NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17

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1 NS6-0 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE REQUIRED Understands division as fitting into Understands /n as one of n equal parts of a whole Can use number lines to represent whole numbers Understands fractions of lengths, areas, capacities, and number lines MATERIALS pre-cut pieces from BLM Fraction Parts and Wholes (pp. J-4 J-) die per pair of students / cup measure cup measure enough counters to fill a cup Review division as fitting into. Remind students that division can be looked at as fitting into. For example, to divide 6, you can ask how many objects of length fit across an object of length 6: SAY: Three s fit into 6, so 6 =. Dividing by a unit fraction. Give students the prepared cutouts from BLM Fraction Parts and Wholes ( whole, halves, thirds, 4 fourths, and fifths for each student). ASK: How many /s fit into? () Students should show their answer by lining up pieces. Write on the board: = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION ASK: How many /s should fit into? () Students should check this with their cutouts. Have a volunteer write the division equation. ( / = ) Repeat for how many fourths fit into ( /4 = 4) and how many fifths fit into. ( / = ) Exercises: Divide. 6 b) c) Bonus: Answers: 6, b), c) 0, d), Bonus: 0 d) Dividing a whole number by a unit fraction. Have students work in groups of four. Ask students to use their fraction pieces from BLM Fraction Parts and Wholes to determine how many /s fit into, b), c), d) 4. The Number System 6-0 J-

2 Then show students how to write the division equations: = = 4 = 6 4 = Repeat for thirds and fourths, but this time have students write the division equations themselves. Take up the answers on the board. Point out that no matter how many fit into, twice as many will fit into as fit into, three times as many will fit into, and four times as many will fit into 4. ASK: How many sixths fit into? (6) How many sixths fit into? ( 6 = ) Write on the board: 6 = 6 so 6 = 6 = Exercises 4 b) c) d) 6 e) f) 0 g) h) Bonus i) 00 j) 000, k) 00 l) 400, 000 Answers: 0, b) 0, c), d) 0, e), f) 0, g) 6, h), Bonus: i) 00, j),000, k),00, l),00,000 Showing division on a number line. Draw on the board: 0 ASK: How many steps of size / fit into? (6) Write on the board: = 6 Tell students that drawing number lines is another way to show how many halves fit into three. Ask a volunteer to extend the number line to find how many halves fit into four. () Then draw a number line from 0 to, divided into fourths. Write on the board: = ASK: How big is each step? (/4) Fill in the first blank. How many of them fit into two? () Fill in the second blank. Exercises: Write the division statement to show how many steps fit into the number line. 0 Bonus b) Answers: /4 =, b) / = 0, Bonus: / = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-6 Teacher s Guide for AP Book 6.

3 Exercises: Draw a number line to determine. Bonus: Draw pizzas divided into fourths to determine 4. Answers: 0 Bonus: = 6 4 = ACTIVITY Students play in pairs. Player rolls a die and takes that many steps. Player tries to take steps that are only / or /4 as long, and cover the same distance. Player decides how many steps Player should take to succeed before Player tries, and records the division equation. Then players switch roles. (MP.4) Different contexts for dividing fractions. Show students a / cup measure, a cup measure, and enough counters to fill up the cup. Tell students that the small measure is labeled as / cup and the big measure as cup. ASK: How many small cupfuls should fill up the big cup? () Ask a volunteer to check that this is the case. Tell students that a recipe calls for cups of flour, but you only have a / cup measure. ASK: How many cupfuls do you need? (6) Have a volunteer write the division equation. ( / = 6) Exercises: Solve the problems. Tegan needs cups of sugar. She only has a / cup measure. How many cupfuls does she need? b) Alex needs cups of water for a recipe. He only has a /4 cup measure. How many cupfuls does he need? c) Mary has feet of ribbon. She uses / of a foot for each gift. How many gifts can she put ribbon on? COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION d) Rosa has apples. She cuts them each into fourths. How many pieces does she have? e) Miki has 6 muffins. He cuts them into halves. i) How many pieces does he have? ii) Four people share the muffins. How many pieces does each person get? Answers: 0, b), c), d), e) i), ii) The Number System 6-0 J-

4 (MP.) Extensions. How can you use: a yard stick to show that = 6? b) two hundreds blocks to show that 00 = 00? c) your hands and fingers to show that = 0? (MP.4). Six people are sharing three oranges. Each orange is cut into eighths. How many pieces does each person get? Answer: 4. Discuss why it is easier to look at division as sharing equally when dividing by whole numbers, but as fitting into when dividing by fractions. Answer: It is hard to see how many pieces of size fit into / so / would be hard to find by thinking of division as fitting into. Also, / would be hard to think of as sharing equally between / of a person. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J- Teacher s Guide for AP Book 6.

