Comparing Fractions - Everyday Math

1 Lesson 8 6 677 Advance PreparationFor the optional Enrichment activity in Part 3, label three sheets of blank 8 1 _ 2 " by 11" paper with one of the following measures: 0, 1 _ 2 , and Concepts and Skills Read Fractions . [Number and Numeration Goal 2] compare Fractions to 1 _ 2 . [Number and Numeration Goal 6] Use an area model to compare Fractions . [Number and Numeration Goal 6] Identify patterns and relationships between numerators and denominators of Fractions . [Patterns, Functions, and Algebra Goal 1]Key ActivitiesChildren use Fraction Cards to identify Fractions that are greater than 1 _ 2 , less than 1 _ 2 , equal to 1 _ 2 , close to 0, and close to 1. Children play Fraction Reference Book, pp. 287 and 288 Home Link 8 5 Fraction CardsPlaying Fraction Top-ItStudent Reference Book, pp. 287 and 288per partnership: 1 deck of Fraction CardsChildren practice Comparing Boxes 8 6 Math Journal 2, p.

2 196 Children practice and maintain skillsthrough Math Box Assessment: Recognizing Student Achievement Use Math Boxes, Problem 2. [Measurement and Reference Frames Goal 3]Home Link 8 6 Math Masters, p. 256 Children practice and maintain skillsthrough Home Link Fraction PatternsMath Masters, p. 257straightedgeChildren construct Fractions on a and Ordering Fractionsper group: 2 six-sided dice, 3" by 5" index cards, 3 sheets of 8 1 _ 2 " by 11" paperChildren compare and order the Les sonOngoing Learning & Practice1324 Differentiation OptionsComparing FractionsObjective To guide children as they compare Fractions using region models. eToolkitePresentationsInteractive Teacher s Lesson GuideAlgorithms PracticeEM FactsWorkshop Game AssessmentManagementFamily LettersCurriculumFocal PointsCommon Core State 6772/23/11 10:55 AM678 Unit 8 Fractions1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASSDISCUSSIONC heck to make sure that children have their unit fraction cards in order from smallest to largest ( 1 __ 6 , 1 __ 5 , 1 __ 4 , 1 __ 3 , and 1 __ 2 ).

3 Have them share their observations about the cards. Expect children to point out that all of the Fractions have 1 in the numerator and that the denominators get smaller from left to right. Guide children to conclude that when the numerators are the same, the larger the denominator, the smaller the shaded part, and, therefore, the smaller the fraction. Ask children to use different fraction cards to show that this holds true for other Fractions with the same numerator. Next, have children find and order the following fraction cards from smallest to largest: 2 __ 10 , 5 __ 10 , and 8 __ 10 . Ask: What do you notice about the cards? They each have 10 in the denominator. Describe which fraction is smallest and which is largest. Sample answer: The smallest fraction has the smallest numerator and the largest fraction has the largest numerator.

4 Guide them to conclude that when the denominators are the same, the larger the numerator, the larger the shaded part, and, therefore, the larger the fraction. Ask children to use different fraction cards to show that this holds true for other Fractions with the same denominator. Getting StartedMath Message Take out your Fraction Cards. Turn them so the picture sides (sides with the shaded parts) are faceup. Find all the unit Fractions ( Fractions that have 1 in the numerator). Put them in order , from the card with the smallest part shaded to the card with the largest part shaded. What pattern do you notice?Home Link 8 5 Follow-Up Have children share their answers for Problems 7 Math and ReflexesPose problems like the following: 3 [30s] 9030 [30s] 900300 [30s] 9,000 70 [60s] 4,200700 [60s] 42,0007,000 [60s] 420,000 50 [400s] 20,000500 [400s] 200,0005,000 [400s] 2,000,000 Mathematical PracticesSMP2, SMP5, SMP6, SMP7, SMP8 Content , , , 6783/12/12 10:12 AMLesson 8 6679 two hundred eighty-seven 287 GamesFraction Top-ItMaterials 1 deck of Fraction Cards (Math Journal 2, Activity Sheets 5 8)Players 2 Skill Comparing fractionsObject of the game To collect more 1.

5 Shuffle the Fraction Cards and place the deck picture-side down on the table. 2. Each player turns over a card from the top of the deck. Players compare the shaded parts of the cards. The player with the larger fraction shaded takes both cards. 3. If the shaded parts are equal, the Fractions are equivalent. Each player then turns over another card. The player with the larger fraction shaded takes all the cards from both plays. 4. The game is over when all cards have been taken from the deck. The player with more cards wins. Players turn over a 3 _ 4 card and a 4 _ 6 3 _ 4 card has a larger shaded area. The player holding the 3 _ 4 card takes both turn over a 1 _ 2 card and a 4 _ 8 shaded parts are equal. Each player turns over another card. The player with the larger Fraction Card takes all the 2872/17/11 10:40 AMStudent Reference Book, p.

