New Colorado P12 Academic Standards
Current Display Filter: Mathematics  All  by Specific Prepared Graduate Competency  (Remove PGC Filter)
Content Area: Mathematics
Grade Level Expectations: First Grade
Standard: 1. Number Sense, Properties, and Operations
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{2} involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (CCSS: 1.OA.1)
^{3} e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (CCSS: 1.OA.2)
^{4} Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.). (CCSS: 1.OA.3)
^{5} For example, subtract 10 8 by finding the number that makes 10 when added to 8. (CCSS: 1.OA.4)
^{6} e.g., by counting on 2 to add 2. (CCSS: 1.OA.5)
^{7} Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). (CCSS: 1.OA.6)
^{8} Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. (CCSS: 1.OA.7)
^{9} For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? 3, 6 + 6 = ?. (CCSS: 1.OA.8)
Content Area: Mathematics
Grade Level Expectations: Kindergarten
Standard: 1. Number Sense, Properties, and Operations
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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

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^{6} e.g., claps. (CCSS: K.OA.1)
^{7} e.g., by using objects or drawings to represent the problem. (CCSS: K.OA.2)
^{8} e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). (CCSS: K.OA.3)
^{9} e.g., by using objects or drawings, and record the answer with a drawing or equation. (CCSS: K.OA.4)
^{10} Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. (CCSS: K.NBT.1)
Content Area: Mathematics
Grade Level Expectations: High School
Standard: 4. Shape, Dimension, and Geometric Relationships
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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Content Area: Mathematics
Grade Level Expectations: Eighth Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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^{1} Lines are taken to lines, and line segments to line segments of the same length. (CCSS: 8.G.1a)
Angles are taken to angles of the same measure. (CCSS: 8.G.1b)
Parallel lines are taken to parallel lines. (CCSS: 8.G.1c)
^{2} For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. (CCSS: 8.G.5)
Content Area: Mathematics
Grade Level Expectations: Seventh Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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Content Area: Mathematics
Grade Level Expectations: Second Grade
Standard: 4. Shape, Dimension, and Geometric Relationships
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

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Evidence Outcomes  21st Century Skill and Readiness Competencies 
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