My Notes CONNECT TO SCIENCE

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1 Mood Rings, Part SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Vocabulary Organizer Tyrell and four of his friends from West Middle School went to a craft fair and they all decided to buy mood rings. When discussing their ring sizes with the ring maker, they learned about anthropometry. Did you know that the average length around a woman s ring finger is about 6 inches and the average length around a man s ring finger is about 6 9 inches? Before they can buy their rings, the friends must first measure their ring fingers.. How big is your ring finger? To measure your ring finger wrap a measuring tape snugly around the base of your finger. Record your measurement to the nearest 6 of an inch. Answers may vary. Sample answer: Ring sizes should vary roughly from to 3 inches.. This table shows the finger sizes of the five friends. Tyrell Bob Jose Nisha Ema 8 in. in. 3 in. 3 6 in. a. Look at this measuring tape to determine Bob s finger size. Write your answer as a mixed number in the table above. 0 3 b. How many inches are in inches? Count the inches on the diagram and write your answer as an improper fraction in. c. Another way to see this is to use a model. Name the shaded parts of this diagram two ways. 5 Mixed Number: Improper Fraction: (wholes + part) (total parts) CONNECT TO SCIENCE ACTIVITY.6 Anthropometry is the study of the measurement of the human body in terms of its dimensions. People who design things for others to use, such as bracelets or rings, have to take typical body measurements into account. Remember, a mixed number is the sum of a whole number and a proper fraction. MATH TERMS A positive improper fraction has a value greater than or equal to. The numerator is greater than or equal to the denominator. ACTIVITY.6 Investigative Mixed Numbers and Improper Fractions Activity Focus Converting between mixed numbers and improper fractions Comparing and ordering mixed numbers and improper fractions Materials Measuring tapes (at least per pair of students) Fraction circles/bars (optional) Chunking the Activity # #5 #3 # #6 #3 # Paragraph Summarize/Paraphrase/Retell The purpose of this question is to engage students in the context of the activity by making a personal connection. Students may need a review mini-lesson on measuring to the nearest 6 inch. Vocabulary Organizer (a, b) This begins a series of four questions that serve as a review of writing mixed numbers and improper fractions using pictures, number lines, and abstract rules. Unit Number Concepts _SB_MS_-6_SE.indd 33 MINI-LESSON: Measuring to the Nearest 6 Inch Give each student a long strip of paper. Have students draw a line at each end of their strips and label the left side 0 and the right side, then fold their strips in half and at the top label this crease,. Students fold their strips in half again and label each crease now with,, just below the label for, and 3. Have students do this two more times in order to create s and 8 s. Encourage students to use different 6 sized lines when labeling the creases. Compare the strips students create to a standard ruler. Let students practice measuring objects to the nearest,, 8, and units of their rulers. 6 /6/09 5:: PM Unit Number Concepts 33

2 ACTIVITY.6 Continued () Think/Pair/ Share, Look for a Pattern (f), Quickwrite (f) Stress the relationships between the parts so that students understand why the trick, or algorithm, works, and do not simply memorize a process. Students may need a vocabulary reminder on the following terms: quotient 3r divisor dividend -6 remainder 3 Create Representations ACTIVITY.6 Mood Rings: Part SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Look for a Pattern, Quickwrite, Create Representations d. Complete this description of how to find the improper fraction for the number of shaded halves: There are whole shaded circles with shaded halves in each. This gives me shaded halves. Plus, there is shaded half in the last circle, making a total of 5 shaded halves. e. Both the mixed number and the improper fraction in Part c describe the same number. Write an equation that shows the two are equal. = 5 f. Without drawing a model, describe a method to use the digits from the mixed number to find its equivalent improper fraction. (Hint: Consider your description in Part d.) Answers may vary. Sample answer: Multiply the denominator by the whole number to get =, then add the numerator to get + = 5. Put 5 over the denominator to get Now convert Nisha s finger size to an improper fraction. a. Use circles: b. Use a number line: 0 c. Use the method you discovered in Part e of Question. Did you get the same answer as you did in Parts a and b? ; yes. Use your method from Question e to convert the other friends sizes to improper fractions. 5 a. Tyrell 8 b. Ema c. Jose /6/09 5::8 P0 3 SpringBoard Mathematics with Meaning Level _SB_MS_-6_SE.indd 3 3 SpringBoard Mathematics with Meaning Level

