres, inches etc?

Perhaps have some maps to hand (borrowed from the geography department). Discuss the different scales used and what they mean.

If I have a line which is 3cm long and the scale is 1cm: 5m, what is the real length of the line? Why? Explain your answer.

Match cards of unitsE.g 1m = 100cm = 1000mm 40 inches etc

Lesson 5 Lesson 6

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Investigate palindromes:Add a two digit number to the reverse of itself. Does it make a palindrome? Do all numbers work? E.g. 92 + 29 = 121Have to include explanation of palindromes!


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Read & interpret scales on a range of measuring instruments

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Ask pupils where they have seen scales before. Different size scales e.g car speeds, weighing scales etc. Explain divisions in scales and how to work out what value these are.

71: Do p274 – 275 Exercise 12:8Extension: p280 Q8

72: Do p282 – 284 Exercise 12:8 & 12:9Extension: p 288 Q7

Extension:




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Make a list of all the conversions you have learnt in the text book and learn them.You will be tested on them at a later date.


Key words:InchFeet YardMillimetreCentimetreMetreKilometreScaleDivisions


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yOn an OHP, have some scales. What are the measurements of these things? If the item measured …., where would the line be?

Test pupils on key words, spellings and definitions.Worksheet: word search ‘Units’

7: Unit 3: Revision and testLesson 1 Lesson 2 Lesson 3

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Countdown:25, 8, 5, 7, 2, 6Target: 252How many ways can you make the target?

In tables, pupils take in turn to test each other on sums: add/ subtract/ multiply/ divide. 1 point for each right answer. 5 bonus points for the table who gets around their table 3 times first!

Testing of :

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See previous references to NNS See previous references to NNS

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Extension:




Extension:


Two sections: non-calculator and calculator.

Give out non-calculator section first. When pupil has finished, they hand in this section and can get their calculators out and do the calculator section

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All: Complete any Questions sections for the test next lesson



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yRecap all the main points from chapters 9 and 10

Recap all the main points from chapters 11 & 12

7: Unit 4: Chapter 13: Algebra: into the unknownLesson 1 Lesson 2 Lesson 3 Lesson 4

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Median sheet: I like..Quadrilaterals sheetPupils ask questions such as do you like shapes with parallel sides? You answer Yes or no. Get 10 questions.

Decimal cards:In pairs/ tables, who can put the cards into order fastest?Discuss the results

Give pupils two sets of data e.g. 2 pupils 100m times. Each table has to make a case for who they would pick to represent them at sport’s day. Idea is to use mean, mode, median and range. 1 minute to argue per table.

Start with 30cm written on the board.Using metric conversions and imperial approximations, what other things can you find that are equal to 30cm?E.g. 0.3m, 1 foot, 12 inches, 300mm etcPerson who finds the most wins!

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Consolidate understanding of the operations of & , their relationship to each other

Know that algebraic operations follow the same conventions & order as arithmetic operations

Solve linear equations, selecting an appropriate method

Construct & solve simple linear equations, selecting an appropriate method

Solve …equations, selecting an appropriate method

Make & justify estimates & approximations (of calculations)

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Emphasise undoing is inverse. +/ and / are inverses of one another.Use idea of function machine and using inverses in those.

71: Do p284 – 287 Exercises 13:1 – 13:3Extension: p301 Q1 & 2

72: Do p292 – 294 Exercises 13:1 – 13:3Extension: p309 Q 1 - 4

Exercise 13:1 and 13:2 could be completed orally with discussion. Exercises are reasonably similar.

Extension:

Go through solving equations, using the undoing idea and whatever you do to one side you must do to the other, so it balances.Do lots of easy examples orally and take onto 2x + 1 = 11 etc.

71: Do p291 – 294 Exercises 13:6 & 13:7Extension: p301 Q 3 - 8

72: Do p298 – 300 Exercises 13:7 – 13:10(maybe odd questions only)Extension: p309 Q9 & 10

Extension:

Show where equations can be used to solve problems in the context of angles work.

71: Do p294 – 295 Exercises 13:8, then finish exercises from yesterdayExtension: p 301 Q9 – 12 & Q17 - 19

72: Do p301 Exercise 13:11, then finish exercises from yesterdayExtension: p309 Q5 - 8

Extension: 7ER chapter 13 p146 – 149 Exercises 13:2 – 13:4

Go through trial and improvement methods. Encourage good setting out and emphasise is on NCT papers!

