A C E. Answers Investigation 3. Applications. 2 are equivalent. It takes 3 thirds to. 1 or 1. 4 or. 2 or

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1 Applications Answers Investigation. and are equivalent. It takes thirds to make whole, so thirds is equivalent to wholes and one third.. B. (See Figure.). Answers will vary. (See Figure.) Pay attention to whether students understand the meaning of greater and less in the context of negative numbers (i.e., do they know that >, or do they think >?) or or 6 or or. Answers will vary. Possible answers include,, 00, 00, and.. a. They moved yards = = b. No. It is because they only got yards forward. Gain and lost makes a gain of. Then gain makes a gain of. Finally, lost makes a total of yards gained forward. 6. F > F. F < 6 F. 0 F > F. F < F 0. The Blue team is the winner, 0 points is the highest point value. You might remind students that numbers on the right of the number line are greater than numbers to the left. 0 is the number furthest to the right of all of them.. a. Ordering # is ordered from least to greatest. b. Ordering # is ordered least to greatest by absolute value. c. Ordering # is ordered from greatest to least. Figure Figure Comparing Bits and Pieces Investigation

2 Answers Investigation. Ordering # (least to greatest):,,,, ; Ordering # (least to greatest by absolute value):,,,, ; Ordering # (greatest to least):,,,, ; One other ordering that could be done is to reverse ordering # (greatest to least by absolute value):,, 6,,. Jeremiah is correct, because the winner is the person closest to zero. They should be concerned about the absolute values of the numbers. Note: The term par, which is included in the phrase that Rosemary rewrote, is the number of strokes an expert golf player would take to complete a particular hole in the golf course.. a. Order from lowest to highest: Death Valley, Indio, New Orleans, Denver, Wenzuan b. Order from least to greatest distance from sea level: New Orleans, Indio, Death Valley, Denver, Wenzuan c. I used absolute value in part b because the order of the cities is in terms of distance, not numerical value. Therefore, it doesn t matter whether the city s elevation level is above or below seal level. The order starts from the city closest to sea level, 0 feet, to the city farthest away from sea level.. The person owes $.00, or has a debt of $ The elevation is 0 feet below sea level.. The quarterback lost yards.. The lemonade stand lost ten dollars.. > 0 0. >. >. <. >. > 6. 6 < 6. 0 < 0. >. < 6. 6 = 0. > For Exercises, answers may vary: between and ; nearer benchmark: 6. between and ; nearer benchmark:. between and ; nearer benchmark:. between 0 and ; nearer benchmark: 0. between and ; nearer benchmark: 0. between. F. D and ; nearer benchmark:. Each person gets 0 or = 0.0 of a 00 pan. ( servings). Each person gets or = 0.0 of a 0 00 pan. ( servings). Each person gets or = 0.0 of a 0 00 pan. ( servings) = = = = Possible answer: 0.60 is greater than 0. because it has a larger value in the tenths place. Also, we can compare these as fractions: 60 < Comparing Bits and Pieces Investigation

3 Answers Investigation 6. Possible answer: 0.6 and 0.60 are equivalent because they both cover the same area of a hundredths grid. Also, we can compare these as fractions: 6 = = = = = = = Possible answers: 0, 0 00,, 0 0. The decimal value 0.0 means If you divide 00 into 0 equal parts or tenths, each tenth will have 0 hundredths in it and of those tenths will have 0 hundredths in it, so 0 0. The step is 0.0. (See Figure.). The step is (See Figure.). The step is 0.. (See Figure.) < = > < 0.0 is equivalent to < 0.6 < , 0., 0., 0., 0. -, 0.00, 0 000, 0.. G 6. Use Pilar s approximation for. a. b. c. 6 = 0.= 0. = 0. =. = 6 0. = d. is equivalent to 6 =, or When Belinda entered into her calculator, the display read 0.. This is the decimal equivalent for. Since is equivalent to, the decimal equivalent is also 0... Possible answer: I would tell the new student to divide the numerator by the denominator on the calculator. I would tell her to round to the nearest hundredth. To show her this makes sense, I would write this decimal as a fraction with a power of ten in the denominator and show her that the original fraction and this fraction are nearly the same amount. I could do this by finding a number to multiply the numerator and the denominator of the original fraction by that gives a denominator close to a power of ten. Figure Figure Figure Comparing Bits and Pieces Investigation

4 Connections Answers Investigation. miles 0. If four days at this rate, the Drama Club can clean 0 miles. So it is correct that they can clean at least they will clean exactly miles, but not that miles.. They are both correct. =. a. 0 or ; 0. b. Possible answer: If every student were to receive one piece of every pizza, each pizza would have to be divided into ten equal pieces, with each piece being of a pizza. Each student would 0 receive eight pieces, giving each 0 of a pizza. The picture below shows one student s share of the pizza. (See Figure 6.). a. Each part represents, 0., or one 0 tenth of a centimeter. (See Figure.) b. Each part represents, 0.0, or one 00 hundredth of a centimeter. c. Each part represents, 0.00, one,000 thousandth of a centimeter , Written as improper fractions, , =, so there are no fractions 0 between them.. is the largest part of a whole. This is a difficult comparison. One way to compare these fractions is based on knowing that if we multiply or divide the numerator and denominator of a fraction by a common factor, we get an equivalent fraction. In comparing to, multiply its numerator 6 and denominator by. The equivalent fraction is. Now that they have the 6 same numerator, we see that is larger 6 (because sixty-eighths are bigger than sixty-ninths). Next, compare 6 to by dividing its numerator and denominator by. reduces to the equivalent 6 fraction,. is greater than so it s the largest part of the whole. Figure 6 Figure Figure Comparing Bits and Pieces Investigation

5 Connections Answers Investigation. (See Figure, previous page.) 00.. Possible explanation: If you break into fourths, or groups of equal size, one group or of will be. (See Figure.) Possible explanation: If you partition into fourths or groups of equal size, one group or or of is 6. of is. Three of those groups 0. Possible explanation: If you partition into ninths or groups of equal size, one group or or of is. Two of those groups of is. (See Figure 0.) 0.. Possible explanation: If you have wholes and partition each whole into fourths, you can take from each of the wholes. You will have one-fourth-size parts, which is of one whole. 0.. Possible explanation: If you partition wholes into parts of equal size, each part will be of whole and of the nine parts 0. or or.. Possible explanation: If you have wholes and partition each whole into fourths, you can take fourth- size pieces or from each of the wholes. You will have one-fourth-size parts or which is equivalent to. or of will be of the one-third size parts or of one of the wholes. is the same as Figure Figure 0 Comparing Bits and Pieces Investigation