Use a Bar Diagram and Write an Equation

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SWBAT use a bar diagram and write an equation to solve multiplication problems.

Big Idea

Bar diagrams and writing an equation are strategies used to solve multiplication problems.


5 minutes

The students have already learned how to solve different types of problems with the different operations.  In today's lesson, they learn a problem-solving strategy to solve word problems that involve bar diagrams and writing an equation.  This gives the students a visual and helps them find the answer when solving word problems.  This aligns with 4.OA.A3 because the students are solving problems with whole numbers using the four operations.

To begin the lesson, I remind the students that we have learned clue words to help solve problems involving addition, subtraction, multiplication, and division.   I ask the students to share some of those words with the class.  I give them a few minutes to think about clue words, then I call on a few students to respond.   One student says, "in all means to multiply or add."  Another students shares, "fewer" means to subtract.  Other words that the students shared were:  "share equally" to divide and "how many more" to subtract.  Their responses let me know that they remember key words that will help them solve problems by using the correct operation.  I let the students know that today they will learn to use a bar diagram and write an equation to solve word problems for addition, subtraction, multiplication, and division.

Whole Class Discussion

10 minutes

To begin the lesson, I call the students to the carpet.  I have the power point for the lesson Draw a Picture and Write an Equation already up on my Smart board. I find that it works better for me if the students are in close proximity.  It helps me keep an eye on the students to make sure that they are attentive to the lesson.

I let the students know that today we will learn to use a bar diagram and write an equation.  We have already learned to use models when solving problems.  I ask the students to give me an example of a model we can use to solve a problem.  I take responses from the students.  One student shares with the class that we can draw an array to help us solve multiplication problems.  Another student shares that we have learned to draw groups to show multiplication.  I let them know that today we will use "bar diagrams" to solve problems.  A bar diagram can be used with any operation: addition, subtraction, multiplication, and division.

I direct the students' attention to the Smart board.  I remind them to ask questions if they are confused about anything that they hear or see during this discussion. 

We start with a problem:


       Susie bought 5 pairs of shoes.  They each cost $12.  How much money did she spend in all?  Let’s find out.


  We can draw a bar diagram to help give us a visual of the problem.








 Notice that at the top of the bar graph, there is a question mark.  The total goes at the top of the bar graph.


What operation will we use to solve this problem? (I give the students a few minutes to think about the question.  Then I call on a student.)


This is a multiplication problem.  The number 12 is repeating 5 times.


The equation is 12 x 5 = 60

Let’s try another one.

       Tim raises cattle.  He owns 528 cows.  He gives 123 to his little brother who now has a farm.  How many cattle does he have left?


 What operation will we use for this problem?  What clue tells you that?






This is a subtraction problem.  The clue that tells you to subtract is “left.” 


The equation is 528-123= 405

I let the students know that now they will have the opportunity to practice

in groups.


Note:  This is a new concept for the students.  I like to expose my students to different methods to solve problems.  As the students work in groups, I will monitor and ask questions to help guide the students through the use of the bar diagrams.

Group or Partner Activity

20 minutes

 During this group activity, the students work in pairs.  Each pair has a copy of the Group Activity Sheet Draw a picture.  The students must work together to find the answer to each word problem.  The students are required to solve problems with whole numbers and whole number answers using the four operations (4.OA.A3). 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 agree upon the answer to the problem.  This takes discussion, critiquing, and justifying of answers by both students (MP3).  As the pairs 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.  It must be evident that they are using clues to help them determine the correct operation. Some of the questions that I ask:

1.  Are there any clues to help you determine the operation to use?  If so, what are they?

2. What are you being asked to find?

3.  Why did you choose that operation?

4.  How does the bar graph connect to this problem?

As I walked around the classroom, I heard the students communicate with each other about the assignment.  I hear the classroom chatter and constant discussion among the students. Groups are discussing how to use the bar graph as a tool to help solve their problems. As we have discussed using models in the past, I hear the students say "the model must match the problem."  This is the conversation that I want to hear with this lesson.  As I prepare the students for the PARCC assessment, they must always make sure that all of their responses to a problem (whether written, model, etc.) must connect with each other.  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 you can see from the Student Work and Student Work - Draw a Picture, these students did well.  The Student Work example shows how the student used the bar diagram to solve an addition problem.  The student knew that the question mark at the top represented the total for the problem. The Student Work - Draw a Picture example shows how the student used a bar diagram to solve a division problem.  The student knew that the equation was 32 divided by 8, and this is shown in the bar diagram with 8 sections with the number 4 for the quotient.  Because of our previous practice with the four operations, the students were able to complete this task.  For instance, learning clue words to help solve word problems were very useful.  They have learned about words, such as "left" and "both."  Also, incorporating task and problem-solving lessons are necessary.  As a teacher, we must provide as many opportunities for the students to practice real-world situations as possible.  It makes for a better rounded student.

 My Observations:

Using the bar diagrams went well for most students.  As I walked around to monitor, I saw that some students didn't know how to draw the bar diagram for the division problems.  One student asked, "How do you know what the bar diagram should look like?"  Because I noticed this with a few of the students, I decided to stop the class and bring the students back together whole class to address this question.  I pointed out to the students that for a division problem, we have been given the dividend.  We are looking for the quotient.  To divide means to share equally.  I point out to the students that we should draw a bar diagram that represent the divisor.  For example, if the divisor is 8, then we need a bar diagram with 8 sections.  I remind the students to use multiplication to help with the division problem.  In this particular case, the students will look for 8 times something to get the amount of the dividend.  After sharing this information with the whole class, I let the students return to their groups to work.

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.


15 minutes


To close the lesson, I have 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  partner sharing will be addressed whole class.  

The biggest misconception from this lesson was the drawing of the bar graph for division and multiplication. A few students were confused by the bar graph.  If the problem was a division problem, they knew that multiplication helps with division because they learned this in previous lessons.  However, they did not know how to draw a division bar graph.  It looks like a multiplication bar graph.  You can see this from the Student Work.  This particular bar graph could be used for a multiplication or divison problem.  It depends on how you write your number sentence.  It can be division as the students have it written on their paper.  Also, it could be multiplication if you write it as 8 x 4 = 32.  For me, by calling the class back together as a whole was the best method to address the misconception.