71: Do p296 - 198 Exercise 13:9Extension:

72: Do p305 – 306 Exercise 13:16Extension: p309- 310 Q16 – 19 & Q20 -23

Extension: 7ER chapter 13 p150 – 152 Exercise 13:5



wk

Have left easier exercises for them to do at home!71: p288 – 290 Exercises 13:4 & 13:572: p295 – 297 Exercises 13:4 – 13:6

(Ensure you have read out answer to equation exercises today please)Do any corrections to your earlier exercisesAnd/ or do 4 more questions from today’s exercise.

Plen

ary Quick fire questions on undoing Discuss answers from exercises – pick out

the harder questions and go through methods used my pupils

Have some triangles/ parallel lines/ opposite angles like exercises today.Make up equations and solve

Go through a question from NCT paper.

Lesson 5 Lesson 6

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I think of a number type puzzles.I think of a number and 4, then add 3. If the answer is 23, what was the number? Etc.


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72 work is not on NNS (so if pushed for time omit)

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Different lessons for groups today!C71: Continue with trial & improvement exercise. Finish p296 - 198 Exercise 13:9Extension: p301 – 302 Q13 – 16 & crossnumber puzzle

72: Explain about ‘subjects’ of formulae. Go through rearranging equations to change the subject!Do p302 – 304 Exercises 13:12 – 13:15Extension: p309 Q11 - 15

Extension: 7ER chapter 13 p153 –154 Exercises 13:6 & 13:7






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71: p388 –389 Help yourself exercise 1172: Finish p302 – 304 Exercises 13:12 – 13:15

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Have fun!……………. Test pupils on key words, definitions & spellings.

7: Unit 4: Chapter 14: Area and perimeterLesson 1 Lesson 2 Lesson 3 Activity 1

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Using number cards:Angle puzzles – in a triangle, around a point, parallel lines, opposite angles & on a straight lineInclude what type of angle is that?

Probability: if I have 2 six sided dice- one with numbers, and one with 2 blue sides; 3 red sides; and 1 green side. Write down all the outcomes. Then ask probability questions, ask to explain answers.

Mini version of bingo. Draw 3 3 grid. Fill with percentages between 0 and 30.Teacher calls out the decimal equivalent, pupils cross out. First to get all out is the winner.

NN

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Calculate the perimeter Use formulae from mathematics, substitute numbers into simple formulae

Calculate the perimeter of compound shapes made up of rectangles

Solve problems in a variety of contexts (shape, space & measures)

Predict, generalise ..by asking ‘What if..’

In simple cases, derive formulae


Key Words:InverseFunction machineEquationSubjectTrial & improvement


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eGo through perimeter and how to approximate areas.

71: Do p306 –308 Exercises 14:1 & 14:2Extension: p327 Q1 & 4


Exercise 14:1 could be completed orally with whole class

Extension:

Go through/ recap area of a rectangle. Explain how given the area and the length of one side, you can work out the other length.

71: Do p309 – 314 Exercise 14:3 & 14:5Extension: p327 Q2 & 3

72: Do p318 - 322 Exercises 14:3 & 14:5Extension:

Extension:

Recap perimeters.

71: Do p316 - 317 Exercise 14:8 & 14:9Extension:

72: Do p324 - 326 Exercises 14:8 & 14:9Extension: p338 Q3

Could do the first 2 questions orally as same for both groups

Extension:

Practical way of finding the formula of a triangle. See separate sheet for teacher’s notes.

Can go onto extend to find the formula of parallelogram.

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71: p314 & 315 Exercises 14:6 & 14:772: p322 & 323 Exercises 14:6 & 14:7

71: p312 Exercise 14:472: p320 Exercise 14:4

Plen

ary What shapes can you draw that have a

perimeter of 20cm? etcReverse questions. If the area is 20cm2 and the length is 10cm, what is the width?

Have some different shapes, e.g. pentagons etc Work out the perimeters?


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Make a chain1.3 + …. ….. + ……. = 1.75How many different ways can you fill the gaps – decimals must be used – no whole numbers- numbers in gaps must be different.Can make up more

Table competition: name 3 things that are about these lengthsa) 20 cm b) 5 foot c) 100m etc.Lots of discussion, so not too long on the doing!


