Mcc Yr 10 Measurement Maths Course Outline Feb19 10

Last Updated: Jan 21st 2010

MURRAYVILLE COMMUINITY COLLEGE

YEAR 10 Mathematics

Semester ONE

Dimensions Topics MQ Chapters

No of Weeks

Number Ch 1 Rational & irrational numbers, ratio, surds Application task

1 3

Space and Geometry Application of Measurement formulae, unit conversion and relationships between quantities

Trig Application Task and Bearings

12 2

Measure and Data Investigative task Trig Graphs 12 2

Structure Ch 3 Linear Graphs, Ch 7 Sim Eq’n, Ch 4&5 Quad 2, 7, 1, 12, 1,1, 2, 2

Work Matem’ly Ch 14 Data Analysis 14 4

Semester TWO

Dimensions Topics MQ Chapters

No of Weeks

Number Ch 8 Exponentials and their functions 8 Term 2

3 weeks

Space and Geometry Circle Geometry 10, 11 3

Measure and Data Ch 13Probability 12, 13 3

Structure Ch 2 Algebra ad equations, Ch 6 Variation 2, 6 3, 1

Work Mathem’ly Structure & Working mathematically across all topics 8

Subject title: YEAR 10 MathematicsMain Dimension Measurement: The content for this topic will enable students to reach each of the following progression Points

conversion between units and between derived units use of pythagoras theorem to calculate the length of a hypotenuse

use of symmetry and scale to calculate side lengths in triangles

calculation and application of ratio, proportion and rate of change such as concentration, density and the rate of filling a container

use of pythagoras theorem to calculate the length of a side other than a hypotenuse

use of trigonometric ratios to calculate unknown sides in a right-angled triangle

conversion between degrees and radians, and use of radians when calculating arc length and area of sectors

use of pythagoras theorem in three-dimensional applications

calculation of unknown angle in a right-angled triangle using trigonometric ratios

Extra and Alternative Activities and Resources to Drawn from as NeededStandard 5Estimate and measurePeople Count: book and/or CD

34 Area, 40 Mass and density, 41 Time: calendar, 42 Time: short durations

Interactive learning for concepts and skills

Metric conversions,

Learning objects

Area of triangles, Area of compound shapes, Inside cubes

Active Learning: Measurement, Chance & Data

M7 Areas for sport, M8 Shadow clocks, M9 Pendulum, M10 History of Melbourne, M11 Perpetual calendar, M15 Cooling coffee, M16 Olympic speeds, M17 Scale factors, M20 Floating, M21 Estimating metric lengths and areas. M22 Estimating irregular areas, M24 Tangram areas, M26 Pick’s rule, M28 Bicycle chain, M29 Non-circular rollers, M35 Volume by displacement, M37 Melbourne’s water, M39 Time and longitude, M40 Tripping around Victoria, M41 Using maps and timetables, M42 The traveller’s problem, M43 Furniture and curtains, M44 A brick barbie and bounce wall, M45 To rain or not to rain

CD5 Estimating lengths using means, CD6 Estimating fractions of lengths, CD9 Reaction times, CD10 The toy car, CD13 Hands – spans and area,

National Library of virtual manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html

standards.nctm.org/document/eexamples/index.htm

5.2 Understanding Distance, Speed, and Time Relationships

The Value of Time

Recreation

Develop and use formulas (for area, perimeter, circles, surface area, volume, rates)Maths300

43 Area of a Circle (Calcs), 44 Area of a Triangle, 45 Circumference of a Circle,

People Count: book and/or CD

35 Area: triangles & parallelograms, 36 Area: circles, 37 Volume, capacity and cuboids, 38 Volume & surface area: prisms and cylinders, 39 Volume: pyramids & cones,


Perimeter of polygon, Circumference, Bike distances and speed, Rectangle, Rectangle area, W,H,A&P, Some areas, Quad areas, Circle and square, Circle area, Value of π, Area of polygon, Cuboids, Box volumes, Boxes, Calendar, Clock, Time calculations, Daylight, Sundial, Time/distance/speed, Planets, Scale/area/volume,

Learning objects

Measures


M12 Walking and running, M13 Bike or car speeds, M14 A rolling ball, M18 Eight fold-up boxes, M19 Making a litre, M23 Rectangles: constant perimeter or area, M25 Design a shape, M27 The relationship c = πd, M30 A historical approach to the value of π, M31 Count the circle areas, M32 Outdoor parallelograms, M33 Outdoor triangles, M34 Side lengths of a box of given volume, M36 Shapes with 1 litre capacity, M38 Estimating small volumes,

http://illuminations.nctm.org/Activities.aspx Free software from the internet

Circle string, Circle ratios, Area parallelograms, Area Trapezoids, Area Triangles, Circle area, Areas in Geometry (rectangle, parallelogram and triangle),

Working Mathematically: Investigations (CC)

Unit 16: Packing containers

Standard 6Estimate and measure (considering scale and errors)People Count: book and/or CD.

