Today’s Lesson: What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions. What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions.

comparison units one equivalent

Three Ways to Write a Ratio: 1)1) 2) 3) Write the following ratios in all 3 ways: 1)The ratio of months that end in the letter “r” to the total number of months in a year (be sure to reduce): 2)The ratio of vowels to consonants in the word “C-A-L-E-N-D-A-R”: 3)The ratio of boys to girls in Ms. Dyson’s class: By using a colon (3 boys : 2 girls) ; using words (three boys to every 2 girls).

What do you notice about the following ratios?? Answer: Each set of ratios are equivalent. Also, their cross-products are the same.

So, in order for two ratios to form a proportion, they must be ________________. Therefore, their cross-products are also equal. That means, we can cross-multiply to find out whether or not two ratios are proportional!! Do the following ratios form proportions? Cross-multiply to find out... equal no yes noyes

You Try (Solve the following proportions): x = 4 x = 10

Real-life Proportions... 1) If 4 tickets to a concert cost $62, how much would it cost for 10 people to go to the concert? x = $155

Real-life Proportions... 2) A certain car drove 110 miles on 5 gallons of gas. How far should it be able to go on 11 gallons? x = 242 miles

Real-life Proportions... 3) For every 4 boys at Simpson Middle School, there are 5 girls. If Simpson has 420 boys, how many total students are at Simpson? x = 525 girls Since there are 420 boys and 525 girls, there are 945 TOTAL STUDENTS!

Real-life Proportions... 4)The ratio of chocolate bars to tootsie rolls is 2 : 5. If there are 20 chocolate bars, how many tootsie rolls are there? x = 50 tootsie rolls

Unit Rates: 5) If four jars of pickles cost $12.80, then how much is one jar? x = $3.20

Unit Rates: 6) If Jill can type 150 words in 5 min., then how many words can she type in 1 min.? x = 30 words per minute

END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

Three Ways to Write a Ratio: 1) 2) 3) Write the following ratios in all 3 ways: 1)The ratio of months that end in the letter “r” to the total number of months in a year (be sure to reduce): 2) The ratio of vowels to consonants in the word “C-A-L-E-N-D-A-R”: 3) The ratio of boys to girls in Ms. Dyson’s class: Math-7 NOTES DATE: ______/_______/_______ What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions. What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions. NAME:

What do you notice about the following ratios?? Answer: So, in order for two ratios to form a proportion, they must be ___________________. Therefore, their cross-products are also equal. That means, we can cross-multiply to find out whether or not two ratios are proportional!! Do the following ratios form proportions? Cross-multiply to find out...

Real-life Proportions... 1)If 4 tickets to a concert cost $62, how much would it cost for 10 people to go to the concert? 2)A certain car drove 110 miles on 5 gallons of gas. How far should it be able to go on 11 gallons? 3)For every 4 boys at Simpson Middle School, there are 5 girls. If Simpson has 420 boys, how many total students are at Simpson? 4) The ratio of chocolate bars to tootsie rolls is 2 : 5. If there are 20 chocolate bars, how many tootsie rolls are there? You Try (Solve the following proportions):

Unit Rates: 5) If four jars of pickles cost $12.80, then how much is one jar? 6) If Jill can type 150 words in 5 min., then how many words can she type in 1 min.?

DATE: ______/_______/_______ NAME:___________________________________________________________________________ Do the following ratios form proportions. Answer “yes” or “no” (cross-multiply): Solve the following proportions:

For each of the below situations, set up a proportion to solve: