Learning Domain: Functions: Building Functions

Standard: Build a function that models a relationship between two quantities

Indicator: Write a function that describes a relationship between two quantities.*

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Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

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Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Prove theorems involving similarity

Indicator: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

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Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

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This is a lesson and assessment task that has many teacher resources. It has ppt, student worksheets, assessment, and lesson plan. It strongly addresses CCSS 7.G.5. Students have to try different ways to find the unknown angle.

Rolling Cups unit presents a non-routine mathematical inquiry situation requiring students to develop experimental and analytical models of a physical situation and to generate and analyze data through the systematic control of variables.

Resources include common misconceptions associated with the target standards along with suggested instructional strategies to ensure students build conceptual understanding.

F-BF.1 – Rating: 3

G-SRT.5 – Rating: 2