lessons featherstone high transition unit; transition ... · make and justify estimates and...
TRANSCRIPT
Lessons
Transition Unit; Transition Booklet
Number 1; number operations, calculation methods
Statistics 1; probability scale, vocabulary, outcomes, experimental, events
CAME Lesson: “Roofs”
Measures 1; angles: measuring, calculating, constructing
Half Term
Algebra 1: sequences and functions
CAME Lesson: “Operating On Numbers”
Number 2; place value, ordering, rounding, calculator methods
Measures 2; reading scales, converting between units, area and perimeter
Assessment
(Christmas)
Statistics 2; averages and range, types of data
CAME Lesson: “Best Desk Size”
Algebra 2; simplifying expressions, expand and factorise, substitution
Number 3; integers, powers and roots
CAME Lesson: “Direction and Distance”
Half Term
Algebra 3; functions and graphs
Measures 3; transformations
CAME Lesson: “Two Step Relations”
Statistics 3: representing data
Assessment
(Easter)
Number 4; fractions, decimals and percentages
CAME Lesson: “Relations”
Measures 4; nets, plans, elevations, surface area and volume
Number 5; ratio and proportion
Half Term
CAME Lesson: “Exploring the Rectangle” Lessons
Statistics 4: specifying, planning and collecting
Featherstone High School
Featherstone High School
A Sports and Community College
Professional
Development
Review (PDR)
2006 — 2007
Name of member of staff
Department Year team Other
Name of reviewer
Date of review
Mathematics Department
Year 7 Scheme of
Work
Algebra 4; equations and formulae
CAME Lesson: “Missing Digits”
Assessment
(Summer)
TRANSITION UNIT: Transition Numeracy Booklet FWK REF:
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Activities
Resources Available in Department Area: P:\Departments\Maths\Curriculum\RESOURCES\Transition2012-13 Hard copies distributed during first department meeting of academic year
Number 1: Number operations and calculation methods FWK REF: 2.4, 2.5, 2.6, 2.8
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Previously...
Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U (Y6)
Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-
digit and three-digit integers by a two-digit integer (Y6)
Understand and use the rules of arithmetic and inverse operations in the context of positive integers and decimals
Use the order of operations, including brackets
MENTAL METHODS: recall number facts, including positive integer complements to 100 and multiplication facts to 10 × 10, and quickly derive associated division facts
Strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple problems mentally
Make and justify estimates and approximations of calculations
WRITTEN METHODS: use efficient written methods to add and subtract whole numbers and decimals with up to two places
Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers
Check results by considering whether they are of the right order of magnitude and by working problems backwards
Next…
use the order of operations, including brackets, with more complex calculations (Y8)
MENTAL: recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8 (Y8)
WRITTEN: use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal places (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
1.1 The calendar
3.6 Column method for addition and subtraction
10.2 The four operations
10.3 BODMAS
10.4 Multiplication and division
10.5 Efficient calculations
17.1 Adding and subtracting decimals
17.2 Multiplying and dividing decimals
G&T TASKS
Number Operations: What Numbers Can We Make? Consecutive Numbers Where Can We Visit? Consecutive Sums
Consecutive Seven Make 100
Mental Calculation Methods:
Missing Multipliers Countdown
Remainders The Remainders Game Number Daisy Got It
Written Calculation
Methods: Dicey Operations Two and Two Multiplying with Lines
Checking Results: Rule of Three
() problems that have detailed Teachers’ Notes
LEVEL 2
use the knowledge that subtraction is the inverse of addition and understand halving as a way of
‘undoing’ doubling and vice versa
use mental recall of addition and subtraction facts to 10
use mental calculation strategies to solve number problems including those involving money and
measures
record their work in writing
choose the appropriate operation when solving addition and subtraction problems
LEVEL 3
derive associated division facts from known multiplication facts
add and subtract two digit numbers mentally
add and subtract three digit numbers using written
method
multiply and divide two digit numbers by 2, 3, 4 or 5 as well as 10 with whole number answers and remainders
use mental recall of addition and subtraction facts
to 20 in solving problems involving larger numbers
solve whole number problems including those involving multiplication or division that may give rise to remainders
LEVEL 4
use a range of mental methods of computation with all operations
recall multiplication facts up to 10 × 10 and quickly derive corresponding division facts
use efficient written methods of addition and subtraction and of short multiplication and division
multiply a simple decimal by a single digit
solve problems with or without a calculator
check the reasonableness of results with reference to the context or size of numbers
LEVEL 5
use known facts, place value, knowledge of
operations and brackets to calculate including using all four operations with decimals to two places
understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three digit number by
any two digit number
apply inverse operations and approximate to check answers to problems are of the correct magnitude
APP Toolkit:
Calculation L3
Calculations L4
Calculations L5 10 ticks
Core (pupil book 2)
2.5 Column method for addition and subtraction
9.2 The four operations
9.3 BODMAS
9.4 Long multiplication and long division
9.5 Efficient calculations
16.1 Adding and subtracting decimals
16.2 Multiplying and dividing decimals
Extension (pupil book 3)
1.6 A function investigation
2.5 Column method for addition, subtraction and multiplication
9.2 The four operations
9.3 BODMAS
9.4 Long multiplication and long division
9.5 Efficient calculations
16.1 Multiplying decimals
16.2 Dividing decimals
KEYWORDS operation, inverse, add, subtract, multiply, divide, sum, total, difference, product, multiple, factor, quotient, divisor, remainder, bracket, order, power, operation, priority
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
Statistics 1; Probability: scale, vocabulary, outcomes, experimental, events FWK REF: 5.4
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Describe and predict outcomes from data using the language of chance or likelihood (Y6)
Use vocabulary and ideas of probability, drawing on experience
Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts; identify all the possible mutually exclusive outcomes of a single event
Estimate probabilities by collecting data from a simple experiment and recording it in a frequency table; compare experimental and theoretical probabilities in simple contexts
Next…
Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable (Y8)
Know that if the probability of an event occurring is p then the probability of it not occurring is 1 − p (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
6.4 Probability
6.5 Experimental probability
G&T Odds and Evens
LEVEL 2
understand vocabulary relating to handling data LEVEL 5
in probability, select methods based on equally
likely outcomes and experimental evidence, as appropriate
understand and use the probability scale from 0 to
APP Toolkit:
Probability Models L5
Probability Scale L5
Experimental Prob L5
Sum of prob L6
Core (pupil book 2)
5.4 Probability
5.5 Experimental probability
15.5 Probabilities from two way tables
Extension (pupil book 3)
5.4 Probability
5.5 Experimental probability
15.5 Comparing experimental and theoretical probabilities
() problems that have detailed Teachers’ Notes
1
understand that different outcomes may result from repeating an experiment
LEVEL 6
find and record all possible mutually exclusive
outcomes for single events and two successive events in a systematic way
know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems
Sample Space L6 Support resources:
worksheets Starter
KEYWORDS certain, chance, even chance, equally likely, event, outcome, fair, likely, unlikely, possible, impossible, probability, probability scale
FHS SKILLS/WRL Be creative (using keywords), use of memory (maths facts), be logical (step by step thinking)
CAME Lesson: “Roofs” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Measures 1; Angle: measuring, calculating and constructing FWK REF: 4.1, 4.3, 4.4
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Estimate, draw and measure acute and obtuse angles using a protractor to a suitable degree of accuracy; calculate angles in a straight line (Y5)
Estimate angles, and use a protractor to measure and draw them, on their own and in shapes; calculate angles in a triangle or around a point (Y6)
Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes
Distinguish between and estimate the size of acute, obtuse and reflex angles
Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles
Identify and use angle, side and symmetry properties of triangles and quadrilaterals
use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree. Construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA)
Next…
