Equivalent Fractions Objective To guide the development and use of a rule for generating equivalent fractions. www.everydaymathonline.com 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 ] Use a rule for generating equivalent fractions. [Number and Numeration Goal ] Develop a rule for generating equivalent fractions. [Patterns, Functions, and Algebra Goal ] Key Activities Students use examples of equivalent fractions to develop a rule for finding equivalent fractions. Playing Fraction Match Student Reference Book, p. Math Masters, pp. and 7 7 Students practice identifying equivalent names for fractions. Fraction and Mixed-Number Addition and Subtraction Math Journal, p. B pattern blocks Students add and subtract fractions and mixed numbers. Math Boxes Math Journal, p. Students practice and maintain skills through Math Box problems. READINESS Identifying Equivalent Fractions on the Fraction Number-Line Poster Math Masters, p. or per group: Fraction Number-Line Poster (Math Masters, pp. and ), straightedge Students use a Fraction Number-Line Poster to identify equivalent fractions. ENRICHMENT Investigating Egyptian Fractions Math Masters, p. Students investigate how early Egyptians represented a fraction as the sum of unit fractions. Ongoing Assessment: Informing Instruction See page. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page. [Number and Numeration Goal ] Key Vocabulary equivalent fractions Equivalent Fractions Rule Materials Math Journal, pp.,, and Study Link 7 Math Masters, p. calculator colored chalk slate pattern blocks (optional) Study Link Math Masters, p. Students practice and maintain skills through Study Link activities. EXTRA PRACTICE Completing Name-Collection Boxes Math Masters, p. 7 Students complete name-collection boxes for fractions. EXTRA PRACTICE -Minute Math -Minute Math, pp., 7, 7, and Students practice finding equivalent fractions. Advance Preparation Teacher s Reference Manual, Grades pp., Lesson
Getting Started Mathematical Practices SMP, SMP, SMP, SMP, SMP7, SMP Content Standards.OA.,.NF.,.NF.,.NF.a,.NF.c,.NF.d Mental Math and Reflexes Have students name all the factor pairs for numbers less than. Suggestions: and ; and and ; and ; and and ; and and ; and ; and and 7 and 7; and ; and ; and ; and ; and and ; and ; and and ; and and ; and 7 Math Message Complete journal page. Study Link 7 Follow-Up Have small groups compare answers. Ask volunteers to draw additional representations of the fractions in Problems. Teaching the Lesson Math Message Follow-Up (Math Journal, p. ) ELL WHOLE-CLASS DISCUSSION Many Names for Fractions Color the squares and write the missing numerators.. Color _ of each large square. Whole square is colored. is colored. is colored. Ask students to examine the squares they colored on journal page. Point out that the three fractions they wrote for each problem all name the same fractional part of the square. Such fractions are called equivalent fractions. To support English language learners, have students write equivalent fractions next to the examples in the journals. Students should notice that whenever the total number of equal parts is doubled (or quadrupled), the number of colored parts is also doubled (or quadrupled), but the fractional part represented by the colored parts does not change. Tell students that in this lesson they will develop a rule for finding equivalent fractions. Developing a Rule for Finding Equivalent Fractions (Math Journal, p. ) ELL WHOLE-CLASS DISCUSSION. Color _ of each large square. is colored. is colored. is colored.. Color _ of each large square. is colored. is colored. is colored. Math Journal, p. -_EMCS_S_MJ_G_U7_7.indd // : PM In each problem on journal page, the numerator and denominator of the first fraction are each multiplied by to obtain the second fraction. They are each multiplied by to obtain the third fraction. To support English language learners, write the following on the board. Problem : _ = _ Problem : _ = _ _ = _ _ = _ Unit 7 Fractions and Their Uses; Chance and Probability
Problem : _ = _ _ = _ Write _ and _ with colored chalk to emphasize that the numerator and denominator were multiplied by the same number. The Equivalent Fractions Rule can be used to rename any fraction: If the numerator and denominator of a fraction are multiplied by the same nonzero number, the result is a fraction that is equivalent to the original fraction. Adjusting the Activity Present a more abstract rationale for this rule: If any number is multiplied by, the product is the number you started with. A fraction with the same numerator and denominator, such as _, is equivalent to. Multiplying the numerator and denominator of a fraction by the same number (not ) is the same as multiplying the fraction by. So, the product is equivalent to the original fraction. Equivalent Names for Fractions Fraction Equivalent Fractions Decimal Percent %, % 7 Math Journal, p. 