Mathscape 9 Teaching Program Page 1

Mathscape 9 Teaching Program Page 1

Stage 5

MATHSCAPE 9

Term / Chapter / Time
1 / 1. Rational numbers / 2 weeks / 8 hrs
2. Algebra / 2 weeks / 8 hrs
3. Consumer arithmetic / 2 weeks / 8 hrs
4. Equations, inequations and formulae / 2 weeks / 8 hrs
2 / 5. Measurement / 3 weeks / 12 hrs
6. Data representation and analysis / 2 weeks / 8 hrs
7. Probability / 1 week / 4 hrs
8. Indices / 3 weeks / 12 hrs
4 / 9. Geometry / 2 weeks / 8 hrs
10. The linear function / 2 weeks / 8 hrs
11. Trigonometry / 3 weeks / 12 hrs
12. Co-ordinate geometry / 2 weeks / 8 hrs

Published by Macmillan Education Australia. © Macmillan Education Australia 2004.

Mathscape 9 Teaching Program Page 29

Chapter 1. Rational numbers

Substrand

Rational numbers /

Text references

Mathscape 9
Chapter 1. Rational Numbers
(pages1–25) /

CD reference

Significant figures
Recurring decimals
Rates

Duration

2 weeks / 8 hours

Key ideas

Round numbers to a specified number of significant figures.
Express recurring decimals as fractions.
Convert rates from one set of units to another. /

Outcomes

NS5.2.1 (page 67): Rounds decimals to a specified number of significant figures, expresses recurring decimals in fraction form and converts rates from one set of units to another.

Working mathematically

Students learn to

·  recognise that calculators show approximations to recurring decimals e.g. displayed as 0.666667 (Communicating)
·  justify that (Reasoning)
·  decide on an appropriate level of accuracy for results of calculations (Applying Strategies)
·  assess the effect of truncating or rounding during calculations on the accuracy of the results (Reasoning)
·  appreciate the importance of the number of significant figures in a given measurement (Communicating)
·  use an appropriate level of accuracy for a given situation or problem solution (Applying Strategies)
·  solve problems involving rates (Applying Strategies)

Knowledge and skills

Students learn about

·  identifying significant figures
·  rounding numbers to a specified number of significant figures
·  using the language of estimation appropriately, including:
§  rounding
§  approximate
§  level of accuracy
·  using symbols for approximation e.g.
·  determining the effect of truncating or rounding during calculations on the accuracy of the results
·  writing recurring decimals in fraction form using calculator and non-calculator methods
e.g. , ,
·  converting rates from one set of units to another
e.g. km/h to m/s, interest rate of 6% per annum is 0.5% per month /

Teaching, learning and assessment

·  TRY THIS
Fermi Problem (page 10): Estimation problem solving
Desert Walk (page 15): Problem solving
Passing Trains (page 20): Travel graph problem
·  FOCUS ON WORKING MATHEMATICALLY
Art, Magic Squares and Mathematics (page 20): If you would like to learn how to make a magic square start with John Webb's article in the June 2000 journal of nrich, the mathematics enrichment page of the Millenium Mathematics Project based at the University of Cambridge http://nrich.maths.org/mathsf/journalf/jun00/art2/ There are many sites which will provide instructions but this is a good one to begin. From January 2004 the nrich web home page can be found at http://nrich.maths.org/public/viewer.php?obj_id=1376 and the home page of the project at http://mmp.maths.org/index.html
The web page http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Durer.html will get you straight to Albrecht Durer. You can scroll through the text to get a look at his engraving Melancholia which is highlighted in blue. From here you can go to the main index and look for "magic squares" under topics, or check out Leonhard Euler under mathematicians.
·  EXTENSION ACTIVITIES, LET’S COMMUNICATE, REFLECTING (page 23)
·  CHAPTER REVIEW (page 24) a collection of problems to revise the chapter.

Technology

Significant Figures: this spreadsheet in designed to round off a given number to a desired number of significant figures. To be used with the text.
Recurring Decimals: this spreadsheet converts recurring decimals to fractions.
Rates: this spreadsheet deals with rates and ratios in units.

Chapter 2. Algebra

Substrand

Algebraic techniques

/

Text references

Mathscape 9
Chapter 2. Algebra
(pages 26–66) /

CD reference

Simplify (with fractional indices)
Expand
Railway tickets

Duration

2 weeks / 8 hours

Key ideas

Simplify, expand and factorise algebraic expressions including those involving fractions or with negative and/or fractional indices. /

Outcomes

PAS5.2.1 (page 88): Simplifies, expands and factorises algebraic expressions involving fractions and negative and fractional indices.