5 NS6- Dividing Fractions by Unit Fractions Pages STANDARDS 6.NS.A. Goals Students will divide fractions by unit fractions in cases where the answer is a whole number. Vocabulary denominator fraction fraction names (halves, thirds, fourths,...) whole number PRIOR KNOWLEDGE REQUIRED Can locate fractions on number lines Can name fractions from pictures Understands division as fitting into Dividing unit fractions by unit fractions when the answer is a whole number. Draw on the board: Ask a volunteer to shade half of each circle. ASK: How many fourths fit into half the circle? () What division equation can you write from that? (/ /4 = ) Repeat for how many sixths fit into half (/ /6 = ) and how many eighths fit into half (/ / = 4). Exercises: Divide using the picture. b) c) 6 4 Bonus: Write another division equation for each picture by dividing the shaded fraction by a whole number. Answers:, b), c) 4; Bonus: / = /6, b) /4 = /, c) / 4 = / COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Exercises: Check your answers using multiplication. Answers: /6 = /6 = /, b) / = / = /4, c) / 4 = 4/ = /, Bonus: a ) /6 = /6 = /, b) / = / = /4, c) 4 / = 4/ = / Dividing fractions by unit fractions with the same denominator. ASK: How many /s are in /? () Write on the board: = ASK: How many /s are in /? () Have a volunteer write the division statement. (/ / = ) The Number System 6- J-

6 Exercises: Divide. 4 b) 6 6 c) d) 0 0 Bonus 4 4 Answers: 4, b), c), d), Bonus: Dividing fractions by unit fractions when the answer is a whole number. Draw on the board a circle divided into sixths as shown in the margin and have a volunteer shade / of it. ASK: How many /6s are in /? (4) Write on the board: 6 = 4 Then show students how they can use a double number line to show the same equation: Step : Draw and label a number line representing the fraction that is being divided. 0 Step : Draw a second number line below the first to represent the number you are dividing by. 0 6 SAY: It takes four /6s to equal /, so / /6 = 4. Exercises: Use the picture to divide. tenths 0 fifths 0 b) 0 c) Answers:, b) 4, c) 6, d), e) 0 0 d) 4 0 e) 0 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-40 Teacher s Guide for AP Book 6.

7 Using multiplication to divide fractions by unit fractions. Tell students that stamps make a strip that is foot long. Draw on the board: foot = SAY: Each stamp is / of the strip. The picture shows that eighths fit into, or that divided by / is. ASK: If stamps fit into strip, how can we know how many stamps fit into /4 of a strip? Allow volunteers to articulate an answer, then SAY: A strip that is /4 of a foot long can only contain /4 as many stamps as one that is foot long. So if stamps fit into, then /4 of stamps will fit into /4 of strip. Write on the board: = so 4 = 4 of = 4 = 6 Exercises: Redo the exercises above using this method. Make sure you get the same answer. Answers: / 0 = 0/ =, b) / 0 = 0/ = 4, c) / 0 = 0/ = 6, d) 4/ 0 = 40/ =, e) / 0 = 0/ = 0 or 0 = 0 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Remind students that this is similar to dividing whole numbers by fractions. SAY: We know that times as many objects will fit into as fit into, so /0 is 0. In the same way, / as many objects will fit into / as fit into, so / /0 = / 0. Exercises: Use = to divide. Bonus: Use d) b) 4 = 00 to divide. e) 00 c) f) Answers: / = 4/ =, b) /4 = 6/4 =, c) /6 = 60/6 = 0, Bonus: d) /4 00 = 00/4 =, e) / 00 = 00/ = 60, f) /0 00 = 00/0 = 0 Exercises: Divide. 6 b) 0 Bonus 4 000, 000,, 000 c) 0 Answers:, b), c), d), Bonus: 4,000 d) The Number System 6- J-4

8 (MP.) Extensions. Divide by finding the missing factor: = so = b) 6 = so 6 = Answers:, b) 4 (MP.4) (MP.). Use pattern blocks to determine 6.. Divide by changing the first fraction to have the same denominator as the second fraction. b) c) 4 0 d) 0 Answers: / / =, b) 0/ / = 0, c) /0 /0 =, d) /0 /0 = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-4 Teacher s Guide for AP Book 6.

9 NS6- Dividing Whole Numbers by Fractions Page 0 (Introduction) STANDARDS 6.NS.A. Goals Students will divide whole numbers by fractions in cases in which the answer is a whole number. Vocabulary phrases such as three times as many or one third as many PRIOR KNOWLEDGE REQUIRED Can divide a whole number by a unit fraction Understands division as fitting into Understands the relationship between multiplication and division Materials BLM Fraction Parts and Wholes (pp.j-4 J-) toothpicks Using pictures and concrete materials to divide whole numbers by fractions. ASK: How many /s fit into? () Draw on the board: ASK: How many fit into 4? (0) SAY: Four times as many fit into 4 as fit into. Extend the picture to show this: Tell students you want to know how many /s fit into 4. Write on the board: 4 = 0 4 =? COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Tell students that instead of just counting /s, they need to count blocks of size /. Demonstrate by drawing the first block and have a volunteer draw the rest to see how many fit into 4: SAY: 0 blocks of size / fit into 4, so 4 / = 0. The Number System 6- J-4

10 (MP.) ACTIVITY Give students (or groups of students) toothpicks and fraction parts and wholes from BLM Fraction Parts and Wholes. To show 4 /: ) Place 4 wholes in a row. ) Line up / size pieces underneath. ) Use toothpicks to mark where the groups of size / end: Six groups of size / fit into 4, so 4 / = 6. Students make pictures like the one above, using toothpicks to mark where a group ends. Students then divide by counting the groups they make. Students draw pictures to divide: b) 4 c) d) 4 4 Answers:, b) 4, c), d) Using division by a unit fraction to divide by a fraction. Refer to the pictures above that show 4 / = 0 and 4 / = 0. Point out that / is twice as long as /, so half as many longer bars fit than shorter bars. Write on the board: 6 = 6 = 6 = (MP.) ASK: How many /s fit into 6? (0) Write in the answer. How many times longer is / than /? (twice as long) SAY: So only half as many / will fit. ASK: What is half of 0? () Write in the answer again. ASK: How many /s fit into 6? (0) How do you know? (/ is three times as long as /, so only one third as many will fit) Exercises: Use 6 = 4 to divide. b) c) Bonus: Divide and match your answers to above. d) e) Answers: 4, b) 6, c), Bonus: d) 6, same as /6, e) 4, same as /6 Write on the board: 0 = (0 ) COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-44 Teacher s Guide for AP Book 6.

11 SAY: 0 = 0 one thirds fit into 0, and two thirds is twice as big as one third, so only half as many will fit. That s why you divide by. Exercises: Divide. 0 b) 4 c) 6 d) 4 Answers: (0 ) = 0 =, b) ( ) 4 = 40 4 = 0, c) (6 ) = 4 =, d) ( 4) = 60 = 0 Checking answers through multiplication. Remind students that they can check their answers using multiplication. Write on the board: 6 = 0 = Have volunteers circle the two numbers you would multiply in each equation to make sure the answer is the other number. Have another volunteer do the multiplication / to check the second division. Exercises: Check your answers to each question above, for b) to d). Answers: b) 4/ 0 = 40/ =, c) / = 4/ = 6, d) /4 0 = 60/4 = Word problems practice. A ribbon is 4 m long. Yu needs a piece / m long for each gift. How many gifts can she wrap? b) Sam lives 0 miles from school. Nina lives / miles from school. How many times farther from school does Sam live than Nina? c) Ravi lives miles from school and 4/ miles from the library. How many times closer is he to the library than to school? Answers: 6, b), c) Extensions COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION (MP.) (MP., MP.). To divide by unit fractions, use the division property that multiplying both terms by the same number doesn t change the answer. For example: = = =. Which do you expect to be greater?,4,6 or,4,6 Explain. Answer:,4,6 / because / = /0 < / = 6/0 and dividing by a smaller number gets a larger answer. The Number System 6- J-4

