In today's lesson, the students learn how to find the value of a variable.
I have the Teaching Tool - Multiplication and Division Equations.pptx displayed on the Smartboard. The students sare sitting at their desks with paper and pencil. I ask the students to write R÷3 = 9 on their papers. I let the students know that this is an equation with a variable. The variable represents the missing number. When we have an equation with a missing number, we can use the inverse operation to solve the equation. I ask, "What is the inverse of division?" Student response: multiplication.
I let the students know that in order to get "R" on the side by itself, I need to multiply both sides by 3. This cancels out the "divided by 3" and "R" is left. Now, we have R = 9 x 3. "What is 9 x 3?" The students know that the product is 27. Therefore, our answer is R = 27. To check to make sure our answer is correct, we put the answer in the equation. The answer checks out correctly.
Let's try another one. I ask the students to write, S x 4 = 28. I explain to the students that because this is a multiplication problem, we should use division to get the variable on the side by itself. We must divide 28 by 4. I remind the students that multiplication helps us with division. What can we multiply 4 times to get 28. The students all know that 4 x 7 = 28. Therefore, S = 7. We check our answer by replacing the variable with 7. The new equation is 7 x 4 = 28. This answer checks out correctly.
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.
For this activity, I put the students in pairs. I give each group an Multiplication and Division Equations.docx and multiplication chart. The students must work together to find the value of the variable. They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem.
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. 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.
1. What is the variable in this equation?
2. What is the inverse operation for this problem?
3. When you check your answer, is the equation true?
Early Finishers: Practice the skill at the following website: http://www.math-play.com/One-Step-Equation-Game.html
To close the lesson, I call on different pairs of students to share their answers. The students must explain why they worked the problem in the order that they did (Video - Multiplication and Division Equations). 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 (Student Work - Multiplication and Division Equations and Student Work - Multiplication and Division Equations), 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.