Solving Linear Equations
1 Warm up
Review the answers as a class.
With a partner write and solve a real-life word problem using the equation 13x = 39. Then rewrite the word problem using division.
2 Create a Book on solving linear equations
Show the students an example of how to build the book.
Create a book on book builder cast. (Create the book in both languages for ELL students)
1) To introduce the lesson use the critical component to literacy: vocabulary
2) The vocabulary word is equation.
3) Define the word equation.
4) Show the steps on how to solve an equation.
5) Give an example on how to solve and actual problem.
3 Book builder Presentations
Students will be presenting the book to the class.
Present the book by groups. (5 minutes presentation)
4 Solving a Two-Step Equation
1) Ask students how they would evaluate the expression
x/8 - 1/2 if they knew the value of x.
2) Ask students what is the first step in solving the equation.
3) Ask students what is the second step in solving the equation. Have students Think-Pair-Share.
Solve the two-step equation, such as x/8 - 1/2 = -7/2.
This is a good way of summarizing how to solve two-step equations.
Explain how the solutions of 4x - 5 = 7 and 4/3x - 5/3 = 7/3 are similar.
Key Standards Supported
Expressions And Equations
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.