Break the Exponent Bricks

Transcription

1 Lesson 7.1 Break the Exponent Bricks Fill in the missing number to complete the number sentence. Shade or cross out the answer in the bricks below to find the route from the left to the right , _ , , _ _ 8. _ _ 11. _ 5 3, _ A N S W E R Problem Number , Stretch Your Thinking Write a number sentence with an exponent where the answer is one of the choices for Problem 7 that you did not cross out. 14. Is 6 4 equal to 4 6? Explain your answer. E49

2 Lesson 7.2 Order of Operations Game Three players are playing a board game. Evaluate the expressions below. Move each player s piece the same number of spaces as the answers. Do not count the start space. Mark the space where each player s piece should be after 4 moves. START FINISH player 1 player 2 player 3 1. (50 2 2) ( ) 4. ( ) 4 ( 13 2 ) 5. (3 1 4) 4 ( 1 1 ) ( ) ( ) 4 ( ) 9. ( ) 3 (11 2 6) 10. ( ) 1 ( ) ( ) ( ) 13. Stretch Your Thinking On his next move, player 1 is given an expression that moves his game piece directly to the finish space on the board. The expression has a division and a subtraction operation and an exponent. Write a possible expression. E50

3 Lesson 7.3 Which Expression Am I? Match each word expression on the left with the correct algebraic expression on the right. a number decreased by 9 4n times the sum of a number and 4 n 3 1 n 15 less than 4 times a number n 2 9 the cube of a number increased by the number the product of a number and 9 9n n 2 1 7n the square of a number, increased by the product of 7 and the number the quotient of a number and 9 9(n 1 4) n times a number, increased by n 4 more than a number divided by n a number increased by 9 4n decreased by 4 times a number n 9 9 decreased by a number n 1 9 E51

4 Lesson 7.4 Tall Math Tales Write sentences using words from the lists, choosing at least one phrase from each column. Then, for each sentence, create a math expression from the number or expression listed next to the phrases you chose. Finally, identify the number of terms in your expression. For example, if you write Oh no! The cow ate my blue pizza! you might create the expression (3n 1 7) 2 2n 3 3. Nouns Verbs Adjectives Exclamations cow 6 sees (5n 2 2) spotted 5n Hooray! 7 elephant 12 ate (3n 1 7) enormous n Oh no! 4 math book 5 became (12 2 n) blue 2n Wow! 9 pizza 3 sat (4n 1 2) wooden 4n Oops! 2 football 10 is carrying n 2 shiny 3n Whoops! 3 computer 4 caught 2n 2 delicious 6n Yikes! 1 Sentence Expression and Terms E52

5 Lesson 7.5 Round and Round They Go Evaluate the expression for each value of a. Circle the correct answer. 8a 2 2(3 1 a) a a a (a 2 1) a a a a 2 3a a a a a E53

6 Lesson 7.6 Find the Formula When an algebraic expression can be used in every example of a certain situation, you can write an equation called a formula. Formulas can have one, two, or more variables. Examples The area of a square is always equal to the square of the side length. A 5 s 2 Distance is always equal to the product of rate and time. d 5 rt Write a formula for each situation. 1. The perimeter P of a rectangle is always equal to the sum of twice the length l and twice the width w. 2. The amount of cheese c in a certain recipe is always equal to 1.5 times the combined amounts of flour f and water w. 3. The number of bags of dog food a certain animal shelter needs each week is always equal to the number of dogs in the shelter divided by 4. (Use d for the number of dogs in the shelter.) 4. The number of violins in Amy s school orchestra is always equal to twice the combined number of flutes, clarinets, and bassoons. 5. How did you choose variables to use in the last two problems? Would the formulas give different results if you chose different letters? E54

7 Lesson 7.7 Shaded Areas Write an expression for the area or perimeter of the figure. Then combine like terms to simplify the expression. 1. Find the area of the shaded region. 2. Find the area of the shaded region. n m n 7 2m 3n 3. Find the perimeter. 4. Find the perimeter. 2m 2n 2 1 n 1 1 3m 3m 7 2 m 2m 1 n 5. Describe how you wrote the expression for the shaded area in Problem 1. E55

8 Lesson 7.8 Powerful Properties Name the property or properties used to generate the equivalent expression. 1. 5b(ac) 5 5(bac) 2. (3s 2 4) 1 (7t 2 s) 5 (7t 2 s) 1 (3s 2 4) 3. 6(3x 1 y 2 5z) 5 6(3x) 1 6(y) 2 6(5z) 4. (5 1 6x) 1 x (6x 1 x) 5. 2(6x x) 5 2(6x 1 x 1 3) 5 2(6x 1 x) 1 2(3) 6. y(2w) 5 2wy 5 2(wy) Write an equivalent expression using the property given. 7. 4(2 1 a 1 b) Distributive Property 8. (8m)(2) Commutative Property of Multiplication 9. Can you use the Commutative Property to justify that 3s 2 4 and 4 2 3s are equivalent expressions? Explain. E56

9 Lesson 7.9 Expression Secret Code Find equivalent expressions to break the code and solve the riddle. Riddle: What did one math book say to the other math book? 3x x 8x x x 1 8 A B C D E F G x x 10x x 2x 8x 2 10 H I J K L M N x 5x x 4x 7x x 6x 1 15 O P Q R S T U 15x 10 6x x 2 7 5x V W X Y Z 5x 1 12x 3(3x 1 2x) 2x x 6x 2 x x 1 10 _ 3(4 2 5x) 2x 1 3x x 1 2x x 8x x _ 4(x 1 3x) 5x 1 5x 2 5 2x 1 (5x? 0) x 1 4x 1 2x! E57