Identify alternate angles and corresponding angles; understand a proof that: - the angle sum of a triangle is 180° and of a quadrilateral is 360° - the exterior angle of a triangle is equal to the sum of the two interior opposite angles (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
8.1 Lines and angles
8.2 Calculating angles
12.1 Measuring and drawing angles
12.3 Solving geometrical problems
G&T Property Chart Shapely Pairs Quadrilaterals Game
() problems that have detailed Teachers’ Notes
LEVEL 2 distinguish between straight and turning movements,
recognise right angles in turns and understand angle as a measurement of turn
LEVEL 5
associated with angle and know and use the angle sum of a triangle and that of angles at a point
measure and draw angles to the nearest degree, when constructing models and drawing or using shapes
LEVEL 6 solve geometrical problems using properties of angles,
of parallel and intersecting lines, and of triangles and other polygons
identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360°
APP Toolkit: Angles L5
Drawing angles L5
Classifying Quad L6
Teaching & Learning: Best Practice Angles (Intro and
Naming).ppt
Angles 90 and 180 (Starter).xls
Modified copy of Angles 90
and 180 (Starter).xls
AngleTypes.ppt
Angles Worksheet.docx
Angles (Parallel Lines).ppt
Alternate_and_corresponding_angles.pdf
Angle Fit EstimatingAnglesStarter
Core (pupil book 2)
7.1 Lines and angles 7.2 Calculating angles 11.1 Measuring and drawing angles 11.3 Solving geometrical problems
Extension (pupil book 3)
7.1 Lines and angles
7.2 Calculating angles
11.1 Measuring and drawing angles
11.2 Constructions
11.3 Solving geometrical problem
KEYWORDS acute angle, obtuse angle, reflex angle, right angle, degree, diagonal, intersection, line segment, parallel, perpendicular, plane, adjacent angles, angles at a point, angles on a straight line, angles in a triangle, vertically opposite angles
FHS SKILLS/WRL Organise information (sort and classify angles), use of memory (angle facts), plan (solving multi step problems)
Algebra 1; Sequences and functions FWK REF: 3.2
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Recognise and continue number sequences formed by counting on or back in steps of constant size (Y4)
Describe integer sequences; generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence)
Generate sequences from patterns or practical contexts and describe the general term in simple cases
Express simple functions in words, then using symbols; represent them in mappings
Next…
Generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculator (Y8)
Use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated
(Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
2.1 Sequences and rules
2.2 Finding terms in patterns
2.3 Function machines
2.4 Double function machines
G&T Picturing Square Numbers
Squares in Rectangles Charlie’s Delightful
Machine
LEVEL 2:
Recognise sequences of numbers, including odd and even numbers
LEVEL 3:
APP Toolkit:
Sequences L3
Number Patterns L4
Number Patterns L5
Core (pupil book 2)
1.2 Sequences and rules
1.2 Finding missing terms
1.3 Functions and mappings
1.5 The general term (nth term)
Triangle Numbers
() problems that have detailed Teachers’ Notes
Recognise a wider range of sequences
LEVEL 4:
Recognise and describe number patterns LEVEL 6:
Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT; write an expression to describe the nth term of an arithmetic sequence
LEVEL 7:
Find the next term and nth term of quadratic sequences and functions and explore their properties
Sequences L6 CIMT:
Number patterns and sequences Extra EXE
Worksheet Creator
Extension (pupil book 3)
1.1 Sequences and rules
1.2 Finding missing terms
1.3 Finding the general term (nth term)
17.3 Dotty investigations
KEYWORDS integer, sequence, term, rule, starting point, difference, function, input, output, combined function, inverse function
FHS SKILLS/WRL Organise information (sequence), be logical (look for patterns and use them), research and explore and be creative (sequences in nature)
CAME Lesson: “Operating On Numbers” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Number 2; Place value, ordering, rounding, calculator methods FWK REF: 2.1, 2.7
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Use knowledge of rounding, place value (Y5)
Use a calculator to solve problems, including those involving decimals or fractions (e.g. find of 150 g); interpret the display correctly in the context of measurement (Y5)
Understand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100, 1000, and explain the effect
Compare and order decimals in different contexts; know that when comparing measurements the units must be the same
