11.WA20.1 Expand and apply understanding of the preservation of equality including solving problems that involve the manipulation and application of formulae for volume and capacity, surface area, slope and rate of change, simple interest, and finance charges.
11.WA20.1.a Verify, using examples, and explain why different forms of the same formula are equivalent.
11.WA20.1.b Verify whether given forms of the same formula are equivalent and justify the conclusion.
11.WA20.1.c Describe, using examples, how a given formula is used in a trade or an occupation.
11.WA20.1.d Create, solve, and verify the reasonableness of solutions to situational questions that involve the use of a formula relevant to self, family, or community.
11.WA20.1.e Analyze solutions to questions that involve formulae to verify the preservation of equality, correct if necessary, and explain the reasoning.
11.WA20.1.f Solve, with or without the use of technology, situational questions that involve the application of a formula that:
11.WA20.3.b Observe, analyze, and compare volume and capacity using examples.
11.WA20.3.c Critique the statement: "Volume and capacity represent the same attribute to measure so the same units of measure can be used for either volume or capacity."
11.WA20.3.d Identify and describe situations in which given SI or imperial volume or capacity units would be used.
11.WA20.3.e Justify and compare the choice of personal referents for surface area, volume, and capacity measurements in both SI and imperial units, (e.g., The bottom half of a two-litre carton of milk has a capacity of one litre, a surface area of 500 cm² or if a top was added to make a prism it would have a surface area of 600 cm² and a volume of about 1000 cm³, or the volume of a box for hockey helmets is approximately 1 ft³ [1800 in³] and the surface area is about 6 ft² [900 in²]).
11.WA20.3.f Justify and apply strategies including use of personal referents to estimate the surface area and volume of 3-D objects, and the capacity of containers.
11.WA20.3.i Determine the surface area and volume of prisms, cones, cylinders, pyramids, spheres, and composite 3-D objects, using a variety of measuring tools such as rulers, tape measures, callipers, and micrometers and explain the strategy used including the manipulation of formulae.
11.WA20.3.j 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 and explain the strategy used.
11.WA20.3.k Analyze and generalize the relationship between the volumes of:
11.WA20.3.k.1 cones and cylinders with the same base and height
11.WA20.3.k.2 pyramids and prisms with the same base and height.
11.WA20.3.l Analyze and illustrate, using examples, the effect of dimensional changes on area, surface area, and volume.
11.WA20.7.d Explain, using examples, the effect of changing different factors on compound interest such as different compounding periods, different interest rates, and starting at a younger age.
11.WA20.7.e Estimate, using the Rule of 72, the time required for a given investment to double in value and explain the reasoning.
11.WA20.8 Demonstrate understanding of financial institution services used to access and manage personal finances, including credit options.
11.WA20.8.a Research and present orally, with the aid of visuals (electronic or other), various types of banking services available from various financial institutions, such as online services, different types of accounts, telephone banking, mobile banking, ATM banking, or credit cards.
11.WA20.8.b Analyze given or personal situations to determine the type of account that best meets the needs of the criteria for each of the situations.
11.WA20.8.c Research and explain various automated teller machine (ATM) service charges.
11.WA20.8.d Describe the advantages and disadvantages of:
11.WA20.8.d.1 online banking
11.WA20.8.d.2 debit card purchases
11.WA20.8.d.3 different types of credit options, including bank and store credit cards, personal loans, lines of credit, and overdraft.
11.WA20.8.e Describe ways that try to ensure the security of personal and financial information (e.g., passwords, encryption, protection of personal identification number (PIN) and other personal identity information).
11.WA20.8.f Research, compare, and report on credit card options from various companies and financial institutions.
11.WA20.8.g Analyze credit options related to the use of credit, such as service charges, interest, payday loans, and sales promotions, to make informed decisions and plans and explain the reasoning.
11.WA20.8.h Describe strategies to use credit effectively, such as negotiating interest rates, planning payment timelines, reducing accumulated debt, and timing purchases.
11.WA20.8.i Solve situational questions that involve credit linked to sales promotions, credit cards, or loans.
11.WA20.8.j Critique the statement, "It is always better to have the lowest possible limit on a credit card."
11.WA20.9 Demonstrate concretely, pictorially, and symbolically (with and without the use of technology) an understanding of slope with respect to: rise over run, rate of change, solving problems.
11.WA20.9.a Research and present contexts that involve slope including the mathematics involved (e.g., ramps, roofs, road grade, flow rates within a tube, skateboard parks, ski hills).
11.WA20.9.b Analyze and generalize relationships between slopes in given contexts such as 3:1 and a 1:3 roof pitch or slopes that are usually described by a colour for downhill skiing and snowboarding, and explain implications of each slope including safety and functionality.
11.WA20.9.c Describe conditions under which a slope will be either 0 or undefined and explain the reasoning.
11.WA20.9.d Critique the statement, "It requires less effort to independently use a wheelchair to climb a ramp of a certain height that has a slope of 1:12 rather than a slope of 1:18."
11.WA20.9.e Justify, using examples and illustrations:
11.WA20.9.f Analyze slopes of objects, such as ramps or roofs, to determine if the slope is constant and explain the reasoning.
11.WA20.9.g Analyze, generalize, and explain, using illustrations, the relationship between slope and angle of elevation (e.g., for a ramp (or pitch of a roof, grade on a road, slope in pipes for plumbing, azimuth in the sky) that has a slope of 7:100, the angle of elevation is approximately 4 degrees).
11.WA20.9.h Solve situational questions that involve slope or rate of change, verify and explain why solutions are reasonable or not.
11.WA20.10 Extend and apply proportional thinking to solve problems that involve unit analysis and scale.
11.WA20.10.a 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 revolutions per second).
11.WA20.10.b Solve situational questions, using unit analysis, and explain the reasoning.
11.WA20.10.c Explain, using examples, 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 or have a constant relationship).
11.WA20.10.d Solve, using personal strategies such as applying proportions or interpreting tables, situational questions that involve conversions of units within and between SI and/or imperial systems of measurement (e.g., km to m or km/h to ft/sec).
11.WA20.10.j Explain the importance of scale in mathematical drawings and/or in situational applications.
11.WA20.11 Extend and apply understanding of representing data using graphs including: bar graphs, histograms, line graphs, circle graphs.
11.WA20.11.a Pose questions that could be answered using histograms, construct the histogram, and draw conclusions.
11.WA20.11.b Analyze and compare sets of bar graphs and histograms.
11.WA20.11.c Analyze sets of data in a variety of contexts to determine and create, with or without technology, possible graphs that could be used to represent the data and explain the advantages and disadvantages of each graph.
11.WA20.11.d Critique the statement, "All histograms are bar graphs and all bar graphs are histograms."
11.WA20.11.e Analyze graphs including bar graphs, histograms, line graphs, and circle graphs to determine and describe trends.
11.WA20.11.f Explain, using examples:
11.WA20.11.f.1 how the same graph can be used to justify more than one conclusion
11.WA20.11.f.2 how different graphic representations of the same data set can be used to emphasize a point of view
11.WA20.11.f.3 what happens if the graph is drawn to the wrong scale
11.WA20.11.f.4 why the graph selected is not reflective of the data set.
11.WA20.11.g Solve, using a variety of strategies including interpolation and extrapolation, contextual problems that involve data analysis and graphs.