10.WA10.2 Analyze puzzles and games that involve spatial reasoning using problem solving strategies.
10.WA10.2.a Determine, explain, and verify strategies to solve a puzzle or to win a game such as:
10.WA10.2.a.1 guess and check
10.WA10.2.a.2 look for a pattern
10.WA10.2.a.3 make a systematic list
10.WA10.2.a.4 draw or model
10.WA10.2.a.5 eliminate possibilities
10.WA10.2.a.6 solve a simpler problem
10.WA10.2.a.7 work backwards
10.WA10.2.a.8 develop alternative approaches.
10.WA10.2.b Observe and analyze errors in a solution to a puzzle or in a strategy for winning a game and explain the reasoning.
10.WA10.2.c Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
10.WA10.3 Demonstrate using concrete, and pictorial models, and symbolic representations, understanding of measurement systems including:
10 The Système International (SI)
10 The British Imperial system
10 The US customary system.
10.WA10.3.a Research and present about a topic related to measurement systems such as:
10.WA10.3.a.1 how the SI system and the Imperial system were developed
10.WA10.3.a.2 the adoption of the SI system in Canada
10.WA10.3.a.3 development of the US customary system and the relationship between the units of this system and those of the Imperial measurement system (e.g., units for length and area are the same; there are differences, however, for mass, weight, and capacity)
10.WA10.3.a.4 early systems of measurement in Canada and contexts in which some are still used today (e.g., hand span and thumbs for measuring horses from the ground to its withers).
10.WA10.3.b Describe situations relevant to self, family, or community in which the SI and/or Imperial systems are used.
10.WA10.3.c Analyze the relationships between:
10.WA10.3.c.1 the base units of the metric system of measurement and the base ten number system
10.WA10.4.b Estimate, using personal referents for SI and Imperial units, linear measurements such as the dimensions of regular 3-D objects or 2-D shapes found in the classroom, at home, or in the community.
10.WA10.4.c Explain why and how the same linear measurement can be expressed using:
10.WA10.4.c.1 equivalent SI units (e.g., 10 centimetres, 0.1 metres, and 100 millimetres)
10.WA10.4.d Measure and record (using Canadian spelling and abbreviations for SI or Imperial units) using a variety of instruments such as trundle or surveyor's wheels, height gauges, metric and Imperial tapes and rulers, carpenter's squares, micrometers, fractional or electronic callipers, and pedometers:
10.WA10.4.d.1 distances at school, at home, and in the community
10.WA10.4.d.2 inside diameters, outside diameters, lengths, and widths of personally relevant 3-D objects.
10.WA10.4.e Develop, generalize, explain, and apply strategies to convert units of linear measurements within the same system (e.g., feet to yards, or metres to millimetres).
10.WA10.4.f Apply knowledge and skills with linear measurement to create and solve or verify the reasonableness of solutions to situational questions relevant to self, family, or community (including perimeter, circumference, and the length + width + height measurement used in shipping and air travel).
10.WA10.4.g Determine the operation that should be used to solve a linear measurement problem and explain the reasoning (e.g., Write the equation that could be used to determine how many lengths of 1/3 of a yard can be cut out of a log measuring 5 1/2 yards).
10.WA10.4.h Develop, generalize, explain, and apply strategies to determine the midpoint of a linear measurement, such as the length, width, height, depth, diagonal length, or diameter of a 3-D object (e.g., A wall measures 5 yards and 6 7/8 inches. If a painting is to be hung centered on the wall, how far is the centre of the painting from each of the adjacent walls?).
10.WA10.4.i Critique the statement "the distance between Regina and Saskatoon is 2 hours".
10.WA10.5 Demonstrate using concrete and pictorial models, and symbolic representations, understanding of area of 2-D shapes and surface area of 3-D objects including units in SI and Imperial systems of measurement.
10.WA10.5.a Describe situations relevant to self, family, or community in which SI and/or Imperial units for area measurement are used.
10.WA10.5.b Justify the choice of referents for area measurements in both the SI and Imperial units (e.g., a dime or a small fingernail is about one cm² and the thumb nail is about 1 in²).
10.WA10.5.c Estimate, using strategies such as personal referents or grids, area and surface area measurements in SI or Imperial units including regular, composite, and irregular 2-D shapes and 3-D objects found in the classroom, at home, or in the community.
10.WA10.5.d Develop, generalize, explain, and apply strategies (including measuring and applying formulae) for determining areas and surface areas of:
10.WA10.5.d.1 regular, composite, and irregular 2-D shapes, including circles
10.WA10.5.f.2 an Imperial unit squared to another Imperial unit squared.
10.WA10.5.g Analyze, with and without the use of dynamic geometry software, the effect of changing the measurement of one or more dimensions on area and perimeter of rectangles and surface area of rectangular prisms.
10.WA10.6.b Observe and analyze a set of triangles to judge if the Pythagorean Theorem could be used to determine an unknown side length and explain the reasoning.
10.WA10.6.c Describe historical and contemporary applications of the Pythagorean Theorem, including the 3:4:5 ratio (e.g., Explain the relationship between a circle of string that has 13 equidistant knots or beads forming 12 spaces of equal length on it to the Pythagorean Theorem).
10.WA10.7.d Draw polygons that are similar to a given polygon using measuring tools and technology, explain the strategies used, and justify why the polygons are similar.
10.WA10.7.e Apply knowledge and skills related to similar polygons to solve situational questions relevant to self, family, or community that involve right triangles with a shared acute angle (e.g., determining the height of a tree).
10.WA10.7.f Create and solve situational questions relevant to self, family, or community that involve similarity of polygons.
10.WA10.7.g Critique the statement "All congruent polygons are similar and all similar polygons are congruent".
