Colorado Academic Standards

Colorado Department of Education

Colorado Academic Standards Online

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clear Content Area: Mathematics - 2019 // Grade Level: Third Grade // Standard Category: 1. Number and Quantity

Mathematics - 2019

Third Grade, Standard 1. Number and Quantity

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More information icon Prepared Graduates:

  • MP6. Attend to precision.
  • MP7. Look for and make use of structure.

More information icon Grade Level Expectation:

3.NBT.A. Number & Operations in Base Ten: Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used.

More information icon Evidence Outcomes:

Students Can:

  1. Use place value understanding to round whole numbers to the nearest \(10\) or \(100\). (CCSS: 3.NBT.A.1)
  2. Fluently add and subtract within \(1000\) using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 3.NBT.A.2)
  3. Multiply one-digit whole numbers by multiples of \(10\) in the range \(10\)–\(90\) (e.g., \(9 \times 80\), \(5 \times 60\)) using strategies based on place value and properties of operations. (CCSS: 3.NBT.A.3)

More information icon Academic Contexts and Connections:

More information icon Colorado Essential Skills and Mathematical Practices:

  1. Flexibly exhibit understanding of a variety of strategies when performing multi-digit arithmetic. (Personal Skills: Adaptability/Flexibility)
  2. Demonstrate place value understanding by precisely referring to digits according to their place value. (MP6)
  3. Recognize and use place value and properties of operations to structure algorithms and other representations of multi-digit arithmetic. (MP7)

More information icon Inquiry Questions:

  1. How is rounding whole numbers to the nearest \(10\) or \(100\) useful?
  2. Do different strategies for solving lead to different answers when we add or subtract? Why or why not?

More information icon Coherence Connections:

  1. This expectation is in addition to the major work of the grade.
  2. In Grade 2, students use place value understanding and properties of operations to add and subtract fluently within \(100\).
  3. This expectation connects to other ideas in Grade 3: (a) an understanding of multiplication, (b) knowing the relationship between multiplication and division, and (c) the concept of area and its relationship to multiplication and division.
  4. In Grade 4, students generalize place value understanding for multi-digit whole numbers and use that understanding and the properties of operations to perform multi-digit arithmetic.

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More information icon Prepared Graduates:

  • MP2. Reason abstractly and quantitatively.
  • MP3. Construct viable arguments and critique the reasoning of others.
  • MP7. Look for and make use of structure.

More information icon Grade Level Expectation:

3.NF.A. Number & Operations—Fractions: Develop understanding of fractions as numbers.

More information icon Evidence Outcomes:

Students Can:

  1. Describe a fraction \(\frac{1}{b}\) as the quantity formed by \(1\) part when a whole is partitioned into \(b\) equal parts; understand a fraction \(\frac{a}{b}\) as the quantity formed by \(a\) parts of size \(\frac{1}{b}\). (CCSS: 3.NF.A.1)
  2. Describe a fraction as a number on the number line; represent fractions on a number line diagram. (CCSS: 3.NF.A.2)
    1. Represent a fraction \(\frac{1}{b}\) on a number line diagram by defining the interval from \(0\) to \(1\) as the whole and partitioning it into \(b\) equal parts. Recognize that each part has size \(\frac{1}{b}\) and that the endpoint of the part based at \(0\) locates the number \(\frac{1}{b}\) on the number line. (CCSS: 3.NF.A.2.a)
    2. Represent a fraction \(\frac{a}{b}\) on a number line diagram by marking off \(a\) lengths \(\frac{1}{b}\) from \(0\). Recognize that the resulting interval has size \(\frac{a}{b}\) and that its endpoint locates the number \(\frac{a}{b}\) on the number line. (CCSS: 3.NF.A.2.b)
  3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (CCSS: 3.NF.A.3)
    1. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (CCSS: 3.NF.A.3.a)
    2. Recognize and generate simple equivalent fractions, e.g., \(\frac{1}{2} = \frac{2}{4}\), \(\frac{4}{6} = \frac{2}{3}\). Explain why the fractions are equivalent, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.b)
    3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express \(3\) in the form \(3 = \frac{3}{1}\); recognize that \(\frac{6}{1} = 6\); locate \(\frac{4}{4}\) and \(1\) at the same point of a number line diagram. (CCSS: 3.NF.A.3.c)
    4. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols \( \gt \), \( = \), or \( \lt \), and justify the conclusions, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.d)

More information icon Academic Contexts and Connections:

More information icon Colorado Essential Skills and Mathematical Practices:

  1. Flexibly describe fractions both as parts of other numbers but also as numbers themselves. (Personal Skills: Adaptability/Flexibility)
  2. Analyze and use information presented visually (for example, number lines, fraction models, and diagrams representing parts and wholes) that support an understanding of fractions as numbers. (Entrepreneurial Skills: Literacy/Reading)
  3. Reason about the number line in a new way by understanding and using fractional parts between whole numbers. (MP2)
  4. Critique the reasoning of others when comparing fractions that may refer to different wholes. (MP3)
  5. Use the structure of fractions to locate and compare fractions on a number line. (MP7)

More information icon Inquiry Questions:

  1. How does the denominator of a unit fraction connect to the number of unit fractions that must be added to make a whole?
  2. When the numerators of two different fractions are the same, how can the denominators be used to compare them?

More information icon Coherence Connections:

  1. This expectation represents major work of the grade.
  2. In Grade 2, students (a) relate addition and subtraction to length, (b) measure and estimate lengths in standard units, and (c) reason with shapes and their attributes, including partitioning circles and rectangles into halves, thirds, and fourths.
  3. In Grade 3, this expectation connects to the solving of problems involving measurement and estimation of intervals of time, liquid volumes, and mass of objects and is further supported by the expectation to represent and interpret data.
  4. In Grade 4, students build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers and extend their understanding of fraction equivalence and ordering. In Grade 6, students apply and extend previous understandings of numbers (including fractions) to the system of rational numbers.

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