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 Generating Equivalent Fractions (Math Journal, pp. and ; Math Masters, p. ) PARTNER Have students turn to the Equivalent Names for Fractions table on journal page. Ask them to write fractions that are equivalent to _. Ask students to explain how they know these fractions are all equivalent to _. Encourage them to use pattern blocks or drawings to support their reasoning. Have students look for patterns in fractions that are equivalent to _. Point out how these patterns relate to the Equivalent Fractions Rule. Equivalent Names for Fractions continued Ongoing Assessment: Informing Instruction Watch for students who note that not every pair of equivalent fractions can be found by multiplying (or dividing) by the same whole number. For example: = _ In this example, the numerator and denominator are both multiplied by the mixed number _. Fraction Equivalent Fractions Decimal Percent 7 7 Working in pairs, students use the Equivalent Fractions Rule to find three equivalent fractions for each of the remaining fractions in the table. Ask students to explain how to use a calculator to find equivalent fractions. Sample answer: Enter a fraction. Multiply it by any fraction whose numerator and denominator are the same. 7 Math Journal, p. Lesson
Name An Equivalent Fractions Rule Margot says the value of a fraction does not change if you do the same thing to the numerator and denominator. Margot says that she added to the numerator and the denominator in _ and got _. _ + + = _ Therefore, she says that _ = _. How could you explain or show Margot that she is wrong? Sample answer: _ does not equal _, because _ equals _. You can multiply or divide the numerator and denominator by the same number and not change the value of the fraction, but you cannot just add or subtract the same number from the numerator and denominator. Math Masters, page When students complete their work on journal pages and ask them to solve the problem on Math Masters, page on their own. Ongoing Assessment: Recognizing Student Achievement Math Masters Page Use Math Masters, page to assess students understanding of equivalent fractions. Students are making adequate progress if they are able to draw a picture or use the Equivalent Fractions Rule to demonstrate that _ (is not equal to) _. Some students may rename the fractions as decimals and show that... [Number and Numeration Goal ] -_EMCS_B_MM_G_U7_7.indd Adjusting the Activity Have a table of equivalent fractions available, such as Math Journal, pages and or Student Reference Book, page. // : AM AUDITORY KINESTHETIC TACTILE VISUAL Ongoing Learning & Practice Playing Fraction Match (Student Reference Book, p. ; Math Masters, pp. and 7 7) SMALL-GROUP Students play Fraction Match to practice naming equivalent fractions. When students have finished playing the game, ask them to select two fractions that match. On an Exit Slip, have them explain how they know the fractions are equivalent. Fraction and Mixed-Number Addition and Subtraction (Math Journal, p. B) Fraction Match Materials deck of Fraction Match Cards (Math Masters, pp. 7 7) Players to Skill Recognizing equivalent fractions Object of the game To match all of your cards and have none left. Directions. Shuffle the deck and deal 7 cards to each player. Place the remaining cards facedown on the table. Turn over the top card and place it beside the deck. This is the target card. If a WILD card is drawn, return it to the deck and continue drawing until the first target card is a fraction.. Players take turns trying to match the target card with a card from their hand in one of possible ways: a card with an equivalent fraction a card with a like denominator a WILD card. is the target card. It can be matched with: an equivalent fraction card such as,, or, or a like denominator card such as,, or, or a WILD card. The player names any fraction (with a denominator of,,,,,,,, or ) that is equivalent to the target card. The player can match by saying,, or. The player may not match by saying.. If a match is made, the player s matching card is placed on top of the pile and becomes the new target card. It is now the next player s turn. When a WILD card is played, the next player uses the fraction just stated for the new target card.. If no match can be made, the player takes card from the deck. If the card drawn matches the target card, it may be played. If not, the player keeps the card and the turn ends.. The game is over when one of the players runs out of cards, when there are no cards left in the Fraction Match deck, or time runs out. The player with the fewest cards wins. Student Reference Book, p. Games Students add and subtract fractions and mixed numbers. Encourage students to use pattern blocks or a method of their choice to solve the problems. Math Boxes (Math Journal, p. ) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-. The skill in Problem previews Unit content. Writing/Reasoning Have students write a response to the following: How did you determine the number of squares you needed to circle in Problem? Sample answer: There are total squares. I divided them into equal groups with squares in each group. Then I circled of the groups. Unit 7 Fractions and Their Uses; Chance and Probability
