1. Algebra Lesson: Solving Algebraic Equations VA SOL: 6.23- The student will a) Model and solve algebraic equations, using concrete materials; b) Solve one-step linear equations in one variable, involving whole number coefficients and positive rational solutions; and c) Use the following algebraic terms appropriately: variable, coefficient, term, and equation. Today’s Objectives: 1.Activity 2.Lesson 3.Discussion 4.Lesson 5.Game 6.Exit Pass

2. Activity !

3. Group 1Group 2 Group 3Group 4 Group 5

4. Solving One-Step Algebraic Equations 1. You are given an isosceles triangle. The length of one of the sides is 7 in. Find the missing side lengths if the perimeter of the triangle is 19 in. 7 in. If one of the side lengths is 7 in, by definition, the other side is 7 in. so now we set up the equation: 7 + 7 + x = 19 14 + x = 19 - 14 x = 5 We let the variable “x” represent the missing side length x

5. Solving One-Step Algebraic Equations In general: To solve a one-step algebraic equation, we do the inverse, or opposite, of the operation in the equation. 14 + x = 19 - 14 x = 5 x - 6 = 12 + 6 + 6 x = 18 4x = 16 ÷4 ÷4 x = 4

6. Directions: Create a word problem using properties you remember from geometry (for example, use the fact that triangles sum to 180 degrees or that a rhombus has 4 sides that are congruent and parallel. Share your problems with a partner.

7. 4. You are given a parallelogram. The length of the side is one more than half the length of the base. If the side length is 4 ft, what are the lengths of the missing edges? Once you’ve found this, calculate the perimeter of the quadrilateral. Solving Two-Step Algebraic Equations 4 ft x Using our knowledge of parallelograms, we know both sides are 4 ft. Now we need to set up an equation to find the length of the base: ½ x + 1 = 4 - 1 -1 ½ x= 3 ÷½ x = 6 ft

8. In general: To solve a two-step algebraic equation, we use multiple inverse operations to find the value of x, similar to one-step equations. Solving Two-Step Algebraic Equations 2x + 3 = 13 - 3 -3 2x= 10 ÷2 x = 5 6x - 5 = 7 + 5 + 5 6x= 12 ÷6 x = 2

9. “I Have, Who Has”

10. Exit Pass What is an inverse operation? Give an example. Solve this equation: ¼ x – 8 = 2 Set up an equation for this word problem: One of the angles in a right triangle is 75º. Find the missing angle. Write down anything from this lesson that made you go “Hmmm…” or “Ah-ha!”