1 / 19

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 _____________ (

kasi
Télécharger la présentation

Today’s Lesson:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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:

More Related