Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 72731
Make a Funny Partial Quotient Division Story
This lesson introduces students to the area model and the partial quotient model to solve division problems with 2-digit divisors. Students are asked
to apply both strategies to solve funny division problems that they help create by inserting information that is left blank in the story problems.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Internet Connection, LCD
Projector, Speakers/Headphones, Microsoft Office
Instructional Time: 2 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Division, Area Model, Partial Quotient, Story Problems, Word Problems
Resource Collection: FCR-STEMLearn Mathematics General
ATTACHMENTS
Simple Division with BaseTen Blocks Review.docx
Make a Funny Division Story Assessment.docx
Make a Funny Partial Quotient Division Story powerpoint.pptx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
The students will increase their understanding of the relationship between multiplication and division.
The students will attend to the role of place value in division.
The students will be able to demonstrate, by solving an equation, how to find the quotient of a division problem with a two-digit divisor and a four-digit dividend.
The students will be able to solve a real-world problem using an area model of division as finding side lengths to illustrate and explain partial quotient.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students know their multiplication facts.
Students understand the place value system.
Students know the vocabulary for division.
Students know where the groups (divisor), how many in all (dividend), and how many in a group (quotients) are placed in an area model.
Guiding Questions: What are the guiding questions for this lesson?
What is the relationship between multiplication and division.
How many hundreds, tens, and ones did you put into each group?
What strategies can we use to find the quotient in a division problem?
How does the area model help us solve division problems?
Teaching Phase: How will the teacher present the concept or skill to students?
Use the Make a Funny Partial Quotient Division Story PowerPoint (attached) to introduce the hook.
page 1 of 5 The Hook: Students will make a funny division story. At the beginning of the math lesson tell the students that they will be writing and solving a funny math story.
Ask:
What is the name of a funny place?
What is the name of a funny game you could play in that place?
Now, insert those answers into the following story problem and write this problem on the board.
"You and 4 of your friends went to the ______________________ and earned 695 tickets in the ______________ game. How are you going to
divide the tickets up?"
This step engages them by making them feel at ease with discussion involving numbers in a fun way.
Ask:
1. Do you think that each of the friends will receive the same amount of tickets? Why? Why not?
(Possible answer: Yes, because 695 ends in 5, and we will be dividing the tickets among five friends.)
2. Teacher must observe students' responses for the following: Do students know that they have to divide amongst 5 students and not 4?
3. Do students know that division involves separating one group into equal groups?
4. Optional: Do students know the divisibility rule for 5?
Teachers, please note: I have attached a document for reviewing simple division with base-ten blocks in multiplication and division. If you feel your students need this
review then you can use this document. If you are sure your students understand that multiplication and division are about making equal groups, then go on to the
next steps in this division strategy.
Introduce the lesson: "Today we will learn how to determine how many tickets you will distribute to each friend using the area model of division. This is a method
of dividing by which we subtract from the dividend, or the tickets, until everyone has the same number of tickets, which is the quotient or the answer to the division
problem."
Tell the students to take out their math journals and to copy what you write on the board as you explain it. (See the Make a Funny Partial Quotient Division Story
PowerPoint attached.)
1. Tell the students to write the number 5 in the far left column, and ask the students, "What does the number 5 represent?" (the number of friends the tickets will be
divided amongst)
2. Tell students to write the number 695 and ask students, "What does 695 represent?" (the tickets to be distributed)
3. "How many hundreds of tickets can you give to each friend to be able to give the same number of hundreds tickets to each of your friends?" (100 tickets)
4. "Can you give 200 tickets to each friend?" (No, because you would need 1,000 tickets to be able to do that.)
5. "If you give 100 tickets to each friend, how many tickets will you have given to the five friends?" (Point to the quotient at the top of the chart and to the number of
friends on the side of the chart) (500 tickets)
6. Click PowerPoint to write 100 on top of the hundreds column and -500 under 695.
7. Ask the students: "If I subtract the 500 tickets I have distributed to my friends how many tickets do I have left to distribute?" (195 tickets)
8. Click PowerPoint to write 195 in the tens column.
9. "From the 195 tickets that are left, how many tens of tickets can you give to each friend to be able to give the same number of tens of tickets to each of your
friends?" (30 tickets)
10. "Can you give 40 tickets to each friend?" (No, because you would need 200 tickets and you only have 195).
11. "Can you give 20 tickets to each friend?" (yes)
12. "If each friend got 20 tickets, how many tickets is that?" (100 tickets)
13. "If you take away those tickets from 195 you will have 95 tickets."