10.WA10.8 Demonstrate an understanding of primary trigonometric ratios (sine, cosine, and tangent).
10.WA10.8.a Observe a set of similar right triangles and analyze and draw conclusions about the ratios of the lengths, with respect to one acute angle of the:
10.WA10.8.d Analyze solutions to situational questions that involve primary trigonometric ratios to determine if they are reasonable and explain the reasoning.
10.WA10.8.e Apply knowledge and skills related to the solving of right triangles using the primary trigonometric ratios to create and solve situational problems relevant to self, family, or community.
10.WA10.9 Demonstrate understanding of angles including:
10 drawing and sketching
10 replicating and constructing
10 relating to parallel, perpendicular, and transversal lines
10 solving problems.
10.WA10.9.a Justify the choice of personal referents for angles measuring 22.5°, 30°, 45°, 60°, 90°, and 180° and use them to estimate angle measurements (e.g., a corner of a sheet of paper is 90° so 1/2 of a corner is 45°).
10.WA10.9.b Sketch or draw angles of various measures, including acute, right, straight, obtuse, and reflex angles, and justify the choice of sketching or drawing in relation to the situation.
10.WA10.9.c Explain, using examples, how to measure angles in different orientations using a variety of instruments such as a protractor, carpenter's square, or dynamic software.
10.WA10.9.d Explain and illustrate how angles can be replicated (e.g., Mira, protractor, compass and straightedge, carpenter's square, and dynamic software).
10.WA10.9.l Provide concrete and pictorial examples that show that there are no angle relationships (excluding vertically opposite angles) when two lines that are not parallel are crossed by a transversal.
10.WA10.9.m Describe and apply strategies for determining if lines or planes are perpendicular or parallel in situations relevant to self, family, or community (e.g., are the walls perpendicular to the floor? Are the corners square? Are the seams on the duvet parallel? Are the joists parallel?).
10.WA10.9.n Analyze personally relevant situations for the impact if lines or planes that are meant to be perpendicular or parallel are not (e.g., What would it be like if the stairs in a staircase were not parallel?).
10.WA10.9.o Create and solve relevant situational questions that involve angles and/or parallel lines and transversals, including perpendicular transversals, and explain the reasoning.
10.WA10.9.p Critique the statement "If two or more lines are perpendicular, then each is a transversal of the other and if two or more lines are transversals of each other, they are perpendicular".
10.WA10.9.q Critique the statement "All lines are either parallel or transversals".
10.WA10.9.r Analyze and describe the role of angles, parallel lines, perpendicular lines, and transversals in games and sports (e.g., chess, curling, pool, hockey, soccer, and basketball).
10.WA10.10 Apply proportional reasoning to solve problems involving unit pricing and currency exchange.
10.WA10.10.a Create and solve problems relevant to self, family, and community that involve best buy, and explain the solution in terms of the cost as well as other factors, such as quality and quantity.
10.WA10.10.b Describe and analyze, using relevant examples taken from print and other media, different sales promotion techniques (e.g., deli meat at $2 per 100g seems less expensive than $20 per kilogram).
10.WA10.10.e Develop using proportional reasoning and mental mathematics strategies, explain, and apply strategies for estimating the cost of items or services in Canadian currency while in a foreign country or when making purchases via the Internet, and explain why this may be important.
10.WA10.10.f Convert between Canadian currency and foreign currencies, such as Mexican or American currencies, using formulas, charts, or tables, and explain how to know if the solution is reasonable.
10.WA10.10.g Analyze solutions to situational questions that involve unit pricing or conversions of currency to determine if they are reasonable and explain the reasoning.
10.WA10.10.h Research advantages and disadvantages for individuals, groups, businesses, and communities of having differences in currency rates between Canada and the United States.
10.WA10.11 Demonstrate understanding of income including:
10 gross pay
10 net pay.
10.WA10.11.a Describe, using examples, various methods of earning income.
10.WA10.11.b Research and record jobs that commonly use different methods of earning income, including hourly wage, wage and tips, salary, commission, contract, bonus, and shift premiums.
10.WA10.11.c Describe the advantages and disadvantages for a variety of methods of earning income, such as hourly wage, tips, piecework, salary, commission, contract work, and self-employment.
10.WA10.11.d Read and explain the information provided on pay stubs.
10.WA10.11.e Determine in decimal form, from a time schedule, the total time worked in hours and minutes, including time and a half and/or double time and explain the strategies used.
10.WA10.11.f Determine gross pay for different situations, including:
10.WA10.11.f.1 base hourly wage, with and without tips, from given or calculated hours worked
10.WA10.11.f.2 base hourly wage, plus overtime (time and a half, double time) from given or calculated hours worked
10.WA10.11.f.3 base wage, plus commission
10.WA10.11.f.4 single commission rate
10.WA10.11.f.5 graduated commission.
10.WA10.11.g Determine the Canadian Pension Plan (CPP), Employment Insurance (EI), and income tax deductions for a given amount of gross pay.
10.WA10.11.h Identify and describe deductions that may be relevant to self in the future which are used when calculating net pay (e.g., health plans, uniforms, union dues, charitable donations, payroll tax).
10.WA10.11.i Investigate, using technology, "what if …" questions related to changes in income (e.g., "What if there is a change in the rate of pay?", "What if there is a change in the method of earning income?", "What if I can qualify for deductions?", "What if I work 80% time instead of full time?", "What if I am sick for a long period of time?").
10.WA10.11.j Create, research, and solve situational questions relevant to self, family, and community that involve income.
10.WA10.11.k Critique the statement "When planning for a budget, it is important to calculate net pay rather than rely only on gross pay".