This task is from Tools 4 NC Teachers. Students explore how the order of operations and placement of parentheses influences the value of each expression. This is remixable.

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Choose one set of expressions.

Set A                                Set B                             Set C                                 Set D

1 + 2 + (3 + 4)                 1 x 2 x (3 x 4)               1 + 2 x (3 + 4)                   (1 x 2) + 3 x 4

(1 + 2) + 3 + 4                 (1 x 2) x 3 x 4               (1 + 2) x 3 + 4                   1 x 2 + (3 x 4)

1 + (2 + 3) + 4                 1 x (2 x 3) x 4               1 + (2 x 3) + 4                   1 x (2 + 3) x 4

1 + 2 + 3 + 4                    1 x 2 x 3 x 4                 1 + 2 x 3 + 4                      1 x 2 + 3 x 4

·       Find the value of each expression.  What patterns do you notice?  What impact does the position of the parentheses have on the value of the expressions? 

·       Find a partner who chose a different set than the one you chose.  What did they notice about their expressions? 

Why do we use parentheses in mathematical expressions?  When is it important to use parentheses?  When are parentheses not necessary?