yr 9 lesson plan – term 3members.iinet.net.au/~rmiln/girrawheen/yr9 programme-adv 2008… ·...

2008 Year 8 Programme & Outline | 1

GSHSGIRRAWHEEN SENIOR HIGH SCHOOL

Year

9 P

rogr

amm

e 20

08

2008 Year 9 Programme and Outline | Forward

Foreward

This document should not be read as definitive nor complete. It is a work in progress that outlines an understanding of the existing year 9 programme and provides a starting point for development of a team approach to curriculum planning and development at Girrawheen Senior High School. Programme outlines from local schools, existing programmes at GSHS and knowledge of the local cohort has been used in devising the programme.

The aim is to use this document for benchmarking what we intend to do, what has been done and what we can do in the future to assist students reach ever higher goals.

This document outlines programme objectives and provides a sample sequence with suggested timing for each lesson. It is realised that each cohort will dictate changes to the timings listed, the order of presentation, teaching strategies used and the achievable outcomes. Each teacher using this programme will need to adopt a common sense approach with the document and note any areas where improvement can be made for subsequent years. It is intended that fortnightly Mathematics meetings are used to monitor the effectiveness of the teaching programme.

Of specific note are the outcomes listed for each lesson. It is not intended that these outcomes are reached by the end of the lesson; but instead each outcome is intended to be introduced at the points referenced, reinforced during subsequent lessons and assessed at defined assessment milestones.

Texts currently in use at GSHS have been referenced by page and chapter. It is not intended that these references are required to be used in each lesson but have been listed only as a ready reference. Alternate text references for each topic have also been listed in the overview.

Furthermore, as documents such as the K-10 Syllabus, COS for upper school or First Steps Mathematics/Stepping out are introduced into GSHS it is intended to use this document to measure the impact on yr 9 and subsequent years.

Koulianos, Humphry, Miln 2007

Version Control

0.1a 11 December 2007 DRAFTDRAFTDRAFTDRAFT

2008 Year 9 Programme and Outline | i

8

9 10 11 12

Index

Assessment Schedule............................................................................................iiiSEMESTER 1...........................iiiTerm 1.....................................iiiTerm 2.....................................iiiSEMESTER 2...........................iiiTerm 3.....................................iiiTerm 4.....................................iii

Working Mathematically Outcomes......................................................................iv

Yr 9 Programme Overview.....................................................................................1SEMESTER ONE......................1Term 1......................................1Term 2......................................2SEMESTER TWO......................3Term 3......................................3Term 4......................................4

GSHS Yr 9 Programme & Lesson Plan...................................................................5SEMESTER 1............................5Term 1......................................5Term 2....................................14SEMESTER 2..........................24Term 3....................................24Term 4....................................34

APPENDIX A – OUTCOMES AUDIT.....................................................................43

2008 Year 9 Programme and Outline | ii

8

9 10 11 12

Assessment Schedule

SEMESTER 1Term 1Week 1 Number Assessment 1Week 3 Number Assessment 2Week 7 Number Assessment 3Week 10 Algebra Assessment 1

Term 2Week 2 Number Assessment 4Week 6 Algebra Assessment 2Week 9 Chance & Data Assessment 1

SEMESTER 2Term 3Week 3 Chance & Data Assessment 2Week 6 Measurement Assessment 1Week 6 Space Assessment 1Week 9 Measurement Assessment 2

Term 4Week 1 Measurement Assessment 3Week 3 Measurement Assessment 4Week 4 Algebra Assessment 3Week 7 Algebra Assessment 4Week 10 Space Assessment 2

2008 Year 9 Programme and Outline | iii

8

9 10 11 12

Working Mathematically OutcomesWM3.4 Students asks questions to clarify essential mathematical features of a problem and uses problem solving strategies

WM3.5 Students extends tasks by asking further mathematical questions and uses problem solving strategies that include those based on developing systematic approaches

WM 4.4 Students checked that answers are roughly as expected and that methods and answers make sense.

WM 4.5 Student checks working and reasoning and checks that answers fit specifications and makes sense in original situations

WM 5.4 Student uses examples

WM 5.5 Student draws on mathematical knowledge

2008 Year 9 Programme and Outline | iv

8

9 10 11 12

Yr 9 Programme OverviewSEMESTER ONETime Contents Text Book Other

ResourcesProgress Maps-Outcome Statements

Assessment Performance (Guidelines only)

Term 1

Week 1-6

Numbers Whole Numbers (Positive and

Negative) Decimal And Fractions Directed Numbers Indices Percentages

Percentages Calculations In Business Percentages In Our Diet Percentages Of Quantities Percentage Change Discount And Commission

Nelson2Ch 8

Maths for WA2 Ch 1,2Worksheets

MZ2 Ch 1,2

HO2 Ch 1,2

Saddler2 Ch1,2,3,4,5

Saddler3Ch 1,2

Saddler4 Ch 2

N6a.4 N6b.4N6.5N6.6 N7.4 N7.5 N8.4 8.5 8.6

N6.5N6.6 N7.5N7.6 N8.5

NUMBER ASSESSMENT 1: TestWeek 1

NUMBER ASSESSMENT 2: TestWeek 3

NUMBER ASSESSMENT 3: Test Week 7

Week 7-9

Algebra and Number Patterns Algebraic Expressions Collecting Like Terms Substitution Formulas Expanding Brackets Factorisation Algebraic Fractions

Nelson2Ch 7

Maths for WA2 Ch 9Worksheets

MZ2 Ch5

HO2 Ch3

Saddler2 Ch 8,9, 12

Saddler3 Ch 7

Saddler4 Ch 5

PA 18.4A 18b.5A 18b.6A 19.5A 19.6

ALGEBRA ASSESSMENT 1: TestWeek 10

2008 Year 9 Programme and Outline | 1

Time Contents Text Book Other Resources

Progress Maps Assessment Performance (Guidelines only)

Term 2Week 1-

2Rates, Ratios & Indicies Ratio And Proportion Simplifying Ratios Using Ratios Rates And Speed, Distance And

Time Graphs And Time Scale Diagrams Index Numbers Index Laws

Nelson2Ch 2,13

Maths for WA2 Ch 6 Worksheets

MZ2 Ch1

HO2 Ch 2

Saddler2 Ch 15

Saddler3 Ch 11

N 6.5N 6.6N 7.6M 10b.5N 7.6M 10b.5, M 9b.5WM 4.5

NUMBER ASSESSMENT 4: Test Week 2

Week 3-6

Solving Linear Equations Simple Equations Solving Equations Using Flow

Charts Inverse Operations Solving Equations With Brackets

Linear Graphs Plotting Points Linear Patterns And Simple Rules Plotting Points From Rules Horizontal And Vertical Lines Gradients Of Straight Lines Finding Equations Of Lines The Gradient And Y-Intercept

Nelson2Ch 3

Maths for WA2 Ch 10

MZ2 Ch6

HO2 Ch 4

Maths for WA2 Ch 11

Saddler2 Ch 9,11

Saddler3 Ch 4

Saddler 4 Ch

PA 19.4

PA 18.4A 17a.5A 17a.6A 18a.5



11Week 7-9

Chance Sample Space Grids Tree Diagrams Simulations Using Sampling

Nelson2Ch 6

Maths for WA2Ch 13

MZ2 Ch9

HO2 Ch 9

Saddler3 Ch 10

Saddler4 Ch 10

C&D 13a.4C&D 13b.5C&D 12.4C&D 12.5C&D 12.6

CHANCE & DATA ASSESSMENT 1: TestWeek 9

SEMESTER TWOTime Contents Text Book Other

ResourcesProgress Maps Assessment Performance

(Guidelines only)Term 3Week 1-2

Statistics Collecting Data Column Graphs And Histograms The Inter-quartile Range Stem And Leaf Plots Mean And Median Line Graphs Scattergraphs

