We will solve equations with squared variables.

Transcription

1 Learning Objective We will solve equations with squared variables. CFU What are we going to do? Activate Prior Knowledge An exponential expression represents repeated multiplication. Bases raised to an exponent of 2 are squared. Exponential Expression exponent base 6 2 Evaluate the squared expressions (-4) 2 4. (-7) 2 Make Connection Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables.

2 Concept Development A square root is a number that is multiplied by itself to form a product. Taking the square root ( ) is used to isolate 1 the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Square Roots x 2 = 36 x 2 = ± 6 2 x = ±6 Perfect Squares 1 2 = = = = = = = = = = 100 CFU Solutions (6) 2 = 36 (-6) 2 = 36 x = 6 and x = -6 both make the equation true. Which equation below can be solved by taking a square root? How do you know? A y 2 = 8 B y 2 = 4 Explain why ±3 are the solutions to the equation z 2 = 9 Vocabulary 1 separate (synonym)

3 Skill Development/Guided Practice A square root is a number that is multiplied by itself to form a product. Taking the square root ( ) is used to isolate the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Solve equations with squared variables. 1 Rewrite the numerical term as a squared expression. 2 Solve the equation by taking the square root of both sides of the equation. 3 Check and interpret 2 the solution(s). 1. a 2 = b 2 = h 2 = k 2 = q 2 = 6. p 2 = CFU 2 3 How did I/you solve the equation? How did I/you check and interpret the solution(s)? Perfect Squares 1 2 = = = = = = = = = = w 2 = m 2 = 49 Vocabulary 2 explain (synonym)

4 Skill Development/Guided Practice (continued) CFU How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? 9. Cameron is tiling his floor with square tiles. He knows the area of each tile is 64 in 2. What is the length of each side of the tile? 8 in 8 in Area = 64 in Vanessa is starting a painting on a square canvas. The area of the canvas is 81 in 2. What is the length of each side of the canvas? 9 in 9 in Area = 81 in 2

5 Relevance A square root is a number that is multiplied by itself to form a product. Taking the square root ( ) is used to isolate the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. 1 Solving equations with squared variables will help you solve real-world problems. Soledad 16 mi Salinas River How long is the Salinas River from King City to Soledad? = r = r = r 2 20 = r 12 mi The Salinas River is 20 miles King City long from King City to Soledad. 2 Solving equations with squared variables will help you do well on tests. Sample Test Question: 87. Choose Yes or No to indicate whether each statement is true about the equation w 2 = 4. A The equation can be solved by taking a square root. B w = 16 C w = ±2 D There are exactly two solutions to the equation. O Yes O No O Yes O No O Yes O No O Yes O No CFU Does anyone else have another reason why it is relevant to solve equations with squared variables? (Pair-Share) Why is it relevant to solve equations with squared variables? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

6 A square root is a number that is multiplied by itself to form a product. Taking the square root ( ) is used to isolate the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Skill Closure Solve equations with squared variables. 1 Rewrite the numerical term as a squared expression. 2 Solve the equation by taking the square root of both sides of the equation. 3 Check and interpret the solution(s). 1. d 2 = n 2 = 81 Perfect Squares 1 2 = = = = = = = = = = 100 Access Common Core Which equation below can be solved by taking a square root? Explain your answer. Explain why the other equations cannot be solved by taking a square root. A x 2 = 25 B y 2 = 16 C z 2 = 13 Word Bank equation square root solution Summary Closure What did you learn today about solving equations with squared variables? (Pair-Share) Use words from the word bank.

7 Independent Practice A square root is a number that is multiplied by itself to form a product. Taking the square root ( ) is used to isolate the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Solve equations with squared variables. 1 Rewrite the numerical term as a squared expression. 2 Solve the equation by taking the square root of both sides of the equation. 3 Check and interpret the solution(s). 1. g 2 = u 2 = c 2 = 1 4. v 2 = 49 Perfect Squares 1 2 = = = = = = = = = = 100

8 Independent Practice (continued) 5. A square portion of Carmen s apartment is tiled. Each tile is 1 ft 2, and there are 25 tiles. How long is each side of the tiled portion of Carmen s apartment? 5 ft 5 ft

9 Periodic Extension: Review 1 Describe in your own words what it means to take the square root of a number: How is squaring a number different from taking the square root of a number?

10 Periodic Extension: Review 1 Find the square of each number below: