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5th Grade
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Numerical Expressions, Patterns, & Relationships

  • Lesson 1: Variables and Expressions
  • Lesson 2: Order of Operations
  • Lesson 3: Evaluating Expressions
  • Lesson4: Addition and Subtraction Expressions
  • Lesson 5: Multiplication and Division Expressions
  • Lesson 6: Patterns: Extending Tables
  • Lesson 7: Problem Solving 
Vocabulary
  • variable: a letter, such as n, that represents a number in an expression or an equation
  • term: a number in a sequence or a variable, such as x or y in an algebraic expression
  • sequence: a set of numbers that follows a pattern
  • algebraic expression: a mathematical phrase involving a variable, or variables, numbers, and operations   Example: x-3
  • order of operations: the order in which operations are done in calculations: parentheses, exponents, multiply AND divide, add AND subtract 
  • corresponding: matching, as in related terms in two sequences. 
Lesson 1: Variables and Expressions
Main Idea: Students translate words into algebraic expressions. They learn how some mathematical phrases can be represented using a variable in an algebraic expression.
Standard (s): 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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Lesson 2: Order or Operations
Main Idea: Students use given values for variables to evaluate numerical or algebraic expressions with three or more numbers and two or more operations. They learn that to simplify a numerical expression, first compute within parentheses. Then do any multiplication and division calculations, followed by any addition and subtraction calculations.
Standard (s): 5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
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Lesson 3: Evaluating Expressions
Main Idea: Students use the order of operations to evaluate expressions with whole numbers and decimals. They learn that there is an agreed-upon order in which operations in a numerical expression are performed.
Standard (s): 5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
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Lesson 4: Addition and Subtraction Expressions
Main Idea: Students study completed tables to determine a rule and write an expression with addition or subtraction. They learn how patterns can sometimes be used to identify a relationship between two quantities. They also learn that some real-world quantities have a mathematical relationship and the value of one quantity can be found if you know the value of the other quantity.
Standard (s): 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
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Lesson 5: Multiplication and Division Expressions
Main Idea: Students study completed tables to determine a rule and write an expression with multiplication or division. They learn how patterns can sometimes be used to identify a relationship between two quantities. They also learn that some real-world quantities have a mathematical relationship and the value of one quantity can be found if you know the value of the other quantity.
Standard (s): 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
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Lesson 6: Patterns: Extending Tables
Main Idea: Students extend patterns in a table using given rules, and then look for the relationship between corresponding terms in the sequences. They learn how patterns that repeat in predictable ways may be used to identify relationships
Standard (s): 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
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Lesson 7: Problem Solving- Use Reasoning 
Main Idea: Students solve problems by showing how to act out the problem. They also use information given in the problem to draw conclusions. They learn how some problems can be solved by using objects to act out the actions in the problem and some problems can be solved by reasoning about the conditions in the problem.
Standard (s): 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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