Workplace+&+Apprenticeship+Mathematics+Grade+11

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toc =Measurement= A1. Solve problems that involve SI and imperial units in surface area measurements and verify the solutions. __Achievement Indicators__ 1.1 Explain, using examples, the difference between volume and surface area. 1.2 Explain, using examples, including nets, the relationship between area and surface area. 1.3 Explain how a referent can be used to estimate surface area. 1.4 Estimate the surface area of a 3-D object. 1.5 Illustrate, using examples, the effect of dimensional changes on surface area. 1.6 Solve a contextual problem that involves the surface area of 3-D objects, including spheres, and that requires the manipulation of formulas.

A2. Solve problems that involve SI and imperial units in volume and capacity measurements.
__Achievement Indicators__ 2.1 Explain, using examples, the difference between volume and capacity. 2.2 Identify and compare referents for volume and capacity measurements in SI and imperial units. 2.3 Estimate the volume or capacity of a 3-D object or container, using a referent. 2.4 Identify a situation where a given SI or imperial volume unit would be used. 2.5 Solve problems that involve the volume of 3-D objects and composite 3-D objects in a variety of contexts. 2.6 Solve a problem that involves the capacity of containers. 2.7 Write a given volume measurement expressed in one SI unit cubed in another SI unit cubed. 2.8 Write a given volume measurement expressed in one imperial unit cubed in another imperial unit cubed. 2.9 Determine the volume of prisms, cones, cylinders, pyramids, spheres and composite 3-D objects, using a variety of measuring tools such as rulers, tape measures, calipers and micrometers. 2.10 Determine the capacity of prisms, cones, pyramids, spheres and cylinders, using a variety of measuring tools and methods, such as graduated cylinders, measuring cups, measuring spoons and displacement. 2.11 Describe the relationship between the volumes of: 2.12 Illustrate, using examples, the effect of dimensional changes on volume. 2.13 Solve a contextual problem that involves the volume of a 3-D object, including composite 3-D objects, or the capacity of a container. 2.14 Solve a contextual problem that involves the volume of a 3-D object and requires the manipulation of formulas.
 * cones and cylinders with the same base and height
 * pyramids and prisms with the same base and height.

NCTM
[|Thinking out of the Box . . . Problem] Student explorations and mathematical generalizations of a classic pre-calculus and calculus problem "The box problem."
 *  Second Look - Volume of a Rectangular Prism **

[|What Else Can You Do with an Open Box?] Starting with the classic Open Box problem, we present extensions of this problem that can be used in high school mathematics classes. We also challenge high school teachers to use this process of problem analysis in their own practice as a way to enrich the content of their lessons and as a means of individualized professional development.

[|Sharing Teaching Ideas: Optimization: A Project in Mathematics and Communication] The mathematics in the problem addresses many of the NCTM's Standards, as well as reform-calculus initiatives. The opportunity for meaningful communication about the mathematics is a vital component that was met well in the context of the assignment.

[|Illuminations Lesson: Popcorn Anyone?] This lesson can be used for students to discover the relationship between dimension and volume. Students create two rectangular prisms and two cylinders to determine which holds more popcorn. Students then justify their observation by analyzing the formulas and identifying the dimension(s) with the largest impact on the volume.

=Geometry= B1. Solve problems that involve two and three right triangles. __Achievement Indicators__ 1.1 Identify all of the right triangles in a given illustration for a context. 1.2 Determine if a solution to a problem that involves two or three right triangles is reasonable. 1.3 Sketch a representation of a given description of a problem in a 2-D or 3-D context. 1.4 Solve a contextual problem that involves angles of elevation or angles of depression. 1.5 Solve a contextual problem that involves two or three right triangles, using the primary trigonometric ratios. media type="custom" key="11247258"

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B2. Solve problems that involve scale. __Achievement Indicator__s 2.1 Describe contexts in which a scale representation is used. 2.2 Determine, using proportional reasoning, the dimensions of an object from a given scale drawing or model. 2.3 Construct a model of a 3-D object, given the scale. 2.4 Draw, with and without technology, a scale diagram of a given object. 2.5 Solve a contextual problem that involves scale.

B3. Model and draw 3-D objects and their views. __Achievement Indicators__ 3.1 Draw a 2-D representation of a given 3-D object. 3.2 Draw, using isometric dot paper, a given 3-D object. 3.3 Draw to scale top, front and side views of a given 3-D object. 3.4 Construct a model of a 3-D object, given the top, front and side views. 3.5 Draw a 3-D object, given the top, front and side views. 3.6 Determine if given views of a 3-D object represent a given object, and explain the reasoning. 3.7 Identify the point of perspective of a given one-point perspective drawing of a 3-D object. 3.8 Draw a one-point perspective view of a given 3-D object.

