Algebra 1A-SE Lesson 1.2 Finding the 10th term of a Sequence Lemonade Anyone? Algebra 1A-SE Lesson 1.2 Finding the 10th term of a Sequence

Scenario Your community is planning a street fair to raise money for the local soup kitchen. You are helping by selling lemonade. You need a lemonade recipe, ingredients to make the lemonade and a sign for your lemonade stand.

Problem 1: Setting up the Stand When creating the sign for the lemonade stand, you decide to decorate the sign’s border with a pattern of lemons. Your design creates a sequence of figures as shown below.

A Continued Draw the lemon pattern that would represent the tenth term of the sequence. Then use a complete sentence describing how you found your answer. Step 1 Step 2 Step 3 Step 4 Step 5

B You find a recipe for lemonade that includes the table below which shows the number of lemons needed for different numbers of pitchers of lemonade. The numbers of lemons form a sequence: 8, 16,24,32,40 Amount of Lemonade (pitchers 1 2 3 4 5 Number of Lemons 8 16 24 32 40

B Continued Complete each statement below to write the number of lemons needed to make the given number of pitchers of lemonade Number of lemons needed to make 2 pitchers of lemonade 2 x (____) = 16 Number of Lemons for 3 pitchers of Lemonade 3 x (_____) = 24

How many lemons are needed for 10 pitchers of lemonade How many lemons are needed for 10 pitchers of lemonade? Check your answer with your spreadsheet document (Sheet 1).

Investigate Problem 1 1) It costs $5 to make the sign and $2 for the ingredients for one pitcher of lemonade. You can use a sequence to model the total cost of making different numbers of pitchers of lemonade. Complete each statement to find the total cost. Do you have to make a new sign for each pitcher of lemonade that you sell? What is the cost of making the sign Is the cost to make that sign constant for this situation or does it change

Total Cost in Dollars to make 1 pitcher of lemonade: 5 + 2 (____) = _____ Total Cost in dollars to make 2 pitchers of lemonade 5 + 2(_____) = ______ Total Cost in dollars to make 3 pitchers of lemonade 5 + 2(_____) = _______

Write the sequence of number formed by the total cost of making 1 pitcher of lemonade, 2 pitchers of lemonade, 3 pitchers of lemonade, and so on…. What is the tenth term of this sequence? Show all your work Use a complete sentence to explain what the 10th term represents.

2) You can pour 14 glasses of lemonade from one pitcher. If you sell the lemonade for $.50 per glass, how much money do you receive from one pitcher of lemonade? Use a complete sentence to explain how you found your answer.

3) Write the sequence of numbers that represents the amount of money that you receive from selling 1 pitcher of lemonade, 2 pitchers of lemonade, 3 pitchers of lemonade, and so on…..

4) The profit is the amount of money that you have left after you subtract the costs from the amount of money you receive. What is your profit from selling 1 pitcher of lemonade? What is your profit from selling 2 pitchers of lemonade?

Write the sequence that represents the profit from 1 pitcher, 2 pitchers, 3 pitchers, and 4 pitchers of lemonade and so on….

Problem 2: Kids Booth At the street fair, there are activity booths for young children. In one of the booths, children can create sand art by layering different colors of sand in a clear plastic tube. One local company is donating the sand and another company is donating the plastic cubes.

You need to contact the sand company and tell them the amount of sand you will need. If the cubes are 6 inches long, 6 inches wide, and six inches tall, then the amount of sand needed to fill one plastic cube can be found by multiplying the length, width, and height of the cube. Write and simplify an expression for the amount of sand needed for one cube _____ X _______ X _____ =____ cubic inches

B. Suppose that the cubes are 8 inches long, 8 inches wide and 8 inches tall. Write and simplify an expression for the amount of sand needed for one cube. ____X_____x_____=____ cubic inches

Suppose that the cubes are 10 inches long, 10 inches wide, and 10 inches tall. Write and simplify an expression for the amount of sand needed for one cube.

Investigate Problem 2 Just the Math: Powers When factors are repeated, you can represent the product by using powers. For instance, the product 6(6)(6) has only one factor, 6, which is repeated 3 times. You can write this product as the power 63

63 = (6)(6)(6) Exponent Base PRODUCT power The base of a power is the repeated factor and the exponent of the power is the number of times that the factor is repeated

Write each power as a product 25 42 65

Write each product as a power 3(3) 1(1)(1) 5(5)(5)(5)

2) Just the Math: Order of Operations When finding the 10th term of a sequence, you may have used the order of operations. These rules ensure that the rest of the combing numbers and operations such as addition and multiplication, is the same every time

ORDER OF OPERATIONS EVALUATE EXPRESSIONS INSIDE GROUPING SYMBOLS SUCH AS () OR [] EVALUATE POWERS MULTIPLY AND DIVIDE FROM LEFT TO RIGHT ADD AND SUBTRACT FROM LEFT TO RIGHT *****REMEMBER PEMDAS********

Perform the indicated operations SHOW YOUR WORK 22 – 3(4) 9(3) + 2(4) 30 - 42

Perform the indicated operations SHOW YOUR WORK 23 + 4(5) (7- 3)5 – 22 8(5) – 3(2 + 5)

3) Suppose that you will have 80 cubes for the street fair and each cube is 9 inches wide, 9 inches long, and 9 inches tall. Write an expression for the number of cubic inches of sand that you will need for the fair.

Find the value of the expression and use a complete sentence to describe the amount of sand that you will need

Summary Now that we have talked about powers and exponents, Write 3-5 sentences describing the similarities and differences between the two ways you can find the 10th term (repeated addition versus multiplication)