Comparing Fractions Objective To provide practice ordering sets of fractions.

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1 Comparing Fractions Objective To provide practice ordering sets of fractions. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Compare fractions. Order fractions. Explain strategies used to compare and order fractions. Use patterns to compare and order fractions. [Patterns, Functions, and Algebra Goal ] Key Activities Students use Fraction Cards to determine whether a fraction is greater or less than another fraction and then order sets of Fraction Cards from to. They also compare fractions to and write different sets of fractions in order. Ongoing Assessment: Informing Instruction See page 67. Ongoing Assessment: Recognizing Student Achievement Use journal page 06. Materials Math Journal, pp. 0 and 06 Study Link 7 Fraction Cards (Math Journal, Activity Sheets and 6) slate calculator (optional) pattern blocks (optional) Playing Over and Up Squares Student Reference Book, p. 7 Math Masters, p. 9 per partnership: six-sided dice colored pencils Students practice plotting ordered number pairs on a coordinate grid. Playing Angle Add-Up Math Masters, pp per partnership: of each of number cards and of each of number cards 0 and 9 (from the Everything Math Deck, if available) full-circle protractor (transparency of Math Masters, p. 9) dry-erase markers straightedge Students draw angles and then use addition and subtraction to find the measures of unknown angles. Math Boxes 7 9 Math Journal, p. 07 Students practice and maintain skills through Math Box problems. Study Link 7 9 Math Masters, p. Students practice and maintain skills through Study Link activities. READINESS Sorting Fractions Math Masters, p. 9 scissors tape Students explore relative sizes of fractions. ENRICHMENT Using Digits to Create Fractions Math Masters, p. 0 Students use digits to create specified fractions. EXTRA PRACTICE Playing Fraction Top-It Student Reference Book, p. 7 Math Masters, p. 06 Fraction Cards (Math Journal, Activity Sheets and 6) Students practice comparing and ordering fractions. Advance Preparation Teacher s Reference Manual, Grades 6 pp Lesson 7 9 6

2 Getting Started Mental Math and Reflexes Write fraction addition problems involving tenths and hundredths on the board. Students find the value of x. Suggestions: _ + _ = x_ 6 _ + = x_ 9 _ + _ = x_ 7 7_ + _ = x_ 0 90 _ + _ = x_ 0 60 _ + _ = x_ 0 0 9_ + + _ 0 = x_ 0 0 = x_ 0 9 6_ + 9_ 0 = x_ 0 79 Math Message Work with a partner to solve Problems and on journal page 0. Study Link 7 Follow-Up Partners compare answers. Ask students to explain how they solved Problems 9 and. Date LESSON 7 9 Nancy Quinn Diego 6 Paula Kiana 6 Time Comparing Fractions Math Message: Eating Fractions Quinn, Nancy, Diego, Paula, and Kiana were given chocolate bars to share. All bars were the same size.. Quinn and Nancy shared a chocolate bar. Quinn ate of the bar, and Nancy ate _. Who ate more? Nancy How much of the bar was left?. Diego, Paula, and Kiana each ate part of the other chocolate bars. Diego ate _ of a bar, Paula ate _ of a bar, and Kiana ate _ 6 of a bar. Who ate more, Diego or Paula? Diego How do you know? Sample answer: Diego ate _, which is more than. Paula ate _, which is less than. Comparing Fractions with Turn your Fraction Cards fraction-side up. Sort them into three piles: fractions less than fractions equal to fractions greater than You can turn the cards over to check your work. When you are finished, write the fractions in each pile in the correct box below. Less than,, 0_,, _, _ 6, _, _ 9, 0,,,, Student Page Equal to, _, _ 6, _,, 6 Greater than _, _, _, _, _, _ 6, 6_, 6_ 9, 6,,,, 9 Teaching the Lesson Math Message Follow-Up (Math Journal, p. 0) WHOLE-CLASS DISCUSSION Students should have had no trouble concluding that Nancy ate more chocolate than Quinn (Problem ), but they may have had more difficulty comparing the amounts eaten by Diego and Paula (Problem ). Ask them to share their solution strategies. Students might have used any of these strategies: If Diego s chocolate bar were divided into equal pieces and Paula s into equal pieces, Diego s pieces would have been larger than Paula s pieces. There would be more chocolate in two of Diego s pieces than in two of Paula s pieces, so Diego ate more chocolate than Paula did. Diego ate more than half a bar ( _ is more than half). Paula ate less than half a bar ( _ is less than half). So Diego ate more. Only of Diego s bar is left, but _ of Paula s bar is left. Since less of Diego s bar is left, he ate more. Next, ask students who ate more, Diego or Kiana. Have them explain their answers. Students might have used any of the following strategies: If Diego s chocolate bar were divided into 6 equal pieces, he would have eaten of the pieces because _ 6 is equivalent to _. Diego ate _ 6 of a bar and Kiana ate _ of a bar, so Kiana ate 6 more chocolate. Kiana has only 6 of her bar left, but Diego has left. Because 6 is less than, Kiana has less left over, so she must have eaten more. Finally, have students determine who ate more chocolate, Diego or Nancy, and give their reasoning. Discuss how they know Diego ate more. Math Journal, p. 0 -_EMCS_S_MJ_G_U07_766.indd 0 /7/ : AM 66 Unit 7 Fractions and Their Uses; Chance and Probability

