1 Teaching the Lesson

Transcription

1 Getting Started Mental Math and Reflexes Children solve division number stories. They write answers on slates and explain their strategies to the class. Provide counters. There are children in the class. They sit in rows of. How many rows are there? 9 rows children share 7 pennies. How many pennies per child? 9 pennies children share strawberries. How many strawberries per child? strawberries, with left over Math Message Take an envelope. Carefully cut apart the Fraction Cards on Activity Sheets at the back of your journal. Put them in the envelope. Home Link Follow-Up Briefly review answers. Place new items in the Fractions Museum. Teaching the Lesson Math Message Follow-Up (Math Journal, Activity Sheets ) Check that children have cut out all Fraction Cards. Using Fraction Cards to Extend Fraction Concepts (Math Journal, Activity Sheets ) DISCUSSION Date Fraction Cards Time Ask children to turn their cards to the picture side. Share observations. (Keep this part of the lesson brief.) Each card represents a whole, or ONE. All cards are the same size. The number of strips (or bars) varies from card to card. Some strips are shaded; others are unshaded. The fraction shown on the back of the card represents the shaded fractional part of the ONE. Some fractions have the same numerator and different denominators. That means the ONE is divided into different numbers of equal parts. The larger the denominator, the more parts the ONE is divided into, and the smaller each part. Point out that any fraction with in the numerator is called a unit fraction. For example, is a unit fraction. Ask children to name other unit fractions. Sample answers:,,, 9 To support English language learners, write unit fraction on the board along with a list of examples. Math Journal, Activity Sheet 7 Unit Fractions

2 Investigating Equivalent Fractions (Math Journal, p. 9) Each partnership uses one set of Fraction Cards. Guide the class through the following activities. Adjusting the Activity Have children find the card. Their task is to find as many other cards in the deck as they can that have exactly the same amount shaded. Demonstrate side-by-side comparisons for exact matches. As children name fractions equivalent to, they record them in the Table of Equivalent Fractions on journal page 9. Remind them that these fractions are called equivalent fractions. Equivalent fractions name the same fractional part of the ONE. Have children find cards with fractions equivalent to the card and record them in the table. Repeat with the card, checking for patterns and predictions before matching equivalent Fraction Cards. Partners then sort the rest of the cards into as many sets of equivalent fractions as they can and record them in the table. Bring the class together to share the equivalent fractions found in the deck and the patterns they observed among the equivalent fractions. Identifying Equivalent Fractions (Math Journal, p. 9) At first, use the cards on Activity Sheets and. Then use the full deck of cards. 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 Discuss how to use the Fraction Number-Line Poster to identify equivalent fractions. Ask: What part of the fourths strip is the same size as of the ONE strip? Is another name for? Yes What are some other names on the Fraction Number-Line Poster for?, Show how to place a straightedge vertically on the page next to the fraction to find fractions equivalent to. Have children use a straightedge to find other names for, for, for, and for. (You may need to point out that equivalent fractions may not line up exactly if they are off slightly in the gluing or cutting. Because the intervals are so large, the error should not prevent children from finding the equivalencies.) Ask: If the ONE strip were divided into equal parts, how many of these parts would be the same size as of the ONE strip? parts What fraction of the ONE strip is this? Date Use your deck of Fraction Cards to find equivalent fractions. Record them in the table. Fraction,,,,, 9 9,, 9,, 9, Describe any patterns you see. Sample answers: Each of the fractions equivalent to has the same numerator and denominator. Except for the row of fractions equivalent to, all the numerators and denominators in each row are multiples of the numerators and denominators of the given fraction for that row. Time Table of Equivalent Fractions Math Journal, p. 9 Equivalent Fractions Whole Halves Fourths Eighths Thirds Sixths A straightedge highlights equal fractions. 7 Lesson 7

