Keeping it in Balance: One Step Equations

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Objective

SWBAT solve for a variable in a one-step equations involving positive whole numbers.

Big Idea

A Balancing Act: Using the properties of equality to solve for a variable in a one-step algebraic equation

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

Engagement

5 minutes

During the opening activity, I will have my students complete addition and subtraction fact families for the number 15 and multiplication and division fact families for the number 12. Each student will come up with two numbers that when added together, equal 15. Then, each students will come up with two numbers that when multiplied to each other, they equal 12. Using their two numbers and the given sum and product, the students will then create fact families.

This activity is for the purpose of demonstrating to my students how the addition, subtraction, multiplication, and division properties of equality work. I will ensure that I make this demonstration during the instructional piece. 

Instruction & Teacher Modeling

10 minutes

In today’s instructional piece, I will first present to my students, the properties of equality, the meaning of one step algebraic equations, and the unit 4 vocabulary and standards. I will then, show my students how to apply the properties of equality for the purpose of solving for a missing value.

To accomplish this, I will use today’s opening activity to show how in every equation presented in every fact family, the left side of the equal sign is equivalent to the right side of the equal sign. I will then select a student’s fact families to further demonstrate the meaning of the properties of equality. I will choose one number in each fact family to change into a variable. After doing this, I will then ask, which equation in the fact family leads us to the solution that will provide us with the value of the variable. After getting the desired response, I will then ask my students what they notice about the original equation and the equation that leads to the solution. The students should notice that the operations are inverses of each other. I will then ask the students to test this with other problems. (MP2 & MP7)

 

4 + b = 18

3z = 45

 

I will then ask students if the same was true with these problems. After receiving several responses from several students, I will then ask, if they believed that this would be true with all one step algebraic equations.

After getting the students to understand that they can use the inverse operation to solve for a missing value, I will then show my students how this relates to the properties of equality.

 

Ex: If I tell you that 5 +3 = 8, then I take 3 away from 5+3, what must I do to 8 in order for the equation to remain true?

 

I will show students how the concept is the same when it comes to one step algebraic equations. To do this, I will demonstrate to students how to isolate the variable by using the inverse operation to remove the other term presented on the same side of the equation as the variable.

Try It Out

10 minutes

To practice solving one-step equations, I will have my students complete a worksheet that will require them to determine which number out of three provided numbers are the solutions to an equation. They will also have to find the solution of given equations without selections, and they will have to solve word problems where they will first have to set up the equation to solve and then solve that equation.

Independent Exploration

20 minutes

To ensure that the students understand the concept of solving one-step equations they will complete a worksheet that contains similar problems as those that they completed during the Try It Out section of this lesson.

Closing Summary

20 minutes

To close out this lesson I will select one student for each problem, on the independent practice worksheet from the independent exploration portion of this lesson. Each of the students will come and present their assigned problem on the board 5 at a time. We will go over each problem, discussing any issues encountered while going through the process of soling the problems. (MP3 & MP6)