M.1.2.6 Solve a problem that involves the capacity of containers.
M.1.2.7 Write a given volume measurement expressed in one SI unit cubed in another SI unit cubed.
M.1.2.8 Write a given volume measurement expressed in one imperial unit cubed in another imperial unit cubed.
M.1.2.9 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.
M.1.2.10 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.
M.1.2.11 Describe the relationship between the volumes of:
M.1.2.11.a cones and cylinders with the same base and height
M.1.2.11.b pyramids and prisms with the same base and height.
M.1.2.12 Illustrate, using examples, the effect of dimensional changes on volume.
M.1.2.13 Solve a contextual problem that involves the volume of a 3-D object, including composite 3-D objects, or the capacity of a container.
M.1.2.14 Solve a contextual problem that involves the volume of a 3-D object and requires the manipulation of formulas.
G.1 Develop spatial sense.
G.11 Solve problems that involve two and three right triangles.
G.1.1.1 Identify all of the right triangles in a given illustration for a context.
G.1.1.2 Determine if a solution to a problem that involves two or three right triangles is reasonable.
G.1.1.3 Sketch a representation of a given description of a problem in a 2-D or 3-D context.
G.1.1.4 Solve a contextual problem that involves angles of elevation or angles of depression.
G.1.1.5 Solve a contextual problem that involves two or three right triangles, using the primary trigonometric ratios.
G.12 Solve problems that involve scale.
G.1.2.1 Describe contexts in which a scale representation is used.
G.1.2.2 Determine, using proportional reasoning, the dimensions of an object from a given scale drawing or model.
G.1.2.3 Construct a model of a 3-D object, given the scale.
G.1.2.4 Draw, with and without technology, a scale diagram of a given object.
G.1.2.5 Solve a contextual problem that involves scale.
G.13 Model and draw 3-D objects and their views.
G.1.3.1 Draw a 2-D representation of a given 3-D object.
G.1.3.2 Draw, using isometric dot paper, a given 3-D object.
G.1.3.3 Draw to scale top, front and side views of a given 3-D object.
G.1.3.4 Construct a model of a 3-D object, given the top, front and side views.
G.1.3.5 Draw a 3-D object, given the top, front and side views.
G.1.3.6 Determine if given views of a 3-D object represent a given object, and explain the reasoning.
G.1.3.7 Identify the point of perspective of a given one-point perspective drawing of a 3-D object.
G.1.3.8 Draw a one-point perspective view of a given 3-D object.
G.14 Draw and describe exploded views, component parts and scale diagrams of simple 3-D objects.
G.1.4.1 Draw the components of a given exploded diagram, and explain their relationship to the original 3-D object.
G.1.4.2 Sketch an exploded view of a 3-D object to represent the components.
G.1.4.3 Draw to scale the components of a 3-D object.
G.1.4.4 Sketch a 2-D representation of a 3-D object, given its exploded view.
N.1 Develop number sense and critical thinking skills.
N.11 Analyze puzzles and games that involve numerical reasoning, using problem-solving strategies.
N.1.1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
N.1.1.1.a guess and check
N.1.1.1.b look for a pattern
N.1.1.1.c make a systematic list
N.1.1.1.d draw or model
N.1.1.1.e eliminate possibilities
N.1.1.1.f simplify the original problem
N.1.1.1.g work backward
N.1.1.1.h develop alternative approaches.
N.1.1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
N.1.1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
N.12 Solve problems that involve personal budgets.
N.1.2.1 Identify income and expenses that should be included in a personal budget.
N.1.2.2 Explain considerations that must be made when developing a budget; e.g., prioritizing, recurring and unexpected expenses.
N.1.2.3 Create a personal budget based on given income and expense data.
N.1.2.4 Collect income and expense data, and create a budget.
N.1.2.5 Modify a budget to achieve a set of personal goals.
N.1.2.6 Investigate and analyze, with or without technology, "what if …" questions related to personal budgets.
N.13 Demonstrate an understanding of compound interest.
N.1.3.1 Solve a problem that involves simple interest, given three of the four values in the formula I=Prt.
N.1.3.2 Compare simple and compound interest, and explain their relationship.
N.1.3.3 Solve, using a formula, a contextual problem that involves compound interest.
N.1.3.4 Explain, using examples, the effect of different compounding periods on calculations of compound interest.
N.1.3.5 Estimate, using the Rule of 72, the time required for a given investment to double in value.
N.14 Demonstrate an understanding of financial institution services used to access and manage finances.
N.1.4.1 Describe the type of banking services available from various financial institutions, such as online services.
N.1.4.2 Describe the types of accounts available at various financial institutions.
N.1.4.3 Identify the type of account that best meets the needs for a given set of criteria.
N.1.4.4 Identify and explain various automated teller machine (ATM) service charges.
N.1.4.5 Describe the advantages and disadvantages of online banking.
N.1.4.6 Describe the advantages and disadvantages of debit card purchases.
N.1.4.7 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.
N.15 Demonstrate an understanding of credit options, including:
N.15.a credit cards
N.1.5.1 Compare advantages and disadvantages of different types of credit options, including bank and store credit cards, personal loans, lines of credit, overdraft.
N.1.5.2 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.
N.1.5.3 Describe strategies to use credit effectively, such as negotiating interest rates, planning payment timelines, reducing accumulated debt and timing purchases.
N.1.5.4 Compare credit card options from various companies and financial institutions.
N.1.5.5 Solve a contextual problem that involves credit cards or loans.
N.1.5.6 Solve a contextual problem that involves credit linked to sales promotions.
A.1 Develop algebraic reasoning.
A.11 Solve problems that require the manipulation and application of formulas related to:
A.11.a volume and capacity
A.11.b surface area
A.11.c slope and rate of change
A.11.d simple interest
A.11.e finance charges.
A.1.1.1 Solve a contextual problem involving the application of a formula that does not require manipulation.
A.1.1.3 Explain and verify why different forms of the same formula are equivalent.
A.1.1.4 Describe, using examples, how a given formula is used in a trade or an occupation.
A.1.1.5 Create and solve a contextual problem that involves a formula.
A.1.1.6 Identify and correct errors in a solution to a problem that involves a formula.
A.12 Demonstrate an understanding of slope:
A.12.a as rise over run
A.12.b as rate of change
A.12.c by solving problems.
A.1.2.1 Describe contexts that involve slope; e.g., ramps, roofs, road grade, flow rates within a tube, skateboard parks, ski hills.
A.1.2.2 Explain, using diagrams, the difference between two given slopes (e.g., a 3:1 and a 1:3 roof pitch), and describe the implications.
A.1.2.3 Describe the conditions under which a slope will be either 0 or undefined.
A.1.2.4 Explain, using examples and illustrations, slope as rise over run.
A.1.2.5 Verify that the slope of an object, such as a ramp or a roof, is constant.
A.1.2.6 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.
A.1.2.7 Explain the implications, such as safety and functionality, of different slopes in a given context.
A.1.2.8 Explain, using examples and illustrations, slope as rate of change.
A.1.2.9 Solve a contextual problem that involves slope or rate of change.
A.13 Solve problems by applying proportional reasoning and unit analysis.
A.1.3.1 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).
A.1.3.2 Solve a problem, using unit analysis.
A.1.3.3 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).
A.1.3.4 Solve a problem within and between systems, using proportions or tables; e.g., km to m or km/h to ft/sec.