Activities

1. How many cookies would each student get if two cookies were divided between four students?
   
   
2. How many brownies would each student get if four brownies were divided between three students?
   
   
3. If three dog bones are divided among 2 dogs, would the answer be a whole number or a fraction?
   
   
4. If there are 5 students on the playground, give two examples of the number of pieces of candy necessary so each student can have an equal number with no partial pieces.
   
   
5. True or false.  Each student in a group of 4 will get 2 ½ cookies if there are 10 cookies.

6. The Blue Group has 20 brownies to be divided evenly between 25 students.  The Red Group has 12 brownies to be divided evenly between 20 students.  Which students will get a bigger piece of brownie?
   
   
7. Sasha has 55 ice cream sandwiches and there are 44 girl scouts in her troop.  She will divide them all up in order to give each girl an equal share.  How many ice cream sandwiches will each girl receive?
   
   
8. If three dog bones are divided among 2 dogs, would the answer be a whole number or a fraction? Explain.
   
   
9. There are 20 students going to the baseball game.  Parents are purchasing 12 subs and four 2-liter bottles of soda.  What fractional part of a sub will each student receive?
   
   
10. There are 5 apples for 4 horses.  Explain why each horse will get at least 1 apple.
    
    
11. 30 students must share 9 submarine sandwiches.  How much does each student receive?
    
    
12. 8 students must share 10 cookies.  Write the number of cookies each student will receive as an improper fraction.
    
    
13. Five pizzas will be shared among 12 students.  What fractional part of all the pizza will each student receive? 
    
    
14. Five cakes will be shared among 7 students.  What fractional part of one cake will each student receive?
    
    
15. What improper fraction represents that solution to the following problem? 
    The museum is being restored and all of the 12 rooms will be painted. Josh figured out the budget will allow him to purchase 9 gallons of paint.  How much paint can be used in each room?

16. Five pizzas will be shared among 12 students.  What fractional part of all the pizza will each student receive?  What fractional part of one pizza will a student receive? Compare what is representative of the whole in the first and second question and explain your reasoning.
    
    
17. The three rectangles below represent pepperoni pizzas.  Draw lines to model how it can be cut to be divided equally among 12 students.  What fractional part a pizza will each student receive?  Three more of the same size pizzas are purchased to share equally among the 12 students but have only cheese on them and are cut differently.  Compare the amount of cheese and pepperoni pizza the students would receive. Explain your reasoning.

18. The Blue Group has 20 brownies to be divided evenly between 15 students.  The Red Group has 12 brownies to be divided evenly between 16 students. How can you tell which students (the Red Group or the Blue Group) will get a larger piece of brownie without doing a single calculation?  Explain your reasoning.
    
    
19. The students in Ms. Rutkowski’s class were asked to create a word problem in which the solution is a fraction.  Zoe created the problem below.  
    
    Q:  There are 6 pans of brownies and each pan is cut into 4 pieces.  How many brownies would 12 students receive?
    
    Zoe solved the problem and indicated that each student would receive ½ brownie.
    What word or phrase (not a number) would need to be changed in Zoe’s question (and also therefore in her answer) in order to get the fraction ½ for the answer? Explain your reasoning.
    
    
20. The students in Ms. Rutkowski’s class were asked to create a word problem in which the solution is a fraction.  Zoe created the problem below.  
    
    Q:  There are 6 pans of brownies and each pan is cut into 4 pieces.  How many brownies would 12 students receive?
    
    Zoe solved the problem and indicated that each student would receive ½ brownie.
    What word (not a number) would need to be changed in Zoe’s answer in order for the solution to be correct? Explain your reasoning.
    
    
21. There are 12 students sharing 5 blankets on the hayride.  What portion of a blanket does each person receive? Is the solution 12/5?  Explain.  Based on the way this question is asked, what is represented as the whole?
    
    
22. Kalee has 4 boxes of ice cream sandwiches with 12 in a box.  Each box cost $3.49.  Kalee has 9 friends coming over for the weekend.  How many ice cream sandwiches will each person get? Is your solution equivalent to 28/5?
    
