Quiz correction
• Reminder: put your homework in the bin!
Which of the following numbers is a solution for the inequality shown below? 7(2x - 3) > 49
A. 10 B. 5C. 0 D. -6
Write a sentence explaining why B is not the correct answer!
Algebra 11/9/2011
Ratios and proportions: setting up and checking a proportion using
units.
Algebra 11/9/2011
Objective: SWBAT set up and solve ratio and proportion problems. SWBAT analyze
a problem using dimensional analysis.
Quote of the day
• "Nothing can dim the light that shines from within." Maya Angelou
Dimensional analysis
• Dimensional analysis is the skill of analyzing a problem using only the units involved.
• In dimensional analysis, you are checking to
make sure that your equation has the correct units. If not, you definitely set up the problem incorrectly!
Example: making a statue
• Dwight Howard is 6 feet 11 inches (6.92 feet) and wears size 18 or 19 shoes (13.26 inches long, or 1.11 feet.) If we were going to make a 30 ft tall statue of Dwight Howard, what would the statue’s shoe length be?
Setup – what goes in the blanks?
Real height 6.92 feet ---------------- = ------------
x Statue’s shoe
Setup – what goes in the blanks?
Real height 6.92 feet 30 feet ---------------- = ------------
1.11 feet x Statue’s shoe
Setup – what goes in the blanks?
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
Questions
• What do the numerators have in common?• What do the denominators have in common?• What does the right side have in common?• What does the left side have in common?
Left side: real Dwight Howard
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
Right side: statue of Dwight Howard
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
Numerators: height
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
Denominators: shoe length
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
Final question: what are the units of x?
Real height 6.92 feet 30 feet Statue’s height
---------------- = ------------Real shoe 1.11 feet x Statue’s shoe
The ratio of cars to trucks in a showroom is 12 to 10. If the number of cars in the showroom is 24, find the number of trucks in the showroom. Write the units for each number below. Is this correct or incorrect?
12 x ---------------- = ------------------
10 24
Big ideas about ratios
• Does your answer make sense? Is this even a ratios problem?
• The ratio setup should work with dimensional analysis!
• Ratio problem – When one amount increases, another amount increases proportionately. When one amount is zero, the other amount must also be zero!
Writing
• 1. If one girl can walk to school in 10 minutes, how fast can two girls walk to school?
• 2. If Huck can paint a fence in two days, then Huck, Tom, and Jim can paint a fence in how many days, assuming they paint at the same rate?
• 3. If one boy makes one model car in 2 hours, then how many model cars can he make in 6 hours?
Classwork
• Textbook page 159 numbers 31 to 35. Setup each problem, write down the correct units, and then solve!
Homework• A car travels 125 miles in 3 hours. How far would it travel in 5 hours?
• If of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?
• Sam works as a dental hygienist. Last week Sam made $500 for 20 hours of work. How many hours must Sam work in order to make $700?
• The Ridilla family plan to drive to their vacation destination in 2 days. On day 1 the family traveled 324 miles in 4.5 hours. On day 2, how many hours will it take the family to complete the 576 mile trip, assuming the travel at the same rate as day 1?
Directions
• Directions: for each problem, set up a proportion and label each part of the proportion. You should also include units and a before/after or part/whole labeling. I know you can solve these, this homework is mainly about the skill and mindset of labeling and checking your units!
