Many Names for Fractions

Transcription

1 Many Names for Fractions Objective To provide practice identifying equivalent 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 Identify fractional parts of regions. [Number and Numeration Goal ] Name equivalent fractions. [Number and Numeration Goal 5] Use patterns in a table to find equivalent fractions. [Patterns, Functions, and Algebra Goal ] Key Activities Students use Fraction Cards to help them start a table of equivalent fractions. Informing Instruction See page 599. Materials Math Journal, pp. and Study Link 7 5 Fraction Cards (Math Journal, Activity Sheets 5 and ) Playing Grab Bag Student Reference Book, p. 9 Math Masters, pp per partnership: six-sided dice Students practice calculating the probability of an event. Adding and Subtracting Fractions and Mixed Numbers Math Journal, p. 00A pattern blocks Students add and subtract fractions and mixed numbers with like denominators. Math Boxes 7 Math Journal, p. 00 Students practice and maintain skills through Math Box problems. Recognizing Student Achievement Use Math Boxes, Problem. [Measurement and Reference Frames Goal ] READINESS Finding Equivalent Fractions Math Masters, pp. 9 scissors glue Students find equivalent fractions by matching fractional parts of circles. ENRICHMENT Modeling Fraction Equivalencies Math Masters, p. Students use a clock face to model equivalencies of fractions with denominators of,,, 5,, 0,, 5, 0, 0, and 0. EXTRA PRACTICE Playing Fraction Match Student Reference Book, p. Math Masters, pp. 89 and 7 7 scissors Students practice identifying equivalent fractions. Study Link 7 Math Masters, p. 8 Students practice and maintain skills through Study Link activities. Advance Preparation If students have not removed Activity Sheets 5 and from the back of the journal and cut the fraction cards apart, have them do so prior to teaching Part of the lesson. Ask students to write their initials on the cards for identification. For the optional Extra Practice activity in Part, consider copying Math Masters, pages 7 7 on cardstock. Teacher s Reference Manual, Grades pp., 598 Unit 7 Fractions and Their Uses; Chance and Probability

2 Getting Started Mathematical Practices SMP, SMP5, SMP, SMP7 Content Standards.NF.,.NF.,.NF.a,.NF.c,.NF.d Mental Math and Reflexes Pose fraction and mixed-number addition and subtraction problems. Have students estimate whether the answer is greater than or less than and explain their answers. Suggestions: _ + _ less 9_ 0 + 7_ 8 greater _ + _ 9 greater _ + _ greater _ 8 + _ greater _ + _ less _ - _ greater _ - _ less _ 7-9_ 8 less _ - _ less _ - _ greater - _ greater Math Message Take out your Fraction Cards. Write down two things that you notice about the cards. Study Link 7 5 Follow-Up Have students discuss how they solved Problems and. Teaching the Lesson Math Message Follow-Up (Math Journal, Activity Sheets 5 and ) Students share observations. WHOLE-CLASS DISCUSSION One side of each card is divided into equal parts, and some of the parts are shaded. A fraction with the numerator or denominator missing appears on the other side of each card. Ask students to write the missing numerator or denominator in order to name the fractional part of the card that is shaded. For example, if the rectangle is divided into equal parts and of them are shaded, the completed fraction on the back should be _. NOTE In the Mental Math and Reflexes activity, you might have students identify the fractions with numerators that are greater than or equal to their denominators. _, _, _ 7, 9_ 8 Fractions like these are sometimes called improper fractions. Informing Instruction Watch for students who make the common error of writing _ for a Fraction Card such as this: Remind students that the numerator is the counting number. It tells how many parts are shaded ( parts). The denominator tells what is being counted. There are parts in all, so sixths are being counted. Tell students that in this lesson they will use the Fraction Cards as a tool to help them name equivalent fractions. Lesson 7 599