3 Ordering Fractions (Math Journal, Activity Sheets and 6) WHOLE-CLASS Tell the class that in this lesson they will use their Fraction Cards (Activity Sheets and 6) as a tool to help them compare and order fractions. Like Numerators Have students take out all the Fraction Cards with in the numerator (,,, and ) and turn them fraction-side up. Ask them to line up the cards from (at the left) to (at the right). They can check by turning the cards over. Ask: What pattern do you notice? As the denominator gets larger, the fraction gets smaller. What is the reason for this pattern? As the denominator gets larger, the pieces get smaller because the whole is being divided into more pieces. NOTE Fractions with in the numerator are called unit fractions. Ongoing Assessment: Informing Instruction Watch for students who reason that, for example, is more than, so fifths must be larger than fourths. Remind students that the denominator represents the number of pieces the whole is divided into. Like Denominators Have students take out all the Fraction Cards with in the denominator ( 0_, _, _, _, 6_, _, and _ ). Ask them to turn the cards fraction-side up and arrange them in a row from fraction to fraction. What pattern do you see? The larger the numerator is, the bigger the fraction is. What is the reason for this pattern? All the pieces are the same size, so more pieces make a bigger fraction. Different Numerators and Denominators Have students take out the cards for, _, _, _, and 6_, and turn them fraction-side up. Have students line up these cards from fraction to fraction. Tell students to place the _ card in front of them. Name one of the other cards (, _, _, or 6_ ), and ask students whether the fraction is more or less than _ and how they know. Ask students to place that card in the correct position to the right or left of the _ card to indicate if it is smaller or larger than _. Name the rest of the cards one by one. Students place the cards in order while you ask for justification for each card s placement. Lesson

