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5-Minute Check on Activity 1-3

5-Minute Check on Activity 1-3. What is the language of Math? What does the variable(s) represent? In step 4 of our problem solving steps, what do we do when we get an answer?. Equations is the language of Math. An unknown value in the problem. Check the answer to see if it makes sense.

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5-Minute Check on Activity 1-3

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  1. 5-Minute Check on Activity 1-3 • What is the language of Math? • What does the variable(s) represent? • In step 4 of our problem solving steps, what do we do when we get an answer? Equations is the language of Math An unknown value in the problem Check the answer to see if it makes sense Click the mouse button or press the Space Bar to display the answers.

  2. Activity 1 - 4 Proportional Reasoning or Being like Mike

  3. Objectives • Use proportional reasoning as a problem-solving strategy • Write a proportion and then solve the resulting proportion

  4. Vocabulary • Ratio – comparisons using quotients • Cross Multiplication – multiplying the numerator of one ratio by the denominator of the other ratio • Proportion – two ratios set equal to each other (solved using cross multiplication) • Percent – a number divided by 100 (100% is the whole) • Equivalent – numbers having the same numerical or decimal value • Proportional Reasoning – ability to recognize when two ratios are equivalent

  5. Ways to Express a Ratio • Verbally – he made 3 out of 4 free-throws • Fraction – he made ¾ of his foul shots • Division – he made 4  12 or field goals • Decimal – his probability of success was 0.33 • Percentage – he made 33% of his field goals 

  6. Activity The following table summarizes Michael Jordan’s statistics during the six games of one of the NBA championship series. What was his points per game average? In which game did he score the most points? In which game did he score the most field goals? free throws? 27.33 Game 3, 36 points Games 3 and 5, 11 Games 4 and 6, 11

  7. Relative Free-Throw Performance The following table summarizes Michael Jordan’s free-throw statistics during the six games of one of the NBA championship series. In which game was his relative free-throw performance the highest? In which game was his actual free-throw performance the lowest? In which game was his relative free-throw performance the lowest? 9/10 9  10 0.90 90% 10/16 10  16 0.625 62.5% 11/11 11  11 1.00 100% 11/13 11  13 0.846 84.6% 4/5 4  5 0.80 80% 11/12 11  12 0.917 91.7% Game 3; 11-11 is 100% Game 5; only made 4 shots Game 2; 10-16 is 62.5%

  8. Equivalent Ratios 9 Fill in the blanksa. 3 out 4 is equivalent to _____ out of 12b. 3 out 4 is equivalent to _____ out of 32c. 3 out 4 is equivalent to _____ out of 100 Write each ratio in faction form and reduce it:a. 27 out of 75b. 63 out of 175c. 36 out of 100 24 75 9/25 also 36% 7/25 also 28% 9/25 also 36%

  9. Proportion Problem Solving Solving any proportion problem generally requires the following: a c --- = --- Write the proportions b d ad = bc Cross-multiplication bc a = ----- Solve for a by dividing by d d

  10. NYPD College Degree A recent survey indicated that 1 out of every 5 New York City Police (NYPD) officers holds a four-year college degree. There were approximately 41,000 NYPD officers when the survey was conducted. How many hold a four-year degree? 1 n --- = --------- Write the proportions 5 41000 41000 = 5n Cross-multiplication 8200 = n Solve for a by dividing by 5

  11. NY High School Graduates New York state has taken a leading position in raising the standards of its high school graduates. In 2003, every graduate needed to pass a series of rigorous subject-matter tests called Regents exams. Currently your cousin lives in a NY county in which only 6 out of 10 graduates receive Regent diplomas. If 5400 students in your cousin’s county earned a Regents diploma last year, how many graduated from high school? 6 5400 --- = --------- Write the proportions 10 n 54000 = 6n Cross-multiplication 9000 = n Solve for a by dividing by 6

  12. Summary and Homework • Summary • Ratios can be expressed in a variety of ways • fraction like a part / whole • verbally like 2 out of 3 • percentage like 58% (58/100) • decimal like 0.58 • Proportions are two ratios set equal • Cross-multiplication is a method to solve for missing values in proportions • Homework • pg 25-7; 1-12

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