lessons featherstone high transition unit; transition ... · make and justify estimates and...

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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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


9.3 BODMAS

9.4 Long multiplication and long division


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


9.3 BODMAS

9.4 Long multiplication and long division


16.1 Multiplying decimals

16.2 Dividing decimals

http://nrich.maths.org/public/

http://nrich.maths.org/7405


http://nrich.maths.org/public/viewer.php?obj_id=31


http://nrich.maths.org/public/viewer.php?obj_id=507&refpage=titlesearch.php






http://nrich.maths.org/public/viewer.php?obj_id=6402&part=





http://nrich.maths.org/public/viewer.php?obj_id=5612&part=index&refpage=monthindex.php


http://www.kangaroomaths.com/free_resources/assessment/app/level3/ch_l3calc1.pdf



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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Previously...

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)



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


15.5 Probabilities from two way tables



http://www.kangaroomaths.com/free_resources/assessment/app/level5/ch_l5hd2.pdf





5.4 Probability


15.5 Comparing experimental and theoretical probabilities


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)









http://www.superteacherworksheets.com/probability.html

http://www.cimt.plymouth.ac.uk/projects/mepres/primary/y4int/29/pb4a_29.html


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


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


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)



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





BestPractices/Angles%20(Intro%20and%20Naming).ppt

BestPractices/Angles%20(Intro%20and%20Naming).ppt

BestPractices/Angles%2090%20and%20180%20(Starter).xls

BestPractices/Angles%2090%20and%20180%20(Starter).xls

BestPractices/Modified%20copy%20of%20Angles%2090%20and%20180%20(Starter).xls

BestPractices/Modified%20copy%20of%20Angles%2090%20and%20180%20(Starter).xls

BestPractices/AngleTypes.ppt

BestPractices/Angles%20Worksheet.docx

BestPractices/Angles%20(Parallel%20Lines).ppt

BestPractices/alternate_and_corresponding_angles.pdf

BestPractices/alternate_and_corresponding_angles.pdf

http://www.transum.org/Software/SW/Starter_of_the_day/starter_May28.ASP







Core (pupil book 2)


1.2 Finding missing terms

1.3 Functions and mappings

1.5 The general term (nth term)

Triangle Numbers


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



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


Number 2; Place value, ordering, rounding, calculator methods FWK REF: 2.1, 2.7

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Previously...

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)


http://www.cimt.plymouth.ac.uk/projects/mepres/book7/y7s7ex.pdf

http://www.cimt.plymouth.ac.uk/projects/mepres/book7/y7s7ex.pdf

http://www.worksheetworks.com/math/numbers/patterns.html



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


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


16.3 Using a calculator



2.1 Decimals

2.2 Ordering decimals

9.1 Rounding


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)






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


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


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)



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













5.1 Mode, median and range

5.2 The mean

15.2 Comparing data


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


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)



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


6.2 Rules of algebra 6.3 Simplifying expressions 13.1 Solving ‘brick wall’ problems




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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Previously...

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)



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


Article: Divisibility Tests



2.3 Directed numbers

10.1 Square numbers and square roots


KEYWORDS directed number, integer, positive, negative, plus, minus, negative number, prime number, factor, square number, square root, triangle number, sequence


CAME Lesson: “Direction & Distance” FWK REF:

Activities


Algebra 3; Functions and graphs FWK REF: 3.2, 4.2

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Previously...

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)




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


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


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)






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


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


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


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)





http://nrich.maths.org/public/viewer.php?obj_id=5459&part=index&refpage=viewer.php


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)



16.1 Pie charts

6.3 Statistical diagrams

16.4 & 16.5 Statistical surveys (will meet again later)

G&T


APP Toolkit: Constructing charts L3

Core (pupil book 2)

15.1 Pie charts


15.3 & 15.4 Statistical surveys (will meet again later)


15.1 Pie charts


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)



5.1 Fractions

5.2 Fractions and decimals

5.3 Adding and subtracting fractions


13.1 Percentages 17.5 Percentages of quantities

G&T Fractions Jigsaw Peaches Today, Peaches

Tomorrow...

Matching Fractions

Decimals Percentages


APP Toolkit:

Core (pupil book 2)

2.3 Fractions, decimals, percentages, ratio and proportion

4.1 Fractions



4.4 Equivalences

16.4 Fractions of quantities

12.1 Percentages

16.5 Percentages of quantities


4.1 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






http://nrich.maths.org/public/viewer.php?time=1202216842&obj_id=1249&part=index

http://nrich.maths.org/public/viewer.php?time=1202216842&obj_id=1249&part=index

CAME Lesson: “Relations” FWK REF:

Activities


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)



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


APP Toolkit:

Core (pupil book 2)

3.3 3-D Shapes

18.4&18.5 Constructing 3-D shapes


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)



13.2 Ratio and proportion 13.3 Calculating ratios and proportions


G&T

Mixing Lemonade


APP Toolkit:

Core (pupil book 2)

12.2 Ratio and proportion

12.3 Calculating ratios and proportions



12.2 Ratio and proportion

12.3 Calculating ratios and proportions


KEYWORDS proportion, ratio, cancel, simplest form, highest common factor




CAME Lesson: “Exploring The Rectangle” FWK REF:

Activities


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…



9.1 Using a tally chart

9.2 Using the correct data 9.3 Grouped frequencies

16.3 Two way tables


G&T

APP Toolkit:

Core (pupil book 2)


8.2 Using the correct data

8.3 Grouped frequencies

8.4 Data collection

15.3&15.4 Statistical surveys




8.2 Using the correct data

8.3 Grouped frequencies

8.4 Data collection


() problems that have


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)



7.5 Equations


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


13.2 Solving square-and-circle problems

17.1 Solving equations

6.4 Formulae

17.2 Formulae




6.3 Expanding and simplifying expressions


13.2 Square-and-circle problems

17.1 Solving equations

17.2 Formulae

6.4 Formulae

17.5 Other types of problem


KEYWORDS problem, equation, solve, formula, substitute, linear, expressions, derive


CAME Lesson: “Missing Digits” FWK REF:

Activities


lessons featherstone high transition unit; transition ... · make and justify estimates and...

Documents