4 Adjusting the Activity ELL Draw a number line from 0 to on the board. Have students estimate the relative size of the fractions and order the fractions by writing them on the number line. 0 6 AUDITORY KINESTHETIC TACTILE VISUAL NOTE On journal page 06, you may want students to identify the relative positions of the fractions in Problems on a number line. Have students work with partners to order the following Fraction Cards:, _, _ 6, _, and _. They should begin with the cards fraction-side up. They can check the order by turning the cards over. Discuss strategies. Comparing Fractions with _ (Math Journal, p. 0) Adjusting the Activity Have students follow the directions at the bottom of journal page 0 to sort the Fraction Cards into three categories: less than, equal to, and greater than. Ask students to look at the equal-to- pile. Have them explain how they know that the fractions in that pile are equal to _. Encourage them to draw pictures or use pattern blocks to justify their answers. Encourage partnerships to compare their sort to that of another group before recording their answers on journal page 0. Have students explain how a calculator can help determine whether a fraction is less than, equal to, or greater than. Possible strategies: Subtract the fraction from. If the difference is positive, it is less than. If the difference is 0, it is equal to. If the difference is negative, it is greater than. Add the fraction to. If the sum is less than, the fraction is less than. If the sum is, then the fraction equals. If the sum is greater than, the fraction is greater than. Find the decimal equivalent by dividing the numerator by the denominator, and compare each decimal to 0.. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Date LESSON 7 9 Ordering Fractions Time Write the fractions in order from to.. _, 7_, _, _,.,, 9,, Student Page 7 Ordering Fractions (Math Journal, p. 06) Students write fractions in order from to. They choose their own set of fractions or mixed numbers and write them in order.. _, _, _ 9, _, _ _,, 7_, 6_, _ 7_. Choose fractions or mixed numbers. Write them in order from to. Answers vary. _ 6. Which fraction is larger: _ or _ 7? Explain how you know. Sample answer: than has a smaller denominator 7, so each fifth is bigger than each seventh. Math Journal, p. 06 Ongoing Assessment: Recognizing Student Achievement Journal page 06 Problem 6 Use journal page 06, Problem 6 to assess students ability to compare fractions and explain their strategies. Students are making adequate progress if their explanations include information such as the following: _ is larger than _ 7. The numerators are the same, so each fraction has the same number of pieces. The size of the pieces (denominator) needs to be compared. The smaller the denominator is, the bigger the pieces are. Some students may include pictures to support their answer or use a calculator to rename the fractions as decimals. -_EMCS_S_MJ_G_U07_766.indd 06 /7/ : AM 6 Unit 7 Fractions and Their Uses; Chance and Probability

5 Ongoing Learning & Practice Playing Over and Up Squares (Student Reference Book, p. 7; Math Masters, p. 9) Students play Over and Up Squares to practice plotting ordered number pairs on a coordinate grid. See Lesson 6-9 for additional information. Playing Angle Add-Up (Math Masters, pp ) To further explore the idea that angle measures are additive, have students draw angles and then use addition and subtraction to find the measures of unknown angles. Note that Round requires students to use addition to find the unknown angle measure. Rounds and require subtraction. The given measures of 90 and 0 degrees provide practice with complementary and supplementary angles. Date LESSON 7 9 Math Boxes. Sari spends of the day at school. Lunch, recess, music, gym, and art make up of her total time at school. How many hours are spent at these activities? hours Show how you solved this problem. Sample answer: of hr = hr; of hr = hr. Adena drew a line segment _ inch long. Then she erased inch. How long is the line segment now? Fill in the circle next to the best answer. A B C D _ 6 in. _ in. in. in.. Complete the table and write the rule. Rule: +.7 in out Math Journal, p. 07 -_EMCS_S_MJ_G_U07_766.indd 07 Student Page 9 Time. Multiply. Use a paper-and-pencil algorithm., = 9 6. Write an equivalent fraction, decimal, or whole number. Decimal a b..0 c. d. 0.6 Fraction Complete. a. 7 in. = ft in. b. in. = ft 7 in. c. 6 ft = yd d. ft = yd ft e. 7 yd = 9 ft 0 0 /7/ : AM Math Boxes 7 9 (Math Journal, p. 07) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 7- and 7-a. The skill in Problem 6 previews Unit content. Writing/Reasoning Have students write a response to the following: Explain why _ inch might have been given as a possible answer in Problem. Sample answer: Some students might incorrectly think that to subtract fractions you subtract the numerators and denominators. If this is done, then an incorrect answer is _ in. in. = _ in. Study Link 7 9 (Math Masters, p. ) INDEPENDENT Home Connection Students compare and order fractions. Name Date Time STUDY LINK 7 9 Compare and Order Fractions Write <, >, or = to make each number sentence true... > _ = Study Link Master < < 0 6. _ 7_ _ > _ 6 7. Explain how you solved Problem. Sample answer: Each fraction has 6 equal parts; parts are more than part.. Explain how you solved Problem. Sample answer: Fourths are bigger than tenths, so fourths are more than tenths. 9. Circle each fraction that is less than _ = Write the fractions in order from to.., 7_,,, _ 7.,, 0,, , _ 0, _, _, _ 0. Practice 6 of 0 =. _ 0 of = 7. _ 6 of = Math Masters, p. 0-6_EMCS_B_MM_G_U07_7696.indd // 9: AM Lesson

