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Brenda's Measurement topic Yr 10 Math 2010

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- 1. Last Updated: Jan 21st 2010 MURRAYVILLE COMMUINITY COLLEGE YEAR 10 Mathematics Semester ONE Dimensions Topics MQ No of Chapters Weeks Number Ch 1 Rational & irrational numbers, ratio, surds Application 1 3 task Space and Geometry Application of Measurement formulae, unit conversion and 12 2 relationships between quantities Trig Application Task and Bearings 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 No of Chapters 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
- 2. Subject title: YEAR 10 Mathematics Main 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 Needed Standard 5 Estimate and measure People 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
- 3. 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, Interactive learning for concepts and skills 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 Active Learning: Measurement, Chance & Data 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 6 Estimate 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 standards.nctm.org/document/eexamples/index.htm 6.3 Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figure
- 4. 7.3 Understanding Ratios of Areas of Inscribed Figures Active Learning: Measurement, Chance & Data 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, 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, Interactive learning for concepts and skills 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’ theorem Maths300 (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, People Count: book and/or CD 47 Pythagoras Interactive learning for concepts and skills Squares and triangle, Pythagoras, Pythagorean triples, Active Learning: Measurement, Chance & Data M68 Dissection proofs, M69 Proving the theorem for Pythagoras, M70 Pythagorean triples, M71 Pythagorean quadruples, M72 Pythagoras and circles, M73 Finding side
- 5. lengths, Geometry Everywhere (MAV) Teaching ideas and worksheets with answers Page 50, 54, worksheet 76; standards.nctm.org/document/eexamples/index.htm 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: Mathematics Topic TWO: Measurement and Outcomes Supporting Dimensions Trigonometry ICT Outcome 1: Structure: Graphs and relations – Working Mathematically Students should be able to define investigating relationships between Identifying variables and constraints, key terms, identify knowledge area, perimeter and volume; using graphs, diagrams and tables of Spread sheets needed for a task. volume, mass and density then sine, values. Formulating conjectures and Students should be able to describe cos and tan and their graphs testing for these. Forming Graphics calculator and explain relationships involved in conclusions based on evidence. trigonometric relationships, Formulating a procedure based on Applets calculations and graphs. prior knowledge and identifying what needs to be learned before Power Point Outcome 2: proceeding. students should be able to analyse Number Space Communication and evaluate evidence from practical Surds, Pythagoras, estimation and Interpreting data of a special nature and theoretical investigations error and transferring that information Power point related to the topic into special relations. Eg bearings, identifying triangles in a shape to Group/class discussion along with Outcome 3: work out distances using Pythagoras’ formal and informal reporting. Students should make correct and rule. appropriate use of technology. Written reports for assessment.
- 6. Weeks T Learning Focus Teaching and Learning Home Work Assessment Sequence) (concepts / knowledge / skill) activities & strategies / Math Resources ICT (hyperlinked / texts / embedded documents) Errors in Measurement and Math Quest Ch 8 PP 338-339 Exercise 8A Sign off of Exercises TERM ONE Calculations Week Four http://illuminations.nctm.org/Activities.aspx Math Quest CoMS #1 Lesson One Determine Prior Knowledge Chapters 8 Are you CoMS Measurement WS 1 from ready? (page 337) http://www.fi.edu/school/math2/april.html#measure Lesson Two Revision of Formulae Refer to Chapter 8 pp 340-370 Exercise 8B Sign off of Exercises Understand the concepts http://illuminations.nctm.org/Activities.aspx associated with perimeter, area, Area parallelograms, Area Trapezoids, Area Triangles volume. http://www.bbc.co.uk/skillswise/numbers/measuring/ volume/quiz.shtml Lesson Understand and apply the concepts CoMS Measurement WS 2 from Exercise 8C Sign off of Exercises Three and associated with perimeter, area, http://www.fi.edu/school/math2/april.html#measure Four volume, mass, density CoMS #2 http://www.learnalberta.ca/Launch.aspx?content= %2fcontent%2fmec%2fhtml%2findex.html 1. Calculating the path width around an estate 2. Estimation and Tollerance
- 7. Weeks T Learning Focus Teaching and Learning Home Work Assessment Sequence) (concepts / knowledge / skill) activities & strategies / Math Resources ICT (hyperlinked / texts / embedded documents) Understand Pythagorus rule Quest worked examples Exercise 8D Sign off of Exercises TERM ONE Week Five CoMS Measurement WS 3 from CoMS #3 Lesson One http://www.fi.edu/school/math2/april.html#measure http://illuminations.nctm.org/Activities.aspx 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) Lesson Two Understand how and when to apply http://argyll.epsb.ca/jreed/math9/strand3/pythagoras.htm Exercise 8E Sign off of Exercises Pythagorus rule http://www.ies.co.jp/math/java/geo/pythasvn/pythasvn.html Homework appltet CoMS #4 http://www.ies.co.jp/math/java/geo/pytha2/pytha2.html See Below http://www.ies.co.jp/math/java/geo/pythafv/pythafv.html Lesson Understand and apply the concepts CoMS WS 4 from Exercise 8F Sign off of Exercises Three and associated with perimeter, area, http://www.fi.edu/school/math2/april.html#measure Four volume, mass, density in Activity based on CoMS #4 conjunction with measurement http://www.shodor.org/interactivate/activities/ rules. 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
