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Mathematics Grade 6
Strand: EXPRESSIONS AND EQUATIONS (6.EE) Standard 6.EE.2
Students will work through Two-Step Equations using algebra tiles, drawing pictures, and writing the step-by-step process.
The Algebra Lab: Middle School, 1990 Creative Publications, 1300 Villa Street, Mountain View, CA 94041
Middle Grades Math, Course 1, Prentice Hall, 2001
Solving two-step equations algebraically has many real world applications. Keeping an equation in balance is a common thread throughout all algebra. Students must learn to automatically perform the same operation with the same number on both sides of the equation.
Linear equations with one variable have only one solution. To find the solution, first simplify by using the properties and the order of operations to rewrite without grouping symbols and to collect like terms. Then isolate the variable by using inverse operations. Addition and subtraction are inverse operations; multiplication and division are inverse operations.
When you solve a two-step equation, whether modeling with tiles or using algebraic properties, you get the variable alone on one side of the equation by reversing the order of operations.
6. Represent mathematical situations.
Invitation to Learn
Choose one task from the following list and write the step-by-step instructions on how to accomplish the task:
Call on students to share their step-by-step instructions. Discuss the importance of completing one step before moving on to the next.
Many math problems need to be handled in a step-by-step method as well.
Step 1: Add or subtract the same number from each side of equation
Step 2: Divide the same number (the number beside the variable) from both sides of equation.
|2x + 3 = 5||2 + 5x = 12|
|3y - 2 = 7||3y - 5 = 10|
Present some real world problems that require a two-step equation to solve the problem.
Economics example—Carmela wants to buy a digital camera for $249. She has $24 and is saving $15 each week. Solve the equation $15w + $24 = $249 to find how many weeks she will take to save enough to buy the camera. (answer: 15 weeks)
Nutrition example—A soccer player wants to eat 800 calories at a meal that includes a roast beef sandwich and potato chips. The sandwich has 570 calories and the potato chips have 23 calories each. Solve the equation 570 + 23p = 800 to find the number of potato chips the soccer player can eat. (answer: 10 chips)
Homework & Family Connection
A family vacation to Disneyland will cost $2,000. Your family has already saved $450 toward the trip and they are saving $300 every month. How many months will you have to save before you can go on your family vacation? Write an equation to solve the problem. Since the solution is not a whole number, discuss with your family about how to round the answer. Should you round up or down?
Give students 2 or 3 two-step equations and ask them to draw algebra tiles to represent the equations, showing the steps involved. Then find the solution to the equations.