B4. Draw and describe exploded views, component parts and scale diagrams of simple 3-D objects. __Achievement Indicators__ 4.1 Draw the components of a given exploded diagram, and explain their relationship to the original 3-D object. 4.2 Sketch an exploded view of a 3-D object to represent the components. 4.3 Draw to scale the components of a 3-D object. 4.4 Sketch a 2-D representation of a 3-D object, given its exploded view.

=Number= C1. Analyze puzzles and games that involve numerical reasoning, using problem-solving strategies. __Achievement Indicators__ 1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g., 1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game. 1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game. Cribbage http://yukon-ed-virtual-math-arcade.wikispaces.com/Cribbage Magic Squares - Under Construction Kakuro/Cross Sums Exploring Krypto @ []
 * guess and check
 * look for a pattern
 * make a systematic list
 * draw or model
 * eliminate possibilities
 * simplify the original problem
 * work backward
 * develop alternative approaches.
 * [|www.kakuro.com]
 * []
 * media type="custom" key="10415880"

C2. Solve problems that involve personal budgets. __Achievement Indicator__s 2.1 Identify income and expenses that should be included in a personal budget. 2.2 Explain considerations that must be made when developing a budget; e.g., prioritizing, recurring and unexpected expenses. 2.3 Create a personal budget based on given income and expense data. 2.4 Collect income and expense data, and create a budget. 2.5 Modify a budget to achieve a set of personal goals. 2.6 Investigate and analyze, with or without technology, “what if …” questions related to personal budgets.

Student Budget Consultation http://www.civix.ca/sbc/

C3. Demonstrate an understanding of compound interest. __Achievement Indicators__ 3.1 Solve a problem that involves simple interest, given three of the four values in the formula I=Prt. 3.2 Compare simple and compound interest, and explain their relationship. 3.3 Solve, using a formula, a contextual problem that involves compound interest. 3.4 Explain, using examples, the effect of different compounding periods on calculations of compound interest. 3.5 Estimate, using the Rule of 72, the time required for a given investment to double in value.

C4. Demonstrate an understanding of financial institution services used to access and manage finances. __Achievement Indicators__ 4.1 Describe the type of banking services available from various financial institutions, such as online services. 4.2 Describe the types of accounts available at various financial institutions. 4.3 Identify the type of account that best meets the needs for a given set of criteria. 4.4 Identify and explain various automated teller machine (ATM) service charges. 4.5 Describe the advantages and disadvantages of online banking. 4.6 Describe the advantages and disadvantages of debit card purchases. 4.7 Describe ways that ensure the security of personal and financial information; e.g., passwords, encryption, protection of personal identification number (PIN) and other personal identity information.

C5. Demonstrate an understanding of credit options, including: __Achievement Indicators__ 5.1 Compare advantages and disadvantages of different types of credit options, including bank and store credit cards, personal loans, lines of credit, overdraft. 5.2 Make informed decisions and plans related to the use of credit, such as service charges, interest, payday loans and sales promotions, and explain the reasoning. 5.3 Describe strategies to use credit effectively, such as negotiating interest rates, planning payment timelines, reducing accumulated debt and timing purchases. 5.4 Compare credit card options from various companies and financial institutions. 5.5 Solve a contextual problem that involves credit cards or loans. 5.6 Solve a contextual problem that involves credit linked to sales promotions.
 * credit cards
 * loans.

=Algebra= D1. Solve problems that require the manipulation and application of formulas related to: __Achievement Indicators__ 1.1 Solve a contextual problem involving the application of a formula that does not require manipulation. 1.2 Solve a contextual problem involving the application of a formula that requires manipulation. 1.3 Explain and verify why different forms of the same formula are equivalent. 1.4 Describe, using examples, how a given formula is used in a trade or an occupation. 1.5 Create and solve a contextual problem that involves a formula. 1.6 Identify and correct errors in a solution to a problem that involves a formula.
 * volume and capacity
 * surface area
 * slope and rate of change
 * simple interest
 * finance charges.

D2. Demonstrate an understanding of slope: __Achievement Indicators__ 2.1 Describe contexts that involve slope; e.g., ramps, roofs, road grade, flow rates within a tube, skateboard parks, ski hills. 2.2 Explain, using diagrams, the difference between two given slopes (e.g., a 3:1 and a 1:3 roof pitch), and describe the implications. 2.3 Describe the conditions under which a slope will be either 0 or undefined. 2.4 Explain, using examples and illustrations, slope as rise over run. 2.5 Verify that the slope of an object, such as a ramp or a roof, is constant. 2.6 Explain, using illustrations, the relationship between slope and angle of elevation; e.g., for a ramp with a slope of 7:100, the angle of elevation is approximately 4º. 2.7 Explain the implications, such as safety and functionality, of different slopes in a given context. 2.8 Explain, using examples and illustrations, slope as rate of change. 2.9 Solve a contextual problem that involves slope or rate of change.
 * as rise over run
 * as rate of change
 * by solving problems.