Round positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place
Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys
Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures)
Next…
Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1 and 0.01 (Y8)
Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places ( Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
3.2 Decimals
3.3 Ordering whole numbers and decimals
3.5 Estimates
10.1 Rounding
17.6 Solving problems
G&T Nice and Nasty Going Round in Circles
() problems that have detailed Teachers’ Notes
LEVEL 3:
Understand place value in numbers to 1000
Use place value to make approximations
Begin to use decimal notation in contexts such as money
LEVEL 4:
Use place value to multiply and divide whole numbers by 10 or 100
Order decimals to three decimal places
APP Toolkit:
Place value L2
L3 Rounding Order decimals L4
Place value and rounding L5
Core (pupil book 2)
2.1 Decimals
2.2 Ordering decimals
9.1 Rounding
9.5 Efficient calculations
16.3 Using a calculator
16.6 Solving problems
Extension (pupil book 3)
2.1 Decimals
2.2 Ordering decimals
9.1 Rounding
9.5 Efficient calculations
16.3 Using a calculator
KEYWORDS place value, decimal number, decimal fraction, zero place holder, less than, greater than, between, order, compare, most, least, significant, digit, round, nearest, to one decimal place (1 dp), approximately, estimate
FHS SKILLS/WRL Use of memory (maths facts), plan (solving multistep problems), be logical (connect your thinking)
Measures 2; Reading scales, converting between units, area and perimeter FWK REF:4.4
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Read and interpret scales on a range of measuring instruments (Y6)
Select and use standard metric units of measure and convert between units using decimals to two places (e.g. change 2.75 litr es to 2750 ml, or vice versa) (Y6)
Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares (Y6)
Read and interpret scales on a range of measuring instruments
Convert one metric unit to another, e.g. grams to kilograms
Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles
Next…
Derive and use formulae for the area of a triangle, parallelogram, and trapezium; calculate areas of compound shapes (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
10.6 Calculating with measurements 4.1 Length, perimeter and area
4.2 Perimeter and area of rectangles
G&T On the Edge
Fence It Can They Be Equal?
Warmsnug Double Glazing
() problems that have detailed Teachers’ Notes
APP Toolkit:
Units of measure L3
Units L4
Scales L4 Area and perimeter L4
Converting between units L5
Core (pupil book 2)
3.1 Length, perimeter and area
3.2 Perimeter and area of rectangles
9.6 Calculating with measurements
Extension (pupil book 3)
3.1 Length, perimeter and area
9.6 Calculating with measurements
KEYWORDS area, estimate, length, width, perimeter, compound shape, millimetre, centimetre, metre, square millimetre, square centimetre, square metre, formula
FHS SKILLS/WRL Use of memory (maths facts), plan and be logical (solving multistep problems)
Statistics 2; Averages and range, types of data FWK REF: 5.2, 5.3
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Describe and interpret results and solutions to problems using the mode, range, median and mean (Y6)
Calculate statistics for small sets of discrete data: - find the mode, median and range, and the modal class for grouped data
- calculate the mean, including from a simple frequency table, using a calculator for a larger number of items
Compare two simple distributions using the range and one of the mode, median or mean
Next…
Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class (Y8)
Compare two distributions using the range and one or more of the mode, median and mean (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
6.1 Mode and range
16.2 The median
G&T M, M and M
Searching for (Mean)ing Litov's Mean Value
Theorem
APP Toolkit:
Mode and range L4
Core (pupil book 2)
5.1 Mode, median and range
5.2 The mean 15.2 Comparing data
Extension (pupil book 3)
5.1 Mode, median and range
5.2 The mean
15.2 Comparing data
() problems that have detailed Teachers’ Notes
KEYWORDS average, data, median, mode, modal class, range, statistic, frequency table, mean, survey
FHS SKILLS/WRL Research and explore (collect and record info), organise info (frequency tables), use of memory (remember the facts)
CAME Lesson: “Best Desk Size” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Algebra 2; Simplify expressions, expand and factorise, substitution FWK REF: 3.1
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Previously...
