4According to professional regulations, a baseball bat

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1 Mixed Numbers MODELING IMPROPER FRACTIONS In Power Players on page 4, you practiced dividing mixed numbers by converting them into improper fractions (fractions in which the numerator is greater than the denominator). To do this, you used a method of multiplication. You can also draw a model to rewrite a mixed number as an improper fraction. EXAMPLE: The circumference of a professional soccer ball is 2 3 feet. Use a diagram to find the equivalent improper fraction. The fraction component of the mixed number 2 3 has a denominator of 3. This tells us to divide each component of our diagram into thirds: To rewrite it as an improper fraction, count the shaded portions. Use the sum as the numerator over the original denominator, 3. Because there are 7 shaded wedges above, the equivalent improper fraction is 7 3. So 2 3 = 7 3. This means the circumference of the soccer ball can also be written as 7 3 feet. Use this method to answer the questions below. A regulation hockey puck must weigh at least 5 2 ounces. Fill in the diagram below to find the improper fraction equal to The diameter of a golf hole is 4 4 inches. Draw a diagram to find the equivalent improper fraction. 3The minimum length of a college-regulation football is inches. Draw a diagram to find the equivalent improper fraction. 4According to professional regulations, a baseball bat can be no more than 7 2 feet long. Draw a diagram to find the mixed number equal to 7 2.

2 Mixed Numbers DIVIDE & CONQUER In Power Players on page 4, you practiced dividing mixed numbers to reveal facts about some spectacular athletes. Use what you learned to answer five more questions involving mixed number division. Solve each problem to find the correct detail to complete a fact about a female sports star. Seven-time WNBA All-Star Becky Hammon recently retired from the league to become the NBA s first female full-time assistant coach. In, Hammon led her WNBA team, the San Antonio Silver Stars, to the best record in the league: Thomas began officiating at high school games in 996, after she graduated from college. In, she became the first woman ever to officiate a college football game A C B D In the 204 Winter Olympics, goalie Shannon Szabados helped Canada s National Women s Team beat their U.S. competitors to 2 in the gold-medal game A C B 0 4 D 7 3Sarah Thomas may become the first-ever female referee in the NFL. In 203, she was selected as one of finalists for the NFL s officiating training program, in which contestants compete for a permanent referee spot with the league A C B D A B C D In 2009, Thomas was one of only five female officials in college football. That year she was assigned a full schedule of games to referee A C B D

3 Ratio Reasoning CONVERSION RATES In Sizing Up a Colossal Cave on page 6, you converted the measurements of big caves into unusual units, such as airplane wingspans and football fields. One way to convert between different units is to express the first measurement as a fraction over, and multiply it by a unit rate of the second measurement. EXAMPLE: Ibrahim is making pancakes. The recipe calls for 2 tablespoons of milk, but Ibrahim has only a teaspoon to measure with. How many teaspoons of milk should he add? STEP : Rewrite the measurement that is being converted as a fraction over : 2 tablespoons Conversion Rates Unit Unit 2 cup 237 milliliters pound 6 ounces yard 3 feet gallon 8 pints tablespoon 3 teaspoons mile 5,280 feet kilometer,000 meters STEP 2: Use the conversion rates chart to find the unit rate that contains both the original unit (tablespoons) and the desired unit (teaspoons). Then multiply your original fraction by the unit rate: 2 tablespoons 5 3 teaspoons tablespoon 2 tablespoons 5 = 3 teaspoons = 6 teaspoons tablespoon So 2 tablespoons equal 6 teaspoons. In the multiplication above, the tablespoon units in the numerator and denominator cancel each other out. Use this method and the conversion rates chart to answer the following questions. The island of Manhattan is about 2.3 miles wide at its widest point. How many feet is this? Jane weighed 7.3 pounds when she was born. What 2 was her weight in ounces? 3Abbie uses 0.75 gallons of gas in a single day. How many pints of gas is this? A recipe for fruit punch calls for 6 cups of seltzer. 4 How many milliliters is this? 5A football player ran yards before being tackled. How many feet did he run?