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Use formulae from mathematics.., substitute numbers into simple formulae

Calculate the perimeter and area of compound shapes made up of rectangles



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eRecap formulae learnt from activity yesterday.Reinforce units are important and must be the same units before working out the areas.(Emphasise perpendicular height – explain perpendicular!)

71: Do p319 - 320 Exercises 14:11 & 14:12Extension: p328 Q7, 8 & 9

72: Do p328 - 330 Exercises 14:11 & 14:12Extension: p338 Q4

Extension: 7ER Chapter 14 p160 - 161 Exercise 14:3

Encourage drawing of shapes and labelling. Then setting out of workings as shown in text book. Explain there is more than one way of dividing up diagrams, but will give the same answer.

71: Do p321 - 323 Exercise 14:13Extension: p328 Q5 & 6

72: Do p331 - 333 Exercise 14:13Extension:

Extension: 7ER Chapter 14 p156 – 160 Exercises 14:1 & 14:2




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71: p323 - 324 Exercise 14:1472: p333 – 334 Exercise 14:14

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Undo the formulae – if the area is 20cm2 and the base is 5cm, what is the perpendicular height?

Have some compound shapes, with triangles and rectangles. Do as a class

Test pupils on key words, spellings & definitions.Worksheet – Area & perimeter – fill in the gaps

7: Unit 4: Chapter 15: Fractions and percentagesLesson 1 Lesson 2 Lesson 3 Lesson 4

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Have a variety of shapes – triangles and quadrilaterals etcWhat are these?What are the angles?How many lines of symmetry? Where?What is the order of rotational symmetry?How many vertices, edges, diagonals?

Using the number cards:Questions on adding and subtracting decimals, upto 2 dp

Another mini bingo:3 3 grid to put fraction in upto tenths, but can have multiples e.g 3/8

Teacher calls out either percentage or decimals equivalent. Pupil who crosses out all fractions first, wins!

Give pupils sets of numbers in context e.g employer and employees’ wages. Workers want a pay rise, which average would they use to support their argument. If you were the employer, which would you use?Have different groups arguing different points?


Key words:PerimeterAreaUnitsHeightBasePerpendicular height


NS

Find fractions of quantities Find fractions of quantities Use the equivalence of fractions Use the equivalence of fractions and percentages in describing proportions

Find fractions and percentages of quantities

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Use proper vocabulary for fractions. Go through fraction of quantities.

71: Do p332 – 334 Exercises 15:1 & 15:2Extension: p353 Q 1, 2 & 3

72: Do p342 – 344 Exercises 15:1 & 15:2Extension: p366 Q4

Extension:

Go through working out fractions of quantities. Encourage mental work, but do not allow calculations hinder understanding.71: Do p335 - 339 Exercises 15:3 - 15:6Extension: p353 Q4

72: Do p345 - 348 Exercises 15:3 & 15:4Extension:

Can do most of 15:3 orally with whole classExtension:

Go through adding and subtracting fractions with/without same denominator.Then extend to / fractions

71: Do p341 - 342 Exercises 15:8 - 15:9Extension: p353 Q5


Extension: 7ER chapter 15 p166 –169 exercises 15:1 & 15:3

Go through connections with fractions and percentages. Recap cancelling down fractions.

71: Do p343 - 344 Exercise 15:10Extension: p354 Q6


Extension: 7ER chapter 15 p169 – 170 exercises 15:3 – 15:5

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71: p339 – 340 Exercises 15:6 (there is two exercise 15:6!?) & 15:772: p349 – 350 Exercises 15:5 & 15:6

71: p345 Exercise 15:1172: p357 Exercise 15:12

Plus any outstanding work that is not complete

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Have some diagrams on the board:What fraction is shaded?Come and shade a quarter of this rectangle etc.

Work backwards:If I kept ¼ of my money, which is worth £10, and put the rest in the bank.How much did I have altogether?

Match the questions with the answers, and discuss why.

Quick fire questions: converting fractions into decimals and visa versa




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l0.10.50.7

0.81.00.3

0.20.40.6

Target = 2.4Like chains, but with decimals

Class counting in decimals & fractions (could use counting sticks)e.g. starting with 0.7, add 0.2 starting with ¼, add ½ etc.

