I let the students know that today we will play a game. We have already learned how to write and evaluate expressions. In today's lesson, the students will practice the skill more by playing "What's My Expression?" I start by asking, "Who remembers why we use variables?" I give the students a few minutes to think about the question. One student answers, "When we have different numbers." I ask, "What do you mean when you say different numbers?" The student responds, "When we can use more than one number for the same variable." I remind students that a variable can be used in the place of more than one number or if the number is unknown. This aligns with 4.OA.A3 because the students are representing problems using equations with a letter standing for the unknown quantity.
I call the students to the carpet as we prepare for a whole class discussion. The Writing Phrases for 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.
I begin by reviewing important vocabulary that the students have already learned. The students will have to know these terms to understand the lesson.
Algebraic expression – A mathematical phrase containing numbers or variables and at least one operation.
We begin with an expression:
r x 3
I remind the students that because this is a multiplication expression, something will be repeating 3 times.
In order to write a phrase for this expression, first decide on who or what you want your word problem to be about.
Let’s use “Bob” for the subject.
Name some objects that may be in multiples. Some objects the students name are cars, circles, computers, radios, and bikes.
Bob has 3 times as many pencils as Rita.
Does this phrase explain “r x 3”?
Let’s try another expression.
What clue words can we use for subtraction?
First, decide on who or what you want your phrase to be about.
Let’s use Teresa.
Next, decide what object or thing will be subtracted in the phrase.
Teresa owns 4 marbles less than John.
Does this phrase explain j - 4?
Yes, this is a phrase that relates to "j - 4" because Teresa = John - 4.
I send the students back to their seats and let them know that they will now have an opportunity to practice this skill by playing a game.
I give the students practice on this skill by letting them work together to play a game. 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 groups of 3. I give each group the rules for What's My Expression (Variables Game). The students must use the expression in the correct context (MP2). 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 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). From the video, you can hear the students discuss the problem and agree upon the answer to the problem. 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 determining if the phrases are correct. I am holding the students accountable for their own learning.
As they work during this activity, I monitor and mentally track the students' understanding. From the Video, you can 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. I heard one student who is usually nonchallant about math say, "No, she does not get a point. She said "more than" when it should be "less than" because she had subtraction." Because the activity was of interest to him, he was energetic and vocal during this lesson. I always tell my students that they must justify their answer or critique other student's answers by referring back to the problem.
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.
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 Student 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 the group activity will be addressed whole class.
In this sample of student work, the student did come up with a phrase to match their expression. The expression that the student pulled from the bag was "p x 6." The student knew to use the word "times" to represent multiplication in their phrase. The student wrote, "Keirrick has 6 times more than Alan." I would have preferred for the student to identify an item to represent the 6 times. For instance, 6 times more "pencils, marbles, erasers, etc."
Difficulty with the lesson:
The biggest problem I noticed in this lesson was the students struggle with composing a phrase to match the expression. My expectation was for the students to list a subject and object in their simple phrases to match their expressions. This was really difficult at first for some of the students. I feel that this is because so many of the students have not been made to think "critically." By the end of the lesson, the majority of the students could write a simple phrase that matched the expression.