A Rational Balancing Act: One Step Equations Continued

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Objective

SWBAT solve for the variable in one-step equations that involve all types of positive rational numbers.

Big Idea

Is This Equation Balanced? Solving for the missing value in equations that include fraction and decimal quantities.

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

In today's opening, I will have the students write down everything that they know about algebra. They are to complete this in their "home" groups (That is the group that they are in when they are in their assigned seats). Each group will create a bullet list that will depict everything that they collectively know about algebra. 

After the time allotted to create the lists, the groups will post them on the whiteboard so that the entire class can see what they have written. At this time, we will compare and contrast the lists and commence with a discussion concerning algebra.

The purpose of this exercise is to review the vocabulary of this unit and to check for retention of concepts that have already been taught. 

Instruction & Teacher Modeling

10 minutes

In today's instructional piece, I will review how to solve one-step equations using the properties of equality. Then, I will demonstrate for my students how these same properties apply to one-step equations that involve fractions and decimals.

To demonstrate this, I will complete 5 examples involving solving one-step algebraic equations that have fractions and/or decimals. 

  • The first two examples will involve fractions. I will have one equation where the inverse operation will be to subtract. The other of the two will involve division of fractions.
  • The next two examples will involve decimals. Like the fraction examples, the first of the two equations will require me to subtract when I do the inverse operation and, the second equation will require me to divide.
  • The last example that I will do for my students will be an equation where the inverse operation required to solve it is division but, I will present an equation with both a fraction and a decimal in it.

During the time that I am completing these examples, my students should be taking notes.

Try It Out

10 minutes

In this part of the lesson, I will guide my students through an attempt to try to solve these types of one-step equations on their own.

To do this, I will provide them with three problems. I will give them one minute to complete each problem, when the minute is up, I will assess whether or not I need to provide them with another minute. While they are working, I will be traveling the room, observing to find misconceptions and common or not so common mistakes. If I should see a misconception or a mistake, I will provide that student with immediate feedback concerning what I have observed.

Once the allotted time has elapsed, I will have the students put their answers on a dry erase paddle and raise their answer up for me to see. This will let me know which students may need to put in a teacher led group during independent practice.

I will then repeat this process with the second and third guided practice problems.

Independent Exploration

20 minutes

For today's independent practice, my students will complete a worksheet where they will solve 12 problems that will require them to find the solution to one-step equations that involve fractions and decimals. (MP1)

Closing Summary

20 minutes

To close out this lesson, I will choose 12 students to come to the board where each of them will place one of the assigned problems and its solution so that the class can determine the accuracy of their work and simultaneously check their own work.

After the students have put the problems on the board, I will go over each problem with the class allowing those who completed the problems to lead me through their solutions. During this time, their peers and I will catch any mistakes and do away with any misconceptions. (MP3)