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Transcript of Strand - mathsbooks.netmathsbooks.net/Activities for Graphics Calculator/9 - 10 A… · Web...
Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Basic introductions to the graphics calculator (TI, Casio, Sharp)
1. Using Graphics Calculators for Basic Operations
(CMA CD/website*)
2. Enhancing Learning with a Graphics Calculator (Casio) Barry Kissane
3. Essential TI-83 Graphics Calculator Companion andEssential Casio 9850/plus Graphics Calculator Companion David Main (Cambridge UP)
*www.canberramaths.org.au under Post-Primary Resources
Home pages
education.ti.com
www.casio.edu.shriro.com.au
sharp-world.com/products/calculator/education
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Revision four operations
Expansion of grouping symbols binomial products collecting terms brackets preceded by a
negative
Factorising review common factors special cases (perfect
squares and difference of two squares)
grouping in pairs factorising trinomials,
including coefficients of x2 other than 1
Access to Algebra 4 Unit 1 Lowe (Curriculum Corporation)
Mathematics at Work Vol 1 Lowe
Enrichment Maths Anne Joshua
Work Samples – National Mathematics Profiles
Working Mathematically with Algebra Thelma Perso
Checking your working out,eg graphing (x+1)(x–1) and x2–1 together
Mathsyear2000.org
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Algebraic fractions
Four operations, including the use of factorising to simplify
Fraction mode
Algebra Change the subject of formulas
Substitution into formulas
Compound Interest(CMA CD/website)
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Linear equations
Include equations with grouping symbols pronumerals on both
sides fractions
Apply to solution of word problems
Solve linear inequations and graph solution sets on a number line
Lesson Enders (WA Test Papers)
Access to Algebra 3 & 4
Assignments in Junior Algebra Books 1 and 2
CFS Blackline Masters
MCTP Vol 1: p216 – Algebra Walk
Use of graphs to solve equations;show the importance of the point of intersection of two lines when the pronumeral is on both sides
Use of shading to show inequalities
SchoolKit – REX
FX Graph
FX Equation
Excel – Spinners
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Solve simultaneous linear equations graphically and
algebraically (by substitution and elimination methods)
apply to solution of word problems
Solve quadratic equations include factorisation,
completing the square and formula methods
apply to solution of word problems
Use graphics or tables to find the intersection of the two lines to give a solution
Access to Algebra – QTP Creating a Tapestry
Simultaneous Equations(CMA CD/website)
Use of graphics/tables to find the roots of a quadratic equation and show what happens to them as the discriminant changes
SchoolKit – Linear Systems by Graphing
Use any graphing packages – FX Graph, Autograph, Graphmatica, etc
SchoolKit Exploring the Discriminant Program the Quadratic Formula
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Coordinate geometry find gradient, length,
midpoint of an interval; geometric applications of these
Graph straight lines using table of values;
gradient/intercept method; x and y intercept method
include horizontal and vertical lines
graph line from equation, write equation from graph
Find the equation of a line given: y-intercept, gradient one point, gradient two points
Transpose between different forms
Recognise linear relationships
Investigate conditions for parallel/perpendicular lines, and find equations using these properties
Graph quadratic functionsFind x/y intercepts, axis of symmetry, vertex, maximum/minimum values. Solve word problems
Battleships
MCTP Vol 1: p213 – Algebra walk
Practical activities, eg slope of ramps, stairs, etc
Graphing software graphics calculators Spinners equation plotter (Green Globs) Graphmatika FX Graph Autograph
Linear experiments – Hooke’s Law
Speed Graphs in MCTP Vol 2, p567
Graphing/table capabilities
Using Graphics Calculators for Coordinate GeometryGraphing Straight LinesGuess the Line StarburstTangrams and Straight LinesWhat’s My LineWalk the Walk (CBR)(CMA CD/website)
Coordinate Geometry Art from The Sub-Atomic Project, QAMT or CMA CD/website
CBR worksheets (TI and Casio) Walk the Line Match the Graph Shape Up
Access to Algebra
SpeedingTemperature ConversionsWhich FuelSketching QuadraticsParabolic AerobicsAlien Attack (CMA CD/website)