14. "Do you have enough tickets left over to give each friend another ten tickets?" (yes)
15. Repeat this until there aren't enough tens to give each friend an even amount.
16. How many tickets are left? (45 tickets) Write 45 in the ones column.
17. Of those tickets that are left, how many can you give to each friend and subtract from the dividend in order to be able to give the same number of tickets to each of
your friends? (9 tickets)
18. Put the 9 on top of the ones column and tell the students, "Nine tickets given to each friend times 5 friends is 45 tickets."
19. Write -45 in the ones column and subtract.
20. "How many tickets are left over?" (0)
21. "Did I distribute all the tickets?" yes
22. "What does it mean if I have tickets left, and I can't make another group of 5?" (It means you have a remainder.)
23. How many hundreds, tens, and ones did you give each friend? (1 hundred, 3 tens, and 9 ones.) (Write an addition sentence with the quotients: 100+30+9) (139
tickets)
Tell the students that this is how you solve a partial quotient problem using the area model. Tell the students that now you will write the partial quotient division
problem to see if anyone can identify where the numbers from the area model are on the partial quotient division problem.
Display the partial quotient model and ask a student to identify or ask several students to identify the dividend, the divisor, and the partial quotient on the partial
quotient model.
Use the PowerPoint to help students locate and compare all the numbers on both models.
Using the PowerPoint, guide students in solving the equation: 7,854 ÷ 33= (238 ) using the area model first, and then the partial quotient model. Remember to use
the following questions:
1. How many hundreds of tickets can I give 33 friends so that they all have equal amounts?
2. Can I give them 100 each? (yes)
3. How much does 100 tickets times 33 friends equal? (3300)
page 2 of 5 4. Was that difficult or easy to multiply? (easy)
5. Tell me how you multiplied. (I know that 33 hundreds is the same number as 3,300.)
6. When I subtract 3300 from 7854, how many tickets do I have left? (4554)
7. Can I give each of the 33 friends 100 more tickets? (yes)
8. If 100 tickets times 33 friends equals 3300 tickets, when I subtract 3300 from 4554, how many tickets do I have left? (1254)
9. Can I give each of the 33 friends another 100 tickets? (No) Why not? (because that 33 friends times 100 tickers equals 3300 tickets, and I only have 1254.)
10. How many tens of tickets can I give 33 friends so that they all have equal amounts? Can I give them 10 each? (yes)
11. How much does 10 tickets times 33 friends equal? (330)
12. When I subtract 330 from 1254, how many tickets do I have left? (924)
13. Can I give each of the 33 friends 10 more tickets? (yes)
14. If 10 tickets times 33 friends equals 330 tickets, when I subtract 330 from 924, how many tickets do I have left? (594)
15. Can I give each of the 33 friends 10 more tickets? (yes)
16. If 10 tickets times 33 friends equals 330 tickets, when I subtract 330 from 594, how many tickets do I have left? (264)
17. Can I give each of the 33 friends another 10 tickets? (No) Why not? (because that 33 friends times 100 tickers equals 330 tickets, and I only have 264.)
18. How many single tickets can I give 33 friends so that they all have equal amounts? Can I give them 7 each? (yes)
19. How much does 7 tickets times 33 friends equal? (231)
20. When I subtract 231 from 264, how many tickets do I have left? (33)
21. Can I give each of the 33 friends 1 more ticket each? (yes)
22. If 1 ticket times 33 friends equals 330 tickets, when I subtract 330 from 924, how many tickets do I have left? (594)
23. Can I give each of the 33 friends 10 more tickets? (yes)
24. If 10 tickets times 33 friends equals 33 tickets, when I subtract 33 tickets from 33 tickets, how many tickets do I have left? (0)
25. Can I give each of the 33 friends another 10 tickets? (No) Why not? (because there are no more tickets to distribute)
26. How much 100+100+10+10+10+7+1 tickets? 238 tickets
27. How many tickets does each friend get? 238 tickets
Next, using the PowerPoint, have students come up to the board to explain how to fill in the partial quotient model step-by-step with the number from the above
problem.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Review rules on the PowerPoint about making funny division stories.
Students will copy word problems from the board and insert the names of people, foods, and objects to make them funny.
Students will solve two problems using the area model and two problems using the partial quotient model.
When everyone has copied the five problems click the PowerPoint back to the previous slide so that students can see the example.
Then, students will solve the problems using the area model or partial quotient.
At this time, walk around the room and check for understanding.