Nelson2Ch 6,11

Maths for WA2Ch 14Worksheets

MZ2 Ch10

HO2 Ch 10

Saddler3 Ch 12

C&D 13a.5C&D 13b.5C&D 14.5C&D 14.4C&D 13b.4C&D 14.4A 17a.5WM 5.5, 5.6

CHANCE & DATA ASSESSMENT 2: TestWeek 3

Week 3-4

Polygons and Polyhedra Naming Angles Complementary And

Supplementary Triangles, Quadrilaterals And

Polygons Angles In Parallel Lines Congruent Shapes Similar Shapes

Nelson2Ch 5,9,14

Maths for WA2Ch 7

MZ2 Ch8

HO2 Ch 8

Saddler2 Ch

M9b.5S16.6M10b.6S15b.4S16.5WM 5.6


Applications Of Similar Triangles 6,10

Saddler3 Ch 3, 13Saddler4 Ch 4

Week5-6 Pythagoras & Trigonometry Pythagoras’ Theorem Pythagorean Triples Compound Shapes

Nelson2Ch 1

Maths for WA2 Ch 4MZ2 Ch4HO2 Ch 7Saddler3 Ch 9

M 10a.5M 10b.6WM 5.5

MEASUREMENT ASSESSMENT 1: Test Week 6

SPACE ASSESSMENT 1: TestWeek 6

Week 7-9

Measurement Converting Units Scale Factors Perimeter Of Shapes Circumference Of A Circle Composite Shapes Area Of Trapezium, Circles And

Sectors Surface Area Of Prisms And

Pyramids Volume Of Prisms And Capacity

Nelson2Ch 4

Maths for WA2 Ch 3

MZ2 Ch3

HO Ch6

Saddler2 Ch 7

Saddler3 Ch 5

M 9a.4M 9a.5M 9a.6M 10a.5M 10a.6N 6.5

MEASUREMENT ASSESSMENT 2: TestWeek 9

Time Contents Text Book Other Resources

Progress Maps Assessment Performance

Term 4

Week 1-2

Trigonometry Right angled triangles Sine, Cosine, Tangent ratios

Nelson 2Ch 9

Worksheets M10b.6 MEASUREMENT ASSESSMENT 2: TestWeek 1

MEASUREMENT ASSESSMENT 2: TestWeek 3

Week 3-4

Simultaneous Equations Graphing Simultaneous

Equations Substitution Method Elimination Method

Nelson2Ch 3


MZ2 Ch6

A 19.5A 19.6

ALGEBRA ASSESSMENT 3:TestWeek 4


Saddler3 Ch 8

Week 5-7

Quadratic Functions Solving Quadratic Equations Worded Problems Sketching Parabolas

Nelson2Ch 12


MZ2 Ch7

HO2 Ch 5

Saddler4 Ch 3,6,11

A 17a.6A 19.6WM 3.6WM 5.6


Week 8-9

Transformations and Location Transformations Enlargements Scale Factors and Maps Networks

Nelson2Ch 10,14

Maths for WA2Ch 8

MZ2 Ch8

HO2 Ch 8

Saddler2 Ch 14

Saddler3 Ch 6

Saddler4 Ch 8,13

S 15c.4S 15c.5M 10b.4S 15a.4S 15a.5, S 15a.6 M 10b.6, WM 3.6

SPACE ASSESSMENT 2: TestWeek 10


GSHS Yr 9 Programme & Lesson PlanSEMESTER 1Term 1Activity Outcomes Links to Pointers Activities

1c

Review Test & CorrectionsPre-test

Place ValueStudents can align numerical values in a

place value chart up to trillionsStudents can identify differences and

advantages of the decimal system over alternatives(eg Roman numerals).

N6a.4 Students can read, write say and count numbers into the millions.

NUMBER ASSESSMENT 1

Modelling: Identifying the ease of Decimal vs Roman numerals

Practice: Nelson1 p.2 Ex 1.1 q1-6

1d

Positive and Negative numbersStudents can place positive and negative

numbers on a number lineStudents can add and subtract positive

and negative numbers using a number line

Students can multiply and divide negative numbers using a number line

N6.5 Students can place negative integers on a number line.

N7.5Students can use the four operators on positive and negative integers.

Practice: Nelson1 Ex 9.1 p.330q. 1-20

2a

Using Positive and Negative NumbersStudents can identify and use negative

numbers in a range of simple applications

Students can name and identify the following symbols <, >, =, <=, >=, ≠

Students can use equality symbols to order integers

N6.5 Students can order positive and negative integers on a number line and can use <>= effectively.

N8.5, N7.5 Students can calculate using a range of written methods on positive and negative integers.

Practice: Nelson1 Ex 9.4 p.338 q. 1-6


2b Directed Number Students can identify which direction to

travel on a number line based on simple number sentences.

N7.4 Students use <=> to complete simple number sentences and can solve simple missing operator problems.


Practice: Nelson1 Ex 9.8 p.350 2008 Term 1 Year 9 Programme and Outline | 6

Activity Outcomes Links to Pointers Activities Students can identify which operation

has been used on a series of numbersq. 1-2

2c

Fractions Students can identify examples where

fractions appear in everyday life. Students recognise equivalent fractions. Students recognise that fractions must

be constructed in equal parts. Students recognise situations where

fractions cannot be used (eg. unequal parts)

Students can define numerator, denominator and venticular.

Students can construct equivalent fractions using multiples

Students can place fractions on a number line

Students can order fractions in ascending and descending order

N6b.4 Students interpret fractional quantities as relating to equal parts of a thing.

N6b.4 Students state fractional equivalents in words and symbols

N6b.4 Students have a sense of the relative magnitude of fractions.

Practice: Nelson1 Ex 7.1 p.240 q. 1-13.


2d Operations on fractions I Students can add and subtract fractions

using pictorial representations. Students recognise that multiplying

fractions involves fractions of quantities Students recognise the word ‘of’

indicates multiplication Students are able to multiply whole

numbers, mixed numerals, improper fractions, proper fractions.

Students understand to convert mixed numerals to improper fractions before multiplying.

Students understand how identifying factors and cancelling can be used to

N6b.3 Students separate collections and objects into equal parts to compare unit fractions

N7.4 Students are beginning to understand the meaning of a whole number and a fraction.

N7.5 Students understand that multiplying or dividing can have the effect of increasing or decreasing a quantity

N8.5 Students use a range of efficient, although not necessarily


Assignment: Nelson1 UMS p.261 q. 1-11.



2008 Term 1 Year 9 Programme and Outline | 7

Activity Outcomes Links to Pointers Activitiessimplify multiplication. standard written methods to

multiply and divide common and decimal fractions

N8.5 Students use calculators efficiently dealing with fractions and their own calculator

3a

Division of fractions Students can divide fractions by

inverting the second term and multiplying numerators and denominators.

N7.5 Students use division in which the divisor is a fractional number


3b

Revision Place Value Positive and Negative numbers Using Positive and Negative Numbers Directed Number Fractions Operations on fractions

N6a.4N6b.3, N6b.4 N6.5N7.4 N7.5N8.5

3c

Test Place Value Positive and Negative numbers Using Positive and Negative Numbers Directed Number Fractions Operations on fractions

N6a.4N6b.3, N6b.4 N6.5N7.4 N7.5N8.5

NUMBER ASSESSMENT 2

3d Decimals Students can identify numbers where

decimal points have been located incorrectly.

Students can place decimal values on a place value chart.

Students can say/verbalise decimal values

N6a.4 Students can place decimal numbers with an equal number of places on the number line

N6.5 Students know that digits to the right of the decimal place have decreasing values in powers

Practice: Nelson1 Ex 2.1 p.32 q. 1.



Activity Outcomes Links to Pointers Activities Students can identify the connection

between expanded notation and numbers placed in a place value chart.

Students can use the a b/c button on a calculator to convert between fractions and decimals

Students can order decimals on a number line

of ten.

4a

Connection between fractions and decimalsStudents recognise that decimals describe

parts of a wholeStudents recognise the connection

between fractions and decimalsStudents can convert freely between

decimals and fractions

N6.5 Students move freely between various ways of representing numbers and quantities


4b

Addition and Subtraction of decimalsStudents can add/subtract decimal values

with and without a calculatorStudents can identify key information

within a worded problem that indicates addition/subtraction is necessary

Students can round numbers accurately

N6.5 Students can round numbers appropriately to a given degree of accuracy.

