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The purpose of this lesson is to have students practice manipulation of literal equations to solve for the variable of interest. A literal equation is an equation that has more than variable (letter).

Students will be able to

Students should already know how to:

Equations with several variables (letters) are called literal equations.

The best way to teach how to solve (manipulate) a literal equation for one variable is by example.

As a learning aid, the teacher may distribute the following hand out: Teaching Phase Notes

Literal Equation Example:

Solve for xmeans to isolate or get x by itself. The process is similar to solving a one-variable equation.

Say: "You want to get x by itself so what did you have to move first?" (Inverse of addition) Say: "x still has a buddy how did you shake him off?" (Inverse of division) Say: x is almost free; what's the next step?" (Inverse of multiplication)

Say: "Is the previous equation and this equation equivalent?" Why?

Say: "What is the value of x when y is 1?"

Answer:

Check for understanding

Teacher now checks for understanding by questioning students.

Say: "Let's review inverse operations"

If you are adding you would?If you are subtracting you would?If you are multiplying you would?If you are dividing you would?If you're squaring you would?If you are square rooting you would?

How do you undo addition or subtraction?How do you undo multiplication or division?How do you undo grouping symbols?How do you undo exponents & radicals?

After the direct instruction is complete and student questions answered, teacher will distribute the literal equation activity worksheet.

Worksheet

Teacher will:

When students have completed the activity, bring them back together to discuss the results. Now you can discuss issues and misconceptions that the students may have and prompt them to brainstorm answers as a group.

This is an additional activity to have the students complete as a home assignment. These problems are graduated in difficulty. To allow students to have success, they may need support on the later problems. The worksheet includes a key with explanations.

Independent Practice

Source: http://www.illustrativemathematics.org/illustrations/393.

Cut out and print the bottom half of the Pre and Post Assessment ("Show me what you've learned about literal equations!"). This is the student exit slip. Give 10 minutes for students to complete, and then collect the exit slip at the door as students leave.

The problems are graduated from easy to hard so that teacher can easily determine each student's level of understanding.

The summative assessment has twelve questions, ranging from simple use of inverse operations to more complex problems including use of grouping symbols and order of operations.

Summative Assessment: Literal Equations SummativeAnswer Key: Literal Equations Summative Key This is a leveled assessment working from low rigor to high rigor, which helps the teacher and student evaluate the learning that has taken place.

This is a leveled assessment working from low rigor to high rigor, which helps the teacher and student evaluate the learning that has taken place.

There is a pre-assessment to be given at the start of the lesson. Administer the pre-assessment on the day prior to doing the activity so teacher can use the information to adjust lesson plan and group students.

Print and cut out for distribution to students: Pre and Post Assessment

Teacher will circulate around the room to provide feedback to students throughout the lesson and to observe whether they are meeting the learning goals. Student sharing supplements the feedback.

Summative Assessment: Literal Equations SummativeAnswer Key: Literal Equations Summative KeyThis is a leveled assessment working from low rigor to high rigor, which helps the teacher and student evaluate the learning that has taken place.

Literal Equation for the surface area of a cylinderSolving for r in the surface area formula of a cylinder requires the use of the quadratic formula.This process would be a great activity for the students to attack as an extension.

;;.Given SA and h, students can solve for r, the radius of the cylinder. Only the positive root is relevant in practical problems.

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