Would know basic arithmetic (add, subtract, multiply and divide)
Use letter symbols to represent unknown numbers or variables; know the meanings of the words term, expression and equation
Understand that algebraic operations follow the rules of arithmetic
Simplify linear algebraic expressions by collecting like terms; multiply a single term over a bracket (integer coefficients)
Substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula
Next…
Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers (Y8)
Simplify or transform algebraic expressions by taking out single-term common factors (Y9)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
2.5 Using letter symbols to represent functions 7.1 Finding unknown numbers
7.3 Algebraic terms and expressions
14.1 Solving ‘brick wall’ problems
7.4 Simplifying expressions
7.2 Calculating using rules
G&T Your Number Is…
Crossed Ends Number Pyramids
More Number Pyramids
APP Toolkit: Substitution L5
Core (pupil book 2)
1.4 Using letter symbols to represent functions
6.1 Algebraic terms and expressions
6.2 Rules of algebra 6.3 Simplifying expressions 13.1 Solving ‘brick wall’ problems
() problems that have detailed Teachers’ Notes
Extension (pupil book 3)
6.1 Algebraic terms and expressions
6.2 Rules of algebra
6.3 Expanding and simplifying expressions
13.1 Solving 'brick wall' problems
KEYWORDS function, mapping, expression, variable, operation, conventions, term, like terms, expansion, simplify, substitute, linear
FHS SKILLS/WRL Be logical (connect thinking), use of memory (learn the facts)
Number 3; Integers, powers and roots FWK Ref: 2.2
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Find the difference between a positive and a negative integer, or two negative integers, in context (Y6)
Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10 (Y6)
Identify pairs of factors of two-digit whole numbers and find common multiples (e.g. for 6 and 9) (Y5)
Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two -digit numbers (Y6)
Understand negative numbers as positions on a number line; order, add and subtract integers in context
Recognise and use multiples, factors, primes (less than 100), common factors, highest common factors and lowest common multiples in simple cases; use simple tests of divisibility
Recognise the first few triangular numbers; recognise the squares of numbers to at least 12 × 12 and the corresponding roots
Next…
Add, subtract, multiply and divide integers (Y8)
Use multiples, factors, common factors, highest common factors, lowest common multiples and primes; find the prime factor decomposition of a number, e.g. 8000 = 26 × 53
(Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
3.3 Ordering whole numbers and decimals 3.4 Directed numbers
11.1 Square numbers
11.2 Triangle numbers
17.3 Divisibility and multiples 17.4 Factors of numbers
G&T First Connect Three How much can we
spend?