12 (MP.). 60 pieces of size fit into 6. How many pieces of size 0 i) 0 will fit into 6? ii) 0 will fit into 6? iii) will fit into 6? 0 b) Find 6. Which answer from part is the same? Why is this so? Answers: i) 0, ii) 0, iii) ; b), iii) is the same because /0 = / 4. Anika lives 4 miles from school and miles from the library. How many times closer to the library is she than to school? Answer: 4 / = 6. To divide, draw a picture with thirds: Group two thirds at a time: 4 pieces remainder Now do the algorithm: = ( ) = = = 4 Now look at the picture. The 4 in 4 is the number of pieces of size, but what does the mean? (It means / of the thing you are dividing by or / of /.) of = The remaining piece is one-half of what you are dividing by. There are four and one-half groups of size / that fit into, so / = 4 /. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-46 Teacher s Guide for AP Book 6.

13 NS6- Dividing by a Fraction Pages STANDARDS 6.NS.A. Goals Students will divide by a fraction, writing the answer as a mixed number and an improper fraction. Vocabulary denominator fraction improper fraction mixed number numerator PRIOR KNOWLEDGE REQUIRED Can convert a mixed number to an improper fraction Knows how many times a given unit fraction fits into Understands division as fitting into MATERIALS several connecting cubes of one color for each student (at least two different colors for the class) grid paper Finding the number of whole parts that fit into. Draw on the board: piece of chocolate This piece of chocolate has pieces, so each piece is /. Write on the board: =? Tell students that you want to know how many pieces of size / fit into. Then outline pieces of size /: COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION ASK: How many whole blocks of size / fit into the whole piece? () SAY: There s some leftover, but we ll think about that part later. Exercises: How many whole blocks fit? b) There are There are Answers:, b) 4 whole pieces of size whole pieces of size in whole. in whole. The Number System 6- J-4

14 Have students shade on grid paper a rectangle consisting of row squares across: ASK: What fraction of the rectangle is each square? (one ninth) Have students draw blocks of size 4/ to find out how many whole blocks of size 4/ fit into one whole. () Now write on the board: whole pieces of size / fit into Have students draw a rectangle on grid paper so that each part is one fifth. ASK: How many squares long is your rectangle? () Be sure everyone drew the correct rectangle before continuing. Then ask them to divide the rectangle into pieces of size two fifths. ASK: How many whole pieces fit into one whole? () Exercises: Draw a picture to decide how many whole pieces fit into. b) c) d) 4 Answers:, b), c), d) Writing the remainder as a fraction of the number you are dividing by. SAY: To divide by /, you need to figure out how many blocks of size / fit into. The answer, in this case, is not a whole number of blocks because there is a leftover part. leftover Point to the leftover piece, and SAY: I want to know what fraction of / the leftover piece is. SAY: Just like a whole number can be a fraction of another whole number, a fraction can be a fraction of another fraction. Draw on the board: ASK: is what fraction of? (/) Exercises is what fraction of? b) is what fraction of? Bonus: is what fraction of,000? Answers: /, b) /, Bonus: /,000 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-4 Teacher s Guide for AP Book 6.

15 Draw on the board: Tell students that this is / and you want to know what fraction / is of /. Ask a volunteer to shade /. ASK: What fraction of the / is shaded? (/) SAY: of the parts are shaded, so / is shaded. Write on the board: is of sevenths is of sevenths / is /4 of 4/ SAY: Just like is / of, / is / of /. Have students draw on grid paper two rectangles each consisting of a row squares long. ASK: What fraction of the rectangle is each square? (/) SAY: You can use your rectangles to answer these questions. Exercises: Shade the first fraction and draw a group showing the second fraction. Then fill in the blank. is of 4? b) is of? Answers: /4, b) / Exercises: Draw a picture to find the answer. is of b) Answers: /, b) /, c) / 6 is of 6 c) is of (MP.) SAY: You don t even need to draw a picture. Write on the board: 00 is of 00 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Have a volunteer fill in the blank. (/) Tell students that of anything is / of of anything, and that s true for thirds, fourths, fifths, hundredths, or baseballs. Exercises: Fill in the missing numbers. is of b) c) is of Bonus: Answers: /, b) 4/, c) /, Bonus: 4/ Dividing by a fraction. Write on the board: 4 is of 4 00, 000 is of 00, 000 The Number System 6- J-4

