Activities

1. Circle the brackets in the expression.  9 ÷ 2[2- 3(1+3)]
   
   
2. If parentheses and brackets are in a numerical expression, which is first for order of operations?
   
   
3. Simplify.  2(3 + 5)
   
   
4. What should be solved first in the following expression:  3[6 + 2(1 + 4)]

5. How many possible solutions are there to the simplification of the expression?  Why?
      33 - 4 + 3(6 + 5) ÷ 5
   
   
6. Circle the expression with the smallest value.
     12 + 6(9 – 1) ÷ 12                9 + 3(2 + 5) ÷ 7
   
   
7. Simplify the expression.  7 + [14 – 16 ÷ 8 + (9 ÷ 3)]
   
   
8. What is the difference between the solution to the expression {[24 – 6(1+1)] + 6} ÷ [1 + (6 – 4)] and the same expression with the braces removed?
   
   
9. Which expression has a greater value?
   
   a.  15 x 4 – 10 ÷ 5 + 2
   b.  (15 x 4 – 10) ÷ 5 + 2
   c.  15 x 4 – 10 ÷ (5 + 2)
   d.  15 x 4 – (10 ÷ 5+ 2)
   
   
10. Roses are in bunches of 12 and tulips are in bunches of 6.  There are 3 bunches of red roses and 4 bunches of white roses.  There are 2 bunches of yellow tulips and 5 bunches of pink tulips.  What expression represents the total number of flowers?
    
    a.   12 + 3 + 4 + 6(2 + 5)
    b.  12(3 + 4 + 6 + 2 + 5)
    c.  12(3 + 4) + 6(2 + 5)
    d.  12(3 + 4 + 2 + 5) + 6
    
    
11. What number can be substituted for B so the expression has a value of 2?
    {[36 – 8(5- 3)] + B} ÷ [7 + (24 ÷ 4)]
    
    
12. Place brackets in the expression so that the solution is 4.       24 – 6(1+1) ÷ 1 + (6 – 4)
    
    
13. Use any combination of brackets, braces and parenthesis in the expression so the solution is 4.  One parenthesis is already placed in the expression.  
    2  +  3 ( 4  –  3  ÷  12  –  7  +  3

Answer Key/Rubric

1. Student circles both [ and ]
   
   
2. Parentheses
   
   
3. 16
   
   
4. 1 + 4

5. One solution.  The order of operations permits only one solution.
   
   
6. Students circle:  9 + 3(2 + 5) ÷ 7
   
   
7. 22
   
   
8. The difference is 8. 

With braces: {[24 – 6(1+1)] + 6} ÷ [1 + (6 – 4)] = 6
Without the braces: [24 – 6(1+1)] + 6 ÷ [1 + (6 – 4)] = 14.

9. A
   
   
10. C
    
    
11. 6
    
    
12. [24 – 6(1+1)] ÷ [1 + (6 – 4)]
    
    
13. [2 + 3 (4 – 3)] ÷ (12 – 7) + 3