Dozens Factors and Multiples
Game Factors and Multiples
Puzzle
APP Toolkit:
Ordering directed numbers L3
Number relationships (factors, multiples...) L4
Core (pupil book 2)
2.3 Directed numbers
10.1 Square numbers and square roots
10.2 Triangle numbers
Article: Divisibility Tests
() problems that have detailed Teachers’ Notes
Extension (pupil book 3)
2.3 Directed numbers
10.1 Square numbers and square roots
10.2 Triangle numbers
KEYWORDS directed number, integer, positive, negative, plus, minus, negative number, prime number, factor, square number, square root, triangle number, sequence
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
CAME Lesson: “Direction & Distance” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Algebra 3; Functions and graphs FWK REF: 3.2, 4.2
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Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids (Y5)
Express simple functions in words, then using symbols; represent them in mappings (met in Algebra 1)
Use conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometrical information
Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise straight-line graphs parallel to the x-axis or y-axis
Plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphs
Next…
Express simple functions algebraically and represent them in mappings or on a spreadsheet (Y8)
Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y = mx + c correspond to straight-line graphs (Y8)
Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
2.3 Function machines 2.4 Double function machines (may have done in alg 1)
8.3 Coordinates
11.4 Naming graphs
11.5 From mappings to graphs
G&T Exploring Simple
Mappings
() problems that have
detailed Teachers’ Notes
APP Toolkit:
Coordinates in first quad L4
Coordinates in all four quads L5
Straight line graphs L6
Real life graphs L6 Core (pupil book 2)
10.3 From mappings to graphs 10.4 Naming graphs 10.5 Naming sloping lines
7.3 Coordinates
17.4 Graphs from the real world
Extension (pupil book 3)
1.4 Functions and mappings
10.3 From mappings to graphs
10.4 More about graphs
17.4 Graphs from the real world
7.3 Coordinates
KEYWORDS coordinates, mapping, x-axis, y-axis, function, equation
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
Measure 3; Transformations FWK REF: 4.2
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Visualise and draw on grids of different types where a shape will be after reflection, after translations, or after rotation through 90° or 180° about its centre or one of its vertices (Y6)
Understand and use the language and notation associated with reflections, translations and rotations
Recognise and visualise the symmetries of a 2-D shape
Identify all the symmetries of 2-D shapes (Y8)
Transform 2-D shapes by: - reflecting in given mirror lines - rotating about a given point
- translating
Explore these transformations and symmetries using ICT
Next…
Transform 2-D shapes by rotation, reflection and translation, on paper and using ICT (Y8)
Try out mathematical representations of simple combinations of these transformations (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
15.1 Line symmetry 15.2 Rotational symmetry
15.3 Reflections
15.4 Rotations
15.5 Translations
18.1 Polygons
G&T Reflecting Squarely
Shady Symmetry Mirror, Mirror…
...on the Wall Attractive Rotations
() problems that have detailed Teachers’ Notes
APP Toolkit: Reflections L3
Transformations L4
Further transformations L5
Core (pupil book 2)
14.1 Line symmetry 14.2 Rotational symmetry
14.3 Reflections
14.4 Rotations 14.5 Translations
18.1 Polygons
Extension (pupil book 3)
14.1 Line symmetry and rotational symmetry
14.2 Reflections
14.3 Rotations
14.4 Translations
18.1 Polygons
KEYWORDS line of symmetry, line symmetry, mirror line, symmetrical, rotate, rotational symmetry, order of rotational symmetry, point of symmetry, object, image, reflection, transformation, translation, angle, symmetry, triangle, quadrilateral, polygon
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems), be creative (visualise)
CAME Lesson: “Two Step Relations” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Statistics 3: Representing data FWK REF: 5.2, 5.3
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Previously...
Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts (Y6)
Construct, on paper and using ICT, graphs and diagrams to represent data, including: - bar-line graphs - frequency diagrams for grouped discrete data - simple pie charts
Interpret diagrams and graphs (including pie charts) and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution
Write a short report of a statistical enquiry, including appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of presentation
Next…
Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem, including: - simple scatter graphs (Y8) - stem-and-leaf diagrams (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