3 Equivalent Fractions Game Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Recognizing fractions that are equivalent Object of the game To collect more Fraction Cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Turn the top card over near the deck of cards.. Players take turns. When it is your turn, turn over the top card from the deck. Try to match this card with a picture-side up card on the table. If you find a match, take the matching cards. Then, if there are no cards left picture-side up, turn the top card over near the deck. If you cannot find a match, place your card pictureside up next to the other cards. Your turn is over.. The game ends when all cards have been matched. The player with more cards wins. Example The top card is turned over and put on the table. The picture shows. Player turns over the card. This card matches. Player takes both cards. There are no cards left picture-side up. So Player turns over the top card and puts it near the deck. The picture shows. Player turns over the card. There is no match. This card is placed next to. It is Player s turn again. Student Reference Book, p. Games Playing the Equivalent Fractions Game (Student Reference Book, pp. and ) Have children read the rules for the Equivalent Fractions Game on page in the Student Reference Book. Demonstrate how to play the game. Before children put their cards in their tool kits, they should store them in an envelope. The Fraction Cards will be used again in Lesson -. Adjusting the Activity Another version of Equivalent Fractions Game has players match the fraction sides of cards with the picture sides of the cards. The rules for this version are on page in the Student Reference Book. 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 Ongoing Learning & Practice Playing The Block-Drawing Game (Math Masters, p. 9; Student Reference Book, pp. and ) SMALL-GROUP Games Equivalent Fractions Game (Advanced Version) Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Recognizing fractions that are equivalent Object of the game To collect more Fraction Cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Turn the top card over near the deck of cards.. Players take turns. When it is your turn, take the top card from the deck, but do not turn it over (keep the picture side down). Try to match the fraction with one of the picture-side up cards on the table. If you find a match, turn the card over to see if you matched the cards correctly. If you did, take both cards. Then, if there are no cards left picture-side up, turn the top card over. If there is no match, place your card next to the other cards, picture-side up. Your turn is over. If there is a match but you did not find it, the other player can take the matching cards.. The game ends when all cards have been matched. The player with more cards wins. Student Reference Book, p. Children practice making and testing predictions by playing The Block-Drawing Game, introduced in Lesson -. Detailed directions are on pages and in the Student Reference Book. Have children record their predictions on an Exit Slip (Math Masters, page 9). Ongoing Assessment: Recognizing Student Achievement Use the Exit Slip to assess children s progress toward making and testing predictions for simple experiments. Children are making adequate progress if they make reasonable predictions based on the data collected from the draws. Some children may be able to make the connection between the number of draws made and the reliability of their predictions. [Data and Chance Goal ] Math Boxes (Math Journal, p. 9) Exit Slip INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -7. The skill in Problem previews Unit 9 content. 7 Unit Fractions

4 Home Link (Math Masters, pp. and ) INDEPENDENT Home Connection Children shade fractions of regions, identify fractions of sets, and identify equivalent fractions. Date Math Boxes. In the number.: the means the means the means ones hundredth tenths the means thousandths Time. Which is true? Fill in the circle for the white best answer. The spinner is blue A unlikely to land on blue B less likely to land on white Differentiation Options. Write fractions equivalent to. Sample answers: C equally likely to land on blue or white D likely to land on green 9 9. Use a straightedge. Draw the other half of the symmetric shape. READINESS Shading Equivalent Fractions of Regions (Math Masters, p. ) SMALL-GROUP Min To provide experience with equivalent fractions, have children shade regions of similar shapes on Math Masters, page.. 9 children share candies. How many candies per child? candies How many candies left over? candies 7 books in all. books per shelf. How many shelves? shelves How many books left over? book Math Journal, p. 9. Solve Home Link Master Name Date Time Home Link Master Name Date Time HOME LINK Equivalent Fractions HOME LINK Equivalent Fractions continued Family Note The class continues fraction work by finding equivalent names for fractions. Different fractions that name the same amount are called equivalent fractions. The fractions that complete Problems are equivalent. If needed, help your child name the fractional parts in these problems. Ask your child to explain the fraction name she or he chooses in Problem 9 a fraction that is equivalent to and describes the fraction of cats circled. 7 Please return this Home Link to school tomorrow. 7. Circle of the cats. The pictures show three kinds of pie. Use a straightedge to do the following:. Divide the peach pie into equal pieces. Shade of the pieces.. Divide the blueberry pie into equal pieces. Shade of the pieces.. Divide the cherry pie into equal pieces. Shade of the pieces.. How many cats did you circle? cats 9. Write a fraction that describes the group of cats you circled and that is equivalent to. Each whole rectangle below is ONE. Write a fraction inside each part.. peach pie blueberry pie cherry pie What fraction of each pie did you shade?. I shaded of the peach pie. Write another name for this fraction:. I shaded of the blueberry pie. Write another name for this fraction:. I shaded of the cherry pie. Write another name for this fraction:. or,, or or Math Masters, p. Math Masters, p. Lesson 7