Working mathematically

Students learn to

·  describe relationships between the algebraic symbol system and number properties (Reflecting, Communicating)
·  link algebra with generalised arithmetic
e.g. use the distributive property of multiplication over addition to determine that (Reflecting)
·  determine and justify whether a simplified expression is correct by substituting numbers for pronumerals (Applying Strategies, Reasoning)
·  generate a variety of equivalent expressions that represent a particular situation or problem (Applying Strategies)
·  check expansions and factorisations by performing the reverse process (Reasoning)
·  interpret statements involving algebraic symbols in other contexts e.g. spreadsheets (Communicating)
·  explain why an algebraic expansion or factorisation is incorrect e.g. Why is the following incorrect?(Reasoning, Communicating)

Knowledge and skills

Students learn about

·  simplifying algebraic expressions involving fractions, such as
·  expanding, by removing grouping symbols, and collecting like terms where possible, algebraic expressions such as
·  factorising, by determining common factors, algebraic expressions such as /

Teaching, learning and assessment

·  TRY THIS
Flags (page 35): Algebraic problem solving
Overhanging the overhang (page 42): Practical
Railway Tickets (page 58): Complete a table and find a rule
·  FOCUS ON WORKING MATHEMATICALLY
Party Magic (page 59): Teachers may wish to down load the Party Magic with Algebra worksheet in the technology folder for chapter 2 Algebra. This worksheet explores the algebraic structure of the games using technology.
The web link http://atschool.eduweb.co.uk/ufa10/tricks.htm at Birmingham in England has great resources for students and teachers.
The web page http://www.umassmed.edu/bsrc/tricks.cfm has good links and lots of activites to show that maths really can be fun.
For the addicted to fun and games check out Martin Gardner's books at http://thinks.com/books/gardner.htm
·  EXTENSION ACTIVITIES, LET’S COMMUNICATE, REFLECTING (page 61)
·  CHAPTER REVIEW (page 62) a collection of problems to revise the chapter.

Technology

Simplify (with fractional indices): algebraic program that simplifies algebraic terms. To be used with the worksheets. Also to be used with the Focus on Working mathematically section.
Expand: this program will expand a given algebraic expression.
Railway Tickets: worksheet to use with the “Try This” problem on page 58.

Chapter 3. Consumer arithmetic

Substrand

Consumer arithmetic /

Text references

Mathscape 9
Chapter 3. Consumer Arithmetic
(pages 67–107) /

CD reference

Money

Duration

2 weeks / 8 hours

Key ideas

Solve simple consumer problems including those involving earning and spending money.
Calculate simple interest and find compound interest using a calculator and tables of values.
Use compound interest formula.
Solve consumer arithmetic problems involving compound interest, depreciation and successive discounts. /

Outcomes

NS5.1.2 (page 70): Solves consumer arithmetic problems involving earning and spending money.
NS5.2.2 (page 71): Solves Consumer arithmetic problems involving compound interest, depreciation, and successive discounts.

Working mathematically

Students learn to

·  read and interpret pay slips from part-time jobs when questioning the details of their own employment (Questioning, Communicating)
·  prepare a budget for a given income, considering such expenses as rent, food, transport etc
(Applying Strategies)
·  interpret the different ways of indicating wages or salary in newspaper ‘positions vacant’ advertisements e.g. $20K (Communicating)
·  compare employment conditions for different careers where information is gathered from a variety of mediums including the Internet
e.g. employment rates, payment (Applying Strategies)
·  explain why, for example, a discount of 10% following a discount of 15% is not the same as a discount of 25% (Applying Strategies, Communicating, Reasoning)

Knowledge and skills

Students learn about

·  calculating earnings for various time periods from different sources, including:
-  wage
-  salary
-  commission
-  piecework
-  overtime
-  bonuses
-  holiday loadings
-  interest on investments
·  calculating income earned in casual and part-time jobs, considering agreed rates and special rates for Sundays and public holidays
·  calculating weekly, fortnightly, monthly and yearly incomes
·  calculating net earnings considering deductions such as taxation and superannuation
·  calculating a ‘best buy’
·  calculating the result of successive discounts /

Teaching, learning and assessment

·  TRY THIS
Sue’s Boutique (page 72): Problem Solving
Telephone Charges (page 92): Problem Solving
Progressive Discounting (page 98): Investigation
·  FOCUS ON WORKING MATHEMATICALLY
Sydney Market prices in 1831 (page 102): The purpose of the learning activities is for students to think about the cost of living in Australia today using market prices in 1831 as a starting point. As an extension students are given opportunity to explore inflation and how the consumer price index (CPI) is calculated. An invitation to a member of the Economics staff to your class could be stimulating. Teachers should note that the further apart the years being compared, the less valid it is to use the relative prices of goods in those years to measure the standard of living. This point is well made in the article by Nell Ingalls published on the web site http://www.sls.lib.il.us/reference/por/features/98/money.html. This is a useful source of information on the value of money.
A good summary of how the CPI is calculated in Australia can be found at http://www.aph.gov.au/library/pubs/mesi/features/cpi.htm
·  EXTENSION ACTIVITIES, LET’S COMMUNICATE, REFLECTING (page 105)
·  CHAPTER REVIEW (page 106) a collection of problems to revise the chapter.

