Transcript Lemonade Anyone?

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
A. 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
Number of
Lemons
8
16 24 32
3
4
5
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?
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.
• 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.
A) 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
1)
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
Exponent
Base
63 = (6)(6)(6)
power
PRODUCT
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
1. EVALUATE EXPRESSIONS INSIDE
GROUPING SYMBOLS SUCH AS () OR []
2. EVALUATE POWERS
3. MULTIPLY AND DIVIDE FROM LEFT TO
RIGHT
4. 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)