ALG1CH5, ALG1PRT1 Apps (TI)
Graphing packages – see Strategies column
SchoolKit – Linear Graphing Intro
FX Graph
FX Equation
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Indices index laws, including
negative, fractional and algebraic indices
scientific notation and the calculator
Access to Algebra
Work Samples – National Mathematics Profiles
Scientific mode on the calculator
Algebra Surds the Real Number
System definition of surds addition and
subtraction of surds multiplication and
division of surds binomial products rationalising the
denominator
Constructing surds on the number line
AAANSWER program (TI) to convert decimal answers to their surd equivalent
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Algebra Sketching Other Graphs relate shape of graph
to equation
parabola cubic hyperbola circle exponential
Identify key features intercepts turning points discontinuities,
asymptotes
Changes to graph shape and position
Translations, dilations, etc
Graphing software graphics calculators Spinners equation plotter
(Green Globs) Graphmatika (shareware) FX Graph Autograph
Graphics and table capabilities
A Classic Example – The Hare and TortoiseLet’s Be RationalThe Best Shape for a Can(CMA CD/website)
Getting Started with Data LoggingSteve Arnold (CMA CD)
TRANSFORM App (TI)
DYNA MENU (Casio)
SUB command (Sharp)
SPGRAPH program (TI)(CMA CD)
Software packages – see Strategies column
SchoolKit – Exponential Regression
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT OpportunitiesChance and Data Probability
Experimental probability
Theoretical probability
Using tables for multiple events
Simple tree diagrams
Probability trees for independent events and dependent events
Multiplication and addition rules
Venn diagrams
Chance and Data Investigations Volumes 1 and 2 Lovitt and Lowe (Curriculum Corporation) eg Lotto game
Various simulations
Maths for the Real WorldUnit 6
MCTP, pp 561, 549, 555
Random-number generator, graphing of data, analysis tools
Probably Finding π(CMA CD/website)
Probability Simulation App (TI)
Enhancing Learning with a Graphics Calculator (Casio) Barry Kissane
Probability and Statistics with the TI-83 Plus Jones and Barling (Cambridge UP)
Getting Started with Probability and Statistics Steve Arnold(CMA CD)
SchoolKit Happy Birthday to You Too Tree Diagrams and
Permutations
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT OpportunitiesChance and Data Statistics
Collecting data
Organising data (including grouped data) into frequency tables
Analysing data measures of central
tendency
Display data histogram polygon for both
frequency and cumulative frequency
stem plots box-and-whisker
diagrams
Use cumulative frequency polygon (ogive) to find
median quartiles percentiles deciles
Measures of spread range interquartile range standard deviation
Normal-distribution curve
ABS website, publications and software
MCTP, Chance and Data and Real-Life Data – social statistics, eg smoking, drink driving, mortality
Use of data from students, eg personal measurements, birthdays, etc
Statistics and graphing capabilities, analysis tools
Enhancing Learning with a Graphics Calculator (Casio) Barry Kissane
Probability and Statistics with the TI-83 Plus Jones and Barling (Cambridge UP)
Reaction Times and StatisticsStatistics from Birthdays (CMA CD/website)
Getting Started with Probability and Statistics Steve Arnold(CMA CD)
Excel – use spreadsheets to enter data and do calculations; also use graph wizard
SchoolKit Box-and-Whisker Plots Normal-Distribution Curve Stem-and-Leaf Plots and
Histograms Standard Deviation
www.abs.gov.au
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Number Consumer Arithmetic
Earning, saving, borrowing and spending money
Simple interest
Compound interest
Depreciation
Foundations Maths for the Real World Pearson Education
Graphing capabilities, tables
TVM calculators
Enhancing Learning with a Graphics Calculator (Casio) Barry Kissane
Time, Value, Money on the TI-83Hofman and Hofman (TI)
Compound Interest(CMA CD/website)
AMORT program (TI)(CMA CD/website)
CelSheet App (TI)
Excel Spinners spreadsheets
SchoolKit Investment Calculator Analysing Financial Data
Bank websiteswww.stgeorge.com.auwww.allhomes.com.auwww.combank.com.auwww.dollarsandsense.com.au (worksheets & lesson plans available)
Coolmath.com
Moneyopolis.com
Sharemarket Game