4 Ratio Reasoning massive measurements In Sizing Up a Colossal Cave on page 6, you compared the sizes of familiar objects with the measurements of giant cave chambers to get a better sense of the caves size and scale. Use what you learned and the table below to answer five more size comparison questions. Round your answers to the nearest whole number. Common Size Comparisons Measurement Object Size Width Area Height Volume Wingspan of a Boeing airplane Football field Statue of Liberty in New York City Olympic-sized pool 225 feet 57,000 square feet 305 feet 88,263 cubic feet The Sarawak Chamber in Malaysia has a volume of 338 million cubic feet. It would take the water from how many Olympic-sized swimming pools to fill this chamber? 2The Big Room in New Mexico s Carlsbad Caverns has a volume of 35 million cubic feet. How many Big Rooms can fit into the Sarawak Chamber in question No.? 3At its widest point, the Big Room measures about 2,000 feet. How many Boeing airplanes lined up wingtip to wingtip would span this distance? 4The Big Room has a floor area of 357,480 square feet. How does this area compare with the area of a football field? 5The deepest level of Carlsbad Caverns measures,027 feet below ground. About how many Statues of Liberty stacked on top of each other would fit in this depth?

5 Comparing Populations RANDOM SAMPLES In The Bugs on Us on page 8, you compared populations of microbes on different body parts. In statistics, the population is the total group being referenced, and a sample is a small portion of that population. A random sample is a sample that was chosen by chance. In general, the characteristics of a random sample should be representative of the population as a whole. EXAMPLE: Aidan buys a bag of 40 marbles. He pulls 0 marbles out of the bag at random: 3 red, blue, 4 yellow, and 2 black. What can Aidan expect the population of marbles to look like? In the chart below, we can predict the composition of the marble population by multiplying each marble selection by 4, because Aidan pulled of the 40 total marbles out of the bag. 4 Aidan s Marbles Sample Calculation Population 3 red marbles = red marbles blue marble = blue marbles 4 yellow marbles = yellow marbles You can also use random samples to draw comparisons between two different populations. Use this information and the chart above to answer the following questions. Charlotte buys a bag of 40 marbles. She pulls 0 marbles out of the bag at random: 6 blue, yellow, and 3 black. Fill in the calculation and population columns of the chart below based on this random sample. 2 black marbles Sample Calculation Population 6 blue marbles yellow marble 3 black marbles Charlotte s Marbles = black marbles 2Which bag likely contains more yellow marbles: Charlotte s or Aidan s? 3Which bag likely contains more blue marbles? Is it probable that Charlotte s bag contains more red 4 marbles than Aidan s bag? Explain your answer.

6 Comparing Populations MICROBE math In The Bugs on Us on page 8, you compared the population distributions of three types of microbes on different parts of the human body. Use what you learned and the chart below to draw more comparisons about microbes and the parts of the body where they live. Percentage Breakdown of Microbe Populations on Select Human Body Parts Body Part Bacteria % Fungi % Viruses % Nostrils Behind the knee Heel of the foot 92 7 Behind the ear Forearm Back Cheek Outside of the ear Webbing between fingers A. Which human body part in the table above has the smallest percentage of bacteria? B. Which body part has the highest percentage of fungi? 2Where would you expect to find a distribution of microbes very similar to that on the webbing between your fingers? Explain. Toenail 90 9 SOURCE: Julie Segre, NATIONAL INSTITUTE OF HEALTH 3Where would you expect to find a distribution of microbes very similar to that on the heel of your foot? Explain. 4On average, there are about million microbes per square centimeter of skin. On a square centimeter on the outside of your ear, how many viruses can you expect to find? 5How many viruses can you expect to find on a square centimeter of skin behind your ear?