N7.4 Students understand the meaning, use and connections between the four operations on decimal numbers

N7.4 Students select the appropriate operation to deal with a wide range of operations


4cPercentages

Students can convert between fractions decimals and percentages

N6.6 Students convert flexibly between various forms decimals, percentages and fractions.


4d Recurring Decimals N 6.6 Express fractions as a Practice: Nelson2 p.253 Ex 8.6


Activity Outcomes Links to Pointers Activities Students can convert fractions to

decimals for recurring numbersrecurring or terminating decimal q1-5

5a

Percentages Students can calculate percentages of

quantities

N8.5 Students calculate simple percentages of amounts

Practice: Nelson2 p.257 Ex 8.8 q1-23Practice: Nelson2 p.263 Ex 8.10 q1-16

5b

Percentages Students can increase and decrease

amounts by percentages

N8.6 Students calculate by an increase or decrease of a percentage


5c

Indices Students can move between factor and

index form Students can recognise exponential

graphs Students can read information from an

exponential graph

N6.5 Student can write indices in factor form for whole number powers and can apply their knowledge of powers and roots to practical problems.


5d

Index Laws Students can multiply indices

appropriately eg. 2b4c3 x 8b2c3 = 16b6c6

N6.6 Students use and understand positive and negative integer powers and roots.

N7.6 Students have an understanding of index laws as they apply to simplifying expressions with common base and integer powers for multiplication, division and powers


6a Index Laws II Students can divide indices appropriately

N6.6 Students use and understand positive and negative



Activity Outcomes Links to Pointers Activitiesinteger powers and roots.


6b

Index Laws III Students can recognise that when an

index is raised to a power Students can raise bracketed terms to a

powereg. (a2)2

N6.6 Students use and understand positive and negative integer powers and roots.



6c

Index Laws IV Students can recognise distributive

patterns with respect to index laws Students are able to switch between

standard form and extended form

N8.6 Students can find the product and quotient of numbers expressed with integer powers and can raise numbers to a power.


6d

Revision Decimals Connection between fractions and

decimals Addition and Subtraction of decimals Percentages Recurring Decimals Indices Index Laws

N6a.4N6.5, N6.6N7.4, N7.6N8.5, N8.6


Activity Outcomes Links to Pointers Activities

7a

Test Decimals Connection between fractions and

decimals Addition and Subtraction of decimals Percentages Recurring Decimals Indices Index Laws

N6a.4N6.5, N6.6N7.4, N7.6N8.5, N8.6

NUMBER ASSESSMENT 3

7b

Algebraic expressions Students are able to convert worded

problems into algebraic expressions Students can recognise pronumerals,

coefficients, terms, expressions, equations and indexes.

A18a.5 Students can find a general rule to relate each element of a sequence to it’s position where one or two operations are involved

A18b.5 Students appreciate that letters are used to represent a variable number and not objects. They translate straight forward linguistic statements involving one variable into symbolic statements by representing the variable quantity with a letter.


7c

Simplification of expressions Students understand that like terms

must have the same pronumerals and each pronumeral has the same index

Students can identify like terms Students are able to collect like terms

A19b.5 Students can use an array to show the equality of a distributive property and can deduce equivalency and factorise.


7d Multiplying and dividing expressions Students understand shorthand notation

for multiplying and dividing (eg no x or ÷ sign)

Students can multiply and divide

A19.5 Students can use an array to show the equality of a distributive property and can deduce equivalency and factorise.



Activity Outcomes Links to Pointers Activitiesalgebraic expressions A19.5 Students can solve one and

two step equations using strategies that include working backtracking, balancing and guess and check.

8a

Substituting into Algebraic Expressions Students are able to recognise values

given for pronumerals Students are able to substitute numerical

values for pronumerals Students are able to substitute values

into algebraic expressions

A19.5 Students can guess a solution to an equation, substitute this value into the equation and use the result as feedback.

A19.6 Students use analytic methods to solve equations, they can simplify expressions by removing brackets and can simplify those requiring factorisation before simplification.


8bUsing formulas

Students substitute for simple examples using speed, distance and time.

A18a.5 Students generate formula from known data and use this pattern to generate sequences in two different scales

Practice: Worksheets

8c

Expanding expressions Students recognise when and how to use

the distributive law with algebraic expressions

Students can expand simple algebraic expressions using the distributive law

A19.5 Students can use an array to show the equality of a distributive property and can deduce equivalency and factorise.

A19.5 Students can solve one and two step equations using strategies that include working backtracking, balancing and guess and check.


8d Expanding binomial products Students can identify binomial products Students recognise binomial expressions

A19.6 Students use analytic methods to solve equations, they can simplify expressions by



Activity Outcomes Links to Pointers Activities Students are able to expand binomial

products and simplify Students can use FOIL and distributive

law to expand binomial products

removing brackets and can simplify those requiring factorisation before simplification.

9a

Factorising by common factors Students understanding that expanding

is the removal of brackets and factorising is the insertion of brackets

Students understand and recognise the highest common factors for algebraic terms

Students are able to factorise simple algebraic expressions



9b

Factorising by grouping Students can factorise by grouping

Factorising using difference of perfect squares Students recognise perfect squares Students can factor perfect squares Students are able to factorise DOPS




9c

Algebraic fractions Students recognise an algebraic fraction Students can simplify algebraic fractions Students are able to factorise numerator

& denominator to use cancellation

A18b.6 Students use algebraic symbols to write one or two variable equations from a description of a single constraint.



9d Revision Algebraic expressions Simplification of expressions

A18a.5A18b.5, A18b.6A19.5, A19.6


Activity Outcomes Links to Pointers Activities Multiplying and dividing expressions Substituting into Algebraic Expressions Using formulas Expanding expressions Expanding binomial products Factorising by common factors Factorising by grouping Factorising using difference of perfect

squares Algebraic fractions

10a

Test Algebraic expressions Simplification of expressions Multiplying and dividing expressions Substituting into Algebraic Expressions Using formulas Expanding expressions Expanding binomial products Factorising by common factors Factorising by grouping Factorising using difference of perfect

squares Algebraic fractions

A18a.5A18b.5, A18b.6A19.5, A19.6

ALGEBRA ASSESSMENT 1


GSHS Yr 9 Programme & Lesson Plan Term 2Activity Outcomes Links to Pointers Activities

1aFractions and ratios

Students can convert freely between fractions and ratios

N6.5 Students move freely between various ways of representing numbers and quantities

Practice: Nelson 2 Ex 13.1 p.413 q.1-12

1b

Ratios of two quantities Students can create ratios from simple

word problems Students can find the simplest form of

ratios

N8.6 Students use computations confidently using ratios.


1cRatio and Proportion

Students can find equivalent ratiosN6.6 Students order ratios by changing parts and comparing them.


2aRates

Students can use ratios to convert between standard units

N6.6 Students order ratios by changing parts and comparing them.


2b

Rates Students can interpret information from

graphs to determine simple rates

N6.6 Students interpret published materials to interpret given situations



2c

Mini Test Fractions and ratios Ratios of two quantities Ratio and Proportion Rates

N6.5, N6.6N8.6

NUMBER ASSESSMENT 4

2d Solving equations graphically Students are able to substitute numerical

values for pronumerals for the RHS for a simple linear equation

Students can produce a numerical value for the LHS

A19.5 Students use an array to show the equality of the distributive property, they can use this rule in reverse to factorise linear expressions.



Activity Outcomes Links to Pointers Activities Students are able to identify the x & y

axis on the coordinate plane Students are able to identify x & y values

on the coordinate plane

A17a.5 Students plot the pairs of values obtained, inspect the result and comment on whether or how the quantities are related.

3a

Guess and Check Students are able to estimate values for

RHS of simple equations Students can check the accuracy of their

estimation Students can use their guess and check

to solve simple linear equations

Backtracking Students are able to convert simple

linear equations into flow charts Students are able to recognise the

inverse operations required Students are able to solve linear

equations using backtracking




Practice: Nelson Ex 3.3 p.63 q.1-2.