Study Link (Math Masters, p. ) Home Connection Students identify the missing numerator or denominator of equivalent fractions to complete name-collection boxes. Fraction and Mixed-Number Addition and Subtraction Add and subtract. Use pattern blocks to help you.. _ + _ _ =, or. _ _ + _ =. = 7. 7 _ + _ _ =, or 7. _ _ + _ =, or. _ + _ + _ =, or 7. _ + _ _ =, or. ( _ _ ) + ( _ _ ) =, or. ( _ + _ ) ( _ + _ ) =. ( + ) ( ) =. ( _ _ ) ( _ _ ) =. ( _ + _ ) + ( _ _ ) =, or, or Differentiation Options READINESS Identifying Equivalent Fractions on the Fraction Number-Line Poster (Math Masters, pp.,, and or ) SMALL-GROUP Min. Paulo, Regina, and Ted picked a bucket of apples on the field trip to the apple orchard. Paulo took _ of the apples, Regina took _ of the apples, and Ted took of the apples. They decided to give the rest of the apples to the teacher. Who took the most apples? What fraction of the apples did their teacher get? How do you know?. Julie was making a quilt. She had _ yard of fabric. She bought another 7_ yard of fabric. She gave _ yard of the fabric to her friend. Regina How many yards of fabric does she have left?, or Sample answer: I added + + and I got. Since I know that the total number of apples was, I subtracted from that and I got. That s how many the teacher gets. Math Journal, p. B, or yard To explore equivalent fractions using a number-line model, have students use a straightedge to vertically line up fractions on the Fraction Number-Line Poster (see the optional Readiness activity in Lesson 7-) that are equivalent to _, _, _, _, and so on. Ask students to record the results of their exploration in a Math Log or on an Exit Slip. -_EMCS_S_MJ_G_U7_7.indd B // : PM Whole Halves Fourths Eighths Math Boxes Thirds Sixths 7. Circle _ of all the squares. Mark Xs on _ of all the squares. Sample answer:. Insert parentheses to make these number sentences true. a. ( + ) = b. = ( - ) c. ( - ) = d. + = ( + ) A straightedge highlights equivalent fractions.. Plot and label each point on the coordinate grid. A (,) B (,) C (,) D (,) E (,) A C D E. A bag contains green blocks, red blocks, blue block, and yellow 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 blue block? B. Draw and label a angle. T This angle is an obtuse (acute or obtuse) angle. Sample answer: O P. If inch on a map represents miles, then how many inches represent miles? Fill in the circle next to the best answer. A B C D in. _ in. _ in. in. Math Journal, p. -_EMCS_S_MJ_G_U7_7.indd /7/ : AM Lesson 7
Study Link Master py g g p Name STUDY LINK Fraction Name-Collection Boxes In each name-collection box: Write the missing number in each fraction so that the fraction belongs in the box. Write one more fraction that can go in the box.. _. _.. Make up your own a. b. name-collection box problems like the ones above. Ask a friend to solve your problems. Check your friend s work. Practice R -_EMCS_B_MM_G_U7_7.indd Answers vary. Answers vary. Answers vary.. =. 7 = 7. = Math Masters, p. _ Answers vary. // : AM ENRICHMENT Investigating Egyptian Fractions (Math Masters, p. ) SMALL-GROUP Min To apply students understanding of fraction addition and equivalent fractions, have students investigate how early Egyptians represented a fraction as the sum of unit fractions. To solve Problems and, students need to divide the rectangle into more regions than indicated by the denominator of the fraction. NOTE Egyptians also used the fraction _. EXTRA PRACTICE Completing Name-Collection Boxes (Math Masters, p. 7) Min To provide practice generating equivalent names for fractions, have students complete name-collection boxes. Encourage students to complete the boxes with equivalent fractions and mathematical expressions that include fractions. Use Math Masters, page 7 to create problems to meet the needs of individual students or have students create and solve their own problems. Name Teaching Master Egyptian Fractions Ancient Egyptians only used fractions with in the numerator. These are called unit fractions. They wrote non-unit fractions, such as _ and _, as sums of unit fractions. They did not use the same unit fraction more than once in a sum. Examples: 7 EXTRA PRACTICE SMALL-GROUP -Minute Math Min To offer students more experience with equivalent fractions, see -Minute Math, pages, 7, 7, and. _ = _ + = _ + _ Use drawings and what you know about equivalent fractions to help you find the Egyptian form of each fraction. _ + _. _ =. _ = * _ + _. _ 7_ + _ =. _ = _ +. _ + _ =. _ 7 = _ + _ Math Masters, p. -_EMCS_B_MM_G_U7_7.indd // : AM Unit 7 Fractions and Their Uses; Chance and Probability