16 Teacher s Guide for AP Book 6. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-0 From the previous exercises, students should know that / is / of /. Or students could extend the leftover piece to make a whole block of size /: Exercises: An extra block was added. What fraction of the last block is the remainder? remainder b) remainder c) remainder Answers The remainder is / of the last block. b) The remainder is / of the last block. c) The remainder is /4 of the last block.

17 Demonstrate how to finish the division for part above: = of another piece of size fits into whole pieces of size fit into Have volunteers demonstrate completing the next two divisions: b) = c) 4 = 4 (MP., MP.) Exercises: Divide. = b) = c) = Answers: /, b) /, c) 4/ Exercises: Draw a picture to divide. = b) 4 = c) = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Answers: 4 /, b) /4, c) / Writing the answer as an improper fraction. Review converting mixed numbers to improper fractions. = = ( ) + Exercises: Write the answers above as improper fractions. Answers: /, b) /, c) /, d) / Using a shortcut way to divide by a fraction. Tell students to look at their answers. ASK: How can you change the fraction you are dividing by to get the answer? (swap the numerator and denominator or turn the fraction upside down) The Number System 6- J-

18 (MP.) NOTE: In the next lesson, students will learn more formally why a/b = b/a. Exercises: Divide by turning the fraction upside down. b) c) 0 Bonus: 0 Answers: /, b) 0/, c) /, d) /4, Bonus: 0/ d) 4 Have students draw a picture to check the answer to part. Discuss why it would be difficult to draw a picture to check the bonus problem. (the numbers are too large) (MP.) Extensions. Divide by a fraction by writing as a fraction with the same denominator. For example, = So just like: apples apples in each group = groups We also have: fifths fifths in each group = groups So you can just divide the numerators: = = = (MP.). Divide by a fraction by multiplying both terms by the denominator. = = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J- Teacher s Guide for AP Book 6.

19 NS6-4 Dividing by Fractions Pages STANDARDS 6.NS.A. Goals Students will divide fractions by fractions. Vocabulary commutative property denominator fraction improper fraction mixed number numerator proper fraction whole number PRIOR KNOWLEDGE REQUIRED Can multiply fractions Can divide by a fraction Understands division as fitting into Understands the relationship between multiplication and division Multiplying fractions with swapped numerator and denominator. Write on the board: ASK: How do you multiply fractions? (multiply the numerators and multiply the denominators) ASK: What is? () What is? () Write on the board: = = Remind students that when the numerator and denominator are equal, the fraction is equal to. Ask volunteers to explain why that s true. Then SAY: When you take all the parts in the whole, you get the whole. Exercises: Multiply. 4 4 b) c) 4 d) 4 Answers: / =, b) 4/4 =, c) 4/4 =, d) 6/6 = Point out that a fraction multiplied by its upside down version is always going to be because the same numbers you multiply to get the numerator are the numbers you multiply to get the denominator. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Understanding the rule for dividing by a fraction. Write on the board: = 6 ASK: What division equations can you write from this? (6 = and 6 = ) Exercises: Write two division equations from the multiplication. 4 4 = b) = c) = d) 4 4 = Answers: /4 = 4/, 4/ = /4; b) / = /; / = /, c) / = /, / = /; d) 4/ = /4, /4 = 4/ The Number System 6-4 J-