Probing questions for this section of the lesson include:
How many equal groups of (hundreds/tens) of tickets can you make for ___ friends?
Can you give each friend 100 tickets?
How much is 100 tickets times _____ friends?
If you subtract that amount from the dividend, how many tickets do you have left? What is different about the last problem?
* After enough students have completed the problems, one student from each group will read their problem and share how the group solved one of the problems.
The last group will share what was most difficult about this activity and what was the least difficult part to this activity.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
1. The students will copy from the PowerPoint the following 4 problems to solve using the area model and the partial quotient model. Then, they will write a story
about the problem:
1. 648 ÷ 18 = (36)
2. 584 ÷ 73 = (8)
3. 3186 ÷ 62 = (51 remainder 24)
4. 1831 ÷ 51 = (35 remainder 46)
2. When most students are done reviewing the answers to the problems using the PowerPoint, ask students the following questions:
Explain how you solved this problem?
Which method do you prefer, the area model or the partial quotient model?
What is different about problems 3 and 4? (they have a remainder)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Ticket Out: Students will solve the following problem using either the area model or the partial quotient model: 2964 ÷ 82 = (36 r.12). Students are also to answer
the following questions in complete sentences: How did you solve this problem? Why did you choose the method you chose?
Summative Assessment
The summative assessment for this lesson is teacher-created (see attached) Make a Funny Division Story worksheet, where students will again make a funny
division problem. They will also solve the problems using either the area model or the partial quotient model.
Formative Assessment
During the discussion after the hook. The teacher must observe that students know that they need to divide amongst 5 students and that students know that division
involves separating one group into equal groups?
Listen to the conversations between the students as they work in groups. Do their conversations show understanding of the learning objectives?
Ask students: Do you see a pattern as you work? What is it? Can it help you? Check to see if the students know that they must multiply the quotient by the divisor
and subtract it from the dividend several times.
page 3 of 5 Check the students' algorithms (math problem). Are they following the correct steps to solve the problem? Are they struggling with math facts?
Check the students' independent work for understanding. Can they follow the steps in the algorithm? Do they know their math facts? What do they understand?
Where might they need additional assistance? Can they identify the remainder?
Feedback to Students
The feedback to students is almost continuous during this lesson especially since much of the lesson is based on discussion.
Students will be provided with feedback during the hook to assist with needed prior knowledge and to correct misconceptions.
Students will be provided with feedback during the guided lesson since the teacher will respond to questions and assist students who struggle with this concept.
The teacher will provide feedback while he/she walks around the room while the students are using the cubes to create groups. Stop to help students who are not
quite sure what they are doing and praise students who understand and are working confidently.
Feedback will be provided when the students are working on the algorithms both in groups and individually to check for understanding. Make sure to correct
misconceptions, praise those who understand the lesson and encourage those who are not sure that they are on the right track.
Feedback will be given after the summative assessment.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Some students may find it helpful to use graph paper to help them keep the place values separated. Some students may need additional practice with smaller
numbers.
* This short video from LearnZillion might be helpful for struggling learners.
Extensions:
Have the students create their own funny division word problems and trade them with a partner. I often let them create questions for a test which they love, but they
also have to make an answer key. They love it when one of their problems shows up on the test.
Suggested Technology: Document Camera, Computer for Presenter, Internet Connection, LCD Projector, Speakers/Headphones, Microsoft Office
Special Materials Needed:
Teachers supplies:
Base-Ten blocks for the students
Math journal Work sheet for summative assessment
Students supplies:
Math journals
Further Recommendations:
Make sure that the worksheets you need are printed.
Check to make sure that you have enough base ten blocks.
Additional Information/Instructions
By Author/Submitter
Students engage in looking for and making use of structure when they repeat the pattern of finding a quotient, multiplying it by the divisor, and subtracting that from the
dividend.
Students make sense of problems and persevere in solving them as well as model with mathematics as they set up division story problems using the area model or the partial
quotient model, and as they explain how they solved the problems.
SOURCE AND ACCESS INFORMATION
Contributed by: Cristina Gonzalez
Name of Author/Source: Cristina Gonzalez
District/Organization of Contributor(s): Miami-Dade
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate
and explain the calculation by using equations, rectangular arrays, and/or area models.
page 4 of 5 MAFS.5.NBT.2.6:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
The extension from one-digit divisors to two-digit divisors requires care. This is a major milestone along the way to
reaching fluency with the standard algorithm in grade 6 (6.NS.2).
page 5 of 5