Student Actions

Teacher Actions

• Develop the ability to communicate mathematically by constructing arguments using concrete representations such as manipulatives, pictures, drawings, and models with applicable mathematical language.

• 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 and 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, e.g. 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 an understanding of when and how to use parentheses.

• Establish mathematics goals to focus learning on multiple opportunities to apply the 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 and multiplication are completed with whichever comes first, and the same with subtraction and addition. (It could also be PEDMAS or PEMDSA).

• Solve expressions and equations with multiple operations correctly.

• Equations must be on the left of the equal sign and the answer on the right.

• A series of numbers and operation signs together with several equals signs is acceptable.

• EX.  (8 + 4 = 12 + 5 = 17)

• There is no connection between the arithmetic properties and algebraic statements of the same properties.

• They understand 3+4 = 4+3 but a+b = b+a is untrue.

• 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.

• Always “multiply before divide and add before subtract”, based on PEMDAS.

  Knowledge Connections

Prior Knowledge

Leads to 

• Use strategies and algorithms (commutative, associative, and distributive properties) to solve division problems. (4.N.2.5)

• Determine unknowns in equivalent and non-equivalent expressions. (4.A.2.3) 

• Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems. (6.A.2.1) 

Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

• 5.A.2.1 Distributive
• 5.A.2.1 Distributive Property