20 Point out that when you divide by a fraction, proper or improper, you always get the fraction turned upside down. Exercises: Divide. b) 6 c) Answers: /, b) 6/, c) /, Bonus: /6 Bonus: 6 Using pictures to understand why the fraction is turned upside down when dividing by the fraction. Draw on the board: ASK: How does / compare to /? Emphasize that / is twice as large as /, so only half as many will fit. But pieces of size / fit into, so / of, or /, pieces of size / fit into. Dividing any whole number by any fraction. Remind students that if you know how many of any object fit into, then twice as many fit into, times as many fit into, and so on. Write on the board: = so 4 = 4 SAY: Four times as many will fit into 4 as will fit into. Have a volunteer do the multiplication. (0/) Exercises: Divide. = b) 4 = so = so 4 = c) 4 d) e) f) 6 4 Bonus: 0 00 Answers: /, /; b) 4/, /; c) /; d) /; e) /; f) 0/4; Bonus: 6,000/ Dividing any fraction by any fraction. Remind students that if you know how many of any object fit into, then /4 as many will fit into /4. Write on the board: = so 4 = 4 Exercises: Write the missing fraction. =? b) 4 6 = 4? c) =? Answers: /, b) 6/, c) / COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-4 Teacher s Guide for AP Book 6.

21 (MP.) (MP.) Ask a volunteer to multiply the fractions in the example above: /4 /. (/) Remind students that to multiply fractions, they can multiply the numerators to get the numerator and multiply the denominators to get the denominator. Exercises: Divide. b) 4 Bonus: , c) 4 d) 6 4 Answers: /, b) 4/0 = /, c) /, d) 4/4, Bonus: /00,000 Exercises: Check your answers using multiplication. Selected solution: / /4 = 4/40 = /0 = / (MP.) Dividing mixed numbers. Write on the board: 4 4 ASK: How are these problems the same? PROMPT: Do you think they will have the same answer? (yes) Why? (because they are dividing the same numbers) How do you know that they are dividing the same number? (because / = /) Have a volunteer circle the easier one to do. (/ 4/) Point out that students have a way to divide improper fractions, so they can use that way to divide mixed numbers they just have to change the mixed numbers to improper fractions. Exercises: Change the mixed numbers to improper fractions. Then divide the improper fractions. 4 b) c) 4 d) Answers: /4 / = /, b) / /4 = 44/, c) / / = 0/4, d) / 0/ = /0 = /0 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Remind students that when the question asks you to divide mixed numbers, it means the answer should be written as a mixed number as well, unless it is less than. Demonstrate the first exercise below for students. Exercises: Use division with remainders to write your answers above as mixed numbers when they are greater than. Answers: = 4 R so / = 4 /, b) 4/, c) 0/4, d) /, e) /0 or /0 Exercises: Divide the mixed numbers. Write any improper fraction answers as mixed or whole numbers. 4 b) 4 c) 4 Answers: /0, b), c) /, d) / d) The Number System 6-4 J-

22 Context problems. Tell students that containers of food items often tell you the size of an expected serving. For example, a single serving of yogurt might be / cup. ASK: If you have cup of yogurt, how many servings do you have? (/) What is that as a mixed number? ( /) (MP.4) Exercises: Solve the problems. How many / cup servings are in / cup of yogurt? b) How many / cup servings are in / cups of yogurt? Answers: / / = 6/ = / servings, b) / / = / / = /4 = /4 servings (MP.4) Exercises: Solve the problems. A rectangle has width / inches and area / square inches. How long is the rectangle? b) A park with area / square miles is / miles long. How wide is it? Answers: 0/ 0/ = 0/0 = 0/0 or / inches long, b) / / = 4/ or / miles long For students who struggle with these exercises, you can prompt them with whole number problems: A rectangle has width inches and area square inches. How long is it? What did they do with the and to get 4? Now compare to the actual problem and have students draw the two rectangles: inches inches square inches square inches Tell students that it is sometimes easier to replace the fractions with whole numbers and reread the problems. That will help them know what to do with the numbers in the problem. Extensions. Divide a fraction by a fraction by writing both fractions with the same denominator. For example: 4 = 0 = (multiply both terms by 0) 0 = COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION J-6 Teacher s Guide for AP Book 6.

23 . Divide. Then describe a rule for dividing unit fractions by unit fractions. i) 4 ii) iii) Answers: i) 4/ or /, ii) / or 4, iii) /; Rule: Divide the second denominator by the first denominator. b) Divide. Then describe a rule for dividing fractions with the same numerator. i) ii) iii) iv) 4 4 Answers: i), ii), iii), iv) ; Rule: Same as part : Divide the second denominator by the first denominator. c) Divide /4 / by using a common numerator for the fractions. Solution: /4 / = 6/ 6/ = = / COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION The Number System 6-4 J-