Colorado Academic Standards Online
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clear Content Area: Mathematics - 2019 // Grade Level: Fourth Grade // Standard Category: 2. Algebra and Functions
Mathematics - 2019
Fourth Grade, Standard 2. Algebra and Functions
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- MP1. Make sense of problems and persevere in solving them.
- MP2. Reason abstractly and quantitatively.
- MP4. Model with mathematics.
- MP7. Look for and make use of structure.
4.OA.A. Operations & Algebraic Thinking: Use the four operations with whole numbers to solve problems.
Students Can:
- Interpret a multiplication equation as a comparison, e.g., interpret \(35 = 5 \times 7\) as a statement that \(35\) is \(5\) times as many as \(7\) and \(7\) times as many as \(5\). Represent verbal statements of multiplicative comparisons as multiplication equations. (CCSS: 4.OA.A.1)
- Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix, Table 2) (CCSS: 4.OA.A.2)
- Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (CCSS: 4.OA.A.3)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Make sense of multi-step word problems by understanding the relationships between known and unknown quantities. (MP1)
- Reason quantitatively with word problems by considering the units involved and how the quantities they describe increase or decrease with addition and subtraction or scale with multiplication and division. (MP2)
- Use mathematics to model real-world problems requiring operations with whole numbers and contextually interpret remainders when they arise. (MP4)
- Look for structures of commutativity and inverses of operations in solving whole number problems with the four operations. (MP7)
- What makes a multiplicative comparison different from an additive comparison?
- How can you recognize whether a comparison is multiplicative or additive?
- This expectation represents major work of the grade.
- In Grade 3, students represent and solve problems involving multiplication and division, apply properties of multiplication and the relationship between multiplication and division, solve problems involving the four operations, and identify and explain patterns in arithmetic.
- This expectation connects to other ideas in Grade 4: (a) using place value understanding and properties of operations to perform multi-digit arithmetic, (b) extending understanding of fraction equivalence and ordering, (c) building fractions from unit fractions, and (d) solving problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- In Grade 5, students apply and extend previous understandings of multiplication and division to multiply and divide fractions by fractions.
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- MP2. Reason abstractly and quantitatively.
- MP7. Look for and make use of structure.
- MP8. Look for and express regularity in repeated reasoning.
4.OA.B. Operations & Algebraic Thinking: Gain familiarity with factors and multiples.
Students Can:
- Find all factor pairs for a whole number in the range \(1\)–\(100\). Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range \(1\)–\(100\) is a multiple of a given one-digit number. Determine whether a given whole number in the range \(1\)–\(100\) is prime or composite. (CCSS: 4.OA.B.4)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Reason quantitatively to recognize that a number is a multiple of each of its factors. (MP2)
- Use the relationship between factors and multiples for whole numbers. (MP7)
- Look for, identify, and explain the regularities in determining whether a given number is a multiple of a given one-digit number and in determining if a given number is prime or composite. (MP8)
- How can you use arrays to explore and determine all of the factors of a given number?
- How are multiples and factors helpful in solving problems related to fractional parts of a whole number, such as \(\frac{3}{5}\) of \(20\)?
- This expectation supports the major work of the grade.
- In Grade 3, students multiply and divide within 100.
- In Grade 6, students compute fluently with multi-digit numbers, find common factors and multiples, and extend previous understandings of arithmetic to algebraic expressions.
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4.OA.C. Operations & Algebraic Thinking: Generate and analyze patterns.
Students Can:
- Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add \(3\)” and the starting number \(1\), generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. (CCSS: 4.OA.C.5)
Academic Contexts and Connections:
Colorado Essential Skills and Mathematical Practices:
- Explore and generate sequences of numbers or shapes that can be described mathematically. (Entrepreneurial Skills: Creativity/Innovation)
- Notice when calculations are repeated and describe patterns in generalized, mathematical ways. (MP8)
- If you were given a rule to add \(4\) to a starting number then to each number that follows, can you generate a sequence of odd numbers? How?
- This expectation is in addition to the major work of the grade.
- In Grade 3, students solve problems involving the four operations and identify and explain patterns in arithmetic.
- In Grade 5, students analyze pairs of patterns created from two given rules and describe and graph the corresponding relationships.
Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us