Colorado Academic Standards Online
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clear Content Area: Mathematics - 2019 // Grade Level: Third Grade // Standard Category: 3. Data, Statistics, and Probability
Mathematics - 2019
Third Grade, Standard 3. Data, Statistics, and Probability
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Prepared Graduates:
- MP1. Make sense of problems and persevere in solving them.
- MP4. Model with mathematics.
- MP5. Use appropriate tools strategically.
Grade Level Expectation:
3.MD.A. Measurement & Data: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Evidence Outcomes:
Students Can:
- Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. (CCSS: 3.MD.A.1)
- Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (This excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (This excludes multiplicative comparison problems, such as problems involving notions of “times as much.” See Appendix, Table 2.) (CCSS: 3.MD.A.2)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Use units of measurement appropriate to the type and magnitude of the quantity being measured. (Professional Skills: Information Literacy)
- Make sense of problems involving measurement by building on real-world knowledge of time and objects and an understanding of the relative sizes of units. (MP1)
- Represent problems of time and measurement with equations, drawings, or diagrams. (MP4)
- Use appropriate measures and measurement instruments for the quantities given in a problem. (MP5)
Inquiry Questions:
- How can elapsed time be modeled on a number line to support the connection to addition and subtraction?
Coherence Connections:
- This expectation represents major work of the grade.
- In Grade 2, students measure and estimate lengths in standard units and work with time and money.
- In Grade 3, this expectation connects to developing an understanding of fractions as numbers, solving problems involving the four operations, and identifying and explaining patterns in arithmetic.
- In Grade 4, students solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
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Prepared Graduates:
- MP2. Reason abstractly and quantitatively.
- MP4. Model with mathematics.
Grade Level Expectation:
3.MD.B. Measurement & Data: Represent and interpret data.
Evidence Outcomes:
Students Can:
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent \(5\) pets. (CCSS: 3.MD.B.3)
- Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. (CCSS: 3.MD.B.4)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Analyze data to distinguish the factual evidence offered, to reason about judgments, to draw conclusions, and to speculate about ideas the data represents. (Entrepreneurial Skills: Literacy/Reading)
- Abstract real-world quantities into scaled graphs. (MP2)
- Model real-world quantities with statistical representations such as bar graphs and line graphs. (MP4)
Inquiry Questions:
- How can working with pictures and bar graphs connect mathematics to the world around us?
- How does changing the scale of a bar graph or line plot change the appearance of the data?
Coherence Connections:
- This expectation supports the major work of the grade.
- In Grade 2, students represent and interpret length by measuring objects, make line plots, and use picture and bar graphs to represent categorical data.
- In Grade 3, this expectation supports developing an understanding of fractions as numbers.
- In Grade 4, students represent and interpret data by making line plots representing fractional measurements and solving addition and subtraction problems using information presented in line plots.
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Prepared Graduates:
- MP3. Construct viable arguments and critique the reasoning of others.
- MP5. Use appropriate tools strategically.
- MP6. Attend to precision.
- MP7. Look for and make use of structure.
Grade Level Expectation:
3.MD.C. Measurement & Data: Geometric measurement: Use concepts of area and relate area to multiplication and to addition.
Evidence Outcomes:
Students Can:
- Recognize area as an attribute of plane figures and understand concepts of area measurement. (CCSS: 3.MD.C.5)
- A square with side length \(1\) unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. (CCSS: 3.MD.C.5.a)
- A plane figure which can be covered without gaps or overlaps by \(n\) unit squares is said to have an area of \(n\) square units. (CCSS: 3.MD.C.5.b)
- Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). (CCSS: 3.MD.C.6)
- Use concepts of area and relate area to the operations of multiplication and addition. (CCSS: 3.MD.C.7)
- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. (CCSS: 3.MD.C.7.a)
- Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. (CCSS: 3.MD.C.7.b)
- Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths \(a\) and \(b + c\) is the sum of \(a \times b\) and \(a \times c\). Use area models to represent the distributive property in mathematical reasoning. (CCSS: 3.MD.C.7.c)
- Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. (CCSS: 3.MD.C.7.d)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Defend calculations of area using multiplication and by tiling the area with square units and comparing the results. (MP3)
- Understand how to use a one-dimensional measurement tool, like a ruler, to make two-dimensional measurements of area. (MP5)
- Be precise by describing area in square rather than linear units. (MP6)
- Use areas of rectangles to exhibit the structure of the distributive property. (MP7)
Inquiry Questions:
- Given three pictures of different rectangles with unknown dimensions, how can you determine which rectangle covers the most area?
- How does computing the area of a rectangle relate to closed arrays?
- How can the area of an E-shaped or H-shaped figure be calculated?
Coherence Connections:
- This expectation represents major work of the grade.
- In Grade 2, students measure and estimate lengths in standard units and reason with shapes and their attributes.
- This expectation connects to other ideas in Grade 3: (a) recognizing perimeter as an attribute of plane figures and distinguishing between linear and area measures, (b) applying properties of multiplication and the relationship between multiplication and division, and (c) solving problems involving the four operations and identifying and explaining patterns in arithmetic.
- In Grade 4, students solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit. In Grade 5, students relate volume to multiplication and to addition and also extend previous understandings of multiplication and division to multiply and divide fractions.
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Prepared Graduates:
- MP1. Make sense of problems and persevere in solving them.
- MP4. Model with mathematics.
Grade Level Expectation:
3.MD.D. Measurement & Data: Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Evidence Outcomes:
Students Can:
- Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. (CCSS: 3.MD.D.8)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Make sense of the relationship between area and perimeter by calculating both for rectangles of varying sizes and dimensions. (MP1)
- Model perimeters of objects in the world with polygons and the sum of their side lengths. (MP4)
Inquiry Questions:
- What are all the pairs of side lengths that can create a rectangle with the same area, such as \(12\) square units?
- Is it possible for two rectangles to have the same area but different perimeters?
- Is it possible for two rectangles to have the same perimeter but different areas?
Coherence Connections:
- This expectation is in addition to the major work of the grade.
- In Grade 2, students measure and estimate lengths in standard units.
- In Grade 3, this expectation connects to understanding concepts of area, relating area to multiplication and to addition, and solving problems involving the four operations.
- In Grade 4, students solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us