*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 two’s or five’s, 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.

The relationship between addition and multiplication is well explained by the fact that, multiplication is more so known to be just repeated addition. This statement is well explained by use of an example. Take into consideration a case where in a group of four students each holding three books. If a question is posed to calculate the total number of books the students are holding, then this calculation can be done this way; by adding 3+3+3+3 and obtain the required solution as 12 books. To explain this, since there are four students and each is holding three books, therefore adding the number of books four times gives the required answer as twelve. Similarly, if you have 5×3, you combined a total of 5 parts in 3 groups, represented as 5+5+5, to obtain 15 an equivalence of 5×3=15. This clearly explains the relationship between addition and multiplication. (Matzke, 2012).

Math uses multiplication and addition, so as to enable students to have a good understanding of the addition concepts like manipulating the groups to obtain the total products. It also helps students find it easy in finding out the quantity or even size of elements in the given groups of same size. A good instance is that where you have a total of 8 sweets in a pack and then you purchase 5 more similar packs, then how many sweets do you have in total at that instance? The solution to this can be obtained by general addition, that is to say, 8+8+8+8+8=40, more so called repeated addition that can be replaced by a multiplication statement, 8×5=40. (Matzke,2012).

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