Name:______Class:______Date______
SWBAT use models to divide fractions by fractions
Do Now[N1]1.) Use a picture to show 4 1/3
2.) Use a picture to show 1/3 4
Class Notes[N2]
Suppose you have half of a large chocolate bar and your cookie recipe calls for 1/8 of a bar. How many cookie recipes can you make with a half bar of chocolate.
Method 1 Method 2:
Bachelors Practice [N3]
Part A: Rasheed and Ananda have summer jobs at a ribbon company. Answer the questions below.
- Use written explanations or diagrams in each to show your reasoning.
- Write a number sentence to show your calculations.
1.)½ yard
Number Sentence:______
2.)¾ yard
Number Sentence:______
3.)2 2/3 yards (Remember 2 2/3 = 8/3)
Number Sentence:______
Part B: Ananda is working on an order for bows. She uses 2/3 yard of ribbon to [N4]make one bow. How many bows can Ananda make from each of the following amounts of ribbon?
4.)1.) 4/5 yard
Number Sentence:______
5.)1 ¾ yards
Number Sentence:______
6.)2 1/3 yards
Number Sentence:______
Dividing Fractions By Fractions Homework
Must show all work and answer all problems to get full credit. Use PENCIL!!!
1.)What algorithm (procedure) makes sense for dividing any fraction by any [N5]fractions?
2.)To solve ¾ 2/5, Elisha writes, “ ¾ 2/5 is the same as 15/208/20. So the answer to ¾ 2/5 is the same as 15 8.”
a.)Is Elisha’s first claim that ¾ 2/5 is the same as 15/208/20 correct? Explain.
b.)Is her second claim that the answer to ¾ 2/5 is the same as 15 8 correct? Explain.
c.)Use Elisha’s method to solve 3/5 1/3. Does this method give you a correct solution? Explain.
[N1]7 minutes
5 minutes work
2 minutes review
Put student work on the board and ask the student to explain.
4 1/3
Draw 4 wholes. Divide each whole into 3 sections . Count the number of 1/3’s
Answer: 12
Have students vote
1/3 4
Put student work on the board and ask the student to explain.
Draw 1 whole. Split it into 1/3’s . Slit the thirds into four equal rows.
Each piece is worth 1/12
Have students vote
[N2]8 minutes
Say:”We have already learned to divie fractions that have either the dividend or the divisor as a whole number. Now we are going to look at problems that involve two fractions.
Do: Have a student read the problem
Say: Take a minute to think about his then share your thinking with your partner (1:30)
Ask: What are we trying to find in this problems?
Answer: How many 1/8’s there are in ½ .
Ask:Does anyone have any ideas about this?
Possible Methods:
1. ) Common Denominator ½ -4/8 so there are 4 8ths in ½.
2.) Draw diagram. Cut into eight pieces then see how many are in ½.
[N3]14 minutes
8 minutes work
6 minutes review
Say: Now I would like you to work on Question A part I by yourselves. Then you can talk with your partners and share your strategies. For the rest of the questions, try each alone and then talk about what you did to your partner. Be prepared to explain your reasoning to the class. You may drawing diagrams to be helpful but if you’re struggling to draw a picture try the common denominator method we discussed in our Class Notes
Answers:
1.)3 There will not be any extra ribbon
2.) 4 ½ There will be 4 whole ribbon badges and ½ of a ribbon badge
16. There will not be any extra ribbon
Summarize:
Say: Okay, Let’s look at some of the problems. Who can tell me their strategy for solving Part A # 1?
Answer: We need to find ½ divided by 1/6. We have 1/3 yd of ribbon and we need 1/6 yd per badge. This means we need to find how many sixths are in ½. I drew a diagram an d counted.
Ask: Does anyone have another way to think about this one?
Answer: I got a common denominators. So I wrote ½ as 3/6. Then I had to find how many sixths are in 2/6. This is the division problem 3/6 1/6 or 3 1., which is 3
Ask: “Who can tell us about question # 2?
“What is different about this question”
Answer: you have a non unit fraction amount of ribbon
Ask: So does the same strategies work?
Answer: Yes you can still ask the question: “how many 1/6’s are in ¾?” You can still draw a diagram or do common denominators.
Say: Ok, Let’s look at a possible strategy.
Do: Use common denominators to write ¾ as 9/12 and 1/6 as 2/12. Divide 9 by 2 to get 4 ½ badtes. Show diagram.
Do: Draw three fourths of the whole and divide the strip into thirds to make 12ths Since 1/6 = 2/12, Out of the 9 1/12 we're working with shade in groups of two. There are 4 and 1/2 groups.
[N4]14
8 minutes work
6 minutes review
Answers:
1.)1 1/5 bows
2.)2 5/8 bows
3.)3 ½ bows
Summarize:
Ask: Which question was harder A or B?
Answer: B because it took 2/3 yard to make one bow. Unit fractions in A seem easier.
Ask: Did your strategies have to change a lot for Part B?
Answer: No actually the same ideas worked.
Ask: For question what what question are we trying to answer?
Answer: How many 2/3’s are in 4/5.
Ask: Who can tell us how you found the answer?
Answer: I tried the common denominators. I wrote both of the givens as 15ths. This gave me 10/15 as the amount of ribbon each bow needed and 12/15 as the amount of ribbon I have. So I have 12 parts and it takes 10 parts to make a bow. I can make 1 bow and have 2/10 left over for another bow. This means I can make 1 2/10 of a bow
Ask similar questions for the remaining problems. Have students show drawings.
[N5]
1.) Possible Answers:
- Find a common denominator for each fractions. Then divide the numerator of the second fraction into the numerator of the first fraction.
- Multiply the first fraction by the denominator of the second fraction and divide the result by the numerator of the second fraction.
- Multiply the first fraction by the reciprocal of the second fraction.
2.)
a.) Elisha’s claim is correct. Possible explanation: The fractions are equivlanet.
b.) Elisha’s claim s correct. Possible explanation: Elisha’s new problem is asking how many groups of 8 twentiths can be made with 15 twentieths. This is the same as asking how many groups of 8 cookies can be makde with 15 cookies. The number sentence for the cookie problem is 15 divided by 8.
Yes. 9/5 or 1 4/5