Quick fire probability questions around class, discussing answers given

Checklist for chapter 15 N

NS

Use the equivalence of fractions, decimals and percentages in describing proportions and convert between them (e.g. to order fractions

Use the equivalence of fractions, decimals and percentages in describing proportions and convert between them (e.g. to order fractions

Understand the relationship between ratio & proportion & use ratio & proportion to solve simple problems

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Go through changing fractions into decimals and visa versa. (Will need to recap division without a calculator)



Extension: 7ER chapter 15 p 170 exercise 15:6

Go through briefly ordering fractions: either change to decimal or same denominator.


72: Do p361 - 363 Exercises 15:14 - 15:15Extension:

Can do quite a lot of 71 15:13 (same as 72 15:14) orally/ on board with class

Extension: 7ER chapter 15 p171 – 174 exercises15:7 & 15:8

Lesson on ratio and proportion – not in text book

Use worksheets ‘Ratio and proportion’ etcDifferent levels for different abilities





Key words:NumeratorDenominatorImproper fractionMixed numberEquivalent fractionPercentageRecurring decimal


wk

As a poster/ in the back of your book, make a conversion chart of %, decimals & fractions for frequently used values e.g. half, quarter, three quarters, thirds etc.

Finish ratio worksheetsPl

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y Have some fractions and decimals on the board. Divide the class into teams. Teacher calls out a fraction or decimal, first one to cross out the equivalent one wins a point.

Have some fractions on the board: tables have got to order them as fast as possible. Discuss answers.

Discuss where you might find ratio in real life situations. Make up example questions.

Test pupils on key words, spellings and definitions

7: Unit 4: Chapter 16: Statistics: what does it all mean?Lesson 1 Lesson 2 Lesson 3 Lesson 4

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Have bags of decimals numbers. Pupils take in turns to pull out a number and add it onto the total, once given a starting number. Can do subtraction too.

Have some coloured patterns on OHP. What is the ratio of blue beads to red beads? Is there another way of saying that?If I had 8 blue beads, how many red ones would I need to make the same pattern?

331/3 % = 12What other facts can you find?

Give tables some shapes. Tables have decide how to group them. Using their own rules. They then have to explain why they have grouped them in the way they have to the rest of the class. How many different ways could the shapes be grouped?

NN

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Calculate the mean of a set of discrete data; using a calculator for a large number of items

Calculate the mean of a set of discrete data; using a calculator for a large number of items

Find the mode of a small data set Find the median of a small number of

items

Find the median of a small number of items

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Go through mean. Use first two questions in 16:1 as examples.

71: Do p358 - 360 Exercises 16:1 Extension: p376 Q1

72: Do p370 - 372 Exercises 16:1 Extension:

Extension:

Go onto mean in grouped frequency tables – use 71 16:2 (same as 72 Q1) as example

71: Do p361 - 362 Exercise 16:2Extension: p376 Q3

72: Do p373 - 375 Exercise 16:2 Extension: p391 Q2

Extension: 7ER chapter 16 p176 – 177 exercise 16:1

Got through other types of average – mode and median

71: Do p363 - 366 Exercises 16:3 & 16:4(Q1 & 2)Extension: p376 - 377 Q2 & 4

72: Do p376 - 380 Exercises 16:3 & 16:4 (Q1 – 4) Extension: p391 Q1

Extension: 7ER chapter 16 p 178 – 179 exercises 16:2 & 16:3

Go through median in grouped frequency tables, and explain modal group.

Do 72 p381 Exercise 16:5 with whole class as class discussion.

Extension:



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71: Finish exercise 16:2 72: Finish exercise 16:2

71: Do p366 Exercise 16:4 (Q3 & 4)

72: Do p380 Exercises 16:4 (Q5)

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Put some numbers on the board, what is the mean?If there are 5 numbers and the mean is 10. Another number is added 8, will that make the mean larger or smaller? New mean?

Go through another question as class group Here are some numbers and here are the averages. Which average is which?

Go through median question as whole group


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Using 1 – 100 grid, split class into teams. Ask questions based around fractions, decimals and percentages. First one to cross out the correct answer wins a point for their team. Pupils in the team must take turns.E.g. what is 1/6 of 42?

Probability questions around the class Checklist for chapter 16

NN

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Find and use the range of a set of values

Draw inferences from simple statistics fro single distribution

Compare two simple distributions using the range & one of the measurements of average



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eGo through range and how to work it out. Explain about small range is better etc when using to help analyse data.