3 Mood Rings: Part SUGGESTED LEARNING STRATEGIES: Identify a Subtask, Quickwrite ACTIVITY.6 Continued 5 Identify a Subtask, Debriefing Suggested Assignment CHECK YOUR UNDERSTANDING p. 38, # UNIT PRACTICE p. 59, #0 6 Quickwrite Students are expected to use prior knowledge and compare the whole numbers. Quickwrite Students compare the unit fractions using prior knowledge the smaller the denominator, the bigger the unit fraction. 8 Quickwrite Students use knowledge from Activity.5 to solve this problem. Make a quick informal assessment using anecdotal records to identify students in need of reteaching for comparing fractions. Encourage students to share and compare their different approaches. 5. You can use two methods to change from an improper fraction to a mixed number: drawing a model or dividing. a. Draw a model of 9. Then write a mixed number to represent the whole and fractional parts of your model. b. Divide 9 by. Express the remainder as a fraction to get a mixed number. 9 = The five friends want to compare finger sizes to see whose ring finger is the largest and whose is the smallest. 6. Nisha and Jose compare their finger sizes. Write an inequality symbol in the circle to make the statement true. Explain your thinking. Nisha Jose 3 < Explanations may vary. Sample answer: Jose; the whole numbers are different so I compare them: <, so 3 <.. Next, Bob and Jose compare. Which of them has the larger ring finger? Explain your thinking. Bob Jose > Explanations may vary. Sample answer: Bob; the whole numbers are the same so I compare the fractions. and are unit fractions, and halves are bigger than fourths, so >. 8. Then Nisha and Tyrell compare their sizes of 3 and 8. Whose finger is larger? Express your answer as an inequality. Explain your thinking. Tyrell s finger is larger: 8 > 3. Students explanations may vary depending on the process they choose to arrive at their answers. ACTIVITY.6 WRITING MATH A fraction is a way of writing a division problem: 9 = 9. Unit Number Concepts 35 M33-038_SB_MS_-6_SE.indd 35 /6/09 5::53 PM Unit Number Concepts 35

4 ACTIVITY.6 Continued 9 Think/Pair/Share, Quickwrite (b) Students should write names and sizes. They then compare Ema to Jose and see that 6 would be equal to which is Jose s fraction, so Ema s size is smaller, as her fraction is 3 6. Students know Ema s finger size is bigger than Tyrell s though because her mixed number has a whole number of. 0 The purpose of this question is for students to discover that they can use common denominators to compare multiple fractions at the same time. ACTIVITY.6 Mood Rings: Part SUGGESTED LEARNING STRATEGIES: Quickwrite, Think/ Pair/Share, Create Representations, Debriefing 9. You have compared the sizes of four friends, two at a time. a. Use what you have learned to order the friends by their ring finger sizes, going from smallest to largest. Nisha, Tyrell, Jose, Bob b. Where does Ema fit into this order? Explain. Ema fits in between Tyrell and Jose. 0. Ema tells her friends that they could order their fractions all at once by using common denominators. Show how this can be done. Change the mixed numbers to improper fractions with 6 as the denominator. Tyrell: 8 = 5 8 = 30 ; Bob: 6 = 5 = 0 6 ; Jose: = 9 = 36 ; Nisha: 3 6 = = 8 6 ; Ema: 3 6 = 35 6 ; then compare the numerators to find that the order from smallest to largest is Nisha, Tyrell, Ema, Jose, and Bob. a Create Representations, Debriefing Students practice ordering on a number line as another way of ordering. Be sure students are plotting points and not shading the line. b Create Representations, Quickwrite, Think/Pair/ Share This question is meant to give students the opportunity to think about a variety of possibilities and decide how they can use what they already know to answer the questions. CONNECT TO AP Looking at the pattern of points on a number line can help you decide if the numbers are getting close to a particular number. Discovering such patterns is a fundamental concept in advanced math courses.. Order the friends ring finger sizes from least to greatest on the number line below. Label each point with each person s initial as shown for Bob. N T EJ B 3. You now know different ways to order measurements. How would you order the measurements of several other friends? Describe your method. Karen Ahmed Ileana Keisha Hunter Answers may vary. Sample answer: First change all numbers to either mixed numbers or improper fractions, and then compare them as done earlier. The finger sizes are easy to order since the fractions are all in s, s, s, or 8 s, like the increments on a ruler. However, 6 many numbers, such as 5 3, 98 00, 3, and, do not have denominators that are as simple to compare. 36 SpringBoard Mathematics with Meaning Level Connect to AP Students will need to be able to graph and order fractions on a number line or in the coordinate plane when they study sequences and series, especially, those that converge to a real number. Consider the sequence, 3, 3, 5,, 9 0, 99,. Have your class graph these fractions on a 00 number line. They can then observe that the points are getting closer and closer to the number. However, no number in the sequence will ever equal or be greater than. An activity like this will set the stage for future understanding of limits, a fundamental concept in calculus _SB_MS_-6_SE.indd 36 /6/09 5::58 P0 36 SpringBoard Mathematics with Meaning Level

