Addition and Subtraction Expressions

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SWBAT model addition and subtraction patterns shown in tables with two-color counters and write rules for the patterns.

Big Idea

Two-color counters can be used to show addition and subtraction patterns in expressions.


5 minutes

In today's lesson, the students model addition and subtraction patterns shown in tables and write rules for the patterns.  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 take a few student responses.  I choose a student with his hands raised.  "It means to solve the expression."  The class agrees with his response.  I let the students know that in todays lesson, we learn to write an expression for a table, then model with the two color counters.  The model provides a visual of the expression, as well as help 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 Addition and Subtraction Expressions.pptx 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.


Variables – A symbol that stands for a number.

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

We begin our lesson, with an addition expression.

What is the rule for the table?






n +






To find the rule,  we can use the inverse operation of addition.  What is the inverse of addition?

Yes, subtraction is the inverse of addition.

 To make sure you have the correct rule, you must subtract each problem in the table.

22 – 7 = 15

23 – 8= 15

24 – 9 = 15

25 – 10 = 15

The rule for the table is n + 15.

How can we model this?

We can use two-color counters to model.  I use the power point slide to show the students how to Model of addition and subtraction expressions.pptx with two-color couners. I explain to the students that the two-color counters can help them by giving them a visual model of their answer.

Next, I show the students a subtraction expression.  







r - ____







100 – 67=33

115 – 82 = 33

121 – 88= 33

138 – 105 = 33

The rule is r - 33

I let the students know that now they will practice the skill in groups.

Group or Partner Activity

20 minutes

I 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, I put the students in pairs.  I give each group a Group Activity Addition and Subtraction Expressions and two-color counters.  The two-color counters are a resource the students can use, if needed, to gain a conceptual understanding through a visual model. The students must work together to find the rule for the table and model the problem as evident in the Student model for 35 - 7 = 28.  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 both students (MP3).  In the Video Addition and Subtraction Expressions, you can hear a student justify his answer to the problems.  He states very clearly in the video, that "I got all of my answers right."  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).  They must look for a pattern (MP7).  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 operation must you use to solve the problem?

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

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


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.  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 approached one group, one of the students asked me a question.  I always encourage the students to ask questions if they do not undertand something.  The student asked, "Can the answer be different from the others?"  The student was referring to the problems in the table.  "Good question," I respond to the student.  "If it is an expression for the table, then when you evaluate all of the problems in the table, your solution should be the same number."  I made a mental note to clarify this point with the whole class during the closure. Sometimes as teachers, we think we have made a clear point but some students are still confused about the skill.

Some of the students were confused at first about how to find the expression.  From this example of Student work - Misconception, you can see that for problem numbers 1 and 4 on the Group Activity Addition and Subtraction Expressions, this pair did not know what operation to use to find the expression.  However, in problems 2 and 3, they did a good job.  Through questioning, I was able to get the students to see their mistakes.   With that being said, I still like to pull students for small group to reinforce the skill the next day.  This pair of students will work with me first thing the next day to make sure they can determine the correct operation to solve an expression.


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 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.