In a brief essay (suggested length of 3 pages): A. Explain the relationship between multiplication and addition. B. Describe how understanding the relationship between multiplication and addition contributes to students understanding of these operations. For example, how does multiplication extend addition concepts (e.g., manipulation of groups for a total product)? C. Explain the commutative, associative, and distributive properties using examples. D. For each property, describe how it is connected to thinking strategies students might use in performing computations (e.g., counting by twos or fives, groupings or many sets of items, adding several equal groups together). E. Provide specific examples of at least two common conceptual errors. 1. Describe an instructional strategy that would serve to correct and/or avoid each of these conceptual errors (1 strategy per conceptual error for a total of at least 2 strategies). 2. Explain how each of the instructional strategies serves to correct and/or avoid its associated conceptual error. F. When you use sources, include all in-text citations and references in APA format.

In a brief essay (suggested length of 3 pages): A. Explain the relationship between multiplication and addition. B. Describe how understanding the relationship between multiplication and addition contributes to students understanding of these operations. For example, how does multiplication extend addition concepts (e.g., manipulation of groups for a total product)? C. Explain the commutative, associative, and distributive properties using examples. D. For each property, describe how it is connected to thinking strategies students might use in performing computations (e.g., counting by twos or fives, groupings or many sets of items, adding several equal groups together). E. Provide specific examples of at least two common conceptual errors. 1. Describe an instructional strategy that would serve to correct and/or avoid each of these conceptual errors (1 strategy per conceptual error for a total of at least 2 strategies). 2. Explain how each of the instructional strategies serves to correct and/or avoid its associated conceptual error. F. When you use sources, include all in-text citations and references in APA format.