3 Equivalent Names for Fractions Fraction Equivalent Fractions Decimal Percent 0 0 0%, Starting a Collection of Fraction Names (Math Journal, pp. and ) ELL 00% Math Journal, p. Have one student in each partnership put his or her Fraction Cards away. Model the following procedure:. Ask students to find the card with out of parts shaded and the card with out of parts shaded. Point out that the fractions on the back of the cards ( _ and _ ) are not the same, but the same amount is shaded on each of these cards. So _ and _ are names for the same fraction.. Ask students to find all of the other cards that are half-shaded. _, _ 8, 0, _. Have students turn to the Equivalent Names for Fractions table on journal page. Next to the fraction _ in the table, have them record all the fractions for the cards that are half-shaded. _, _, _ 8, 0, _ To support English language learners, make the connection between the Equivalent Names for Fractions table and the name-collection boxes completed in prior lessons. Links to the Future Students begin filling in the column for decimals in Lesson 7-8 and the column for percents in Unit 9. Continuing a Collection of Fraction Names (Math Journal, pp. and ) PROBLEM SOLVING Instruct partners to sort the remaining cards into groups that have the same amount shaded. Then have them record the fractions in each of these groups on the appropriate lines in the Equivalent Names for Fractions table. Games Grab Bag Materials deck of Grab Bag Cards (Math Masters, pp. 8 8) Grab Bag Record Sheet for each player or team (Math Masters, p. 85) six-sided dice Players, or two teams of Skill Variable substitution; calculating probabilities of events Object of the game To score more points by calculating the probabilities of events. Directions. Shuffle the deck of Grab Bag cards and place it problem-side down on the table.. Players (or teams) take turns. When it is your turn: Note Draw a card and place it problem-side up on the table. Two quantities are missing from each card. They are shown with the variables x and y. Roll the dice and substitute the numbers rolled for the variables x and y in the following way: Replace x with the number shown on of the dice. Replace y with the sum of the numbers on the other dice. Solve the problem and give an answer. The opposing player (or team) checks the answer. Your score for the round is calculated as follows: 0 points: if the event is unlikely (probability is less than ). 0 points: if the event is likely (probability is greater than ). 50 points: if the event has a chance (probability exactly ).. The player (or team) with the higher score after 5 rounds wins. Paul draws the card shown to the right. He rolls,, and, and substitutes for x and 0 for y. Lina s grab bag has red, blue, pink, and 0 green ribbons. The probability of Lina picking a green ribbon is 0 out of 5 or 0 5 or. Picking a green ribbon is likely (probability is greater than ). Paul scores 0 points. Use a strategy when replacing x and y by the dice numbers to earn the most points possible for that turn. Ongoing Learning & Practice Playing Grab Bag (Student Reference Book, p. 9; Math Masters, pp. 8 85) Algebraic Thinking Students play Grab Bag to practice calculating the probability of an event. Adjusting the Activity Have students draw pictures to model the problems they generate while playing Grab Bag. 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 ELL Student Reference Book, p Unit 7 Fractions and Their Uses; Chance and Probability

