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5-A-2-1

Page history last edited by Brenda Butz 6 years, 2 months ago

5.A.2.1 Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents).

In a Nutshell

In objective 5.A.2.1, students will find equivalent expressions and solve problems based on the following number properties: commutative, associative, and distributive. In fourth grade, they have been introduced to number properties. Order of operations is also included in this objective. This year is the first time they will begin working with order of operations. They will solve order of operations with all four operations and parentheses. They will not have to operate with exponents.

Student Actions	Teacher Actions
Develop the Ability to Communicate Mathematically by constructing arguments using concrete representations such as manipulatives, pictures, and drawings. Develop the ability to make conjectures, model, and generalize by explaining calculations based upon models and properties of operations and rules that generate patterns. Develop Accurate and Appropriate Procedural Fluency by exploring representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, and creating equations. Develop mathematical reasoning by using the distributive property to describe the relationship between the two numerical patterns by reasoning that 6 + 6 + 6 = 2 (3 + 3 + 3).	Support productive struggle in learning mathematics by facilitating real world problem solving activities that allow for a connection of student-generated strategies and methods to more efficient procedures as appropriate. Elicit and use evidence of student thinking by having students summarize their new knowledge and connect their prior knowledge to the new understanding of properties and equivalents. Implement tasks that promote reasoning and problem solving by providing students with multiple expressions that use grouping symbols to develop understanding of when and how to use parentheses. Establish mathematics goals to focus learning on multiple opportunities to apply order of operations and number properties in real-world situations.
Key Understandings	Misconceptions
Understand the commutative property of addition and multiplication. Understand the associative property of addition and multiplication . Understand the distributive property. Realize that the distributive property can be represented in multiple ways. Use partial products. Know that “PEMDAS” is a tool that they can use to help them solve a problem with more than one operation, but must understand that they read the equation from left to right and that. division/multiplication is completed with whichever comes first, and the same with subtraction/addition. Solve expressions and equations with multiple operations correctly.	Think numbers on the left of the equation have the operation followed by the equals sign and the answer on the right. If the answer is on the left followed by the equals sign and the operation is on the right, it is backwards and can't be solved (c = a+b). Think they can string a series of numbers and operation signs together with several equals signs. EX. 8 + 4 = 12 + 5 = 17) Think there is no connection between the arithmetic properties they already understand and the algebraic statements of the same properties. They understand 3+4 = 4+3 but not a+b = b+a is non-sensical. Know the commutative and associative property of addition or multiplication but fails to apply it to simplify the “work” of addition or multiplication. Misapply the commutative and associative properties in subtraction situations Solve problems from left to right no matter what the operations are. Not distribute multiplication to all terms in the parentheses. Think “multiply before divide and add before subtract”, based on PEMDAS.