    
23. Compare the work of Johanna and Kajeet when solving the problem below.  Did they both do the work correctly?  Who has the correct answer?  Explain you reasoning.
    There are 12 candy bars that must be shared equally by 8 people.   Explain how you would divide the candy equally.  How much does each person get?

Johanna                                  
I would distribute one candy bar to each of the 8 people, thus leaving 4 candy bars.  Then I would take the 4 candy bars and divide them into fourths, giving each person two fourths. The total amount of candy each person would receive is 1 2/4.

Kajeet
Divide each candy bar into 8 equal parts.  Each person gets 1/8 of each candy bar for a total of 12/8 per person.

24. Compare the work of Kenya and Thomas when solving the problem below.  Did they both do the work correctly?  Who has the correct answer?  Explain you reasoning.
    There are 4 submarine sandwiches that must be shared equally by 9 people.   Explain how you would divide the sandwich equally.  How much does each person get?

Kenya                         
I would distribute 1/3 of each sub to each of the 9 people.  1/3 times 4 subs is 4/3.  The total amount of sandwich each person would receive is 1 and 1/3.

Thomas
Put all of the subs in one long line and divide the entire length into 9 equal parts. Each person would get 1/9 of the long line.  Since there are 4 single subs, 4 times 1/9 equals 4/9 of a single sub.   Each person would get 4/9 of a single sub.

25. Give an example of a situation where something is being shared equally and the portion is greater than 1 whole.  Compare this with a situation where the portion is less than a whole.  Explain the difference between the situations in regard to the portion being greater or less than 1.

Answer Key/Rubric

1. ½ cookie each
   
   
2. 1 1/3 brownie
   
   
3. Fraction
   
   
4. 10, 20, additional answers are possible; any number that is a multiple of 5 will work
   
   
5. True

6. Blue Group – the blue group will get 4/5 and the red group will get 3/5
   
   
7. 1 ¼ sandwich
   
   
8. Fraction, because 2 does not divide evenly into 3
   
   
9. 3/5 of a sub
   
   
10. 4 goes into 5 at least 1 time with a remainder
    
    
11. 3/10 of a sub
    
    
12. 5/4 of a cookie
    
    
13. 5/12
    
    
14. 1/7
    
    
15. ¾ of a gallon (must have gallon)

16. 5/12, 1/12  The whole is represented by five pizzas in the first question whereas in the second questions the whole is one pizza.  The indicators in the questions are “all” and “one” respectively
    
    
17. Students must draw lines that will represent equal pieces and show exactly 12 equal portions – many solutions can be drawn and the fraction should be equivalent to ¼.  The cheese and pepperoni portions would be the same because the whole is the same in both situations.

18. The Blue Group will get more brownie per student because this group has more brownies than students and students will get at least one whole brownie.  Whereas the Red Group has more students than brownies therefore when the brownies are divided each student will get a fraction of a whole brownie.
    
    
19. Change the word brownie to “pans of brownies”.  This changes the whole from brownies to pans and thus 6 pans of brownies divided by 12 students would give each student ½ a pan of brownies.
    
    
20. Change the word brownie to “pan”.  The whole then is represented by the pan instead of the whole being a single brownie.
    
    
21. The solution is not 12/5 because this would mean that each student would have 2 and 2/5 blankets.  There are only 5 blankets total and 12 students must share so each student gets less than one blanket.  The whole is referring to total blankets.
    
    
22. Each person will get 4 and 4/5 ice cream sandwiches.  Since she has 9 friends coming over, that means there are 10 people total to split up 48 sandwiches.  No.
    
    
23. Both did the work correctly and got a correct answer.  Student must explain how the work is correct for both Johanna and Kajeet.  They must include that 1 2/4 is the same as 12/8.
    
    
24. Kenya did the work incorrectly and her answer is incorrect.  Student must explain why work is incorrect.  Thomas did the work correctly and has a correct answer.  Student must explain why the work is correct.
    
    
25. Situations will vary. Most importantly, student is able to articulate that when the portion is greater than 1, the number of people is less than the number of objects to be divided.  Conversely, when the portion is less than 1, the number of objects to be shared is less than the number of people.