Multiplication and Division Expressions

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Objective

SWBAT find a rule and write multiplication and division expressions from a completed table.

Big Idea

From a completed table, students can study to find the relationship between numbers, then write an expression for the table.

Opener

5 minutes

In today's lesson, the students model multiplication and division patterns shown in tables, determine the rule and write an expression.  This aligns with 4.OA.A3 because the students are representing these problems using equations with a letter standing for the unknown quantity.

To get the students started, I remind students that we have learned how to evaluate expressions.  "What does it mean to evaluate an expression?"   I let the students think about that question for a few minutes.  I call on a student to respond. One student replies, "It is when you work the problem." I add on to the student response by reminding the students that when you evaluate an expression, you replace the variable with a number, then solve.  I let the students know that in todays lesson, we determine a rule from a completed table, then write an expression.  Also, the students will make a model by using two-color counters.  The model provides a visual of the expression, as well as helps the students count to get the correct answer.

Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The Multiplication and Division Expressions power point is already up on the Smart board.  I like for my students to be near so that I can have their full attention while I'm at the Smart board.  

At the beginning of each lesson, I like to review all relevant skills that we have learned that will help with the new skill. I find that this helps the lesson run smoothly by having the important information in the forefront of the students' minds.

I begin by reviewing the vocabulary.

Review:

Variables – A symbol that stands for a number.

Algebraic expression – A mathematical phrase containing numbers or variables and at least one operation.

We begin with the multiplication expression. A completed table is used for an example to help the students write an expression.

What is the rule for the table? 

n

1

2

3

4

n x

8

16

24

32

Notice that the numbers are increasing.  Since the numbers are increasing, we need to multiply.  How much is it increasing?

I like for my students to interact with me during our whole group discussion.  I like to ask questions of them to make sure they are understanding the skill. 

I feel that all answers should not be given to students.  During whole class discussion and group activity, students should have to "think" to come up with some information.  I feel that when they discover some things on their own or use skills that they have learned, then this information stays with them.

Yes, it is increasing by 8.

1 x 8=8

2 x 8 =16

3 x 8 = 24

4 x 8 = 32

The expression for the table is n x 8.

How can we model this?

We can use counters to Model of Multiplication and Division Expressions.

Next, we worked an example of a division expression.

What is the rule for the table?

r

45

50

55

60

r ÷____

9

10

11

12

In my class, we discussed that if a number is decreasing, it is either subtraction or division. Because the students are familiar with their multiplication facts, when they saw 45 and 9, they knew that 9 x 5 is 45.  Therefore, because of fact families, they knew that 45 divided by 5 would give them 9.

Yes, the rule is divide by 5.

45 ÷ 5 = 9

50 ÷ 5= 10

55 ÷ 5 = 11

60 ÷ 5 = 12

Now, you will work with your classmates to practice the skill.

Group or Partner Activity

20 minutes

Give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).

For this activity, put the students in groups of 3.  I give each group a Group Activity Sheet Multiplication and Division Expressions and counters.  The students must work together to find the rule to completed tables. This is evident in their completed Student Work.  They must communicate precisely to others within their groups (MP6).  They must use clear definitions and terminology as they precisely discuss this problem (MP1).

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by the students (MP3).  As the groups discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  What is the value of each number?

2. Did you work all of the problems in the table?

3.  What result did you get for each of the problems?

As I walk around the classroom, I hear the students communicate with each other about the assignment.  From the Video Multiplication and Division Expressions, you can hear the classroom chatter and constant discussion among the students, as well as the student justifying her answer to the problem.  Before Common Core, I thought that a quiet class working out of the book was the ideal class.  Now, I am amazed at some of the conversation going on in the classroom between the students.  As I walk around the room,  I hear students justify their answers.  This is evident in the video.    They cannot just tell me what their answer is, there should always be a "because" or "I got my answer by..."   I always tell my students that they must justify their answer by referring back to the problem.  Also, the students use skills that were learned previously.  The Student Work - Relating Multiplication and Division shows how the students related multiplication and division in their work.  Even though the activity did not require it, the students knew the relationship and applied it.  This is what I want of my students.  I want them to take ownership of their learning and apply skills previously learned in their work.

In the Student Work, you can see how the students drew a table to help solve the problem.  In the table, the students replaced "s" with the appropriate number.  The students used their understanding and knowledge of multiplication to complete the table.  In this example, the students knew that "s" was multiplied by 4 in order to get the numbers listed in the table.

 

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.

Closure

15 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during student independent and partner sharing will be addressed whole class.  

Misconception(s) for this lesson:

The only problem that I had with this lesson was some of the students did not work all of the problems in the table.  After they worked one or two problems and got the same answer, they went to the next problem.  I explained to the students that it is always best to work all of the problems in a table because as the lessons progress to higher levels, the rule may not be the same.  For example, in patterns, the students may start out by adding 1 to the first number, then 2 to the second number, and so on.  My goal is to get the students to work efficiently and accurately.  I need to put emphasis on using the correct approach to problem-solve in 4th grade so that they will be successful in 5th grade.