Technology

Money: series of worksheets to use with spreadsheets to explore Commission, Net Income, Piece Work, Salaries, Wages and a Weekly Budget.

Chapter 4. Equations, inequations and formulae

Substrand

Algebraic techniques /

Text references

Mathscape 9
Chapter 4: Equations, inequations and formulae (pages 108–40) /

CD reference

Evaluating
Floodlighting

Duration

2 weeks / 8 hours

Key ideas

Solve linear and simple quadratic equations of the form
Solve linear inequalities /

Outcomes

PAS5.2.2 (page 90): Solves linear and simple quadratic equations, solves linear inequalities and solves simultaneous equations using graphical and analytical methods.

Working mathematically

Students learn to

·  compare and contrast different methods of solving linear equations and justify a choice for a particular case (Applying Strategies, Reasoning)
·  use a number of strategies to solve unfamiliar problems, including:
-  using a table
-  drawing a diagram
-  looking for patterns
-  working backwards
-  simplifying the problem and
-  trial and error (Applying Strategies, Communicating)
·  solve non-routine problems using algebraic methods (Communicating, Applying Strategies)
·  explain why a particular value could not be a solution to an equation (Applying Strategies, Communicating, Reasoning)
·  create equations to solve a variety of problems and check solutions (Communicating, Applying Strategies, Reasoning)
·  write formulae for spreadsheets (Applying Strategies, Communicating)
·  solve and interpret solutions to equations arising from substitution into formulae used in other strands of the syllabus and in other subjects. Formulae such as the following could be used:
(Applying Strategies, Communicating, Reflecting)
·  explain why quadratic equations could be expected to have two solutions (Communicating, Reasoning)
·  justify a range of solutions to an inequality (Applying Strategies, Communicating, Reasoning)

Knowledge and skills

Students learn about

Linear and Quadratic Equations
·  solving linear equations such as
·  solving word problems that result in equations
·  exploring the number of solutions that satisfy simple quadratic equations of the form
·  solving simple quadratic equations of the form
·  solving equations arising from substitution into formulae
Linear Inequalities
·  solving inequalities such as /

Teaching, learning and assessment

·  TRY THIS
A Prince and a King (page 129): Two Ancient Problems
Arm Strength (page 132): Formulae Investigation
Floodlighting by formula (page 136): Formulae Investigation
·  FOCUS ON WORKING MATHEMATICALLY
Bushfires (page 137): Teachers may wish to use a spreadsheet to evaluate F given C and vice versa. Go to the Evaluatingthesubject.xls spreadsheet in the technology folder for Chapter 4. There is also a useful worksheet. Extension students could discuss whether F=9C/5+32 is a formula or an equation and what constitutes the difference -- see page 136 on Floodlighting for example. For newspaper reports of the fires try the Sydney Morning herald web site http://www.smh.com.au/. If you type 'Sydney bushfires' into a search engine you will get a range of options.
http://www.gi.alaska.edu/ScienceForum/ASF13/1317.html will give you a short account how the two men Daniel Fahrenheit and Anders Celcius constructed their scales. This will be very useful link with the study of science.
·  EXTENSION ACTIVITIES, LET’S COMMUNICATE, REFLECTING (page 138)
·  CHAPTER REVIEW (page 139) a collection of problems to revise the chapter.

Technology

Evaluating: students analyse a spreadsheet and then design their own.
Floodlighting: activity to complement the “Try This” problem on page 136.

Chapter 5. Measurement

Substrand

Algebraic techniques /

Text references

Mathscape 9
Chapter 5:.Measurement
(pages 141–205) /

CD reference

Perigal
Measuring plane shapes
Circle measuring

Duration

3 weeks / 12 hours

Key ideas

Develop formulae and use to find the area of rhombuses, trapeziums and kites.
Find the area and perimeter of simple composite figures consisting of two shapes including quadrants and semicircles.
Find area and perimeter of more complex composite figures. /

Outcomes

MS5.1.1 (page 126): Use formulae to calculate the area of quadrilaterals and find areas and perimeters of simple composite figures.
MS5.2.1 (page 127): Find areas and perimeters of composite figures.

Working mathematically

Students learn to

·  identify the perpendicular height of a trapezium in different orientations (Communicating)
·  select and use the appropriate formula to calculate the area of a quadrilateral (Applying Strategies)
·  dissect composite shapes into simpler shapes (Applying Strategies)
·  solve practical problems involving area of quadrilaterals and simple composite figures (Applying Strategies)
·  solve problems involving perimeter and area of composite shapes (Applying Strategies)
·  calculate the area of an annulus (Applying Strategies)
·  apply formulae and properties of geometrical shapes to find perimeters and areas e.g. find the perimeter of a rhombus given the lengths of the diagonals (Applying Strategies)
·  identify different possible dissections for a given composite figure and select an appropriate dissection to facilitate calculation of the area
(Applying Strategies, Reasoning)

Knowledge and skills