34 Area, 40 Mass and density, 41 Time: calendar, 42 Time: short durations

Learning objects

Measures


6.3 Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figure

7.3 Understanding Ratios of Areas of Inscribed Figures


M46 Imperial units and conversions, M47 Solar system model, M48 Earth-moon model and phases, M49 Sports fields, M51 Renovating a garden, M52 Kite areas, M53 Athletics tracks, M54 The Gregorian calendar, M55 Racetrack simulation game, M56 The speed of sound, M57 Experiments on a slope, M58 Finding densities, M59 Area of a dam, M60 Distances you can’t measure directly, M61 As the crow flies, M62 Plane table surveying, M63 A large protractor, M64 Estimating angles and slopes, M65 The height-measurer, M66 Triangle of forces, M67 Ski slopes,

Use formulas (for area, perimeter, circles, surface area, volume, rates)Maths300

80 Cylinder Volumes, 81 Biggest Volume, 100 Planets, 109 Newspaper Pathways,

Problem Solving Task Centre

84 Rectangle Nightmare, 85 Time Swing, 126 Planets, 156 Photo Angles, 219 The Hole In The Triangle,


35 Area: triangles & parallelograms, 36 Area: circles, 37 Volume, capacity and cuboids, 38 Volume & surface area: prisms and cylinders, 39 Volume: pyramids & cones,


Boxes, Sun position, Max volume cone, Volume of pyramid, Decibels, Surface area to volume, Pyramid and cone, Truncated pyramid, Truncated cone, Floating, Day of year, Earth-moon,

RIME: Measurement, Space, C&D

18 Biggest volume

Maths at work

21 Creating an image, 22 Making maps,

Pythagoras’ theoremMaths300 (CC) Lesson plans

157 Pythagoras & Other Polygons,

Problem Solving Task Centre

97 Pythagoras Rods, 155 ‘64 = 65’, 175 Pythagoras, 189 Pythagoras 3, 196 Cross & Square,


47 Pythagoras


Squares and triangle, Pythagoras, Pythagorean triples,


M68 Dissection proofs, M69 Proving the theorem for Pythagoras, M70 Pythagorean triples, M71 Pythagorean quadruples, M72 Pythagoras and circles, M73 Finding side lengths,

Geometry Everywhere (MAV) Teaching ideas and worksheets with answers

0, 54, worksheet 76;


6.5 Understanding the Pythagorean Relationship Using Interactive Figures

http://illuminations.nctm.org/Activities.aspx

Pythagorean theorem,

http://nlvm.usu.edu/en/nav/vlibrary.html

Duration of subject: 4 weeks Domain: MathematicsTopic TWO: Measurement and Trigonometry

Outcomes Supporting Dimensions

ICT

Spread sheets

Graphics calculator

Applets

Power Point

Outcome 1:Students should be able to define key terms, identify knowledge needed for a task.Students should be able to describe and explain relationships involved in trigonometric relationships, calculations and graphs.

Outcome 2:

Structure: Graphs and relations – investigating relationships between area, perimeter and volume; volume, mass and density then sine, cos and tan and their graphs

Working MathematicallyIdentifying variables and constraints, using graphs, diagrams and tables of values. Formulating conjectures and testing for these. Forming conclusions based on evidence. Formulating a procedure based on prior knowledge and identifying what needs to be learned before proceeding.


students should be able to analyse and evaluate evidence from practical and theoretical investigations related to the topic

Outcome 3:Students should make correct and appropriate use of technology.

Communication

Power point

Group/class discussion along with formal and informal reporting.

Written reports for assessment.

NumberSurds, Pythagoras, estimation and error

SpaceInterpreting data of a special nature and transferring that information into special relations. Eg bearings, identifying triangles in a shape to work out distances using Pythagoras’ rule.