16.1 Pie charts
6.3 Statistical diagrams
16.4 & 16.5 Statistical surveys (will meet again later)
G&T
() problems that have detailed Teachers’ Notes
APP Toolkit: Constructing charts L3
Core (pupil book 2)
15.1 Pie charts
5.3 Statistical diagrams
15.3 & 15.4 Statistical surveys (will meet again later)
Extension (pupil book 3)
15.1 Pie charts
5.3 Statistical diagrams
15.3 & 15.4 Statistical surveys
KEYWORDS bar chart, line graph, pie chart, percentage, data, statistics, tally, frequency
FHS SKILLS/WRL Research and explore (collect and record info), organise info (frequency tables), use of memory (remember the facts), be creative (different ways to represent your data)
Number 4; Fractions, decimals and percentages FWK REF: 2.3
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Express a smaller whole number as a fraction of a larger one (e.g. recognise that 5 out of 8 is ); find equivalent fractions (e.g. = , or = 1 ); relate fractions to
their decimal representations (Y5)
Express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents or 1 pizzas); simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator (Y6)
Understand percentage as the number of parts in every 100 and express tenths and hundredths as percentages (Y5)
Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000); find equivalent percentages, decimals and fractions (Y6)
Express a smaller whole number as a fraction of a larger one; simplify fractions by cancelling all common factors and identify equivalent fractions; convert terminating decimals to fractions, e.g. 0.23 = 23/100; use diagrams to compare two or more simple fractions
Add and subtract simple fractions and those with common denominators; calculate simple fractions of quantities and measurements (whole-number answers); multiply a
fraction by an integer
Understand percentage as the ‘number of parts per 100’; calculate simple percentages and use percentages to compare simple pr oportions
Recognise the equivalence of percentages, fractions and decimals
Next…
Recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals (Y8)
Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multipl y and divide an integer by a fraction (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
5.1 Fractions
5.2 Fractions and decimals
5.3 Adding and subtracting fractions
5.4 Solving problems
13.1 Percentages 17.5 Percentages of quantities
G&T Fractions Jigsaw Peaches Today, Peaches
Tomorrow...
Matching Fractions
Decimals Percentages
() problems that have detailed Teachers’ Notes
APP Toolkit:
Core (pupil book 2)
2.3 Fractions, decimals, percentages, ratio and proportion
4.1 Fractions
4.2 Fractions and decimals
4.3 Adding and subtracting fractions
4.4 Equivalences
16.4 Fractions of quantities
12.1 Percentages
16.5 Percentages of quantities
Extension (pupil book 3)
4.1 Fractions
4.2 Fractions and decimals
4.3 Adding and subtracting fractions
4.4 Calculations and equivalences
16.4 Fractions of quantities
12.1 Percentages
16.5 Percentages of quantities
KEYWORDS numerator, denominator, mixed number, proper fraction, improper fraction, equivalent, cancel, lowest terms, simplest form, decimal number, decimal place, digit, order, tenth, hundredth, thousandth
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
CAME Lesson: “Relations” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Measures 4; Nets, plans, elevations, surface area and volume FWK REF: 4.1, 4.3, 4.4
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Identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes, and to identify and draw nets of 3-D shapes (Y5)
Use 2-D representations to visualise 3-D shapes and deduce some of their properties
Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square based pyramid, triangular prism
Calculate the surface area of cubes and cuboids
Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids (Y8)
Next…
Visualise 3-D shapes from their nets; use geometrical properties of cuboids and shapes made from cuboids; use simple plans and elevations (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
4.3 3-D shapes
18.4 & 18.5 Constructing 3-D shapes
G&T Marbles in a Box Cuboids
Painted Cube Cuboid Challenge
Sending a Parcel () problems that have
detailed Teachers’ Notes
APP Toolkit:
Core (pupil book 2)
3.3 3-D Shapes
18.4&18.5 Constructing 3-D shapes
Extension (pupil book 3)
3.3 3-D shapes
18.4 & 18.5 Constructing 3-D shapes
KEYWORDS edge, face, vertex, isometric grid, net, 3-D shape, polyhedron, cube, cuboid, cylinder, sphere, hemisphere, prism, pyramid, tetrahedron, surface area
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems), be creative (visualise)
Number 5; Ratio and proportion FWK REF: 2.3