- 8. Weeks T Learning Focus Teaching and Learning Home Work Assessment Sequence) (concepts / knowledge / skill) activities & strategies / Math Resources ICT (hyperlinked / texts / embedded documents) Assessment of measurement, Test on measurement rules Review TEST TERM ONE number and calculation skills. Week Six Lesson One Lesson Two Review of the Use of degrees and Angles and the calculator (page 475) WE 1a-b, 2, 3a-b, 4a- Ex 12A Angles and Sign off of Exercises radians as units of measurement for b the calculator (page CoMS #5 angles and convert between units 479 CoMS #5 Use Pythag theorem and trig ratios People Count: book and/or CD to obtain lengths of sides, angles 46 Scale drawing & trigonometry, and the area of right-angled triangles Use degrees and radians and convert between units Scale drawing Lesson Using trigonometric ratios to find WE 4a-b, 5 Ex 12B Using Sign off of Exercises Three and side lengths (page 480) trigonometric ratios WE 6a-b, 7a-b Four to find side lengths Using trigonometric ratios to find Maths300 (CC) Lesson plans angles (page 486) 108 Trigonometry Walk. Working mathematically Interactive learning for concepts and skills Ex 12B Using Sign off of Exercises TERM ONE trigonometric ratios Week Seven Select and use technology in various Trigonometry, Triangle, Projectiles, Great circle distance, Venus, Lesson One Clifftop, River, Sun position, Daylight, Sundial, Sound waves to find side angles combinations to assist in mathematical inquiry, to Learning objects manipulate and represent data, to analyse functions and carry out symbolic manipulation.
- 9. Weeks T Learning Focus Teaching and Learning Home Work Assessment Sequence) (concepts / knowledge / skill) activities & strategies / Math Resources ICT (hyperlinked / texts / embedded documents) Lesson Two Practice using trig ratios Mathletics to practice trig and measurement skills Ex 12C Using trig Sign off of Exercises ratios to find angles CoMS #6 CoMS #6 Lesson Carry out computations to a Maths at work (MAV) Student text on CD Ex 12D Applications Sign off of Exercises Three and required accuracy in terms of 23 Measuring from afar (page 496) Four decimal places and/or significant Assignment Spreadsheets from Interactive Learning (MAV) figures Perspective, Prism, Cylinder, Pyramid, Truncated pyramid, Spread sheet Cone, Truncated cone, Solar house, Applications (page 493) Max volume cone, Volume of pyramid, Decibels, Surface area to volume, Pyramid and cone. Understand how to interpret WE 10a-b, 11a-b, 12a-c, 13a-c Ex 12E Bearings Sign off of Exercises TERM TWO Bearings to assist in working on (page 505) Week One Active Learning: Measurement, Chance & Data Lesson One mathematical tasks (page 500) M74 Latitude, longitude and trigonometry, M75 Identities and equations, M76 The sliding ladder, M77 Practical projectiles, Use Pythagoras' theorem Structure M78 Finding angles, M79 Trigonometry out of this world! Ritemaths - Shot on Goal on Moodle Lesson Two Number Explore to introduce the idea of radian measure and the Ex 12F The unit Sign off of Exercises approximation of the circumference for small angles and circle – quadrant 1 Computations involving natural CoMS #10 the opposite side of the circle triangle subscribed and (page 512) numbers, integers and finite circumference for angles near 90 degrees and the decimals using mental and/or adjacent side of the triangle subscribe. Use the link: written algorithms to a required accuracy in terms of decimal places http://illuminations.nctm.org/LessonDetail.aspx?id=L575 and/or significant figures The unit circle – quadrant 1 (page 508) WE 14, 15, 16a-d Ritemathe – Sine and Cosine Transformations Xsl spreadsheet on Moodle
- 10. Weeks T Learning Focus Teaching and Learning Home Work Assessment Sequence) (concepts / knowledge / skill) activities & strategies / Math Resources ICT (hyperlinked / texts / embedded documents) Lesson Looking for patterns and recording Understanding Circular functions (page 514) Ex 12G Circular Sign off of Exercises Three and as tables of values and graphs. functions (page Four WE 17a-b, 18a-b, 19a-b, 20a-b 519) CoMS #11 Working Mathematically CoMS #8 Ex 12H Graphs of CoMS #8 TERM TWO Week TWO Graphs of y = sin x and y = sin x and y = SAC 1A Lesson One cos x (page 522) Investigation y = cos x (page 521) Report. SAC 1A Investigation. Lesson Two EXAM Practice and Techniques TSSM Exam style questions Practice for test exam MathQuest. Working Mathematically Summary (page 524) + Chapter review (page 526) Mathletics Lesson Study Techniques SAC 1B: SAC 1B: Three and Four Application Task Application Task
- 11. Homework Applets Number http://www.ronblond.com/M10/rootAP/index.html (square root applet) http://illuminations.nctm.org/Activities.aspx Measurement http://illuminations.nctm.org/Activities.aspx 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
- 12. 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

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