6 287 Student PageGames288 two hundred eighty-eightFraction Top-It (Advanced Version)Materials 1 deck of Fraction Cards (Math Journal 2, Activity Sheets 5 8)Players 2 Skill Comparing fractionsObject of the game To collect more 1. Shuffle the Fraction Cards and place the deck picture-side down on the table. 2. Each player takes a card from the top of the deck but does not turn it over. The cards remain picture-side down. 3. Players take turns. When it is your turn: Say whether you think your fraction is greater than,less than, or equivalent to the other player s fraction. Turn the cards over and compare the shaded parts. Ifyou were correct, take both cards. If you were wrong,the other player takes both cards. 4. The game is over when all cards have been taken from the deck. The player with more cards wins. Joel draws a 2 _ 8 card.

7 Sue draws a 1 _ 4 card. It is Sue s turn, and she says that her fraction is less than Joel s. They turn their cards over and find that the shaded areas are equal. The Fractions are equivalent. Sue was wrong, so Joel takes both 2882/17/11 10:40 AMStudent Reference Book, p. 288 Student Page Comparing Fractions to 1 _ 2 , WHOLE-CLASS ACTIVITY0, and 1 Ask children to take out the following Fraction Cards: 1 _ 2 , 1 _ 4 , 2 _ 10 , 10 _ 12 ,4 _ 8 , 4 _ 5 , 3 _ 9 , 0 _ 4 , 2 _ 2 , and 2 _ 3 . Guide them in the following activities: Use the 1 _ 2 card to help you find all the cards that are less than half-shaded. 1 _ 4 , 2 _ 10 , 3 _ 9 , and 0 _ 4 compare the numerators anddenominators of these Fractions . What do you observe? Thenumerator is less than half of the denominator. Ask children to name a fraction that is less than half and has a denominator of 8.

8 Sample answers: 3 _ 8 , 2 _ 8 , 1 _ 8 , 0 _ 8 Find all the cards that are more than half-shaded. 4 _ 5 , 2 _ 2 , 10 _ 12 , and 2 _ 3 compare the numerators and denominators of these Fractions . What do you observe? The numerator is more thanhalf of the denominator. Ask children to name a fraction that ismore than half and has a denominator of 8. Sample answers: 5 _ 8 ,6 _ 8 , 7 _ 8 , 8 _ 8 , 9 _ 8 , and so on Find all the cards that are exactly half-shaded. 1 _ 2 and 4 _ 8 compare the numerators and denominators of these do you observe? The numerator is exactly half of the denominator. Ask children to name a fraction that is equal tohalf and that has a denominator of 12. 6 _ 12 Put all the cards back in the deck and take out the following cards: 1 _ 4 , 3 _ 4 , 1 _ 5 , 4 _ 5 , 1 _ 6 , 5 _ 6 , 2 _ 10 , 8 _ 10 , 2 _ 12 , and 10 _ 12 Find all the cards that show more than 3 _ 4 of the card shaded.

9 5 _ 6 , 10 _ 12 , 4 _ 5 , and 8 _ 10 Ask children which card they used to guide their comparisons. 3 _ 4 What do you observe about the numerators and denominators of these Fractions ? When most of a card is shaded, the numerator of the fraction is close to the denominator. The difference between the numerator and denominator is small. Find all the cards that show less than 1 _ 4 of the card shaded. 1 _ 5 , 2 _ 10 , 1 _ 6 , and 2 _ 12 Ask children which card they used to guide their comparisons. 1 _ 4 What do you observe about the numerators and denominators of these Fractions ? When a very small part of a card is shaded, the numerator of the fraction is very small compared to the denominator. The difference between the numerator and denominator is large. Playing Fraction Top-It WHOLE-CLASS ACTIVITY(Student Reference Book, pp.)

10 287 and 288)Have children read the rules for Fraction Top-It in the Student Reference Book on page 287. Demonstrate a few rounds and then have partners play the the ActivityPlay the advanced version of Fraction Top-It. Directions are on page 288 in the Student Reference KINESTHETIC TACTILE 67910/5/11 10:39 AM680 Unit 8 FractionsName Date TimeComparing Fractions to 1 _ 2 HOME LINK8 6 Your child s class is Comparing Fractions to determine whether they are larger, smaller, or equal to 1 _ 2 . Ask your child to explain how to tell which category a fraction fits into. For more on this topic, see Student Reference Book pages 13, 31, and return this Home Link to school Note1331 32 Shade each rectangle to match the fraction below it.