5 Name Date Time Equivalent Fractions in Shapes. Shade of each circle. Complete the fractions.. Shade of each rectangle. Complete the fractions.. Make up your own: Shade of each square. Write the fractions. Answers vary. Teaching Master 9 ENRICHMENT Looking for a Rule (Math Journal, p. 9; Math Masters, p. ) PARTNER Min To apply children s understanding of equivalent fractions, have them look for a rule about how fractions equivalent to are related to one another. (For example, equivalent fractions can be generated by multiplying the numerator and the denominator by the same whole number.) They use their rule to complete the remaining problems on Math Masters, page. NOTE Not every pair of equivalent fractions can be found easily with this rule, for example, and. However, applying the rule when one of the fractions is a unit fraction is usually easy. For example, if the numerator and denominator of are multiplied by, the result is the equivalent fraction ; if the multiplier is, the result is 9, and so on. Math Masters, p. ENRICHMENT Making Name-Collection Boxes for Fractions SMALL-GROUP Min To apply children s understanding of fraction concepts, have them work in small groups to make poster-size name-collection boxes for familiar fractions. Encourage them to include region, collection, and number-line representations as well as equivalent fractions, expressions with numbers, and expressions with words. Assign each small group a fraction for their name-collection box for example, or. Name Date Time Teaching Master Rules for Equivalent Fractions. Look at Math Journal, page 9. Record the fractions equivalent to below. As you record them, put them in an order that will help you find a pattern.. Use your pattern to write a rule for finding equivalent fractions. Write your rule on the lines below. Sample answer: Multiply the numerator and denominator by the same whole number to find equivalent fractions. ELL SUPPORT Building a Math Word Bank (Differentiation Handbook) SMALL-GROUP Min To provide language support for fractions, have children use the Word Bank template found in the Differentiation Handbook. Ask children to write the term equivalent fraction, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information. Try your rule to see whether it works. List other fractions equivalent to using your rule. (Use pictures or counters to check your fractions.) 7 9. Use your rule to find fractions equivalent to. Check your answers with the Fraction Cards. Try This 9. Use your rule to find equivalent fractions for the fractions in the table below. Show any work that you do on the back of this page. Fraction Equivalent Fractions Sample answers:,,,,, 9,, 7 Math Masters, p. 7 Unit Fractions

6 Objective To guide children as they compare fractions using region models. Teaching the Lesson Key Activities Children use Fraction Cards to identify fractions that are greater than, less than, equal to, close to, and close to. Children play Fraction Top-It. Key Concepts and Skills Read fractions. [Number and Numeration Goal ] Compare fractions to. [Number and Numeration Goal ] Use an area model to compare fractions. [Number and Numeration Goal ] Identify patterns and relationships between numerators and denominators of fractions. [Patterns, Functions, and Algebra Goal ] Ongoing Learning & Practice Children play the Equivalent Fractions Game. Children practice and maintain skills through Math Boxes and Home Link activities. Ongoing Assessment: Recognizing Student Achievement Use journal page 9. [Measurement and Reference Frames Goal ] READINESS Differentiation Options Children construct fractions on a grid. ENRICHMENT Children compare and order fractions. materials Student Reference Book, pp. 7 and Home Link Fraction Cards materials Math Journal, p. 9 Student Reference Book, pp. and Home Link Master (Math Masters, p. ) Fraction Cards materials Teaching Master (Math Masters, p. 7) dice " by " index cards sheets of " by " paper straightedge See Advance Preparation Additional Information Advance Preparation For the optional Enrichment activity in Part, label three sheets of blank -by- paper with one of the following measures:,, and. Technology Assessment Management System Math Boxes, Problem See the itlg. Lesson 77

7 Getting Started Mental Math and Reflexes Pose problems like the following: [s] 9 [s] 9 [s] 9, 7[s], 7[s], 7,[s], [s], [s],,[s],, 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 DISCUSSION Have children share their observations about the unit fraction cards,,,, and. Guide them to conclude that the larger the denominator, the smaller the shaded part and therefore, the smaller the fraction. Clarify with children that this is the case in this problem because all the numerators are. Comparing Fractions to,, and Ask children to take out the following Fraction Cards:,,,, 9,,, and. Guide them in the following activities:, Use the card to help you find all the cards that are less than half-shaded.,, 9, and 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:,,, Find all the cards that are more than half-shaded.,,, 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:,, 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., 7 Unit Fractions

8 Put all the cards back in the deck and take out the following cards:,,,,,,,,, and. Find all the cards that show more than of the card shaded.,,, and 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.,,, 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. 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 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. Games Playing Fraction Top-It (Student Reference Book, pp. 7 and ) Student Reference Book, p. 7 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. Adjusting the Activity Play the advanced version of Fraction Top-It. Directions are on page in the Student Reference Book. 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 Ongoing Learning & Practice Playing the Equivalent Fractions Game (Student Reference Book, pp. and ) PARTNER The Equivalent Fractions Game was introduced in Lesson -. If necessary, children can read the rules in the Student Reference Book on pages and. 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. 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. Example 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. Student Reference Book, p. Lesson 79

9 Date. Solve. Fill in the circle that shows the best answer. ( 9) 7 A 9 B 99 C 7 Math Boxes. Write fractions equivalent to. Sample answers:. 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 minutes hour minutes hour 7. Draw a set of Xs. Circle 9 of them. What fraction of the whole set are the 9 Xs? 9 or. Solve. Use your calculator. Pretend the division key is broken. Christopher and Rochelle are packing cookies in boxes. Each box holds cookies. How many full boxes can they pack? Answer: boxes (unit) Math Boxes (Math Journal, p. 9) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit 9 content. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem INDEPENDENT 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 minutes in a day and the number of hours in days. [Measurement and Reference Frames Goal ] D 9 Math Journal, p. 9 Home Link (Math Masters, p. ) 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. Home Link Master Name Date Time HOME LINK Comparing Fractions to Family Note 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. Shade each rectangle to match the fraction below it. Example: List the fractions above that are greater than.. List the fractions above that are equal to., Insert,, or in each problem below. Draw pictures to help you Solve. Practice, 7, Math Masters, p. means is less than means is greater than means is equal to Unit Fractions

10 Differentiation Options Teaching Master Name Date Time 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 to find the fraction that names the next smallest section,. Continue with the pattern to find the next smallest section., and so on. ENRICHMENT Comparing and Ordering Fractions SMALL-GROUP Min. 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 This is the WHOLE or ONE. To apply children s understanding of comparing and ordering fractions based on relationships between numerators and denominators, have them make a set of Fraction Cards to compare. Lay out the three labeled in. by in. papers in line from 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 in. by in. index card. When they have written fractions, have them decide whether to place each fraction between or on the,, 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