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.

WA20.1.e: Analyze solutions to questions that involve formulae to verify the preservation of equality, correct if necessary, and explain the reasoning.

Area of Triangles
Solving Formulas for any Variable

WA20.2: Demonstrate the ability to analyze puzzles and games that involve numerical reasoning and problem solving strategies.

WA20.2.a: Determine, explain, and verify strategies to solve a puzzle or to win a game such as:

WA20.2.a.4: draw or model

Estimating Population Size

WA20.3: Extend and apply understanding of surface area, volume, and capacity using concrete and pictorial models and symbolic representations (SI or imperial units of measurement).

WA20.3.a: Observe, analyze, generalize, and explain using examples including nets, the relationships between area, surface area, and volume.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

WA20.3.g: Solve situational questions that involve:

WA20.3.g.1: the volume of 3-D objects and composite 3-D objects in a variety of contexts

Prisms and Cylinders

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.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

WA20.3.l: Analyze and illustrate, using examples, the effect of dimensional changes on area, surface area, and volume.

Perimeter and Area of Rectangles
Surface and Lateral Areas of Prisms and Cylinders

WA20.3.m: Solve using a variety of strategies, including the manipulation of formulae, situational questions that involve:

WA20.3.m.1: the surface area of 3-D objects, including spheres

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

WA20.3.m.2: the volume of 3-D objects, including composite 3-D objects

Prisms and Cylinders

WA20.4: Solve problems that involve at least two right triangles.

WA20.4.a: Analyze and sort a set of illustrations of triangles in a given context according to whether they are right triangles or not, and justify the sort.

Classifying Triangles

WA20.4.d: Apply personal strategies including the primary trigonometric ratios to solve situational questions that involve:

WA20.4.d.1: angles of elevation or angles of depression, and explain the reasoning

Sine, Cosine, and Tangent Ratios

WA20.4.d.2: more than two right triangles and explain the reasoning.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

WA20.5: Extend and apply understanding of 3-D objects including: top, bottom, and side views, exploded views, component parts, scale diagrams.

WA20.5.a: Describe and sketch or draw, with or without technology, using a variety of strategies including the use of isometric paper:

WA20.5.a.5: 2-D representations of 3-D objects, given their exploded view.

Surface and Lateral Areas of Prisms and Cylinders

WA20.5.b: Draw to scale:

WA20.5.b.1: top, front, and side views of given actual 3-D objects

Dilations

WA20.7: Demonstrate understanding of compound interest.

WA20.7.a: Solve situational questions that involve simple interest, given three of the four values in the formula I=Prt and explain the reasoning.

Compound Interest

WA20.7.b: Analyze and generalize the relationship between simple interest and compound interest.

Compound Interest

WA20.7.c: Solve, using a formula, situational questions that involve compound interest.

Compound Interest

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.

Compound Interest

WA20.8: Demonstrate understanding of financial institution services used to access and manage personal finances, including credit options.

WA20.8.h: Describe strategies to use credit effectively, such as negotiating interest rates, planning payment timelines, reducing accumulated debt, and timing purchases.

Compound Interest

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.

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).

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope-Intercept Form of a Line

WA20.9.c: Describe conditions under which a slope will be either 0 or undefined and explain the reasoning.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

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."

Distance-Time and Velocity-Time Graphs - Metric

WA20.9.e: Justify, using examples and illustrations:

WA20.9.e.1: slope as rise over run

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

WA20.9.e.2: slope as rate of change.

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

WA20.9.f: Analyze slopes of objects, such as ramps or roofs, to determine if the slope is constant and explain the reasoning.

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

WA20.10: Extend and apply proportional thinking to solve problems that involve unit analysis and scale.

WA20.10.e: Describe, using examples, contexts in which scale representations are used.

Dilations

WA20.10.h: Draw, with or without technology, a scale diagram of 3-D objects.

Dilations

WA20.11: Extend and apply understanding of representing data using graphs including: bar graphs, histograms, line graphs, circle graphs.

WA20.11.a: Pose questions that could be answered using histograms, construct the histogram, and draw conclusions.

Histograms
Real-Time Histogram
Stem-and-Leaf Plots

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.

Stem-and-Leaf Plots

WA20.11.e: Analyze graphs including bar graphs, histograms, line graphs, and circle graphs to determine and describe trends.

Histograms

WA20.11.f: Explain, using examples:

WA20.11.f.2: how different graphic representations of the same data set can be used to emphasize a point of view

Stem-and-Leaf Plots