Colorado Academic Standards

Colorado Department of Education

Colorado Academic Standards Online

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clear Content Area: Mathematics - 2019 // Grade Level: Fifth Grade // Standard Category: 4. Geometry

Mathematics - 2019

Fifth Grade, Standard 4. Geometry

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More information icon Prepared Graduates:

  • MP2. Reason abstractly and quantitatively.
  • MP5. Use appropriate tools strategically.

More information icon Grade Level Expectation:

5.G.A. Geometry: Graph points on the coordinate plane to solve real-world and mathematical problems.

More information icon Evidence Outcomes:

Students Can:

  1. 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. 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., \(x\)-axis and \(x\)-coordinate, \(y\)-axis and \(y\)-coordinate). (CCSS: 5.G.A.1)
  2. Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. (CCSS: 5.G.A.2)

More information icon Academic Contexts and Connections:

More information icon Colorado Essential Skills and Mathematical Practices:

  1. Use the first quadrant of the coordinate plane to represent real-world and mathematical problems. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
  2. Analyze and use information presented visually in a coordinate plane. (Entrepreneurial Skills: Literacy/Reading)
  3. Reason quantitatively about a problem by abstracting and representing the situation in the first quadrant of the coordinate plane. (MP2)
  4. Use the first quadrant of the coordinate plane as a tool to represent, analyze, and solve problems. (MP5)

More information icon Inquiry Questions:

  1. What are things in the real world that are designed like a coordinate plane or that use a coordinate system?
  2. Why are the axes of the coordinate plane made to form right angles instead of acute and obtuse angles?

More information icon Coherence Connections:

  1. This expectation is in addition to the major work of the grade.
  2. In previous grades, students use number lines to represent whole and fractional number distances from zero.
  3. In Grade 6, students extend the number line and the coordinate plane to include negative numbers and solve real-world and mathematical problems by graphing points in all four quadrants.

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More information icon Prepared Graduates:

  • MP3. Construct viable arguments and critique the reasoning of others.
  • MP5. Use appropriate tools strategically.
  • MP7. Look for and make use of structure.

More information icon Grade Level Expectation:

5.G.B. Geometry: Classify two-dimensional figures into categories based on their properties.

More information icon Evidence Outcomes:

Students Can:

  1. Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. (CCSS: 5.G.B.3)
  2. Classify two-dimensional figures in a hierarchy based on properties. (CCSS: 5.G.B.4)

More information icon Academic Contexts and Connections:

More information icon Colorado Essential Skills and Mathematical Practices:

  1. Observe and analyze attributes of two-dimensional figures to classify them. (Entrepreneurial Skills: Inquiry/Analysis)
  2. Critique the reasoning of others’ classifications of two-dimensional shapes. (MP3)
  3. Strategically use measurement tools to help improve the classification of shapes. (MP5)
  4. Look for and use attributes of two-dimensional shapes to classify the shapes in a hierarchy of figures. (MP7)

More information icon Inquiry Questions:

  1. How can you use the words "always," "sometimes," and "never" to develop a classification of two-dimensional figures?

More information icon Coherence Connections:

  1. This expectation is in addition to the major work of the grade.
  2. In Grade 4, students draw and identify lines and angles and classify shapes by properties of their lines and angles.

Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us