D3. Solve problems by applying proportional reasoning and unit analysis. __Achievement Indicators__ 3.1 Explain the process of unit analysis used to solve a problem (e.g., given km/h and time in hours, determine how many km; given revolutions per minute, determine the number of seconds per revolution). 3.2 Solve a problem, using unit analysis. 3.3 Explain, using an example, how unit analysis and proportional reasoning are related; e.g., to change km/h to km/min, multiply by 1h/60min because hours and minutes are proportional (constant relationship). 3.4 Solve a problem within and between systems, using proportions or tables; e.g., km to m or km/h to ft/sec.

=Statistics= E1. Solve problems that involve creating and interpreting graphs, including: __Achievement Indicators__ 1.1 Determine the possible graphs that can be used to represent a given data set, and explain the advantages and disadvantages of each. 1.2 Create, with and without technology, a graph to represent a given data set. 1.3 Describe the trends in the graph of a given data set. 1.4 Interpolate and extrapolate values from a given graph. 1.5 Explain, using examples, how the same graph can be used to justify more than one conclusion. 1.6 Explain, using examples, how different graphic representations of the same data set can be used to emphasize a point of view. 1.7 Solve a contextual problem that involves the interpretation of a graph.
 * bar graphs
 * histograms
 * line graphs
 * circle graphs.

Census @ School
//**Census at School**// is an international classroom project for students aged 8 to 18. They complete a brief online survey, analyze their class results and compare themselves with students in Canada and other countries. [|More]...
 * []
 * [] (Français)

Other

 * Mathematics learning resources can be found @ [] (English) and [] (Français)
 * [|Aboriginal Studies: Key Resources] - This page brings together the most useful articles, maps, reference material and external links on Aboriginal people in Canada. [|(Français)]
 * [|Feature-archives] ([|Français])
 * 2010
 * 2010-04-14: [|Earth Day]
 * 2010-03-17: [|2010 Paralympics]
 * 2010-02-05: [|Valentine's Day]
 * 2009
 * 2009-11-16: [|Sport in Canada and the 2010 Winter Olympics]
 * 2009-10-13: [|Hallowe'en]
 * 2009-10-06: [|Federal elections]
 * 2009-08-21: [|Back to school... by the numbers]
 * 2009-04-08: [|Spring]
 * 2009-03-13: [|St. Patrick's Day]
 * 2009-02-10: [|Valentine's Day]
 * 2009-01-08: [|Chinese New Year]
 * 2008
 * 2008-12-02: [|Christmas]
 * 2008-11-27: [|Portrait of the school-age population]
 * 2008-10-29: [|Hallowe'en]
 * 2008-09-22: [|Back to school], [|Federal elections]
 * 2008-03-31: [|Spring]
 * 2008-03-14: [|Wealth and income tax], [|St. Patrick's Day]
 * 2008-02-04: [|Chinese New Year], [|Valentine's Day]
 * 2007
 * 2007-12-07: [|Winter]
 * 2007-11-06: [|Autumn]
 * 2007-10-26: [|Hallowe'en]
 * 2007-10-08: [|Back to school]
 * 2007-06-20: [|Summer]
 * [|Canada at a Glance] - The 2009 print version is now available: you can order free class sets while supplies last. This annually updated booklet is full of statistics about Canada! Its tables and charts cover topics like population, health, the economy and the environment, as well as some international comparisons. [|(Français)]
 * [|Community Profile] - These profiles present community-level information from the 2006 Census of Population. Users can search for an area of interest by typing its 'place name' in the box or by clicking on a province or territory from the list and selecting the area from a list. ([|Français])

=Curriculum Wide Resources=

Education World

 * Education World Math Worksheet Library

LearnNowBC

 * Charged Up For Math & Science []

Math Trax (From NASA)
This online graphing calculator can be used to graph equations, do physics simulations or plot data files. The graphs have descriptions and sound so you can hear and read about the graph. Blind and low vision users can access visual math data and graph or experiment with equations and datasets. This free download is already on the image of computers in Yukon schools. It is also a free download @ http://prime.jsc.nasa.gov/mathtrax/download.htm.

Open School BC
Note: The resources from Open School BC are not free.
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PBS Teachers

 * @http://www.pbs.org/teachers/classroom/9-12/math/resources/

Saskatchewan Ministry of Education
[] [] (Français) Workplace and Apprenticeship Mathematics 20 > Core Learning Resources

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