5 Mood Rings: Part SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Create Representations, Quickwrite, Debriefing, Self Revision/Peer Revision To order numbers like these, think about how close each fraction is to benchmark numbers, such as 0,,, and so on. For example, 5 is a little less than 3, because half of 3 is 6. Thus, place 3 5 just before the mark Continue using benchmarks to order 00 98, 3, and on the number line above.. Summarize your findings on comparing and ordering mixed numbers and improper fractions by discussing the following cases. a. Whole numbers are different: 9 3 and 3 Answers may vary. Sample answer: Just compare the whole numbers. The bigger the whole number, the bigger the mixed number. ACTIVITY.6 MATH TERMS Benchmark numbers are numbers used as points of comparison when estimating. ACTIVITY.6 Continued TEACHER TO Read and Think Aloud is TEACHER a good teacher strategy to use while reading the information before Question 3. Paragraph Summarize/Paraphrase/Retell C Create Representations Students reason that 98 is just 00 a little less than 3, 3 is a little greater than because of is, and is a little greater than but less than. d Quickwrite, Debriefing, Self Revision/Peer Revision Students form generalizations for comparing and ordering different combinations of mixed numbers and improper fractions. Suggested Assignment CHECK YOUR UNDERSTANDING p. 38, # UNIT PRACTICE p. 59, # b. Whole numbers are the same: 5 3 and 5 9 Answers may vary. Sample answer: Compare the fractions by either writing equivalent fractions or using crossmultiplication. c. Both are improper fractions: 3 5 and Answers may vary. Sample answer: Compare them the same way you compare common fractions. d. One mixed number and one improper fraction: 6 3 and 3 5 Answers may vary. Sample answer: Either change the improper fraction to a mixed number or the mixed number to an improper fraction, then solve using the methods discussed earlier. Unit Number Concepts 3 M33-038_SB_MS_-6_SE.indd 3 /6/09 5:5:0 PM Unit Number Concepts 3

6 ACTIVITY.6 Continued ACTIVITY.6 Mood Rings: Part Answer Key a. 53 b Kendra, Miley, Bryson, Wyatt 3. Juan. See answer to # below. 5a. 8 9 > b < , 3 0, 5, 6. Answers may vary. Sample answer: Fractions can be expressed as proper fractions, improper fractions, or mixed numbers. Comparing mixed numbers and improper fractions is like comparing proper fractions because you can find equivalent fractions if you need to and then use common denominators or common numerators to compare; comparing mixed numbers and improper fractions is different from comparing proper fractions because with mixed numbers sometimes you can just compare the whole number parts and sometimes you have to convert the mixed number to an improper fraction. CHECK YOUR UNDERSTANDING Write your answers on notebook paper. Show your work.. Order each of the following numbers Show your work. by placing them on a number line. Use. Convert the improper fraction to a mixed benchmark numbers to determine their number and the mixed number to an placement. improper fraction. a. b , 5, 0 8, and 3 5. Compare.. Mr. White s students are playing a game. a. 8 9 and He gives each student in a group a fraction 6 b and 5 to help them decide the order in which they will play. The person with the largest fraction goes first, and so on. The table 6. Order from least to greatest: 6, 5,, 3 0 below shows the fractions for the students in one group.. MATHEMATICAL REFLECTION Describe the three forms in which fractions can be Wyatt Kendra Miley Bryson List the order in which they will take their turns. 3. Kim and Juan are measuring their wrists to purchase watches. Kim s measures in. and Juan s measures 5 3 in. Who has the larger wrist? written. Explain how to compare the three forms. Give examples using different forms of fractions. 38 SpringBoard Mathematics with Meaning Level _SB_MS_-6_SE.indd 38 /6/09 5:5:0 P SpringBoard Mathematics with Meaning Level

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