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Use the vocabulary of ratio and proportion to describe the relationship between two quantities (Y4)
Solve simple problems involving direct proportion by scaling quantities up or down (Y6)
Understand the relationship between ratio and proportion; use direct proportion in simple contexts; use ratio notation, simpl ify ratios and divide a quantity into two parts in a given ratio; solve simple problems involving ratio and proportion using informal strategies
Use the equivalence of fractions, decimals and percentages to compare proportions (Y8)
Next…
Apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units, recognising links with fraction notation;
divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple problems involving ratio and direct proportion (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
13.2 Ratio and proportion 13.3 Calculating ratios and proportions
13.4 Solving problems
G&T
Mixing Lemonade
() problems that have detailed Teachers’ Notes
APP Toolkit:
Core (pupil book 2)
12.2 Ratio and proportion
12.3 Calculating ratios and proportions
12.4 Solving problems
Extension (pupil book 3)
12.2 Ratio and proportion
12.3 Calculating ratios and proportions
12.4 Solving problems
KEYWORDS proportion, ratio, cancel, simplest form, highest common factor
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
CAME Lesson: “Exploring The Rectangle” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons
Statistics 4: Specifying, planning and collecting FWK REF: 5.1
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Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask (Y6)
Suggest possible answers, given a question that can be addressed by statistical methods
Decide which data would be relevant to an enquiry and possible sources
Plan how to collect and organise small sets of data from surveys and experiments:
- design data collection sheets or questionnaires to use in a simple survey - construct frequency tables for gathering discrete data, grouped where appropriate in equal class intervals
Collect small sets of data from surveys and experiments, as planned
Next…
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
9.1 Using a tally chart
9.2 Using the correct data 9.3 Grouped frequencies
16.3 Two way tables
16.4 & 16.5 Statistical surveys
G&T
APP Toolkit:
Core (pupil book 2)
8.1 Using a tally chart
8.2 Using the correct data
8.3 Grouped frequencies
8.4 Data collection
15.3&15.4 Statistical surveys
Extension (pupil book 3)
8.1 Using a tally chart
8.2 Using the correct data
8.3 Grouped frequencies
8.4 Data collection
15.3 & 15.4 Statistical surveys
() problems that have
detailed Teachers’ Notes
KEYWORDS average, data collection sheet, database, hypothesis, questionnaire, survey
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems), research and explore (ask questions), be creative (ask interesting useful questions and collect and record data in a variety of ways)
Algebra 4; Equations and formulae FWK REF: 3.1
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Use simple expressions and formulae in words then symbols (e.g. the cost of c pens at 15 pence each is 15c pence) (Y6)
Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations)
Use simple formulae from mathematics and other subjects; substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula (met in Algebra 2)
Next…
Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate method s (e.g. inverse operations, transforming both sides in same way) (Y8)
Use graphs and set up equations to solve simple problems involving direct proportion (Y8)
Use formulae from mathematics and other subjects; substitute integers into simple formulae, including examples that lead to an equation to solve; substitute positive integers
into expressions involving small powers, e.g. 3x2 + 4 or 2x3; derive simple formulae (Y8)
NEW FRAMEWOKRING MATHS Enrichment G&T Assessment Criteria Teaching Resources
Support (pupil book 1)
7.5 Equations
14.1 Solving ‘brick wall’ problems
14.2 Solving square-and-circle problems
7.2 Calculating using rules
G&T Your Number Was…
APP Toolkit:
Core (pupil book 2)
6.5 Equations
13.1 Solving ‘brick wall’ problems
13.2 Solving square-and-circle problems
17.1 Solving equations
6.4 Formulae
17.2 Formulae
Extension (pupil book 3)
6.3 Expanding and simplifying expressions
13.1 Solving ‘brick wall’ problems
13.2 Square-and-circle problems
17.1 Solving equations
17.2 Formulae
6.4 Formulae
17.5 Other types of problem
() problems that have detailed Teachers’ Notes
KEYWORDS problem, equation, solve, formula, substitute, linear, expressions, derive
FHS SKILLS/WRL Use of memory (use of maths facts), be logical (do things step by step), plan (solving multi stage problems)
CAME Lesson: “Missing Digits” FWK REF:
Activities
Resources Available in Department Area: P:\ /Departments/Maths/Curriculum/SOW - KS3/CAME lessons