3b Inverse Operations Students are able to recognise where

inverse operations are required to solve simple algebraic equations

Students can solve simple algebraic equations using inverse operations (LHS & RHS)


A18b.6 Students can use linear expressions to make general arguments.


Practice: Nelson Ex 3.4 p.65 q. 1-7.


Activity Outcomes Links to Pointers ActivitiesA19.6 Students use analytic methods to solve equations, they can simplify expressions by removing brackets and can simplify those requiring factorisation before simplification.

3c

Solving equations Students are able to use combinations of

backtracking, flowcharts and inverse operation to solve difficult linear equations.



Practice: Nelson Ex 3.5 p.69 q.1-7.

3d

Manipulating Formula Students recognise that formula can be

rearranged or transposed to make the subject suit their requirement

Students are able to use various methods to solve formula



4a Plotting points on a Cartesian Plane Students are able to recognise four

quadrants on the Cartesian plane Students are able to plot points in all

quadrants Students recognise coordinates are

ordered pairs

Linear Patterns and Simple Rules Students are able to identify ordered

A17a.5 Students plot the pairs of values obtained, inspect the result and comment on whether or how the quantities are related.


Practice: MFWA 11a p.308 q. 1-3.

Practice: MFWA 11b p.311 q. 1-


Activity Outcomes Links to Pointers Activitiespairs from points on the coordinate plane

Students are able to identify patterns derived from a list or coordinates on the Cartesian plane

Students are able to produce simple rules based on sets from the coordinate plane

Students are able to identify basic algebraic equations from coordinate (x,y) tables

A18a.5 Students generate formula from known data and use this pattern to generate sequences in two different scales

7.

4b

Determining linear equations Students are able to identify 1st

difference patterns from (x,y) tables Students can determine whether sets of

(x,y) coordinates form linear equations based on 1st difference patterns

Students can use 1st difference patterns to find equations of lines

A18a.5 Students can identify the linear rule connecting pairs on a graph. They can find the general rule to relate each element of a sequence to its position where one or two operations are involved.

A18a.6 Students can recognise the nature of a relationship by examining difference patterns and ratios from tables. They can recognise that a constant first difference pattern indicates that a relationship is linear and can relate the constant to the slope of the line.

Practice: MFWA 11c p.314 q. 1-4.

4c Plotting Points from equations Students understand a linear

relationship is a set of points that form a straight line when plotted.

Students can plot coordinates accurately in the Cartesian plane to form straight

A17a.6 The student recognises and represents linear relationships in tables symbols and graphs.

Practice: MFWA 11d p.315 q. 1-4.


Activity Outcomes Links to Pointers Activitieslines

Students can determine x or y values based on simple linear rules to form x,y coordinates

4d

Horizontal and Vertical Lines Students are able to recognise aspects of

a horizontal line when plotted on a Cartesian plane

Students are able to recognise aspects of a vertical line when plotted on a Cartesian plane

Students understand that for vertical lines the x value does not change

Students understand that for horizontal lines the y value does not change

Students can accurately plot horizontal and vertical lines

Students recognise parallel and perpendicular lines in relation to vertical and horizontal lines

A17a.6 The student recognises and represents linear relationships in tables symbols and graphs.

Practice: MFWA 11e p.317 q. 1-8.

5a Gradient of a line Students recognise the relationship

between vertical and horizontal change Students are able to determine values of

vertical and horizontal change given two coordinates

Students can recognise that gradient of a line is equal to vertical change(rise) ÷ horizontal change(run)

Students recognise that m in y=mx+c represents gradient and c represents the y intercept/vertical shift/constant.

Students understand that gradient is steepness of a line

A18a.6 Students can recognise the nature of a relationship by examining difference patterns and ratios from tables. They can recognise that a constant first difference pattern indicates that a relationship is linear and can relate the constant to the slope of the line.A17a.6 Students read and interpret the gradient and intercepts and can use these to sketch the graph of y=mx+c.



Activity Outcomes Links to Pointers Activities Students relate large values of m to

steep line and values less than 1 to a shallow line

A17a.6 Students can express the linear relationships by measuring rise, run and y intercept.

5b

Finding equations of lines from graphs Students are able to identify two key

coordinates from a given straight line Students are able to calculate the

gradient from these points Students are able to find the value of c

by using the y intercept Students are able to find the value of c

by solving an equation Students are able to construct the

equation of a line from two points

A17a.6 Students can use two points to find the linear relationship y=mx+c.

A17a.6 Students relate constants to the context to which variables come.

Practice: MFWA2 Ex 11G p.323 q. 1-3.

5c

Nature of a line Students recognise at a glance key

aspects of linear equations such as gradient, y intercept and equation.

Students can use this information for error checking when plotting points and drawing lines.

A17a.6 Students can use two points to find the linear relationship y=mx+c.

A17a.6 Students relate constants to the context to which variables come.

A17b.6 Students can recognise linear relationships between variables in symbolic expressions and graphs.

Practice: MFWA2 Ex 11H p.324 q. 1-5.

5d

Sketching Lines Students understand that sketching lines

is different to drawing lines Students can identify key aspects to

include on a sketch to uniquely identify a line

A17b.6 Students can recognise linear relationships between variables in symbolic expressions and graphs.

Practice: MFWA2 Ex 11I p.327 q. 1-7.

6a Revision Solving equations graphically

A17a.5, A17a.6A18a.5, A18a.6


Activity Outcomes Links to Pointers Activities Guess and Check Backtracking Inverse Operations Solving equations Manipulating Formula Plotting points on a Cartesian Plane Linear Patterns and Simple Rules Determining linear equations Plotting Points from equations Horizontal and Vertical Lines Gradient of a line Finding equations of lines from graphs Nature of a line Sketching Lines

A18b.6A19.5, A19.6

6b

Test Solving equations graphically Guess and Check Backtracking Inverse Operations Solving equations Manipulating Formula Plotting points on a Cartesian Plane Linear Patterns and Simple Rules Determining linear equations Plotting Points from equations Horizontal and Vertical Lines Gradient of a line Finding equations of lines from graphs Nature of a line Sketching Lines

A17a.5, A17a.6A18a.5, A18a.6A18b.6A19.5, A19.6


7a Probability – Understanding ChanceTerms & Estimation of Probability

Students understand the terms chance, probability, certain, uncertain, outcome,

C&D12.3 Understanding ChanceStudents distinguish certain from uncertain, likely from unlikely and can order events based on

Modelling: Making the connection between the real world and the number line.


Activity Outcomes Links to Pointers Activitieslikely, unlikely

Students can use a scale/number line to show estimations of probability

Students have examined various words that indicate probability and ordered them

personal experience. Practice: Nelson2 p.179 Ex 6.1 q1-10

Worksheets

7b

Probability – Understanding ChanceEqually likely Outcomes

Students can define ‘equally likely’Students understand the term ‘event’Students can construct a probability

statement based on PStudents recall that P must be 0 ≤ P ≤ 1Students recognise that P can be a

fraction or a decimalStudents can determine P for basic

problems

C&D12.3 Understanding ChanceStudents recognise equally and not equally likely events.

C&D12.4 Understanding ChanceStudents order events on the basis of numerical information.

Activity: Spinners (Kagan p.?)


Worksheets

7c

Probability – Venn Diagrams Students understand that a group of

things with the same properties are a set Students understand that things

belonging to a set are called elements of a set

Students recognise Venn diagrams Students recognise that all elements in

the Venn diagram are the universal set Students can populate basic Venn

diagrams using a range of problem solving skills.

C&D14.4 Students describe information from diagrams including Venn diagrams.

C&D14.5 Students use systematic strategies for ordering their data.


7d Probability – Venn Diagrams II Students are able to identify elements

from within worded problems Students can identify the number of

elements in the universal set from a

C&D14.5 Students use systematic strategies for ordering their data.



Activity Outcomes Links to Pointers Activitiesworded problem

Students can identify where elements of a Venn diagram overlap (intersection)

Students are able to correctly label Venn diagrams

8a

Exploring SetsStudents are able to construct sample

space gridsStudents are able to identify probabilities

and outcomes based on sample space grids

C&D12.6 Students use systematic strategies to calculate probabilities for two stage events using two way tables.

