2. Find the next term in the sequence given above.

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1 1. Find the rule for the following sequence. 2, 6, 18,... Warm Up 2. Find the next term in the sequence given above. 3. Find the 1st three terms of the sequence given by the rule: start at 3 and multiply the previous number by Find the temperature in degrees Fahrenheit if an ant is moving at a speed of 2.5 inches/sec using the rule: T = 11s What would the speed be if the temperature was 75.5 degrees outside? Use the formula in problem 4. 1

2 Lesson 8.1B Content Objective: I can substitute a number in for a variable and solve the expression. I can turn a word problem into an expression, equation, or inequality and solve for a variable. Language Objective: I can write a word problem that can be expressed using an algebraic expression. Assignment 8.1B Due Quiz 8.1 after 8.1E

3 Lesson 8.1B Expressions I can substitute a number in for a variable and solve the expression I can turn a word problem into an expression, equation, or inequality and solve for a variable How would you write 3 less than a number? How old is AJ's sister, if she is 3 years less than AJ who is 15? Tips and Tricks Words that tell you to: ADD: more, added to, increased by, sum, plus, (be careful of words like total which can have other meanings) SUBTRACT: fewer than, less than, subtracted from, difference, decreased by, minus MULTIPLY: product, times, doubled, tripled, of, twice DIVIDE: out of, over, quotient, goes into, per. You have seen that algebraic expressions can be used to represent situations in which a quantity (number) changes or varies. In this lesson, you will write algebraic expressions to describe many other situations. 3

4 Jay, Lamar, Davina, Bart, Tara, and Freda live in a row of houses that are numbered 1 to 6. Use the clues below to help you solve the following problems. Jay owns some DVDs. Lamar lives next to Jay and three houses from Freda. Lamar has 2 fewer DVDs than Jay. Davina lives on the other side of Jay and has three times as many DVDs as Lamar. Bart lives in house 2 and has 4 more DVDs than Jay. If Tara had 13 more DVDs, she would have four times as many as Jay. Jay acquired (got) all his DVDs from Freda, who lives in house 6. Freda had 17 DVDs before she gave p of them to Jay. The person in house 5 owns the most DVDs ) Determine who lives in each house. (Hint: Focus on where the people live and ignore the other information.) 2.) Let p stand for the number of DVDs that Jay has. Write an expression containing the variable p for the number of DVDs that each person has. Jay = Bart = Davina = Lamar = Freda = Tara = 3.) Use your expressions to help determine how many DVDs Jay has. (Hint: Experiment with different values of p. Only one value of p gives the person in house 5 the most DVDs.) Set your expressions equal to the amount when p = 5. You can sometimes make sense of an expression by inventing (making up) a meaning for its symbols. For example for the expression k 4 could stand for (represent) the number of kittens in the shop after four have been sold. 4.) Create a meaning for (make up a situation) each expression below. 4a.) d b.) 3a 4c.) f 4 4

5 April 16, 2018 In problems 1 3, the variable p could have only one value. The variable was used to represent the unknown quantity: Jay's number of DVDs. As you saw, it is helpful to be able to use a variable to represent an unknown quantity. Now you have two ways to think about variables. A variable is a quantity that can change or an unknown quantity. An algebraic expression contains at least one variable and may contain operations. For these situations, the variables represent unknown quantities rather than quantities that change. 5.) Esteban bought N apples. 5a.) Granny Smith bought four times as many apples as Esteban. Write an expression to show how many apples she bought. 5b.) Esteban used 11 apples in a pie. How many does he have left? 6.) Suppose a bag of potatoes weighs t pounds. Write an expression for the number of pounds in each bag of vegetables below. Each expression should include the variable t. 6a.) a bag of carrots weighing 3 pounds more than a bag of potatoes 6b.) a bag of corn weighing 2 pounds less than a bag of potatoes 6c.) a bag of broccoli weighing 5 pounds less than a bag of corn 6d.) a bag of beans weighing 3 pounds more than a bag of broccoli 6e.) Order the five bags from lightest to heaviest. 5

6 7.) Baby Leanne is L inches tall. Write expressions, in terms of (using) the variable L to represent the heights in inches of the members of Leanne's family. 7a.) her 4 year old brother Tim, who is twice as tall as Leanne 7b.) her 6 year old sister Kerry, who is 5 inches taller than Tim 7c.) her mother, who is 15 inches shorter than four times Leanne's height 7d.) her father, who is 15 inches shorter than twice Kerry's height 7e.) Baby Leanne is about 20 inches long. Check the expressions you wrote above by substituting this value and determining (figuring out) whether the heights are reasonable. Tim's Kerry's mom's dad's 8.) Sasha has k nickels in her pocket. 8a.) Write an expression for the value (amount it is worth) of Sasha's nickels in cents (pennies). Find the value of the expression for k = 4. 8b.) Sasha also has 60 cents in other coins. Write an expression for the total value, in cents, of all her change. 8c.) Find the total value for k = 5 and k = 12. 8d.) Yesterday Sasha had k nickels in her pocket and no other money. She spent 70 cents on pencils. What was the total value of her coins after she bought the pencils? 8e.) Could k be any whole number? Explain. 6