Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.

MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).

MAT-06.AR.RP.01 Describe the concept of a ratio relationship between two quantities using ratio language and visual models.

MAT-06.AR.RP.03 Make and use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios, rates, and unit rates.

MAT-07.AR.RP.02 Analyze the relationships between the dependent and independent variables of a proportional relationship using graphs and tables. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, k) where k is the unit rate.

MAT-07.AR.RP.03 Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by an equation of the form y = kx, where k is the constant of proportionality, and describe the meaning of each variable (y, k, x) in the context of the situation.

MAT-07.AR.RP.04 Use proportional relationships to solve multi-step problems involving ratios, percents, and scale drawings of geometric figures, including authentic problems.

MAT-08.AR.EE.03 Explain the characteristics of a linear relationship, including identifying the slope and yintercept in tables, graphs, equations, and descriptions.

MAT-08.AR.EE.04 Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.

MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.

MAT-10.GM.15 Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MAT-10.GM.16 Prove similarity theorems about triangles.

MAT-10.GM.18 Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.

MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30°-60°-90° and 45°-45°-90°).

MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.

MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

MAT-10.GM.36Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).

MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context.

Units of Measurement

MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.

MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.

MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.

MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.

MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.

MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.

MAT-10.GM.36Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).

MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.

MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.

MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data
displays.

MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.