Activities

1. Add 9 and 4, is represented by the numerical expression 9 - 4.  True or false?
   
   
2. When a number is doubled it is _________ by 2.
   
   
3. 8 – 3 is not the same as writing three less than 8.  True or false?
   
   
4. 8 + a is half of 2(8 + a).  True or false?
   
   
5. Write 12 ÷ 4 in word format.

6. Write an expression for the phrase.   Subtract 9 from 12 and then multiply by 2
   
   
7. Write a phrase for the following expression: 12 ÷ (2 + 4)
   
   
8. How many times larger is the first expression than the second expression?
    h ( 12 + 42)                             12 + 42
   
   
9. Write an expression that is half of 2(4 – a).  The “a” represents a positive whole number.
   
   
10. Which expression is three times as large as 3(8 – 3) + 12 – 2(6 + 4)?
    
    a.   3(8 – 3) + 12 – 2(6 + 4)
    b.  3(24 – 3) + 12 – 2(18 + 4)
    c.  6(8 – 3) + 12 – 6(6 + 4)
    d.  9(8 – 3) + 36 – 6(6 + 4)
    
    
11. Compare the two expressions, which is smaller?  The “a” represents a positive whole number.
    a(9 – 5) ÷ 33                a(9 – 5) ÷ 33a 
    
    
12. Compare the two expressions, are they the same or is one smaller than the other?  The “b” represents a positive whole number.
    2[8(b – 4)]÷ 10                        8(b – 4) ÷ 5
    
    
13. Which statement is true about the expression 7(8 – 1) + 12?
    
    a.  The expression will be three times as large if the 7 is multiplied by 3.
    b.  The expression will be twice as large if the 7 is multiplied by 2 and the 12 is multiplied by 2
    c.   The expression will be three times as large if the 8 and 12 are multiplied by 3.
    d.  The expression will be twice as large if the 8 is multiplied by 2 and the 12 is divided by 2.
    
    
14. Compare the two expressions, 6[a(9 – 4) ]+ 10 and a(9 – 4) + 10.  The “a” represents a positive whole number.  Which statement is true?
    
    a.  The first expression is larger
    b.  The second expression is larger
    c.  The expressions are equivalent
    d.  There is not enough information to make a statement

15. Would you need parenthesis when writing 9 divided by 3 multiplied by 2 as an expression if the solution is 1 ½?  Explain.
    
    
16. Explain why the calculation for “add 6 and 7, then multiply by 3” must have a set parentheses.
    
    
17. There are two calculations “add 2 and 4 then divide by 12” and “add 2 and 4 divided by 12”.  Write a numerical expression for each calculation and explain why parentheses were necessary.
    
    
18. Given the expression b(11 – 5) ÷ 9 where “b” is a positive whole number.  Rewrite the expression and make an adjustment which makes the expression three times as large.  Explain why it is three times larger.
    
    
19. Compare the two expressions, 6[b(4 – 2)]+ 7 and b(4 – 2) + 7.  The “b” represents a positive whole number.  Explain how you know the first expression is larger, even though “b” is unknown.
    
    
20. Select an expression that is 4 times as large as the expression 7 + 2(16 – b) – 4.  Explain.
    
    a.   7 + 8(16 – b) – 4
    b.  4[7 + 2](16 – b) – 4
    c.  28 + 8(16 – b) – 16
    
    
21. Given the expression 25 ÷ (3 + c), write two different expressions that are 4 times larger than the one given.  Explain.
    
    
22. Given the rule “add 4 and 16, then divide by 2”, write the numerical expression and explain.
    
    
23. Casey tells Mrs. Smith that she has multiplied the expression on the board by three.  Is she accurate?  Why?  Why not?

Expression on the board:    7 + 2(16 – b) – 4
Casey’s expression:  21 + 2(16 – b) – 12

Answer Key/Rubric

1. False
   
   
2. Multiplied
   
   
3. False
   
   
4. True
   
   
5. Twelve divided by four or the quotient of twelve and four

6. 2(12 – 9) or (12 – 9)2
   
   
7. Answers will vary.  One example:  Divide 12 by the solution to 2 added to 4.
   
   
8. H times larger
   
   
9. Answers will vary.  Example:  4 - a
   
   
10. D
    
    
11. a(9 – 5) ÷ 33a
    
    
12. The same
    
    
13. B
    
    
14. A

15. Yes parentheses are necessary.  Explanations will vary.  This expression can be written as 9 ÷ 3 x 2, where 9 ÷ 3 is 3 and then 3 multiplied by 2 is 6, which is not 1 ½.  When parentheses are inserted as follows 9 ÷ (3 x 2), 3 x 2 is first so 9/6 = 1 ½
    
    
16.  Explanations will vary.   The calculation says “add 6 and 7, then multiply by 3” because of the word “then” it means that 6 and 7 are to be added first then the resulting number is multiplied by three.
    
    
17. The first calculation uses the word “then”, which means 2 and 4 are added first and the result is divided by 12.  (2+4) ÷ 12 = ½
    The way the second calculation is written there is no “then”.  Therefore, it is written as 2 + 4 ÷ 12 = 2 1/3, where 4 is divided by 12 and then two is added.
    
    
18. 3b(11 – 5) ÷ 9 or b(11 – 5) ÷ 3 Explanations will vary.  Example:  Since 11 – 5 = 4 and 4 times b is 4b, if 4b is multiplied by 3 that will make what is being divided by 9, three times larger. Since it is three times larger than the original number being divided by nine, the solution will also be three times larger. Students may use an example with numbers to demonstrate.
    
    
19. Explanations will vary.  Students must explain that what is inside the brackets is six times larger in the first expression than the second no matter what the number because it is being multiplied by six.  The second part of both expressions is adding 7, but it is done to both equations.
    
    
20. C.  Explanations will vary. Students must somehow state that every term in the expression was multiplied by 4 therefore the solution will be 4 times larger.  Since 2(16 – b) is considered one term, the 2 is multiplied by 4.
    
    
21. 100 ÷ (3 + c) and 4[25÷ (3 + c)]  Explanations will vary. Students must explain that since 100 is 4 times larger than 25 and they are both being divided by the same number, the solution will be 4 time larger.  In the second expression, the solution is being multiplied by 4 therefore it will be 4 times larger.
    
    
22. (4 + 16)/2 or (4 + 16) ÷ 2.  Explanations will vary.  Student must explain that parenthesis are necessary around the addition because the word “then” in the rule indicates that division is the last step.  If the parentheses were not there 16 would be divided by 2 first.
    
    
23. Casey is not accurate.  Explanations will vary.  The first term (7) she did multiply by three accurately to get the 21.  The third term (4) she multiplied by three correctly to get 12; however the second term, 2(16 – b), she did not multiply by three at all, and here is the error.