Practice: MFWA p.365 Ex 13B q1-5

8b

Tree Diagrams Students can define sample space Students can create a simple sample

spaceStudents can construct tree diagrams for

simple samplesStudents can determine probability of

events based on a tree diagramStudents understand that they need to

carefully read the question to determine if order is important and answer the question correctly

C&D12.6 Students use systematic strategies to calculate probabilities two stage events using tree diagrams.

Practice: MFWA p.369 Ex 13C q1-5

8c

SimulationsStudents can use simple experimentation

to obtain data and construct experimental probabilities

Students can compare experimental probability with theoretical probability

C&D12.5 Students begin to explore the notation of simulations using chance equipment.

C&D13a.6 Students conduct checks that data has been accurately recorded

Practice: MFWA p.369 Ex 13E q1-3

8d Estimating proportions using Sampling C&D13a.6 Students understand Practice: MFWA p.374 Ex 13F


Activity Outcomes Links to Pointers ActivitiesStudents are aware that at times

obtaining information from large groups is not practical

Students recognise the need to obtain samples from large populations for data gathering to obtain valid probabilities

Students understand the relationship between proportions in probability and theoretical probability

the difference between the sample and the population in situations in which the distinction is straightforward.

q1-5Or Worksheets

9a

Probability – Understanding ChanceModelling/Experimental/Proportional Probability

Students understand the difference between experimental and theoretical modelling

Students can construct a basic sample space

Students understand that experimental and theoretical modelling are related but the solutions for each will not necessarily agree

Tree Diagrams Students can define sample space Students can create a simple sample

spaceStudents can construct tree diagrams for

simple samplesStudents can determine probability of

events based on a tree diagramStudents understand that they need to

carefully read the question to determine if order is important and answer the question correctly

C&D12.5 Students begin to explore the notation of simulations using chance equipment.

C&D12.6 Students use systematic strategies to calculate probabilities two stage events using tree diagrams.




9b

Probability – Multiple Events C&D12.5 Understanding ChanceStudents are able to construct a sample space for a 1 step event allocating numerical values to possible events.

C&D12.6 Understanding ChanceStudents use tree diagrams to determine probability.

Modelling: One step and Multiple step problems. Counter in bag, dice, coin problems.

Practice: Nelson p.437 Ex 11.3 q1-6

Worksheets

9c

Revision Terms & Estimation of Probability Equally likely Outcomes Probability – Venn Diagrams Exploring Sets Tree Diagrams Simulations Estimating proportions using Sampling Modelling/Experimental/Proportional

Probability

C&D12.3, C&D12.4, C&D12.5, C&D12.6C&D13a.6,C&D14.4C&D15.5

9d

Test Terms & Estimation of Probability Equally likely Outcomes Probability – Venn Diagrams Exploring Sets Tree Diagrams Simulations Estimating proportions using Sampling Modelling/Experimental/Proportional

Probability

C&D12.3, C&D12.4, C&D12.5, C&D12.6C&D13a.6,C&D14.4C&D15.5

CHANCE ASSESSMENT 1


GSHS Yr 9 Programme & Lesson PlanSEMESTER 2 Term 3


1a

Statistics - Collecting and Organising DataCreating Tables

Students recognise that a table has a title, headings, units, totals, lines should be ruled

Students present information in table form such that it can be understood without further explanation

C&D 13a.3 Collect and Process DataStudents organise data in tables using simple tallies or organised lists

Pre-test: Students to create a table from random data on board.

Modelling: Information required in a table [OHP].


1b Statistics – Variables Students are able to distinguish

between quantitative/qualitative data Students can identify continuous,

discrete, ordinal and nominal data types


1c Statistics – Summarising and Representing dataGraphing

Students recognise that bar and column graphs are used for discrete data and line graphs and histograms for continuous data.

Students can draw and read column, bar and line graphs.

Students can read pie chartsStudents can use Excel to draw pie,

column, bar and line graphsStudents can plot cumulative frequency

graphs based on information from box plots

C&D 13a.4 Collect and Process DataStudents construct and use their own categories to answer specific questions

C&D 13a.5 Collect and Process DataStudents use a range of graphs such as Stem and leaf plots, bar graphs, compound column graphs and histograms


Group Discussion: How can we present data from previous class in a meaningful way?

Graph: Students use information from 1a,1b to create bar, pie and column graphs.

Application: Students reproduce information in poster form for display in


Activity Outcomes Links to Pointers Activitiesclass.Text: Nelson1 5.3, 5.4, 5.5, 5.7Text: [MFWA2 Ex 14A p.392]Text: [HOM2 Ex 10H p.455]

1d Statistics – Summarising and Representing dataMeasures of central tendency (Revision)

Students recognise there are three types of average – Mean, Mode and Median

Students can calculate Mean, Mode, Median & Range for simple examples

Students use the measures of central tendency to provide solutions for simple word problems

C&D 13b.4 Summarise and Represent DataStudents investigate a practical problem not obviously mathematical but where mathematics may help

Notes: Students copy notes on Mean/Mode/MedianModelling: Model calculation of mean mode and medianExcel: Use Excel to measure determine mean/mode/medianPractice: Nelson 1 Ex 5.8 Practice: [MFWA2 Ex 14C p.398]Practice: [MFWA2 Ex 14E p.406 q1-13]Practice: [HOM2 Ex 10B p.431]

2a Statistics – Summarising and Representing dataMeasures of central tendency

Students can read Stem and leaf plots and box plots to determine individual values

Students can use Stem and Leaf Plots to determine lowest & highest value, percentages within intervals, mode, range and median

Students can use Stem and Leaf plots to solve simple word problems

C&D 13a.5 Collect and Process DataStudents use a range of graphs such as Stem and leaf plots for univariate data


Broadcast: DM[HH p.240]

Text: Nelson1 Ex 5.9Text: [MFWA2 Ex 14D p.402]Text: [DM2 Ex14F p.242]

2b Statistics – Summarising and Representing dataMeasures of central tendency

Students can use box plots to plot four

C&D 13b.6 Students use the range of scores in a set of data as a measure of spread. They can calculate means and quartiles



Activity Outcomes Links to Pointers Activitiesquartiles accurately.

Students are able to visually observe inter-quartile range on box plots.

Students can determine the range and median from box plots.

Students can use Box plots to solve simple word problems

and use them to construct a box and whisker plot.

2c

Statistics – Interpreting dataStudents can distinguish data types from

line graphs and use estimation to give approximate values

Students are able to interpret line graphs with relation to mean mode and median

C&D 14.5 Students interpret a variety of graphs where the scales and axis must be read between calibrations.

Practice: MFWA2 Ex 14F p.408 q1-4

2d

Statistics – ScattergraphsStudents are able to construct scatter

plotsStudents are able to find a line of best fitStudents are able to find an equation of

the lineStudents are able to estimate mean,

mode and median based on data from the scatter plot

Students are able to recognise outliers

C&D 13b.6 Students use a scatter plot to show a relationship between bi-variate data and where warranted draw a line of best fit by eye.

A17a.6 Students read and interpret the gradient and intercepts and can use these to sketch the graph of y=mx+c.

A17a.6 Students can express the linear relationships by measuring rise, run and y intercept.

Practice: MFWA2 Ex 14G p.411 q1-3

3a

Revision Creating Tables Variables Graphing Measures of central tendency Interpreting data

C&D13a.3, C&D13a.4, C&D13a.5C&D13b.4, C&D13b.6C&D14.5A17a.6

3b Test C&D13a.3, C&D13a.4, CHANCE ASSESSMENT 2


Activity Outcomes Links to Pointers Activities Creating Tables Variables Graphing Measures of central tendency Interpreting data

C&D13a.5C&D13b.4, C&D13b.6C&D14.5A17a.6

3c

Measuring Angles Students can recognise and define

vertex & ray Students are able to name angles Students recognise acute, straight,

obtuse, reflex, right angles Students are able to use a protractor to

measure an angle. Students understand the standard units

of measure for angles (degrees, minutes, seconds)

S16.4 Students recognise figures and objects on the basis of spatial features using conventional geometric criteria.

