New Colorado P12 Academic Standards
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Content Area: Mathematics
Grade Level Expectations: Sixth Grade
Standard: 2. Patterns, Functions, and Algebraic Structures
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Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
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^{1} For example, express the calculation "Subtract y from 5" as 5 – y. (CCSS: 6.EE.2a)
^{2} For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. (CCSS: 6.EE.2b)
^{3} For example, use the formulas \(V = s^3\) and \(A = 6s^2\) to find the volume and surface area of a cube with sides of length s = 1/2. (CCSS: 6.EE.2c)
^{4} For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. (CCSS: 6.EE.3)
^{5} i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Reason about and solve onevariable equations and inequalities. (CCSS: 6.EE.4)
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{6} For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. (CCSS: 6.EE.9)
Content Area: Mathematics
Grade Level Expectations: Fourth Grade
Standard: 2. Patterns, Functions, and Algebraic Structures
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Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
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Inquiry Questions:
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^{1} For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. (CCSS: 4.OA.5)
Content Area: Mathematics
Grade Level Expectations: High School
Standard: 4. Shape, Dimension, and Geometric Relationships
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{11} For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, \(\sqrt{3}\)) lies on the circle centered at the origin and containing the point (0, 2). (CCSS: GGPE.4)
^{12} e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point. (CCSS: GGPE.5)
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{13} Use dissection arguments, Cavalieri's principle, and informal limit arguments. (CCSS: GGMD.1)
Content Area: Mathematics
Grade Level Expectations: Sixth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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Content Area: Mathematics
Grade Level Expectations: Fifth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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Inquiry Questions:
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^{2} Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. (CCSS: 5.G.1)
Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). (CCSS: 5.G.1)
^{3} For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. (CCSS: 5.G.3)
Content Area: Mathematics
Grade Level Expectations: Fourth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{6} Based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (CCSS: 4.G.2)
^{7} as a line across the figure such that the figure can be folded along the line into matching parts. (CCSS: 4.G.3)
Identify linesymmetric figures and draw lines of symmetry. (CCSS: 4.G.3)
Content Area: Mathematics
Grade Level Expectations: Third Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
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Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
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^{1} e.g., rhombuses, rectangles, and others. (CCSS: 3.G.1)
^{2} e.g., having four sides. (CCSS: 3.G.1)
^{3} e.g., quadrilaterals. (CCSS: 3.G.1)
^{4} For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. (CCSS: 3.G.2)
Content Area: Mathematics
Grade Level Expectations: First Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
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Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:

^{1} e.g., triangles are closed and threesided. (CCSS: 1.G.1)
^{2} e.g., color, orientation, overall size. (CCSS: 1.G.1)
^{3} rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles. (CCSS: 1.G.2)
^{4} cubes, right rectangular prisms, right circular cones, and right circular cylinders. (CCSS: 1.G.2)
^{5} Understand for these examples that decomposing into more equal shares creates smaller shares. (CCSS: 1.G.3)
Content Area: Mathematics
Grade Level Expectations: Kindergarten
Standard: 4. Shape, Dimension, and Geometric Relationships
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Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:

^{1} lying in a plane, "flat". (CCSS: K.G.3)
^{2} "solid". (CCSS: K.G.3)
^{3} e.g., number of sides and vertices/"corners". (CCSS: K.G.4)
^{4} e.g., having sides of equal length. (CCSS: K.G.4)
^{5} e.g., sticks and clay balls. (CCSS: K.G.5)
^{6} For example, "Can you join these two triangles with full sides touching to make a rectangle?" (CCSS: K.G.6)