Weeks T Sequence)

Learning Focus(concepts / knowledge / skill)

MathICT

Teaching and Learning activities & strategies /

Resources(hyperlinked / texts / embedded documents)

Home Work Assessment

TERM ONE Week FourLesson One

Errors in Measurement and Calculations

Determine Prior Knowledge

Math Quest Ch 8 PP 338-339


CoMS Measurement WS 1 from http://www.fi.edu/school/math2/april.html#measure

Exercise 8A

Math Quest Chapters 8 Are you ready? (page 337)

Sign off of Exercises

CoMS #1

Lesson Two Revision of Formulae

Understand the concepts associated with perimeter, area, volume.

Refer to Chapter 8 pp 340-370


Area parallelograms, Area Trapezoids, Area Triangles

http://www.bbc.co.uk/skillswise/numbers/measuring/

volume/quiz.shtml

Exercise 8B Sign off of Exercises

Weeks T Sequence)


MathICT




Lesson Three and Four

Understand and apply the concepts associated with perimeter, area, volume, mass, density


http://www.learnalberta.ca/Launch.aspx?content=

%2fcontent%2fmec%2fhtml%2findex.html

1. Calculating the path width around an estate

2. Estimation and Tollerance

Exercise 8C Sign off of Exercises

CoMS #2

TERM ONE Week FiveLesson One

Understand Pythagorus rule Quest worked examples



Pythagorean theorem_ investigate the approximation using Pythagoras’ theorem and using the circumference measurement of the distance around the earth.

http://nlvm.usu.edu/en/nav/vlibrary.html (great circle measurements and unit conversion)

Exercise 8D Sign off of Exercises

CoMS #3


Weeks T Sequence)


MathICT




Lesson Two Understand how and when to apply Pythagorus rule

http://argyll.epsb.ca/jreed/math9/strand3/pythagoras.htm

http://www.ies.co.jp/math/java/geo/pythasvn/pythasvn.html

http://www.ies.co.jp/math/java/geo/pytha2/pytha2.html

http://www.ies.co.jp/math/java/geo/pythafv/pythafv.html

Exercise 8E

Homework appltet

See Below


CoMS #4


Understand and apply the concepts associated with perimeter, area, volume, mass, density in conjunction with measurement rules.

CoMS WS 4 from http://www.fi.edu/school/math2/april.html#measure Activity based on

http://www.shodor.org/interactivate/activities/

surfaceareaandvolume/

Students explore relationships between volume and change in side lengths and graph results. Formulate conclusions about the effect of doubling lengths on volume and SA etc.

Work Sheet of Excel Spreadsheet

Exercise 8F Sign off of Exercises

CoMS #4

TERM ONE Week SixLesson One

Assessment of measurement, number and calculation skills.

Test on measurement rules Review TEST

Weeks T Sequence)


MathICT




Lesson Two Review of the Use of degrees and radians as units of measurement for angles and convert between units

Use Pythag theorem and trig ratios to obtain lengths of sides, angles and the area of right-angled triangles

Use degrees and radians and convert between units

Scale drawing

Angles and the calculator (page 475) WE 1a-b, 2, 3a-b, 4a-b

CoMS #5


46 Scale drawing & trigonometry,

Ex 12A Angles and the calculator (page 479


CoMS #5


Using trigonometric ratios to find side lengths (page 480)

Using trigonometric ratios to find angles (page 486)

WE 4a-b, 5

WE 6a-b, 7a-b

Maths300 (CC) Lesson plans

108 Trigonometry Walk.

Ex 12B Using trigonometric ratios to find side lengths


TERM ONE Week SevenLesson One

Working mathematically

Select and use technology in various combinations to assist in mathematical inquiry, to manipulate and represent data, to analyse functions and carry out symbolic manipulation.


Trigonometry, Triangle, Projectiles, Great circle distance, Venus, Clifftop, River, Sun position, Daylight, Sundial, Sound waves

Learning objects

Ex 12B Using trigonometric ratios to find side angles


Lesson Two Practice using trig ratios Mathletics to practice trig and measurement skills

CoMS #6

Ex 12C Using trig ratios to find angles


CoMS #6

Weeks T Sequence)


MathICT





Carry out computations to a required accuracy in terms of decimal places and/or significant figures

Spread sheet

Applications (page 493)

Maths at work (MAV) Student text on CD

23 Measuring from afar

Spreadsheets from Interactive Learning (MAV)

Perspective, Prism, Cylinder, Pyramid, Truncated pyramid, Cone, Truncated cone, Solar house,

Max volume cone, Volume of pyramid, Decibels, Surface area to volume, Pyramid and cone.

