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Order of Operations: Patterns and Algebra

Explore the convention for the order of operations and how it ensures consistent results in solving number sentences involving multiple operations. Discover how grouping symbols can change the order of operations. Solve problems and reflect on the process.

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Order of Operations: Patterns and Algebra

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  1. 14 - 8 + 3 = 9 OR 14 - 8 + 3 = 3 Which one is correct? 14 - 8 + 3 = 9 14 - 8 + 3 ≠ 3 Convention: Addition an subtraction left to right Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

  2. 24 ÷ 4 x 6 = 36 OR 24 ÷ 4 x 6 = 1 Which one is correct? 24 ÷ 4 x 6 = 36 24 ÷ 4 x 6 ≠ 1 Convention: Multiplication and division left to right Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

  3. 8 + 5 x 2 = 26 OR 8 + 5 x 2 = 18 Which one is correct? 8 + 5 x 2 ≠ 26 8 + 5 x 2 = 18 Convention: First multiplication and division left to right, then addition an subtraction left to right Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

  4. (8 + 5) x 2 = 26 8 + 5 x 2 = 18 • The bracket is a grouping symbol that tells us to perform that operation first. • So in this number sentence with the brackets as grouping symbols, we will add 8 and 5 first to make 13, then multiply the total by 2 to make 26. Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

  5. Investigation: Select cards to make a number sentence (equation) involving more than one operation. Solve the number sentence (equation) by performing the operations using the convention for the order of operations. Reflection: How does the convention for the order of operations make sure we all get the same answer? Problem Solving Lola said this number sentence equals 44. 3 + 8 x 4 = 44 Do you agree? Why? Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

  6. Investigation: Select cards to make a number sentence (equation) involving more than one operation. Solve the number sentence by performing the operations using the convention for the order of operations. Insert a grouping symbol to change the order of operations. Solve the number sentence by performing the operations in the new order. Did you get different answers? Why? Reflection: How do grouping symbols change the order of operations? Problem Solving Kerry said this number sentence equals 44. (3 + 8) x 4 = 44 Do you agree? Why? Multiplication and Division 29 Addition and Subtraction 33 Patterns and Algebra 31

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