Activities

1. Identify the denominator in the fraction ¼.
   
   
2. What is the solution to ½ + ½ ?
   
   
3. How many quarters are there in a whole?
   
   
4. Identify the numerator in the fraction ¾.
   
   
5. What is ¾ - ¼ ?

6. Solve 2/3 + 5/8.
   
   
7. Rewrite the expression 5/6 – ½ using twelfths and then solve.
   
   
8. What is the solution to 5/3 + 9/12?
   1. 19/12
   2. 28/12
   3. 2   5/12
   4. 2   4/12
      
      
9. What equation is modeled in the figure below?

10. What equation is modeled in the figure below?

11. 18/4 +1/2 = ?
    
    
12. Write the solution to 18/4 – ¾ as an improper fraction.
    
    
13. Write the solution to 13/4 – ½ as a mixed number.
    
    
14. Is the solution to the following expression a whole number or a mixed number?     2  5/7  + 19/21
    
    
15. Write the solution to the expression 1  2/3 – 1/3 as a mixed number and an improper fraction.

16. What needs to be changed in the problem below to make the solution 4 ¼?  Explain your reasoning.
    Bill had 1 2/3 of a bowl of carrots, ¾ of a bowl of apples, ½ a bowl of bananas, and 1 ½ of a bowl of oranges left over at the food kitchen after lunch was finished being served.  He must log the total amount of leftover food for his inventory.  What did he log?
    
    
17. Four students are combining their bags of Halloween candy.  John has 2/3 of a bag, Sierra has ¾ of a bag, Liam has ¾ of a bag, Jess has 1 1/6 of a bag.  What is the whole or 1 in this situation?  Explain.  How many bags of candy do the students have?
    
    
18. Sam is giving out coupons for a free soda.  He notices that several people have come to his booth for a coupon more than one time.  He decides to keep track of those visiting more than once because he only has 54 coupons to hand out.  Below is his data.

Boy with a cowboy hat – 4 coupons
Girl with braids – 6 coupons
Lady with a blue dress – 3 coupons
Man with red hair – 9 coupons

Write an expression that is modeled by this situation and will answer the following question.   All fractions must be in simplest form.  

What is the fraction of coupons handed out to the people visiting Sam more than once?  Explain how the expression connects to the situation.

19. Insert the appropriate signs ( +, -, x, ÷, =)  into the model below.  Write the expression for the model.  Explain the connection between the model and the expression.

20. What can you tell about the solution to the expression below?  Explain.
    1/2a + 3a / 2a
    
    
21. The work of two students for solving the expression ½ + 5/2 – 2 is listed below.  Find the any errors and explain why it is an error.
    
    Kevin                                                         Ashley
     ½ = 2/4     5/ 2 = 10/4                              ½ = 2/4     5/ 2 = 10/4
    2/4 + 10/4 – 2                                           2/4  +10/4 – 2
    12/4 - 2                                                     12/4 + 2
    4 – 2 =  2                                                   3 + 2 = 5
    
    
22. Use the fractions listed below to create an expression with a solution of 1 ¼.  Use only addition and subtraction.  The fractions can be used more than once.  Show all work.
    ¾     5/6    5/3     1/3   ¼
    
    
23. Use at least one addition sign and at least two of the fractions listed below to create an expression with a solution of  1/24.  Use only addition and subtraction.  The fractions can be used more than once.  Show all work.
    7/8       ½       1/8      ¼       5/12
    
    
24.  Show two different ways to solve the expression.  Give two equivalent solutions.
     1/8 + 3/12 – 1/4
    
    
25. What is incorrect about this model?  Explain. Make a change to make it correct.

Answer Key/Rubric

1. 4
   
   
2. 1
   
   
3. 4
   
   
4. 3
   
   
5. 2/4  or ½

6. 31/24 or 1  7/24
   
   
7. 10/12 – 6/12 answer 4/12 or 1/3
   
   
8. c
   
   
9. ½ + ¾ = 1 ¼ or 5/4
   
   
10. ¾ - ½ = ¼
    
    
11. 20/4 = 5
    
    
12. 15/4
    
    
13. 2  ¾
    
    
14. Mixed Number
    
    
15. 4/3 or equivalent improper fraction.  Mixed number is 1  1/3

16. Answers will vary.  An example would be:  Change 1 2/3 to 1 2/4.  Then when all of the food items are added: 1 2/4 + ¾ + ½ + 1 ½ you get 4 ¼.  Student must explain the process of getting common denominators in order to add the fractions.
    
    
17. Explanations will vary.  The whole is a bag of candy because that is how the candy is being measured or accumulated.  The total is 3 1/3 bags of candy
    
    
18. 4/54 + 6/54 + 3/54 + 9/54 = 22 / 54    In simplest form:  2 /27 + 1/9 + 1/18 + 1/6 = 11/27   Answers will vary.  Since 54 is the total amount of coupons Sam has, it is the denominator.  The amount of coupons given to each repeater is the numerator.  So 22 of the 54 coupons were given to repeaters, or 11 out of 27 coupons in simplest form.
    
    
19. 1 ¼ - ¾ = ½  Answers will vary.  Student must first explain how each drawing represents the fraction given in addition to the reasoning for the inserted signs.
    
    
20. Answers will vary.  The solution to the expression is an improper fraction because the second fraction in the expression is improper.  3/2 is improper no matter what “a” is.  OR  The solution to the expression is 1+3a/2a.  When adding fractions with like denominators, you add the numerators and keep the denominator the same.
    
    
21. Kevin’s error is in the conversion of 12/4.  To simplify this fraction, both the numerator and denominator are divisible by 4 which gives you 3/1 or 3; Kevin wrote 4.  Ashley’s error was in the last step when she wrote +2 instead of -2, thus giving her an incorrect answer of 5 instead of 1.  The correct answer is 1.
    
    
22. Answers will vary. Students must produce an expression that equals 1 ¼ and all work must be shown.   One example is    ¾ + 5/6 – 1/3 = 1 1/4
    
    
23. Answers will vary. Students must produce an expression that equals 1/24 and all work must be shown.   One example is    1/8 + 5/12 – 1/4 – ¼ = 1 1/4
    
    
24. Answers will vary. Students must produce two methods for solving the expression that equals 1/8 and all work must be shown.   One possible example: Students can simplify the fraction 3/12 to ¼ and then convert it to 2/8 or convert all fractions to 24ths.  The solutions are all fractions equivalent to 1/8. 
      
25.  Answers will vary.  There are two “easy” corrections.  One is to change the “+” sign to a “-“ sign.  Another is to change the solution to 3 shaded rectangles or 3.  Student must explain why it is wrong and how they propose to change it.  Theoretically, a student could make more than one change.