Ex 12D Applications (page 496)


Assignment

TERM TWO Week OneLesson One

Understand how to interpret Bearings to assist in working on mathematical tasks (page 500)

Use Pythagoras' theorem Structure

WE 10a-b, 11a-b, 12a-c, 13a-c


M74 Latitude, longitude and trigonometry, M75 Identities and equations, M76 The sliding ladder, M77 Practical projectiles, M78 Finding angles, M79 Trigonometry out of this world!

Ritemaths - Shot on Goal on Moodle

Ex 12E Bearings (page 505)


Lesson Two Number

Computations involving natural numbers, integers and finite decimals using mental and/or written algorithms to a required accuracy in terms of decimal places and/or significant figures

Explore to introduce the idea of radian measure and the approximation of the circumference for small angles and the opposite side of the circle triangle subscribed and circumference for angles near 90 degrees and the adjacent side of the triangle subscribe. Use the link:

http://illuminations.nctm.org/LessonDetail.aspx?id=L575

The unit circle – quadrant 1 (page 508)

WE 14, 15, 16a-d

Ritemathe – Sine and Cosine Transformations Xsl spreadsheet on Moodle

Ex 12F The unit circle – quadrant 1 (page 512)


CoMS #10


Looking for patterns and recording as tables of values and graphs.

Understanding Circular functions (page 514)

WE 17a-b, 18a-b, 19a-b, 20a-b

Ex 12G Circular functions (page 519)


CoMS #11

Weeks T Sequence)


MathICT




TERM TWO Week TWOLesson One

Working Mathematically CoMS #8

Graphs of y = sin x and

y = cos x (page 521)

SAC 1A Investigation.

Ex 12H Graphs of

y = sin x and y = cos x (page 522)

CoMS #8

SAC 1A Investigation Report.

Lesson Two EXAM Practice and Techniques

Working Mathematically

TSSM Exam style questions

Summary (page 524) + Chapter review (page 526)

Mathletics

Practice for test exam MathQuest.


Study Techniques SAC 1B:

Application Task

SAC 1B:

Application Task

Homework Applets

Number

http://www.ronblond.com/M10/rootAP/index.html (square root applet)


Measurement


http://www.shodor.org/interactivate/activities/ShapeExplorer/

http://www.mathsnet.net/geometry/solid/nets.html

http://www.shodor.org/interactivate/activities/surfaceareaandvolume/

http://www.bbc.co.uk/skillswise/numbers/measuring/volume/quiz.shtml

http://www.learnalberta.ca/Launch.aspx?content=%2fcontent%2fmec%2fhtml%2findex.html

Pythagouas’ Rule

http://matti.usu.edu/nlvm/nav/frames_asid_164_g_4_t_3.html?open=instructions

http://www.ies.co.jp/math/java/geo/pythasx/pythasx.html

http://www.ies.co.jp/math/java/geo/pitha1/pitha1.html

http://www.ies.co.jp/math/java/geo/pythafor/pythafor.html

http://www.ies.co.jp/math/java/geo/pythathr/pythathr.html

http://www.ies.co.jp/math/java/geo/pythashi/pythashi.html

http://argyll.epsb.ca/jreed/math9/strand3/pythagoras.htm

Trigonometry

http://argyll.epsb.ca/jreed/math9/strand3/trigonometry.htm

VCAL

Year 10 Measurement (3 weeks)

Towards VELS 4 Towards VELS 5 Towards VELS 6

Practical measurement and money

http://www.bbc.co.uk/skillswise/numbers/measuring/perimeterareaandvolume/arearectangle/quiz.shtml

http://www.mathsnet.net/geometry/solid/nets.html

http://www.bbc.co.uk/skillswise/numbers/measuring/volume/quiz.shtml

Formulas & Pythagoras’ theorem in 2D

Active Learning (Measurement, C&D) M68 Pythagorean dissections

Maths at Work #13 Leisure costs Active Learning (Measurement, C&D) M69 Proving

Active Learning (Measurement, C&D) M70 Pythagorean triples

Maths at Work #13 Leisure costs Active Learning (Measurement,C&D) M32 Outdoor parallelograms

Active Learning (Measurement)

Maths at Work #13 Leisure costs Active Learning (Measurement,C&D) M33 Outdoor triangles

Active Learning (Measurement,C&D) M72 Pythagaoras & circles

Maths at Work #13 Leisure costs Active Learning (Measurement,C&D) M49 Sports fields

Active Learning (Measurement,C&D) M73 Finding side lengths

Maths at Work #13 Leisure costs Active Learning (Measurement,C&D) M51 Renovating a garden

Active Learning (Measurement,C&D) M54 Gregorian calendar

Mcc Yr 10 Measurement Maths Course Outline Feb19 10

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