S16.4 Students select figures and objects based on sides, edges, angles and faces

S16.5 Students explore and use angle relationships such as the sum of angles in a triangle or quadrilateral, vertically opposite angles, supplementary and complementary angles.

M9a.5 Students are practical in their choice of measuring things.

M9b.5 Students read and take accurate measurements using a variety of graduated scales.


3d Angles and Lines Students recognise complementary and

supplementary angles Students recognise vertically opposite

angles Students recognise C, F and Z angles

(co-interior, corresponding, alternate)

S16.5 Students explore and use angle relationships such as the sum of angles in a triangle or quadrilateral, vertically opposite angles, supplementary and complementary angles



Activity Outcomes Links to Pointers ActivitiesS16.6 Students identify and use angle relationships including those in isosceles and equilateral triangles and angles formed by a line through two or more parallel lines such as alternate, corresponding and co-interior angles

4aConstructing Polygons

Students can use a compass to construct various polygons

S15b.6 Students use a range of geometric tools and techniques to make accurate drawings


4b

Congruent Triangles Students are able to define congruent

triangle Students are able to recognise

components that create congruent triangles.

Students recognise and apply rules for congruency when comparing triangles (SSS,SAS,ASA,RHS)

S16.6 Students know the condition under which triangles are congruent and can tell what information they need about a triangle in order to produce on exactly the same


4cAngle Properties in Triangles

Students are able to apply knowledge of angles and triangles to calculate a range of angle sizes.

S16.6 Students identify and use angle relationships including those in isosceles and equilateral triangles and angles formed by a line through two or more parallel lines such as alternate, corresponding and co-interior angles


4d

Properties of Quadrilaterals Students can define quadrilateral Student recognise the six forms of

quadrilaterals Students can define the angle

properties of various quadrilaterals

S16.6 Students understand and use basic properties of triangles and rectangles.




5a

Similar Figures / Triangles Students are able to apply their

knowledge of scale to reproduce shapes

S15b.6 Students use a range of geometric tools and techniques to make accurate drawings

S16.6 Students know the conditions under which triangles are similar


5b

Applications of Similar Triangles Students are able to apply their

knowledge of scale and angle properties to reproduce similar triangles

Students recognise properties of similar triangles

Students are able to apply ratio rules to determine similar triangles

S16.6 Students know the conditions under which triangles are similar.

N8.6 Students use computations confidently using ratios.


5c

Pythagoras Theorem Students are able to define a right angle

triangle Students are able to name the sides of a

right angled triangle Students recognise Pythagoras’

theorem Students are able to apply Pythagoras’

theorem

M10a.5 Students can confidently apply Pythagoras’ theorem to calculate the side length of a right triangle given the lengths of the other two sides

Practice: MFWA2 Ex 4B,C p.92 q1-2, 1-11.

5d Pythagorean Triples Students can define Pythagorean Triple Students can recognise a Pythagorean

triple.

Finding the length of a side Students are able to rearrange

Pythagoras Theorem using algebraic rules

Students are able to apply number rules

M10a.5 Students can confidently apply Pythagoras’ theorem to calculate the side length of a right triangle given the lengths of the other two sides

Practice: MFWA2 Ex 4D p.97 q1-3.

Practice: MFWA2 Ex 4E p.98 q1-9.


Activity Outcomes Links to Pointers Activitiesto determine the length of a given size

Students can use a calculator to solve an algebraic equation to find the side of a right angle triangle.

6aApplications of Pythagoras M10b.6 Students use

Pythagoras’ theorem to solve practical measurement problems.

Practice: MFWA2 Ex 4F p.101 q1-5

6b

Composite Shapes Students can use Pythagoras in

conjunction with known measurement principles to solve perimeter problems of known shapes.

M10b.6 Students use Pythagoras’ theorem to solve practical measurement problems.

Practice: MFWA2 Ex 4G p.9104 q1-4.

6c

Revision Measuring Angles Angles and Lines Constructing Polygons Congruent Triangles Angle Properties in Triangles Properties of Quadrilaterals Similar Figures / Triangles Applications of Similar Triangles Pythagoras Theorem Pythagorean Triples Applications of Pythagoras

M9a.5M9b.5M10a.5M10b.6

S15b.6S16.4, S16.5, S16.6

N8.6

6d Test Measuring Angles Angles and Lines Constructing Polygons Congruent Triangles Angle Properties in Triangles Properties of Quadrilaterals Similar Figures / Triangles Applications of Similar Triangles

M9a.5M9b.5M10a.5M10b.6

S15b.6S16.4, S16.5, S16.6

N8.6

MEASUREMENT ASSESSMENT 1SPACE ASSESSMENT 1


Activity Outcomes Links to Pointers Activities Pythagoras Theorem Pythagorean Triples Applications of Pythagoras

7a

Converting UnitsStudents are able to move freely between

common standard units of measure (mm, cm, m, km, mL, L, °C, sec ,month ,week, day ,year ,hour ,min)

Students are able to use estimation to give approximate lengths of standard objects

Students are able to recognise appropriate units

Students are able to apply appropriate units

M10b.3 Students can predict or calculate the size of the parts in scale version

M9a.4 Students can express measures of length using common metric prefixes and appropriate notation

Practice: MFWA2 Ex 3A p.61 q1-5

7b Scale FactorStudents are able to determine factors of

scaleStudents are able to construct scale

ratios from scale diagramsStudents are able to use scale ratios to

determine actual measurements

M10b.4 Students use a whole number or unit number scale fraction to calculate or estimate measurements.

M10b.4 Students can predict or calculate the size of the parts in scale version

M9b.5 Students read and take accurate measurements from a variety of graduated scales

M11.4 Students uses the known size of familiar things to help make and improve estimates

M11.5 Students makes sensible estimate of length, area volume,



Activity Outcomes Links to Pointers Activitiesangle and time in standard units and identifies unreasonable estimates

7c

Perimeter of shapes Students can calculate the perimeter of

a variety of quadrilateral and triangular shapes.

M9a.4 Students understand the differences between perimeter and area

M10a.3 Students understands and measures perimeter directly and uses straightforward arithmetic to determine perimeter

M10a.4 Students use perimeter for a variety of polygons

Practice: Nelson2 Ex 4.4 p.111 q.1-10

7d

Circumference of a circle Students can use a calculator to find an

approximation of pi Students recognise that pi is a special

constant. Students can calculate the

circumference of a circle using radius and diameter

M10a.5 Students understands and applies directly circumference of a circle


8a Perimeter of shapes Students can calculate the perimeter of

a variety of shapes.

M9a.4 Students understand the differences between perimeter and area

M10a.3 Students understands and measures perimeter directly and uses straightforward arithmetic to determine perimeter

M10a.4 Students use perimeter



Activity Outcomes Links to Pointers Activitiesfor a variety of polygons

8b

Area of rectangles Students can find the area of a

rectangle using l x w

Students use appropriate units when calculating area.

Area of parallelograms and triangles I Students can find the area of

parallelograms and triangles

M10a.5 Students understands and applies directly areas based on rectangles and circles and uses similarity to solve.



8c

Area of a circle & composite shapes Students are able to use pi x r2

calculate area of a circle Students are able to use area of circles

and rectangles to determine the area of area of composite shapes

M10a.5 Students understands and applies directly areas based on rectangles and circles and uses similarity to solve.


8d

Surface Areas of Prisms, Pyramids and Cylinders

Students can determine the surface area of various shapes by deconstructing objects into nets

Students are able to apply known area formula to determine surface area of various objects

Students are able to use known mathematical processes to construct surface area from various area formula

M10a.5 Students use area formula to calculate the surface area of prisms and pyramids

M10a.6 Students use a wide range of formula to calculate the areas and surface areas of prisms and pyramids


9a Surface Areas of Prisms, Pyramids and Cylinders II

M10a.5 Students use area formula to calculate the surface area of prisms and pyramids

M10a.6 Students use a wide range of formula to calculate the

Worksheets


Activity Outcomes Links to Pointers Activitiesareas and surface areas of prisms and pyramids

9b

Volume of prisms Students can define Volume Students recognise that volume is 3

dimensional Students use the correct units for

volume problems eg mm3

Students define prisms as a three dimensional shape with parallel sides

Students can determine the volume of a prism using area of the base x height

M10a.5 Student understands and applies directly volume relationships for shapes based on prisms.