4 Adding and Subtracting Fractions and Mixed Numbers (Math Journal, p. 00A) Students use pattern blocks to add and subtract fractions and mixed numbers with like denominators. Math Boxes 7 (Math Journal, p. 00) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-8. The skill in Problem previews Unit 8 content. 7 Adding and Subtracting Fractions and Mixed Numbers Use pattern blocks to help you solve the problems.. _ +. _ +, or _. _ + _, or _. _ 5 + _ 5 _ 5 _ 5. _ + _, or. _ + _ 5 0, or 0 8. _ + _, or _ 7. 0_ 0 + _ _ 9 _ 9, or _ 0. _. _ 8 _ 8 _ 8, or _. _ 7 _ 7 _ 7. _ 9 _ 9 _ 9. 5 _ _ 5 5 _ 5 7. Ryan and Reggie baked an apple pie that was cut into equal pieces. Ryan had _ of the pie, and Reggie ate. Reggie Who ate more? What fraction of the pie did the boys eat all together? 8, or _ 8. Alice and Cherice run at the same park. On Saturday, Alice ran _ 8 of a mile, and Cherice ran 7_ 8 of a mile. Who ran the shorter distance? Alice 0 How far did Alice and Cherice run all together? 8, or _ miles Recognizing Student Achievement Math Boxes Problem Use Math Boxes, Problem to assess students ability to estimate the measure of an angle. Students are making adequate progress if they are able to identify the angle as obtuse. Some students may be able to measure it with a full- or half-circle protractor to within degrees. [Measurement and Reference Frames Goal ] Math Journal, p. 00A Study Link 7 (Math Masters, p. 8) Home Connection Students match fractions with pictures of shaded regions and collections of objects. Study Link Master Name STUDY LINK 7 Many Names for Fractions 7 Math Boxes Write the letters of the pictures that represent each fraction.. _ C, F, I. _ B, D. _ E, H 5. _ A, G 5. Practice A B C D E F G H I _, or + _. _ 8. -, or _ 9. Math Masters, p. 8 _ + _ 7. _ + _ - _, or 0. _ - _ 9. Which fraction is another name for _ 8? Fill in the circle next to the best answer. A B C D. Use pattern blocks to help you solve these problems. a. b. c. d. _ + + +, or _ +, or _ 5. Next month 8 students, teachers, and parents are going on a field trip to the zoo. Each bus holds 5 people. How many buses are needed for the trip? buses Math Journal, p. 00. A bag contains blue blocks, red blocks, 5 green blocks, and 0 black blocks. You put your hand in the bag and, without looking, pull out a block. About what fraction of the time would you expect to get a black block? 0 0, or _. TAP is an obtuse (acute or obtuse) angle. T The measure of TAP is 5. A. Tell if each of these is closest to inch, foot, or yard. a. the length of your smile inch b. the length of your journal foot c. the distance from your waist to your feet yard d. the width of your wrist inch P Lesson 7 0

5 Name 7 Equivalent Fractions Follow these steps to find equivalent fractions: Cut out each circle on Math Masters, page 9. Label the parts of each circle with a fraction, and cut them apart along the dashed lines. Glue the cutout pieces onto the circles on this page and Math Masters, page as directed. Fill in the missing numerators to complete the equivalent fractions.. Cover _ of the circle with fourths.. Cover _ of the circle with eighths. 9 Differentiation Options READINESS Finding Equivalent Fractions (Math Masters, pp. 9 ) 5 0 Min To explore equivalent names for fractions, have students find equivalent fractions by matching fractional parts of circles. 8 py g g p ENRICHMENT Modeling Fraction Equivalencies (Math Masters, p. ) 5 5 Min Math Masters, p. 0 To further explore equivalent fractions, have students use a clock face to model equivalencies of fractions with denominators that are factors of 0. Have students discuss how the clock faces might be used to help them model fraction addition and subtraction. EXTRA PRACTICE Playing Fraction Match (Student Reference Book, p. ; Math Masters, pp. 89 and 7 7) SMALL-GROUP 5 5 Min To practice identifying equivalent fractions, have students play Fraction Match. Have students describe on an Exit Slip how they know that two of the fractions are equivalent. See Lesson 7-7 for additional information. Name 7 Equivalent Fractions continued. Cover _ of the circle with eighths.. Cover _ of the circle with sixths Cover _ of the circle with sixths.. Cover _ of the circle with sixths. Name 7 Equivalent Clock Fractions. Explain why a hexagon pattern block is useful for modeling equivalencies of fractions with denominators of,, and. Sample answer: A hexagon is made up of triangles, so each triangle is _ of a hexagon; each rhombus is made up of triangles, which is _ or _ of a hexagon; and each trapezoid is made up of triangles, which is _ or _ of a hexagon.. Study the clock face. Which denominators can be modeled on the clock face? 0, 0, 0, 5,, 0,, 5,,, and. Explain your answer. Sample answer: These denominators are all factors of 0, and there are 0 marks on the clock face.. Using the denominators from Problem, name the fraction represented on each clock face in as many different ways as you can. Sample answers: a. b. c. _, _, 0, 0 _, _, _, 0, _, 0_ 0, 0, 0_ 0 _, 0 py g g p d. e. f. _, _, _, 5, 0_ 0, 0_ 0, 0 _, 9_, 0, 0 Math Masters, p. Math Masters, p. 0 Unit 7 Fractions and Their Uses; Chance and Probability