# Words to Expressions 1

Alignments to Content Standards: 5.OA.A.2

Write an expression that records the calculations described below, but do not evaluate.

Add 2 and 4 and multiply the sum by 3. Next, add 5 to that product and then double the result.

## IM Commentary

This problem allows student to see words that can describe the expression from part (c) of "5.OA Watch out for Parentheses." Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.

## Solution

Taking the instructions step by step we have:

1. Add 2 and 4 and multiply the sum by 3: $3(2+4)$ or possibly $(2+4)3$.
2. Add 5 to that product gives $5+3(2+4)$ or $3(2+4)+5$ or even $(2+4)3+5$.
3. Then double the result means we need to multiply the entire expression by 2: $$2(5 + 3(2 + 4))$$ or $$(5 + 3(2 + 4))2$$ or $$2(3(2+4)+5)$$ or $$(3(2+4)+5)2$$ or $$2((2+4)3+5)$$ or $$((2+4)3+5)2$$ Additionally, this can be written as $$(5 + 3(2 + 4)) + (5 + 3(2 + 4)).$$

The differing ways the calculations can be expressed also help to illustrate the commutative laws of multiplication and addition.