71: Do p367 - 36 Exercise 16:5 Extension: p377 Q 5 & 6



Explain how statistics can be used to mislead people.

Work through exercise as whole class, as discussion

71: Do p370 - 372 Exercise 16:7

72: Do p386 - 387 Exercise 16:7

Extension:

71: Do p379 - 380 ‘Test Yourself’ section72: Do p393 - 394 Test Yourself’ section



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71: p369 exercise 16:672: p384 exercise 16:6

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range is 25. What was the largest number in the data? etc

Pull discussion together and recap. Test pupils on key words, spellings and definitions.

7: Unit 4: AT1, revision and testLesson 1 Lesson 2 Lesson 3 Lesson 4

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Countdown75, 5, 2, 8, 4, 9Target 328How many different ways can you get the target?

Have two dice, roll them and multiply answers together

Throw a dice – have to draw a shape that has that many sides. Other pupils have to name the shape.(Let 1 and 2 stand for 8 and 10)

Using the numbers 5,6, 7& 8 and any operations. Make all the numbers between 1 – 20. You can only use each number once and depending on ability depends whether you have to use them all.


Key words:MeanMedianModeModal groupRange


NS

See previous references to NNS Choose and justify the use of an appropriate & efficient method of solving a problem

Explain methods & reasoning, orally & in writing. Predict, generalise and suggest extensions by asking ‘What if..’

See previous references to NNS Choose and justify the use of an appropriate & efficient method of solving a problem


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Go through chapters 13 and 14

71: chapter 13 p299 – 300 Questions 72: chapter 13 p307 – 308 Questions

Extension:

Start investigation ‘Crosses’

DiagramsTable of resultsPredictionTest predictionPatterns

Go through chapters 15 & 1671: chapter 15 p351 – 352 Questions 72: chapter 15 p36 – 365 Questions

Extension:

Continue with investigation.

Go onto rules, testing rules and drawing graphs. Try to explain the rules relating to the diagrams.Extend the investigation onto 3D.

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71: chapter 14 p325 – 326 Questions 72: chapter 14 p335 – 336 Questions

71:chapter 16 p374 – 375 Questions 72: chapter 16 p389 – 390 Questions

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Divide the board in half, pupils write up all the important points of chapters 13 & 14

Recap what pupils should have completed and what they need to do next lesson.

Divide the board in half, pupils write up all the important points of chapters 15 & 16

Recap what pupils should have completed and what they need to do next lesson.

Lesson 5 Lesson 6

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Write some number patterns on the board.What is the pattern? What is the rule?

Testing of:



NS

Choose and justify the use of an appropriate & efficient method of solving a problem


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Follow the same ideas, but continue and finish the investigation

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Finish the write up of the investigation.

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This is what you should have done. Go through the check list for all pupils.

Test pupils on key words, spellings and definitions.



Year 7 - Crosses Investigation

Pattern number: 1 2 3

Number of counters 1 5 ….

Teacher Notes:

DIAGRAMS: Copy these three diagrams, and add the next two diagrams

TABLE OF RESULTS: Put your results into a table

PREDICTION: Predict how many counters would be in pattern number 6I think that for pattern number 6 will use …………

TEST PREDICTION: Draw diagram number 6 and see if you are rightMy prediction was ………..

PATTERN: Look at the counter column, can you see a pattern in the numbers.I have noticed that the number of counters goes up in……….

RULE: Find what you have to do to the pattern number to get to the number of countersWrite your rule in words, use a number machine and then in algebraPattern number …….. ……. = number of counters

TEST THE RULE: Put numbers into your rules, do they come out with the right answersMy rule ………….

GRAPH: Pattern number on the horizontal axis. Label the axis and give it a title.You can draw a bar chart, but for the extension draw a line graph.From my graph, I can see that it goes up in………… I can predict number pattern ….. would be …. from my graph

EXPLANATION: Can you explain why the rule works in relation to the shape!

EXTENSION: Change the pattern into three dimensions, with cross growing up, down and outI am going to make the problem harder by ………..

Could use multi-link for three dimensions to help pupils. Can extend by changing shape if pupils are very weak.

4P 3 = C in two dimensions

6P – 5 = C in three dimensions


westfield community school – mathematics · web viewcount the number of letters in each word in...

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