7 Bar Graphs CHOOSING SCALE In Birds on the Move on page 4, you made a double-bar graph to compare two different sets of data. When you re making a graph, it s important to choose a scale that suits the data. To do so, you can follow these four steps: STEP : Identify the highest value in your data set. STEP 3: Divide your scale maximum by the total number of grid lines on your axis. The quotient will be your approximate scale. STEP 2: Set a scale maximum that exceeds this value. STEP 4: Round up your approximate scale to a friendly number: a multiple of 2, 5, or 0. After you ve determined your scale, label your grid lines and plot the data. The data should take up most of the space in the graph. If the data looks very small within your graph, your scale is probably too big. Use this information and the data table below to answer the following questions about scale. Predicted 2080 Range for Select U.S. Bird Species Range Bird Species (square miles) Long-billed curlew 27 A. What is the maximum value of this data set? B. Based on this value, what is a reasonable scale maximum for your graph? 2If you were graphing this data on a plot with 5 grid lines, what would be your approximate scale? 3Choose a final scale by rounding your answer from question 2 to a friendly number. Sharp-tailed grouse 839 Red-naped sapsucker 772 Pygmy nuthatch 20 Dunlin 88 SOURCE: THE NATIONAL AUDUBON SOCIETY A. Will the minimum value in the data set above be 4 visible on a graph with the scale you ve chosen? B. Will the maximum value take up most of the height of the graph? On a separate piece of graph paper, create a 5-line 5 grid and plot the data in the table using the scale you ve chosen. After seeing your final bar graph, would you make any changes to your scale?

8 Bar Graphs EVALUATING RANGE REDUCTION In Birds on the Move on page 4, you compared the past and future ranges of select bird species by creating a double-bar graph. Use what you learned and the graph below to answer five more questions about the decreasing ranges of certain bird species. 5,000 Ranges of Select U.S. Bird Species Range (square miles) 4,000 3,000 2,000,000 Range in 2000 Predicted Range in Bohemian waxwing SOURCE: The National Audubon Society Brown-headed Sage thrasher nuthatch Bird Species Worm-eating warbler Which bird species on the graph is expected to have the smallest range by 2080? 2Without doing the math, use the graph to predict which bird species is expected to lose the most square miles of range between 2000 and Calculate the approximate decline in square miles of the range for each bird. Was your prediction in question No. 2 correct? 4Without doing the math, use the graph to predict which bird species is expected to experience the greatest percent decline in its range. 5Calculate the approximate percent decline in range for each bird. Round your answers to the nearest whole percent. Was your prediction in question No. 4 correct?

9 Practice Test Solve this equation to fill in the fact below: = In the 204 Winter Olympics, Canadian ice hockey goalie Shannon Szabados stopped goals in the goldmedal game, helping lead Canada s National Women s Team to victory. ISSUE SKILLS REVIEW 6At its widest point, the Miao Room is 2,795 feet across. The wingspan of a Boeing airplane is 225 feet. About how many planes, lined up wingtip to wingtip, could fit across the width of the Miao Room? 2Solve this equation to fill in the fact below: = As goalie for the Columbus Cottonmouths, Szabados is the first woman to play in her team s professional league. In November 204, she made saves to become the first female goalie to win a game in the league. 3In 2000, the range of the greater sage-grouse was 62 square miles. Scientists predict it will decrease to 47 square miles by By what percent will the area of the range decrease between these years? Round to the nearest whole percent. 4The mountain bluebird s range is predicted to decrease from 4,532 square miles to,232 square miles over the same time period. Which bird will experience a greater percent decrease in its range? 5The Miao Room cavern in China has a volume of million cubic feet. The Big Room inside New Mexico s Carlsbad Caverns has a volume of 35 million cubic feet. About how many Big Rooms can fit inside the Miao Room? 7On average, there are about million microbes per square centimeter of skin. If the microbe breakdown of your forearm is 85% bacteria, 5% fungi, and 0% viruses, how many viruses would you expect to find on a square centimeter of your forearm? 8The microbe breakdown of your toenails is 90% bacteria, % fungi, and 9% viruses. How many more bacteria would you expect to find on a square centimeter of toenail than on a square centimeter of your forearm? 9Classify this triangle according to its angles: Classify this triangle 0 according to the lengths of its sides: