Comparing Fractions Objective To guide children as they compare fractions using region models.

Transcription

1 Comparing Fractions Objective To guide children as they compare fractions using region models. 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 Read fractions. [Number and Numeration Goal ] Compare fractions to _. [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 ] Key Activities Children use Fraction Cards to identify fractions that are greater than _, less than _, equal to _, close to 0, and close to. Children play Fraction Top-It. Materials Student Reference Book, pp. 7 and Home Link Fraction Cards Playing Fraction Top-It Student Reference Book, pp. 7 and per partnership: deck of Fraction Cards Children practice comparing fractions. Math Boxes 6 Math Journal, p. 96 Children practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem. [Measurement and Reference Frames Goal ] Home Link 6 Math Masters, p. 6 Children practice and maintain skills through Home Link activities. READINESS Exploring Fraction Patterns Math Masters, p. 7 straightedge Children construct fractions on a grid. ENRICHMENT Comparing and Ordering Fractions per group: six-sided dice, " by " index cards, sheets of _ " by " paper Children compare and order fractions. Advance Preparation For the optional Enrichment activity in Part, label three sheets of blank _ " by " paper with one of the following measures: 0, _, and. Lesson 6 677

2 Getting Started Mental Math and Reflexes Pose problems like the following: [0s] 90 0 [0s] [0s] 9, [60s], [60s],000 7,000 [60s] 0,000 0 [00s] 0, [00s] 00,000,000 [00s],000,000 Mathematical Practices SMP, SMP, SMP6, SMP7, SMP Content Standards.NF.,.NF.a,.NF.b,.NF.d Math 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 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 Follow-Up Have children share their answers for Problems 7 9. Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Check to make sure that children have their unit fraction cards in order from smallest to largest ( 6,,,, and ). Have them share their observations about the cards. Expect children to point out that all of the fractions have 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: 0, 0, and. Ask: What do you notice 0 about the cards? They each have 0 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. 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. 67 Unit Fractions

3 6 Comparing Fractions to _ 0, and, WHOLE-CLASS Ask children to take out the following Fraction Cards: _, _, _ 0, 0_, _, _, _ 9, 0_, _, and _. Guide them in the following activities: Use the _ card to help you find all the cards that are less than half-shaded. _, _ 0, _ 9, and 0_ Compare the numerators and denominators of these fractions. What do you observe? The numerator is less than half of the denominator. Ask children to name a fraction that is less than half and has a denominator of. Sample answers: _, _, _, 0_ Find all the cards that are more than half-shaded. _, _, 0_, and _ Compare the numerators and denominators of these fractions. What do you observe? The numerator is more than half of the denominator. Ask children to name a fraction that is more than half and has a denominator of. Sample answers: _, 6_, 7_, _, 9_, and so on Find all the cards that are exactly half-shaded. _ and _ Compare the numerators and denominators of these fractions. What do you observe? The numerator is exactly half of the denominator. Ask children to name a fraction that is equal to half and that has a denominator of. 6_ Put all the cards back in the deck and take out the following cards: _, _, _, _, _ 6, _ 6, _ 0, _ 0, _, and 0_ Find all the cards that show more than _ of the card shaded. _ 6, 0_, _, and _ 0 Ask children which card they used to guide their comparisons. _ 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 _ of the card shaded. _, _ 0, _ 6, and _ Ask children which card they used to guide their comparisons. _ 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 (Student Reference Book, pp. 7 and ) WHOLE-CLASS Have children read the rules for Fraction Top-It in the Student Reference Book on page 7. Demonstrate a few rounds and then have partners play the game. Fraction Top-It Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Comparing fractions Object of the game To collect more cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. 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.. 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.. The game is over when all cards have been taken from the deck. The player with more cards wins. Players turn over a _ card and a _ 6 card. The _ card has a larger shaded area. The player holding the _ card takes both cards. Players turn over a _ card and a _ card. The shaded parts are equal. Each player turns over another card. The player with the larger Fraction Card takes all the cards. Student Reference Book, p. 7 Games Fraction Top-It (Advanced Version) Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Comparing fractions Object of the game To collect more cards. Directions Games two hundred eighty-seven 7 Adjusting the Activity Play the advanced version of Fraction Top-It. Directions are on page in the Student Reference Book. AUDITORY KINESTHETIC TACTILE VISUAL. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Each player takes a card from the top of the deck but does not turn it over. The cards remain picture-side down.. 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. If you were correct, take both cards. If you were wrong, the other player takes both cards.. The game is over when all cards have been taken from the deck. The player with more cards wins. Joel draws a _ card. Sue draws a _ 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 cards. two hundred eighty-eight Student Reference Book, p. Lesson 6 679

4 Date LESSON 6 Math Boxes. Write fractions equivalent to _. Sample answers: 0 0 _ 6 _ 00. If I wanted to have an equal chance of taking out a circle or a square, I would put in circle(s). Time. Complete. hours = day _ hours = day weeks = days 0 minutes = hour minutes = _ hour 0 7. Draw a set of Xs. Circle 9 of them. What fraction of the whole set are the 9 Xs? 9_ or _ Ongoing Learning & Practice Playing Fraction Top-It (Student Reference Book, pp. 7 and ) PARTNER Children continue to practice comparing fractions by playing Fraction Top-It. Have children use half-sheets of paper to record each round using <, >, or = to compare the fraction pairs.. Solve. Fill in the circle that shows the best answer. ( 90) + 7 = A 9 B 99 C 7 D Solve. Use your calculator. Pretend the division key is broken. Christopher and Rochelle are packing cookies in boxes. Each box holds 0 cookies. How many full boxes can they pack? Answer: 0 boxes (unit) Math Boxes 6 (Math Journal, p. 96) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem 6 previews Unit 9 content. Math Journal, p. 96 Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem Use Math Boxes, Problem to assess children s ability to describe relationships between equivalent units of time. Children are making adequate progress if they successfully complete Problem. Some children may be able to describe the relationship between the number of hours in day and the number of hours in days. [Measurement and Reference Frames Goal ] Name Date Time HOME LINK 6 Family Note Home Link Master Comparing Fractions to _ Your child s class is comparing fractions to determine whether they are larger, smaller, or equal to _. Ask your child to explain how to tell which category a fraction fits into. For more on this topic, see Student Reference Book pages,, and. Please return this Home Link to school tomorrow. Home Link 6 (Math Masters, p. 6) INDEPENDENT Home Connection Children shade rectangles to represent given fractions. They use the shaded rectangles to determine which fractions are greater than or equal to _. Then they compare fractions without using shaded rectangles. Shade each rectangle to match the fraction below it. Example: _ 9. List the fractions above that are greater than _., 7_, _ 9 _ 0. List the fractions above that are equal to _. 6, _ 0 Insert <, >, or = in each problem below. Draw pictures to help you.. 6. > 9 < < means is less than. _ 0 _. 6 > means is greater than > = = means is equal to 7 9 Practice Solve.. 7 = 6 6. = =. 9 = 7 Math Masters, p Unit Fractions

5 Differentiation Options Name Date Time LESSON 6 Teaching Master Exploring Fraction Patterns For each problem, record your work on the grid below. READINESS Exploring Fraction Patterns (Math Masters, p. 7) PARTNER Min. Use a straightedge to divide the square into halves. Label each on your drawing. To explore the patterns between the numerators and denominators of fractions, have children use a straightedge to construct fractions on a grid. When children have finished with Math Masters, page 7, have them discuss the patterns they see. Sample answer: Every time the unit fractions are divided in half, the numerators stay the same and the denominators double. The numerators and denominators of the equivalent fractions are multiples. Multiply _ 6 _ to find the fraction that names the next smallest section, _. Continue with the pattern to find the next smallest section. _ _ = _, and so on. 6 ENRICHMENT Comparing and Ordering Fractions SMALL-GROUP 0 Min This is the WHOLE or ONE.. Use a straightedge to divide one of your halves into equal parts. What fraction of the WHOLE is each new section worth? Write the fraction equivalent to.. Use a straightedge to divide one of your smallest sections into equal parts. What fraction of the WHOLE is each new section worth? Write the fraction equivalent to.. If you were to divide your smallest section into equal parts, what fraction of the WHOLE would each new section be worth? Write the fraction equivalent to On the back of your paper, list at least three patterns you notice in the fractions you have made on the grid and the fractions you have written on this paper. Math Masters, p. 7 To apply children s understanding of comparing and ordering fractions based on relationships between numerators and denominators, have them make a set of 0 Fraction Cards to compare. Lay out the three labeled _ " by " papers in line from 0 to with space between them. (See Advance Preparation.) Children roll two dice, and make and record a -digit number from the digits. They repeat this. They use one of the numbers as the numerator of a fraction and the other as the denominator. (They should begin by making all their fractions less than or equal to one.) They write each fraction on a " by " index card. When they have written 0 fractions, have them decide whether to place each fraction between or on the 0, _, and labels. Some children may be able to put some of the fractions in order Variation: Roll only die each time instead of to generate -digit numbers. Lesson 6 6