9.2.3: Measurement: Investigate measurement using a variety of tools, units, systems, processes and techniques in various cultures. Explain and reason with attributes, estimations and formulas to communicate measurement(s) and relationships effectively. Justify decisions and consider the reasonableness of the measurement.

Measurement: Investigate measurement using a variety of tools, units, systems, processes and techniques in various cultures. Explain and reason with attributes, estimations and formulas to communicate measurement(s) and relationships effectively. Justify decisions and consider the reasonableness of the measurement.

9.2.3.01Apply the Pythagorean Theorem and distance formula to compute perimeters of polygons and areas of right triangles and rectangles on coordinate planes. (MP1)9.2.3.02Apply properties of 45-45-90 and 30-60-90 triangles to solve situations and logically justify results. (MP1, MP4)9.2.3.03Use trigonometric ratios and the Pythagorean Theorem and its converse to solve contextual situations, including right triangles or polygons that can be decomposed into triangles. (MP4, MP7)9.2.3.04Develop, justify and use decomposition to determine the formula for surface area and volume of various three-dimensional figures. (MP7, MP8)9.2.3.05Use the formulas for surface area and volume of various three-dimensional figures to solve multi-step contextual situations. (MP4, MP5)9.2.3.06Use units of measure and dimensional analysis to solve multi-step situations. Interpret units consistently in formulas. Interpret the scale and the origin in graphs and data displays. (MP1, MP4)9.2.3.07Compute the unit cost and total cost to cover different areas and volumes in applications, such as painting, carpeting and gardening. Optimize costs for various models, including linear and quadratic. Use technology, including spreadsheets. (MP4, MP5)9.2.3.08Use similarity to determine the side ratios in right triangles as properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (MP8)9.2.3.09Apply dilations of scale factor k on length, area and volume and recognize the effect is multiplication by k, k^2, k^3 respectively. (MP2)
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