6 Name Date Time LESSON 7 9 Two-Digit Fractions Any fraction can be made from the digits 0 9. A fraction can have two digits like _ or _ 7 7 or many digits like _ 9. A fraction may not have a denominator of 0. Use any two digits to make each of the following fractions.. The possible fraction greater than 0 _. The fraction less than 9 _. The fraction greater than 9. The possible fraction 9. Make up your own problem. Answers vary. 9_ Differentiation Options READINESS Sorting Fractions (Math Masters, p. 9) Min Math Masters, page 0 To explore comparing fractions, have students sort fractions represented as area and number-line models into groups according to their relative size. When they finish the sort, have students describe how they chose their groups. About? 0 0-6_EMCS_B_MM_G_U07_7696.indd 0 // 9: AM Very small Almost a whole? 0? 0 Fraction Top-It Student Page Materials set of Fraction Cards and (Math Journal, Activity Sheets and 6) Players to Skill Comparing fractions Object of the game To collect the most cards. Directions Advance Preparation Before beginning the game, write the fraction for the shaded part on the back of each card.. Deal the same number of cards, fraction-side up, to each player: If there are players, 6 cards each. If there are players, cards each. If there are players, cards each.. Players spread their cards out, fraction-side up, so that all of the cards may be seen.. Starting with the dealer and going in a clockwise direction, each player plays one card. Place the cards fraction-side up on the table.. The player with the fraction wins the round and takes the cards. Players may check who has the fraction by turning over the cards and comparing the amounts shaded.. If there is a tie for the fraction, each player plays another card. The player with the fraction takes all the cards from both plays. 6. The player who takes the cards starts the next round. 7. The game is over when all cards have been played. The player who takes the most cards wins. Games Fraction Cards Fraction Cards ENRICHMENT Using Digits to Create Fractions (Math Masters, p. 0) Min To extend students ability to compare fractions, have them use digits to create specified fractions. For each problem, have students share their reasoning. EXTRA PRACTICE Playing Fraction Top-It (Student Reference Book, p. 7; Math Masters, p. 06) SMALL-GROUP Min To practice comparing and ordering fractions, have students play Fraction Top-It. See Lesson 7- for additional information. Student Reference Book, p Unit 7 Fractions and Their Uses; Chance and Probability

7 Name Date Time Angle Add-Up Materials number cards ( of each) number cards 0 and 9 ( of each) dry-erase marker straightedge full-circle protractor (transparency of Math Masters, p. 9) Angle Add-Up Record Sheet (Math Masters, p. 09) Players Skills Drawing angles of a given measure Recognizing angle measures as additive Solving addition and subtraction problems to find the measures of unknown angles Objective To score the most points in rounds. Directions. Shuffle the cards and place the deck number-side down on the table.. In each round, each player draws the number of cards indicated on the Record Sheet. Copyright Wright Group/McGraw-Hill. Each player uses the number cards to fill in the blanks and form angle measures so the unknown angle measure is as large as possible.. Players add or subtract to find the measure of the unknown angle and record it in the circle on the Record Sheet. The measure of the unknown angle is the player s score for the round.. Each player uses a full-circle protractor, straightedge, and marker to show that the angle measure of the whole is the sum of the angle measures of the parts. 6. Players play rounds for a game. The player with the total number of points at the end of the rounds wins the game. 07

8 Name Date Time Angle Add-Up Example Example: In Round, Suma draws a, 7,, and. She creates the angle measures and 7 and records them on her record sheet. Round : Draw cards. + 7 = Using addition, Suma finds the sum of the measures of angles ABD and DBC. She records the measure of angle ABC on her record sheet and scores points for the round. Round : Draw cards. + 7 = Suma uses her full-circle protractor to show that m ABD + m DBC = m ABC. A degrees 9 B 7 6 D Copyright Wright Group/McGraw-Hill C 0

9 Name Date Time Angle Add-Up Record Sheet Game Round : Draw cards. + = Round : Draw cards. Round : Draw cards. + = 90 + = 0 Total Points = Copyright Wright Group/McGraw-Hill Game Round : Draw cards. Round : Draw cards. Round : Draw cards. + = + = 90 + = 0 Total Points = 09

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