Equivalent forms: fractions, decimals, and percents Block 1 Student Activity Sheet

Transcription

1 Block 1 Student Activity Sheet 1. List two real-life examples of fractions. 2. List two real-life examples of decimals. 3. List two real-life examples of percents. 4. Consider the table below showing Courtney s batting over the first seven games. Game Total Hits At Bats What would her new batting average be if she got 2 hits for 5 at bats in her next game? Page 1 of 3

2 Block 1 Student Activity Sheet 5. REINFORCE In game nine, Courtney had two hits and her overall batting average for the season was after that game. Game Total Hits At Bats a. Complete the table to show how many times Courtney was at bat in game nine if her overall batting average for the season was after that game. Game Total Hits At Bats b. Explain your process for determining how many times Courtney was at bat in game nine. 6. REINFORCE In professional baseball, one of the best career batting averages of all time was a. If this batter had 4209 career hits, how many times was he at bat during his career? b. If this player had 6 at bats in one game, how many hits would you expect him to get? Page 2 of 3

3 Block 1 Student Activity Sheet c. A baseball legend once said those that fail 'only' seven times out of ten attempts will be the greatest in the game. Explain the meaning of this quote. Page 3 of 3

4

5 Block 2 Student Activity Sheet 1. As you consider the definition of rational numbers, consider these questions. a. What do you notice about the word rational? b. Record what you know about positive rational numbers and provide at least three different examples. 2. REINFORCE Rewrite in the form a b. 3. Complete the table showing the place value names. ones or units. tenths 4. Rewrite as a fraction in simplest form. Page 1 of 2

6 Block 2 Student Activity Sheet 5. Convert the decimals below to their equivalent fraction form in simplest terms. Decimal Fraction 6. REINFORCE Rewrite each decimal as a fraction in simplest form. a b c Page 2 of 2

7 Block 3 Student Activity Sheet 1. After 25 at bats, Courtney had 7 hits. She represented her batting average with a fraction. hits at bats = 7 25 a. Rewrite the fraction 7 25 as a decimal fraction. Then convert the decimal fraction to a decimal to find Courtney s batting average. Batting averages are shown to the thousandth place. b. Use long division to convert 9 20 to a decimal. c. Use long division to convert 5 6 to a decimal. Page 1 of 4

8 Block 3 Student Activity Sheet 2. So far this year, Alyssa has 5 hits and 16 at bats. What is Alyssa's batting average? Explain how you found it. 3. Complete the table below showing the decimal equivalents and batting averages for Courtney s six teammates. Player Hits At Bats Decimal to 4 places Batting average Alyssa Brianna 8 26 Mariah 5 18 Sophie 7 22 Katie 3 14 Melissa 4 20 Page 2 of 4

9 Block 3 Student Activity Sheet 4. REINFORCE Show how to use a standard algorthim to write each fraction as a decimal. a. 4 5 b. 7 8 c d REINFORCE Complete the equivalence table. Decimal notation a. b. c Fraction notation a b in simplest form Fraction notation using mixed numbers in simplest form d h. i e. f. g j. Page 3 of 4

10 Block 3 Student Activity Sheet 6. REINFORCE Give two fractions whose decimal equivalent is REINFORCE Three pans of lasagna were prepared for the school cafeteria. The shaded area represents the amount of lasagna that has been eaten. Represent the lasagna that has been eaten as a fraction and a decimal. 8. REINFORCE Joseph wants to make trail mix. He is buying ingredients in the bulk foods section of his grocery store. However, the food scale at the grocery store is digital and will only display weights as decimals. If Joseph buys the exact weights called for in the recipe, what decimal values will be displayed on the digital scale? Ingredient Almonds Dried apricots Dried cherries Trail Mix Recipe Weight given in fractions pounds a. 5 8 pound b. 2 3 pound c. Weight given in decimals Walnuts pounds d. Page 4 of 4

11 Block 4 Student Activity Sheet 1. Show how to express 5 8 as a percent. 2. What does percent mean? 3. Complete the following activities to explore common benchmark fractions and translate between fractions and percents. a. List as many benchmark fractions as you can. b. Represent 1 4 using a strip diagram, a 10-by-10 grid, and a number line. Page 1 of 4

12 Block 4 Student Activity Sheet c. Represent at least three of your benchmark fractions as percents using strip diagrams, 10-by-10 grids, and number lines. Label each representation with the fraction and the percent. Can you complete the puzzle by representing the correct number of squares that would be shaded in the ten-by-ten grid to represent each of the decimals? would be represented by shading squares would be represented by shading squares would be represented by shading squares would be represented by shading squares would be represented by shading squares. Page 2 of 4

13 Block 4 Student Activity Sheet 5. What is the quickest way to convert any decimal to an equivalent percent? 6. To convert a percent to an equivalent decimal, remove the % and move the decimal point places to the. 7. REINFORCE Find the equivalent percent for each benchmark fraction. Represent each percent with a strip diagram, a 10-by-10 grid, and a number line. a. 3 4 = % b. 7 8 = % Page 3 of 4

14 Block 4 Student Activity Sheet c. 5 9 = % 8. REINFORCE Complete the table to show equivalent fractions, decimals, and percents. Put your fractions in simplest terms. Fraction Decimal Percent 3 5 a. b. c d. e. f. 35% g. 0.2 h i. j. k. l. m n. o. p. 68% Page 4 of 4

15 Block 5 Student Activity Sheet 1. Courtney s goal is to get 16 hits in 40 at bats by the end of the season. She writes the ratio as a fraction 16, and wonders what percent this fraction is equal to. Find what 40 percent the fraction equals. 2. What is a proportion? Page 1 of 3

16 Block 5 Student Activity Sheet 3. Use the following proportion to rewrite 3 5 as a percent. 3 5 = n REINFORCE Use a proportion to rewrite as a percent. 5. Show how to convert 68.75% to a decimal and fraction in lowest terms. Page 2 of 3

17 Block 5 Student Activity Sheet 6. Complete the table to show equivalent forms of rational numbers. Fraction Decimal Percent % Page 3 of 3

18

19 Block 6 Student Activity Sheet 1. Explain how to compare two decimals. 2. The denominator of a fraction tells how many equal parts one whole is divided into. The numerator of a fraction tells how many of those parts we are interested in. For the fraction 3 8 we are interested in three equal parts of a whole that is divided into eight equal parts. Can you describe 5 8 in this way? 3. If two fractions with the same denominators are being compared, how can you tell which one is larger? 4. REINFORCE Locate and label each pair of values on the number line. Then show algebraically which value is greater. a. Which value is greater, 0.34 or 2 5? Page 1 of 3

20 Equivalent forms: fractions, decimals, percents Block 6 Student Activity Sheet b. Which value is greater, 1 25 or 0.025? c. Which value is greater, 0.3 or 9 25? d. Which value is greater, 1 8 or 0.08? Page 2 of 3

21 Equivalent forms: fractions, decimals, percents Block 6 Student Activity Sheet e. Which value is greater, or 0.2? Page 3 of 3

22

23 Block 7 Student Activity Sheet 1. If two fractions with the same numerators are being compared, how can you tell which one is larger? 2. If two fractions have different numerators and different denominators, how can you tell which one is larger? 3. List the rational numbers in order from smallest to largest % % % Page 1 of 2

24 Block 7 Student Activity Sheet 4. REINFORCE Complete the table by writing the correct inequality symbol in the left column. In the right hand column write the least common denominator for the two fractions. a. c. e. g. i. Comparison (> or <) Least common denominator b. d. f. h. j. Page 2 of 2