9c

Volume of Cylinders and Composite Shapes Students recognise that a cylinder is a

special prism. Students can determine the volume of

composite shapes based on their knowledge and understanding 3D shapes

Students can deconstruct composite shapes and use this knowledge to calculate volume.

M10a.5 Students understands and applies directly volume relationships for shapes based on prisms.

Practice: Nelson2 Ex 4.11 p.133 q.1-7 (cont.. from prev exercise)

9dVolume of Cylinders and Composite Shapes II M10a.5 Students understands

and applies directly volume relationships for shapes based on prisms.

WorksheetsMEASUREMENT ASSESSMENT 2 (ASSIGNMENT)


GSHS Yr 9 Programme & Lesson PlanTerm 4Activity Outcomes Links to Pointers Activities

1a

Review Assignment Converting Units Scale Factor Perimeter of shapes Circumference of a circle Perimeter of shapes Area of rectangles Area of parallelograms and triangles Area of a circle & composite shapes Surface Areas of Prisms, Pyramids and

Cylinders Volume of prisms Volume of Cylinders and Composite

Shapes

M9a.4

M9b.5

M10a.3, M10a.4, M10a.5, M10a.6M10b.3, M10b.4

M11.4, M11.5

1b

Validation Test Converting Units Scale Factor Perimeter of shapes Circumference of a circle Perimeter of shapes Area of rectangles Area of parallelograms and triangles Area of a circle & composite shapes Surface Areas of Prisms, Pyramids and

Cylinders Volume of prisms Volume of Cylinders and Composite

Shapes

M9a.4M9b.5

M10a.3, M10a.4, M10a.5, M10a.6M10b.3, M10b.4

M11.4, M11.5

MEASUREMENT ASSESSMENT 3

1c Right Angled Triangles Students are able to define a right

angled triangle

M10b.6 Students use trigonometric ratios for right triangles to find the unknown side



Activity Outcomes Links to Pointers Activities Students are able to name the sides of a

right angle triangle using trigonometric conventions (hyp,adj,opp)

or angle in both mathematical and practical problems.

1d

Trigonometric Ratios – Sine and Cosine Students recognise the trigonometric

ratios sine and cosine Students are able to solve basic

trigonometric problems using sine and cosine ratios

M10b.6 Students use trigonometric ratios for right triangles to find the unknown side or angle in both mathematical and practical problems.


2a

Trigonometric Ratios – Finding the Sides Students are able to calculate side

lengths using sine and cosine ratios

Finding the Hypotenuse Students can rearrange the

trigonometric ratio to find the hypotenuse


Practice: Nelson2 Ex 9.6 p.302 q.1-4Practice: Nelson2 Ex 9.7 p.305 q.1-12

2b

Trigonometric Ratios - Tangent ratio Students recognise Tan ratio Students can use the tan ratio to find

angles in a triangle Student can use the sine and cosine ratio

to find angles in a triangle Student can use their calculator

correctly to find angles using trigonometric ratios

Students can apply the tan ratio to find the sides and hypotenuse of a triangle




2c

Applications of Trigonometry Students recognise and use the acronym

SOH CAH TOA Students can identify the correct ratio to

solve a worded problem Students use the 5 step rule for solving





Activity Outcomes Links to Pointers Activitiestrigonometric equations

2d

Revision Right Angled Triangles Trigonometric Ratios – Sine and Cosine Trigonometric Ratios – Finding the Sides Finding the Hypotenuse Trigonometric Ratios - Tangent ratio Applications of Trigonometry

M10b.6

3a

Test Right Angled Triangles Trigonometric Ratios – Sine and Cosine Trigonometric Ratios – Finding the Sides Finding the Hypotenuse Trigonometric Ratios - Tangent ratio Applications of Trigonometry

M10b.6 MEASUREMENT ASSESSMENT 4

3b

Solving Simultaneous Equations Graphically I Students can define a point of

intersection Students are able to accurately graph

the equation of a line Students are able to accurately

determine the coordinates of points of intersections

Students can solve basic simultaneous equations using graph and points of intersection

A17a.6 Students identify and represent certain families of functions in tables including linear, quadratic and exponential functions.

A17a.6 Students understand how graphs can be used to solve equations and can do so when appropriate.

A17a.6 Students can solve two linear equations simultaneously and understand that the two lines can intersect in no, one or at an infinite number of points.

Practice: Nelson2 Ex 3.9 p.84 q.1-3Worksheets

3c Solving Simultaneous Equations Graphically II Students can solve simple simultaneous

equations using substitution and

A19.6 Students can show that two linear expressions are equivalent both by referring to the



Activity Outcomes Links to Pointers Activitieselimination methods original situation and by calling

on conventions of algebra to prove equivalence.

A19.6 Students can solve two linear equations simultaneously by substitution or elimination.

3dSolving Simultaneous Equations Graphically III

Students can solve simultaneous equations using substitution and elimination methods

A19.6 Students can solve two linear equations simultaneously by substitution or elimination.


4a

Solving Simultaneous Equations Graphically IV Students are able to use mathematical

process to derive equations from worded problems

Students are able to solve simultaneous equations using either substitution or elimination

A18a.6 Students use symbols to describe rules for linear relationships.

A18b.6 Students can use linear expressions to make general arguments.


4bRevision

Solving Simultaneous Equations Graphically

A17a.6A18a.6A19.6

4cTest

Solving Simultaneous Equations Graphically

A17a.6A18a.6A19.6


4d

Quadratic Functions - Plotting Points Students can substitute known values for

x into simple quadratic equations Students can complete tables from

quadratic equations Students can plot points from a table

onto a Cartesian plane for quadratic equations

A17a.6 Students identify and represent quadratic functions in tables symbols and graphs

A17a.6 Students follow symbolic rules to generate input/output pairs and draw graphs


5a Quadratic Functions – Graphing Parabolas A19.6 Students extend their Practice: Nelson2 Ex 12.3 p.393


Activity Outcomes Links to Pointers Activities Students understand negative and

positive coefficients of x2 invert the parabola

Students understand that coefficients of x2>1 will narrow the parabola and x2<1 will widen the parabola

Students recognise the effect of change in the constant will move the parabola up or down on the vertical axis

Students understand the effect of a perfect square on the parabola (eg. moving left or right)

understanding of factorising to quadratic expressions.

A19.6 Students factorise quadratic expressions and use the Null factor law to solve quadratic equations

A17a.6 Students investigate families of functions related to y=a(x+b)2 + c and describe the effects of changing the constants a,b,c.

q.1-5

5b

Quadratic Functions – Solving Graphically Students can define turning point, y

intercept and x intercept Students are able to determine the

turning point from a plotted parabola Students are able to determine the y

intercept from a plotted parabola Students are able to determine the x

intercept from a plotted parabola Students recognise that there may be 0,1

or 2 x intercepts on a plotted parabola


A17a.6 Students investigate families of functions related to y=a(x+b)2 + c and describe the effects of changing the constants a,b,c.


5c

Quadratic Functions – Null Factor Law Students recognise that axb=0 and

either a =0, b=0 or both =0 Students recognise in an equation

y=(x+a)(x+b) that the values of a & b give x values where y=0



5dQuadratic Functions – Null Factor Law II A19.6 Students factorise

quadratic expressions and use the Null factor law to solve quadratic equations

Worksheets



6a

Factorising Quadratic Equations Students understand that to factorise

quadratic equations ax2+bx+c must equal 0, where y=0.

Students understand that they must factorise ax2+bx+c before applying the null factor law

Students are able to apply previous factorisation skills to quadratic equations



6bFactorising Quadratic Equations II A19.6 Students factorise


Worksheets

6cFactorising Quadratic Equations III A19.6 Students factorise


Worksheets

6d

Problem solving using quadratics Students are able to expand and

manipulate equations so as LHS=0 Students are able to use the Null factor

law to determine x intercepts Students are able to decipher worded

problems, identify important features regarding quadratics and write equations to suit.



