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Author:
Kevin Hall
Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/
Rates, Graphs, and Linear Equations
Discussion prompts to activate prior knowledge
See PowerPoint slides.
1). SCENARIO: You work at a car wash. The owner says he’ll pay you $20 for every 2 hours you work.
Worked Example: (Teacher demonstrates, and students explain).
2). SCENARIO: When you buy DVD’s from the website, it costs $15 for every 4 DVD’s, plus a $6.00 flat-rate shipping fee. What expression shows the total bill for 25 DVD’s?
a). Reflections A – B (discuss).
b). Answer (cost for 25 DVD’s): ______
c). Let’s show how the scenario looks on a graph. Please continue the rate pattern: every time you add ____ DVD’s, you increase the cost by ____. Then draw a line through all the points.
Practice:
3). SCENARIO: The tree is 5 ft tall when it’s planted. Then every 3 years, it grows by about 2 feet.
a). How tall would it be in 11 years?
b). What’s the expression for its height after x years? ______
c). On the graph below, please show how the height changes over time.
Worked Example: (Teacher demonstrates, and students explain).
4). SCENARIO: Every year, the school gives the football team 25% of the money that’s raised in the student raffle, plus $5,050. If the students raise x dollars in the raffle, how much does the football team get in total?
a). Reflections A-C (discuss).
c). Final answer: ______
d). Please draw a graph of this situation below.
Practice:
5). SCENARIO: You take 45 copies of your CD to your performance. Every 10 minutes, you sell about 3 CD’s.
a). How many CD’s will you have left after 1 hour (____ minutes)?
b). What expression shows how many CD’s you’ll have left after x minutes? ______
c). On the graph below, please show how the number of CD’s left changes over time.
d). On your graph, please label the point representing “Number of CD’s left after 0 minutes”
Worked Example:
6). SCENARIO: On his birthday, Tanez starts saving money to buy an X-box. The equation for his savings is:
Let x = number of days he saves
Let y = total dollars saved
y=152x+10
Practice:
7). Let’s try it with the equation y=12+6x
Worked Example:
8). Fill in the blank in the equation for this graph:
Class Discussion
9). What equation would represent the graph below?
Guided Problem-Solving: Try on your own, using the questions to help. Start with question a).
10). What equation would represent the graph below?
How could you describe this scenario in words? ______
______
______
Small-Group Practice
11). Ian is using a hose to finish filling up a swimming pool.
a). What equation represents the graph below?
b). If water costs $0.05/gallon, how much money is Ian spending per minute on water? (Show work).
12). What equation represents the graph below?