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Name: Class: Date: ID: A Algebra 2R Skillset 1.2 - Generating Algebraic Expressions from Patterns Are They Saying the Same Thing?

1 Name: Class: Date: ID: A Algebra 2R Skillset Generating Algebraic Expressions from Patterns Are They Saying the Same Thing? Using Patterns to Generate Algebraic Expressions Problem Set Write an expression to represent each pattern. 1. Renetta is creating a design for a craft project. Write an expression to represent the number of shaded squares in each piece of the design. 2. After 1 minute, a file Portia is downloading from the internet is at 0 kilobytes downloaded. After 2 minutes, the file is at 7 kilobytes downloaded. After 3 minutes, the file is at 26 kilobytes downloaded. After 4 minutes, the file is at 63 kilobytes downloaded. Write an expression to model the amount of the file downloaded. Explain your reasoning. 3. A library receives book donations over the course of the year. The number of books received each month is listed in the table. Write an expression to model the number of books received by the library. Explain your reasoning. Time (months) Number of Books Received

2 Name: ID: A 4. A website begins its first week with 3 subscribers. The number of subscribers each week is listed in the table. Write an expression to model the number of subscribers at the website each week. Time (weeks) Number of Subscribers Determine whether the two expressions are equivalent. Explain your reasoning. 5. 6n + 8 and 2(3n + 4) 6. 3x + 5 and 2(x + 3) 7. (y + y y) + 3y and 6y y y and 3(6y 1) 2

The table lists the number of pets that have been adopted over several weeks.

3 Name: ID: A Represent each pattern as an expression and as a graph. Then identify whether the pattern is linear, exponential, or quadratic. Explain your reasoning. 9. A local pet shelter is able to see many of their pets adopted. The table lists the number of pets that have been adopted over several weeks. Time (weeks) Number of Pets Adopted Emilio is looking at bunches of grapes at the market. He starts to notice a pattern in the number of grapes in each bunch. Write an expression for the number of grapes in each bunch. 3

4 Name: ID: A 11. The school swim team holds a car wash to earn money for an upcoming trip. The table lists the number of hours that the car wash runs and the amount of money earned during the car wash. Time (hours) Amount of Money Earned (in dollars)

5 ID: A Algebra 2R Skillset Generating Algebraic Expressions from Patterns Answer Section 1. ANS: The number of shaded squares in each design is one more than the design number. So, the expression is n ANS: The amount of the file downloaded is the cube of the number of minutes, minus 1. So, the expression is n ANS: The number of books received is 3 times the number of months squared, minus 1. So, the number of books received in month n is 3n ANS: The number of subscribers is 2 times the number of weeks cubed, plus 1. So, the number of subscribers in week n is 2n ANS: The expressions are equivalent. Use the distributive property and combine like terms. 2(3n + 4) = 6n ANS: The expressions are not equivalent. 2(x + 3) = 2x + 6, which is not equivalent to 3x

6 ID: A 7. ANS: The expressions are equivalent. Combine like terms. (y + y y) + 3y = 3y y = 6y ANS: The expressions are equivalent. Combine like terms. 8y y = 18y 3 3(6y 1) = 18y 3 2

7 ID: A 9. ANS: The number of pets adopted is the number of weeks squared plus 7. So, an expression to represent the pattern is w The pattern is quadratic. 10. ANS: The number of grapes in each bunch is x squared plus 5 times x. So, an expression to represent the pattern is x 2 + 5x. The pattern is quadratic. 3

8 ID: A 11. ANS: The amount of money earned is 2 times the number of hours plus 18. So, an expression to represent the pattern is 2h The pattern is linear. 4

ALL WORK IS TO BE DONE ON SEPARATE PAPER. SHOW ALL WORK FOR CREDIT. FOLLOW YOUR HOMEWORK GUIDELINES FOR HEADING AND WORK FORMAT.

Chapter 3 Exercise NAME -CLASS PD ALL WORK IS TO BE DONE ON SEPARATE PAPER. SHOW ALL WORK FOR CREDIT. FOLLOW YOUR HOMEWORK GUIDELINES FOR HEADING AND WORK FORMAT. 1. What is the least possible integer