Special Quotients

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SWBAT use multiplication facts with 0 and 1 to learn about special division rules with 0 and 1.

Big Idea

The identity property and zero property of multiplication can help you solve division problems with quotients of 0 and 1.


5 minutes

In today's lesson the students learn about quotients of 0 and 1.  This aligns with 4.NBT.B6 because the students find quotients using properties of multiplication.

I let the students know that division is a part of our every day lives.  When they share things equally with their friends, then they are dividing.  We have learned several properties of multiplication.  We have also learned that multiplication can help with division.  It is very important for the students to use the properties of multiplication to help them diviide to find special quotients.  Using these properties of multiplication allows the students to find their quotients efficiently.  

I tell the students,  "Our lesson for today is Special Quotients.  You use multiplication facts with 0 and 1 to help you with special division rules with 0 and 1."  I ask the students, "When might you need to share 5 items equally among 5 people?"  I let the students think about the question for a minute.  I allow 2 or 3 students to share their answers.

Direct Instruction

15 minutes

I call the students to the carpet for the whole class direct instruction part of the lesson.  I want all of the students near me so that I can see that I have their full attention.  The Special Quotients power point is displayed on the Smart board.  I like to begin with a review of the skills that are important for this lesson.  In this particular lesson, I review the multiplication properties that will help the students with Special Quotients.  I do this because it helps make the lesson go smoothly if the students have all the pertinent information in the forefront of their minds.  

I remind students that the identity property of multiplication says that any number multiplied by 1 is that number.  Also, the zero property of multiplication says that any number multiplied by zero is zero.  I let the students know that this is very important information because it is going to help them with today's lesson.

In the direct instruction lesson, I use real-world scenarios to teach the lesson.  "—Sarah has 5 popsicles.  She wants to share them with 4 of her friends.  How many popsicles will they each get?"  The rationale behind using real-world problems to teach the lesson is that the students can relate to the people in these problems.  I try to make it relevant so that they will be interested in the lesson.  Also, it gives them a clear picture of how this skill fits into their lives. 

I find it works better for me to stop and ask questions as I teach from the power point.  I like to hear feedback from my students.  Most of the time when I ask a question, I want a choral response from the class.  Sometimes I repeat the question 2 or 3 times until I get the level of response that I am looking to get.  As I plan my lessons, I try to think of any misconceptions that the students can have and ways that I can clear them up at the very beginning of the lesson.

Possible Misconception(s):

1.  Using the correct number as the dividend

2.  Trying to divide by 0

Questions that I will include in my direct instruction to clear up these misconceptions:

 1.  What is a dividend?  In this problem, what is the total number of items? How many groups do they have?   What is a divisor?  In this problem, which number represents the number of groups?

 2.  What does it mean to have zero?  If you have zero groups, then do you have anything?  What is the divisor in this problem?  Can you have a number of groups with zero items in those groups?  What would that look like as a division problem?


Group or Partner Activity

20 minutes

After the direct instruction, I put the students in pairs.   If you have 20 students in your class, count the students off 1 to 10.  This will allow the students to work with someone that they may have not had the opportunity to work with in your class.  Each pair will write a "rap" about special quotients.  I want my students to enjoy my math class, so what better way to let them work on the skill but through music?  I find that most of my students love some form of music.  This gives them the opportunity to compose their very own rap song.  Each pair receives a rubric (Special Quotients Rubric) with the guidelines for creating the "rap." (MP4) The students are being provided with a rubric because I want the students to know what is expected of them.  If they know what is expected of them, then they must take responsibility for their own learning (MP6).

Their raps are graded accordingly:  

 Each rap must talk about the identity property of multiplication (25 points), the zero property of multiplication (25 points), an example of a division problem with 1 as the quotient (25 points), and a division problem with 0 as the quotient (25 points).  The total possible points for this lesson are 100 points. (MP1)

After the students have completed writing their raps, I let some of the groups perform their raps for the class. This  Rap Video for Special Quotients is the creative work of a pair of students.


Early finishers can practice dividing at the following site: http://www.funbrain.com/cgi-bin/mb.cgi


Independent Activity

10 minutes

In order for me to know that the students understood how to use multiplication to solve division problems with special quotients, I give my students an independent activity.  This lets me know what each person knows on their own.  I have the directions for the Independent Activity Special Quotients on the Smart board. 



Write a real-world problem with a quotient of 0 or 1.  Write the multiplication sentence that helps you solve the problem.  Tell which multiplication property goes with the multiplication sentence.


10 minutes

To close the lesson, I let some of the students share their real-world problems.  I have the students read their word problem without giving the answer.  Then, I let the other students find the quotient to the word problem and tell what multiplication property helps to solve the word problem.  This provides another whole class teaching opportunity.  Any students who did not have mastery of the lesson will have this chance to hear their classmates' answers and justification for their answers.