7aProblem solving using quadratics II A19.6 Students factorise


Worksheets

7b Revision Quadratic Functions - Plotting Points Quadratic Functions – Graphing

A17a.6A19.6


Activity Outcomes Links to Pointers ActivitiesParabolas

Quadratic Functions – Solving Graphically

Quadratic Functions – Null Factor Law Factorising Quadratic Equations Problem solving using quadratics

7c Revision cont.. A17a.6A19.6

7d

Test Quadratic Functions - Plotting Points Quadratic Functions – Graphing

Parabolas Quadratic Functions – Solving

Graphically Quadratic Functions – Null Factor Law Factorising Quadratic Equations Problem solving using quadratics

A17a.6A19.6


8a Space – Transformation and SymmetryTranslation

Students can define ‘translation’Students understand that an ordered pair

on a Cartesian plane is known as a coordinate

Students can plot coordinates on a Cartesian plane

Students understand that negative horizontal translation is to the left and positive is to the right.

Students understand that negative vertical translation is down and positive is up

Students understand A’ notation and how to construct Cartesian axes

S15c.6 Represent TransformationsStudents follow instructions for moving or sketching things according to one or more transformations.

Text: [N2 Ex 14.1 p.437]

Activity: Drawing students class positions on Cartesian planes

Activity: Student construct snoopy from Cartesian coordinates.

8b Space – Transformation and Symmetry S15c.6 Represent Text: [N2 Ex 14.2 p.440]


Activity Outcomes Links to Pointers ActivitiesDescribing Translation

Students can perform translations using notation (x, y) → (x + a, y + b)

Students can describe translations using notation (x, y) → (x + a, y + b)

TransformationsStudents follow instructions for moving or sketching things according to one or more transformations.

Text: [MFWA2 Ex 8AB p.213]Text: [EM1o Ex 3G p.124]

8c Space – Transformation and SymmetryRotations

Students can define ‘rotation’Students understand that the centre of

rotation, angle of rotation and direction of rotation are required before a rotation can occur

Students can determine the order of rotation of a regular polygon


Text: [N2 Ex 14.3 p.442]Text: [MFWA2 Ex 8D p.218]Text: [EM1o Ex 3I p.131]

8d Space – Transformation and SymmetryReflection

Students can define ‘reflection’Students can identify the line of

symmetry/mirror lineStudents can construct a reflected image

when provided a line of symmetryStudents can determine when an object is

not reflectedStudents can describe reflections along

the x axis, y axis, y=x and y=-x


Text: [N2 Ex 14.4,14.5 p.446]Text: [MFWA2 Ex 8C p.216]Text: [EM1o Ex 3H p.127]

9a Space – Transformation and SymmetryDilation

Students can define ‘dilation’, ‘enlargement/stretch’, ‘reduction/squash’

Students can identify the line of symmetry/mirror line

Students recognise that a dilation requires a scale factor and a centre of dilation.


Text: [N2 Ex 14.6 p.452]Text: [MFWA2 Ex 8E p.219]Text: [EM1o Ex 3J p.135]


Activity Outcomes Links to Pointers ActivitiesStudents can perform basic dilations

9b Space – Topology and NetworksNetworks

Students can define networks, nodes and arcs, vertices, paths, regions.

Students can construct Cayley tablesStudents can draw basic network

diagrams

S15a.5 Represent ArrangementsStudents use diagrams to represent arrangements and movements when solving problems

Broadcast: Describe the nature of networks and define critical terms. [N WE 2 p. 321]Text: [N1 Ex 10.1 p.323] Text: [MFWA2 Ex 8H p.224]

9c Space – Topology and NetworksTraversability of Networks

Students can identify passing, start/finish nodes, Eulerian pathways, fully/semi/not traversable networks

Students can modify networks to make them fully/semi traversable

Students identify traversable meaning all paths covered and no backtracking.


Text: [N1 Ex 10.2 p.326]

Activity: Students play hovercraft racer.

9d Space – Topology and NetworksTravel Routes

Students can identify Travelling salesperson problems

Students can identify that in a travelling salesperson problem that it is allowed to traverse arcs/paths more than once

Students understand that more than one solution may exist – but they are searching for the best/shortest route with the least backtracking

Students can define a Hamiltonian circuit


Text: [N1 Ex 10.3 p.329]Text: [MFWA2 Ex 8I p.226]

Activity: Students identify the shortest route to deliver newspapers in Girrawheen.

10a Revision Translation Describing Translation

S15a.5S15c.6


Activity Outcomes Links to Pointers Activities Rotations Reflection Dilation Networks Traversability of Networks Travel Routes

10b Test Translation Describing Translation Rotations Reflection Dilation Networks Traversability of Networks Travel Routes

S15a.5S15c.6

SPACE ASSESSMENT 2


APPENDIX A – OUTCOMES AUDITWorking Mathematically

Number Measurement Chance and Data

Space Pre-algebra/Algebra

WM3.4

WM3.5

WM4.4

WM4.5

WM5.4

WM5.5

N6a.4Term 1 (1c)

N6b.3Term 1 (2d)

N6b.4Term 1 (2c,3d)

N6.5Term 1 (1a,2a,3d,4a,4b,5c)Term 2 (1a)

N6.6Term 1 (4c,4d,5d,6a,6b)Term 2 (1c,2a,2b)

N7.4Term 1 (2b,2d,4b)

N7.5Term 1 (1d,2a,2d,3a)

N7.6Term 1 (5d,6a,6b)

M9a.4Term 3 (7a,7c,8a)

M9a.5Term 3 (3c)

M9b.4Term 3 (7b)

M9b.5Term 3 (7b)

M10a.3Term 3 (7c,8a)

M10a.4Term 3 (7c,8a)

M10a.5Term 3 (5c,5d,7d,8b,8c,8d,9a,9b,9c,9d)

M10a.6Term 3 (8d,9a)

M10b.3Term 3 (7a)

M10b.4Term 3 (7b)

M10b.6

C&D12.3Term 2 (7a,7b)

C&D12.4Term 2 (7b)

C&D12.5Term 2 (8c,9a,9b)

C&D12.6Term 2 (8a,8b,9a,9b)

C&D13a.3Term 3 (1a)

C&D13a.4Term 3 (1c)

C&D13a.5Term 3 (1c,2a)

C&D13a.5Term 2 (8c,8d)

C&D13b.4Term 3 (1d)

C&D13b.6

S15a.5Term 4(9b,9c,9d)

S15b.6Term 3(4a,5a)

S15c.6Term 4(8a,8b,8c,8d,9a)

S16.4Term 3 (3c)

S16.5Term 3 (3c,3d)

S16.6Term 3 (3d,4b,4c,4d,5a,5b)

A17a.5 Term 2 (2d,4a,4b)

A17a.6 Term 2 (4c,4d,5a,5b,5c)Term 3(2d)Term 4(3b,4d,5a,5b)

A18a.5 Term 1 (7b,8b)

A18a.6 Term 2 (4b,5a)Term 4 (4a)

A18b.5 Term 1 (7b)

A18b.6 Term 1 (9c)Term 2 (3b,4a,5c,5d)Term 4 (4a)

A19.5Term1 (7c,7d,7e,8c)Term 2 (2d,3a,3b,3c)

A19.6Term1 (8a,8d,9a,9b)Term 2 (3a,3b,3c,3d)Term 4

APPENDIX A | 48

N8.5Term 1(2a,2d,5a)

N8.6Term 1 (5b,5c,6c)Term 2 (1b)Term 3 (5b)

Term 3 (6a,6b)Term 4 (1c,1d,2a,2b,2c)

M11.4Term 3 (7b)

M11.5Term 3 (7b)

Term 3 (2b,2d)

C&D14.4Term 2 (7c)

C&D14.5Term 2(7c,7d)Term 3 (2c)

(3c,3d,5a,5b,5c,6a,6b,6c,6d,7a)

APPENDIX A | 49

yr 9 lesson plan – term 3members.iinet.net.au/~rmiln/girrawheen/yr9 programme-adv 2008… ·...

Documents