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities Measurement Trigonometry of
right-angled triangles
Establish the trig ratios (sin, cos, tan) by measuring sides of triangles (similarity)
Use calculator to find trig ratios angles when the ratio
is known
Find unknown sides and angles in right triangles
Construct appropriate diagrams
Solve word problems
Understand bearings; angles of elevation or depression; solve problems
Exact values of the trig functions for 30, 45, 60
Trig ratios for angles of any magnitude
Sine rule, cosine rule
Area of a triangle
Problems involving right triangles
Definition by unit circle; include four quadrants/boundaries
MCTP Vol 1: Trig Walk, p219
MCTP Vol 2: pp 371, 379
Make/use a clinometer, compass
Use as a scientific calculator SchoolKit – Meaning of Trigonometric Functions
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities Measurement Review
perimeter and area of plane shapes, including circles
Pythagoras’ Theorem units and conversions rounding and keeping accuracy until the last step
Working Mathematically with Measurement Thelma Perso
Use as a scientific calculator
Use a table to enter formula to find the length of hypotenuse and shorter sides
Can also use formulas in lists (TI)
AreaForm App (TI)
Excel – use a spreadsheet to enter formula to find the length of hypotenuse and shorter sides
Searching the internet for the history of Pythagoras’ Theorem
Searching the internet for the history of π
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities Measurement Surface area
Identifying prisms and pyramids – naming and drawing.
Surface area of: prisms, including
cylinders pyramids, including
cones spheres composite solids
Practical applications of surface area
Plastic models
MCTP Vol 1: Baby in the car, p105
Make 3D shapes
Use a table or graph to compare surface-area-to-volume ratios of different-sized spheres
Given a fixed surface area of glass, how do you maximise the volume of a fish tank? – use a table or graph to model this
The Best Shape for a Tin Can (CMA CD/website)
CabriJr App (TI)
Getting Started with Interactive Geometry Steve Arnold(CMA CD)
Use Excel spreadsheets to compare surface-area-to-volume ratios of different-sized spheres
Given a fixed surface area of glass, how do you maximise the volume of a fish tank? – use an Excel spreadsheet to model this
Geometers Sketchpad CAD packages
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities Measurement Volume
Volume of: prisms and cylinders pyramids and cones spheres composite solids
Practical applications of volume
MCTP Vol 2: Drink Can Design, p617
Volume of a cylinder – folding an A4 sheet vertically and horizontally
Make 3D shapes
Use a table or graph to compare surface-area-to-volume ratios of different-sized spheres
Given a fixed surface area of glass, how do you maximise the volume of a fish tank? – use graphs and/or tables to model this
The Best Shape for a Can(CMA CD/website)
CabriJr App (TI)
Getting Started with Interactive Geometry Steve Arnold(CMA CD)
Use Excel spreadsheets to compare surface-area-to-volume ratios of different-sized spheres
Given a fixed surface area of glass, how do you maximise the volume of a fish tank? – use an Excel spreadsheet to model this
Geometers Sketchpad
CAD packages
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Space Similarity
Similar figures
Investigating similarity
Ratio and proportion
Conditions for similar triangles
Sides, areas and volumes of similar figures
Drawing package CabriJr App (TI)
Getting Started with Interactive Geometry Steve Arnold(CMA CD)
Any drawing package, such as Geometers Sketchpad or Mathsplot
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Optional Polynomials
Including: four operations Remainder Theorem Factor Theorem finding zeroes sketching
Algebraic and graphical methods
Graphing capabilities and graph tools
Let’s Be Rational(CMA CD/website)
SPCUBIC and SPQUINT programs (TI)(CMA CD/website)
SchoolKit – Polynomial Exploration
Graphing packages
Excel – Spinners
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Year 9 and 10 Course – Level 1Strand Content Strategies Graphics Calculators ICT Opportunities
Optional Geometry
Congruent triangles conditions deductive problems
and proofs
Circles parts properties theorems deductive problems
and proofs
CabriJr App (TI)
Getting Started with Interactive Geometry Steve Arnold(CMA CD)
Geometers Sketchpad
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