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.

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 contexts

4 /
  • 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 rectilinearfigures & 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 likelyoutcomes & 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 StrategyProgramme of Study – Year 7

Numbers & the Number System
Place 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.
Calculations
Number 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; / Algebra
Equations 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 & Measures
Lines 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 Data
Specifying 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!

Year 7 Scheme of work1999 - 2000

Westfield Community School– Mathematics

Year 7 : Unit 1

Topic

/

Time

/ NC /

Descriptors

/ Resources / Notes / Key Words
1 Graphs
1 Statistics: about our school
2 Pie charts
3 Tallying in groups
4 Location
5 Scatter graphs / 1
1
1
1
1 / H3
H5
H3
H4
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
Extension: 7ER Ch1 p10-14 / 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 / Statistics
Data
Bar chart
Represents
Pictogram
Key
Pie chart
Angle
Tally
Grouped data
Co-ordinates
X axis
Y axis
Scatter graphs
Correlation
Test Yourself
/ 1 / Pupils mark and fill in pupil assessment booklet.
WS: Graphs, with key words
2 Symmetry
1 Lines of symmetry
2 Symmetry in everyday life
3 Turnings
4 Rotational symmetry / 1
1
1
1 / S4
S4
S5
S5 / Reflect simple shapes in a mirror line
Use language associated with angles
Know all symmetries of 2D shapes / Extension: 7ER Ch2 p16-19
Extension: 7ER Ch2 p20-22
Extension: 7ER Ch2 p23-26 / Bring in pictures that show symmetry from the real life
Find pictures in real life that show rotational symmetry from real life / Line of symmetry
Mirror line
Vertical
Horizontal
Turn
Clockwise
Anticlockwise
Points of the compass
Rotational symmetry
Order of rotational symmetry
Centre 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 nos
Recognise & describe nos patterns, & relationships including multiple, factor
Recognise & describe nos patterns, & relationships including multiple, factor & square / Extension: 7ER Ch3 p28-32
Extension; 7ER Ch3 p33-38 / *Highest common factor
*Prime factor
WS required- p54/55?
EXCEL program :’Spot the pattern and find the rule’ / Counting numbers
Odd numbers
Even numbers
Multiple
Factor
Prime
Square nos
Triangle nos
Test Yourself / 1 / Pupils mark and fill in pupil assessment booklet.
Word search with key words
4 Arithmetic and the calculator
1 Rounding up and rounding down
2 Mental arithmetic
3 Estimation
4 Priority of operations / 1
1
2
1 / N3
N3
N4
N3
N4
N4? / 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  facts
Use… 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 results by reference to knowledge of the context or to the size of the nos / Extension: 7ER Ch 4 p40-44 / WS required – p73/74?
Snap cards available
Mini investigation: Using 1, 2, 3, and 4 find all the numbers 1 - 30 / Rounding
Estimate
BODMAS
Brackets
Power
Test Yourself / 1 / Pupils mark and fill in pupil assessment booklet.
Mental work / 10 mins every lesson / N3
N4
N5
N6
S2
S3
S5 / Show understanding of place value in nos up to 1000 & use this to make approximations
Use mental recall of +/- facts to 20
+/- nos. with 2 digits mentally
Use mental recall of the 2,3,4,5 & 10  tables & derive the associated  facts
Use their understanding of place value to  whole nos. by 10 or 100
Use 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 places
Use understanding of place value to /  whole nos. & decimals by 10, 100 & 1000
Calculate fractional or percentage parts of quantities & measurements
Understand & use the equivalences between fractions, decimals & percentages
Begin to use standard units to measure length & mass
Classify 2D shapes in various ways using mathematical properties such as reflective symmetry for 2D shapes
Use standard metric units of length, capacity & mass
Use language associated with angle
Convert 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 1
Gnome Homes / 3
Revision and unit test / 3 / Use ‘Questions’ section for revision

Year 7 : Unit 2