Colorado Academic Standards Online
Use the options below to create customized views of the Colorado Academic Standards. For all standards resources, see the Office of Standards and Instructional Support.
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clear Content Area: Mathematics - 2019 // Grade Level: Fifth Grade // Standard Category: 3. Data, Statistics, and Probability
Mathematics - 2019
Fifth Grade, Standard 3. Data, Statistics, and Probability
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5.MD.A. Measurement & Data: Convert like measurement units within a given measurement system.
Students Can:
- Convert among different-sized standard measurement units within a given measurement system (e.g., convert \(5\) cm to \(0.05\) m), and use these conversions in solving multi-step, real-world problems. (CCSS: 5.MD.A.1)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Convert measurements to solve real-world problems. (Professional Skills: Information Literacy)
- Use appropriate precision when converting measurements based on a problem’s context. (MP6)
- What is happening mathematically when we convert from centimeters to meters? What about when we convert from meters to centimeters?
- How can you use fractions to change \(53\) kilograms to grams? How can you use decimals to do this conversion?
- This expectation supports the major work of the grade.
- In Grade 4, students solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- In Grade 5, this expectation connects with performing operations with multi-digit whole numbers and with decimals to hundredths.
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5.MD.B. Measurement & Data: Represent and interpret data.
Students Can:
- Make a line plot to display a data set of measurements in fractions of a unit (\(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{1}{8}\)). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. (CCSS: 5.MD.B.2)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Display fractional measurement data in line plots. (Professional Skills: Information Literacy)
- Participate in discussions of measurement data using information presented in line plots. (Civic/Interpersonal Skills: Literacy/Oral Expression and Listening)
- Strategically determine the scale of line plots to represent fractional measurements. (MP5)
- (Given a data set of fractional measurements with unlike denominators) What will you consider in deciding how to label the tick marks on the line for your line plot?
- This expectation supports the major work of the grade.
- In Grade 4, students represent and interpret data.
- In Grade 5, this expectation connects with using equivalent fractions and applying and extending previous understandings of multiplication and division.
- In Grade 6, students develop understanding of statistical variability and summarize and describe distributions.
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- MP2. Reason abstractly and quantitatively.
- MP5. Use appropriate tools strategically.
- MP7. Look for and make use of structure.
5.MD.C. Measurement & Data: Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition.
Students Can:
- Recognize volume as an attribute of solid figures and understand concepts of volume measurement. (CCSS: 5.MD.C.3)
- A cube with side length \(1\) unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume. (CCSS: 5.MD.C.3.a)
- A solid figure which can be packed without gaps or overlaps using \(n\) unit cubes is said to have a volume of \(n\) cubic units. (CCSS: 5.MD.C.3.b)
- Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (CCSS: 5.MD.C.4)
- Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. (CCSS: 5.MD.C.5)
- Model the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. (CCSS: 5.MD.C.5.a)
- Apply the formulas \(V = l \times w \times h\) and \(V = b \times h\) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. (CCSS: 5.MD.C.5.b)
- Use the additive nature of volume to find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. (CCSS: 5.MD.C.5.c)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Solve real-world problems involving volume. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
- Make connections between the values being multiplied in a volume formula, the concept of cubic units, and the context within which volume is being calculated. (MP2)
- Use unit cubes as a tool for finding or estimating volume and compare those results with those obtained with formulas. (MP5)
- Extend the structure of two-dimensional space and the relationship between arrays and area to three-dimensional space and the relationship between layers of cubes and volume. (MP7)
- How are volume and area related in a solid figure?
- Why is multiplication used when computing the volume of a solid figure, instead of another operation?
- This expectation represents major work of the grade.
- In previous grades, students connect area to the operation of multiplication and understand how to represent area problems as multiplication equations.
- In Grade 6, students solve real-world and mathematical problems involving area of right rectangular prisms with fractional side lengths, using fractional cubic units.
Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us

