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Today’s Lesson:

Today’s Lesson:. What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions. Vocabulary: Ratio – __________________________ of two numbers ( 15 students to 1 teacher ) . Rate – comparing two numbers with different _____________ (

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Today’s Lesson:

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

  2. Vocabulary: Ratio – __________________________ of two numbers (15 students to 1 teacher). Rate– comparing two numbers with different _____________ ( Unit Rate – rate that is out of ________ ( ) . Proportion – two ratios that are _____________________ to one another ( = ). comparison units one equivalent

  3. Three Ways to Write a Ratio: 1) 2) 3) Write the following ratios in all 3 ways: • The ratio of months that end in the letter “r” to the total number of months in a year (be sure to reduce): • The ratio of vowels to consonants in the word “C-A-L-E-N-D-A-R”: • The ratio of boys to girls in Ms. Dyson’s class: By using a colon (3 boys : 2 girls) ; using a fraction ( );and using words (three boys to every 2 girls) . 4 : 12 or 1 : 3 ; or ; one to three 3 : 5 ; ; three to five

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

  5. 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 no yes

  6. Solving a Proportion: Step One: Cross Multiply Step Two: Divide by the coefficient (# with “x”) Example: = 72 = 12x 12 12 x = 6 You Try (Solve the following proportions): x = 10 x = 4

  7. 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

  8. 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

  9. 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!

  10. Real-life Proportions . . . 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

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

  12. 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

  13. 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.

  14. NAME: DATE: ______/_______/_______ Math-7 NOTES What: rates and proportions Why: To introduce essential vocabulary and begin to solve proportions. Vocabulary: Ratio – _________________________________ of two numbers (15 students to 1 teacher). Rate– comparing two numbers with different __________ ( Unit Rate – rate that is out of ___________ ( ). Proportion – two ratios that are _____________________ to one another ( = ). Three Ways to Write a Ratio: 1) 2) 3) Write the following ratios in all 3 ways: 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:

  15. 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 . . . Solving a Proportion: Step One: Cross Multiply Step Two: Divide by the coefficient (# with “x”) Example: = 72 = 12x 12 12 x = 6

  16. You Try (Solve the following proportions): Real-life Proportions . . . • If 4 tickets to a concert cost $62, how much would it cost for 10 people to go to the concert? • A certain car drove 110 miles on 5 gallons of gas. How far should it be able to go on 11 gallons? • 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?

  17. 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.?

  18. NAME:___________________________________________________________________________NAME:___________________________________________________________________________ DATE: ______/_______/_______ Math-7 practice/ homework Do the following ratios form proportions. Answer “yes” or “no” (cross-multiply): Solve the following proportions:

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

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