Calculator Practice: Computation with Fractions

Transcription

1 Calculator Practice: Computation with Fractions Objectives To provide practice adding fractions with unlike denominators and using a calculator to solve fraction problems. 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 Convert between fractions and mixed numbers. [Number and Numeration Goal ] Express fractions and mixed numbers in simplest form. [Number and Numeration Goal ] Compare and order fractions. [Number and Numeration Goal ] Use mental arithmetic, paper-and-pencil algorithms, and calculators to solve fraction and mixed-number addition problems. [Operations and Computation Goal ] Use benchmarks to estimate sums. [Operations and Computation Goal ] Key Activities Students add fractions with unlike denominators using estimation and paperand-pencil computation by playing Fraction Action, Fraction Friction. They use calculators to perform operations with fractions and mixed numbers. Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Number and Numeration Goal ] Materials Math Journal, p. 7 Student Reference Book, pp. 0 and Study Link 8 ; Math Masters, p. 9 slate scissors per partnership: eight " by " index cards cut in half (optional) calculator overhead calculator for demonstration purposes (optional) Math Boxes 8 Math Journal, p. 8 Students practice and maintain skills through Math Box problems. Study Link 8 Math Masters, p. Students practice and maintain skills through Study Link activities. READINESS Charting Common Denominators Math Masters, p. 7 transparency of Math Masters, p. 7 Students use a flowchart to find common denominators. ENRICHMENT Exploring Equivalent Fractions Math Masters, p. 8 calculator Students use calculators to explore fraction-to-decimal conversions. EXTRA PRACTICE -Minute Math -Minute Math, pp., 98, 99, and calculator Students use calculators to add fractions. Advance Preparation For the optional Readiness activity in Part, make a transparency of Math Masters, page 7. Background Information This lesson presents example key sequences for the TI- and Casio fx- calculators. If other calculators are used, edit the key sequences as needed. Teacher s Reference Manual, Grades pp. 9, 9 Unit 8 Fractions and Ratios

2 Getting Started Mental Math and Reflexes Have students decide if each expression is > _, < _, or = _. _ + _ 8 > _ + _ < _ 8 + _ < 8 + _ = _ + _ 0 = _ - _ > _ _ > _ 8 - _ = _ 7_ 8 - _ 9 > _ Math Message Work with a partner. Take one copy of Math Masters, page 9. Cut out the cards. Put them in order from least to greatest. Which fraction is the greatest? _ Which is the least? _ Study Link 8 Follow-Up Have partners compare answers and resolve differences. Teaching the Lesson Ongoing Assessment: Math Message Recognizing Student Achievement Use the Math Message to assess students ability to order fractions. Watch students as they order the cards. Students are making adequate progress if they identify the least, the middle (the benchmark of _ ), and the greatest fractions and correctly place one or two fractions in proximity to these three fractions. Some students may be able to place all of the fractions in order from least to greatest. [Number and Numeration Goal ] Math Message Follow-Up WHOLE-CLASS DISCUSSION Write _ on the board. Ask: How can you use the fraction _ to help you place the other fractions in order? Sample answer: I can use the benchmark _ to place the other fractions as either greater than _ or less than _. Ask a volunteer to write another fraction from the cards on the board, placing it in order as if on a number line. If the fraction is less than _, place it to the left of the fraction. If it is greater than _, place it to the right of the fraction. For example, a student might choose _ and write it to the right of _. _ Continue having volunteers add fractions to the ordered list one by one. When the list is complete, ask students to rename the fractions so they have a common denominator of. Have volunteers write the equivalent names above the original fractions. Ask: Is the order correct? How do you know? The order is correct if the numerators for the twelfths are in order from least to greatest. The complete order not counting repeats: _ 7_ _ Lesson 8 7

3 Games Fraction Action, Fraction Friction Materials Fraction Action, Fraction Friction Card Deck (Math Masters, p. 9) or more calculators Players or Skill Estimating sums of fractions Object of the game To collect a set of fraction cards with a sum as close as possible to, without going over. Directions. Shuffle the deck and place it number-side down on the table between the players.. Players take turns. On each player s first turn, he or she takes a card from the top of the pile and places it number-side up on the table. On each of the player s following turns, he or she announces one of the following: 7 Action This means that the player wants an additional card. The player believes that the sum of the fraction cards he or she already has is not close enough to to win the hand. The player thinks that another card will bring the sum of the fractions closer to, without going over. Friction This means that the player does not want an additional card. The player believes that the sum of the fraction cards he or she already has is close enough to to win the hand. The player thinks there is a good chance that taking another card will make the sum of the fractions greater than. Once a player says Friction, he or she cannot say Action on any turn after that.. Play continues until all players have announced Friction or have a set of cards whose sum is greater than. The player whose sum is closest to without going over is the winner of that round. Players may check each other s sums on their calculators.. Reshuffle the cards and begin again. The winner of the game is the first player to win rounds. Student Reference Book, p. Fraction Action, Fraction Friction Card Deck 7 Adjusting the Activity Have students make their own set of Fraction Action, Fraction Friction cards. They should make up two fractions for each of the following denominators:,,,, 8, 9, 0, and. Each fraction should be less than _, when possible. (With thirds and fourths, this will not be possible.) Using the in. by in. cards, they will have a total of cards, each with a different fraction. Encourage students to make estimates of their sums as they play. AUDITORY KINESTHETIC TACTILE VISUAL Introducing Fraction Action, Fraction Friction (Student Reference Book, p. ; Math Masters, p. 9) WHOLE-CLASS Refer students to the fraction cards from the Math Message or the display on the board, and ask the following questions: What common denominator might you use to find the sum of all the fourths and all the sixths?,, and so on... What common denominator might you use to find the sum of all the thirds and all the sixths?,, and so on... What common denominator might you use to find the sum of all the thirds, fourths, and sixths?,, and so on... What is the least common denominator for all the fractions on the cards? Go over the rules for Fraction Action, Fraction Friction on Student Reference Book, page with the class. Play a few practice rounds against the class before partners play the game on their own. Remind students to compare the fractions with benchmarks to help them estimate the sums. Science Link In physics, friction is a force that resists relative motion. Compare pulling a heavy box across a rough concrete floor versus pulling it across smooth ice. The greater resistance to motion on the concrete is due to greater friction. In the game, a player might call Friction! to ask for resistance to motion if the player does not wish to move any further toward. By calling Action! the player asks to resume moving toward. Students play Fraction Action, Fraction Friction. Circulate and assist. Exploring Fraction-Operation Keys on a Calculator (Student Reference Book, pp. 0 ) WHOLE-CLASS Students can use scientific calculators to perform operations with fractions and mixed numbers. Students explored these calculator operations in Lessons - and -. If you have a calculator for the overhead, have volunteers use it to demonstrate how to enter the following fractions and mixed numbers: Sample answers for TI- and Casio fx-: _ 8 n 8 d, or 8 7 _ 7 Unit n d, or 7 _ 7 n 7 d, or 7 8 Unit 8 Fractions and Ratios

4 Use these same numbers to have other volunteers demonstrate how to convert between fractions and mixed numbers: Sample answers for TI- and Casio fx-:, or Write the following problems on the board or a transparency for students to solve using their calculators: Sample answers for TI- and Casio fx-: _ + _ 8 _, or 9_ _ - 7 _ + _, or 0_ Have the class mirror the volunteers as they explain the key sequences used for their solutions. Discuss any difficulties or interesting occurrences students encountered. Ask: What are some of the important steps to remember when working with a calculator? Expect these types of responses: Clear between operations. Check that the fix function is off or set appropriately. Pay attention to the display as you press keys. Ask students to locate the or key on their calculators. Have them explore how to use this key and what it does. Then ask them to report what they found. Refer students to Student Reference Book, pages 0. As a class, read the section on simplifying fractions, and do the examples together. Calculators The keys to convert between mixed numbers and improper fractions are similar on all fraction calculators. Convert 7 to a mixed number with your calculator. Then change it back. Both and toggle between mixed number and improper fraction notation. Simplifying Fractions Ordinarily, calculators do not simplify fractions on their own. The steps for simplifying fractions are similar for many calculators, but the order of the steps varies. Approaches for two calculators are shown on the next three pages depending on the keys you have on your calculator. Read the approaches for the calculator having keys most like yours. Student Reference Book, p. 0 Pressing is not optional in this key sequence. Pressing is optional in this key sequence. Entering Fractions on a Calculator (Math Journal, p. 7) PARTNER Have students complete the journal page. Circulate and assist. Ongoing Learning & Practice Math Boxes 8 (Math Journal, p. 8) INDEPENDENT Date 8 Time Exploring Fraction-Operation Keys Some calculators let you enter, rename, and perform operations with fractions. Sample answers provided for calculators:. Draw the key on your calculator that you would use to do each of the functions. Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-. The skill in Problem previews Unit 9 content. Writing/Reasoning Have students write a response to the following: Explain how you found the answer to Problem b. Include the strategies and the reasoning that you used. Answers vary. Function of Key Give the answer to an entered operation or function. Enter the whole number part of a mixed number. Enter the numerator of a fraction. Enter the denominator of a fraction. Convert between fractions greater than and mixed numbers. Simplify a fraction. Use your calculator to solve ,97., Key Unit n d, or. In any row, column, or diagonal of this puzzle, there are groups of fractions with a sum of. Find as many as you can, and write the number sentences on another piece of paper. The first one has been done for you. There are 8 possible number sentences, including the example. Example: Number Sentence Math Journal, p. 7 Lesson 8 9

5 Date 8. Add. a. b. 8 c. d. e. Math Boxes. Max worked for hours on Monday and hours on Tuesday. Did he work more or less than 0 hours? More than 0 hours Explain. 0, which is more than 0 hours.. Solve. Solution m a. 0 0 b. 7 n c. k8 8 d. 0 p a e , or, or m 9 n 8 k 8 p a Math Journal, p. 8 Time STUDY LINK 8 More Fraction Problems. Use the patterns to fill in the missing numbers..8. a..,., 8.,,.. b. 0,,.,, c.., 0., 0.,, d.., 7., 7., , e.,, 9,,. Make each sentence true by inserting parentheses. a. 00 ( 0 ) b. / ( ) c. 8 ( / ) d. ( 0 / ) e. ( 0 ) / ( ). Circle the congruent angles. a. b. c. d. Name Date Time. Circle all the fractions below that are greater than Rewrite each expression by renaming the fractions with a common denominator. Then decide whether the sum or difference is greater than, less than, or equal to. Circle your answer Fraction Puzzle. Select and place three different numbers so the sum is as large as possible. Procedure: Select three different numbers from this list:,,,,,. Write the same number in each square. Write a different number in the circle. Write a third number in the hexagon. Add the two fractions. Example: 8 Practice Study Link Master ,09 / 0., or 8 0 Sample answer: Study Link 8 (Math Masters, p. ) INDEPENDENT Home Connection Students compare fractions to _ and solve a fraction addition puzzle. Differentiation Options READINESS Charting Common Denominators (Math Masters, p. 7) SMALL-GROUP 0 Min To explore fraction addition using a common-denominator strategy, have students use a flowchart to find common denominators before solving fraction addition problems. Explain that students can use a flowchart to show the steps and decisions used to find common denominators. Use the prepared transparency, and demonstrate how to read the flowchart on the Math Masters page. Example: Step Write 7_ + _ in the START circle. Step Point to the first triangle and ask: Do the fractions have a common denominator? No Step Follow the No side of the triangle. Step Point to the second triangle and ask: Is one denominator a factor of the other? Yes. is a factor of. Step Follow the YES side of the triangle. Step Rename _ with a denominator of. _ = 0_ Step 7 Follow the line that leads to the next rectangle. Step 8 Add the numerators = 7 Step 9 Write the solution. 7_ + 0_ = 7_, _, or _ 8 Have students use the flowchart as they solve the following problems: _ + 8, _, or _ 8_ + _ 8_, _, or 7_ _ +, or _ _ 8 + _ 79_, or 7_ Math Masters, p. 0 Unit 8 Fractions and Ratios

6 Adjusting the Activity Have students list the steps they take as they decide whether to use the QCD or to find the least common denominator. Name Date Time 8 Teaching Master Charting Common Denominators START 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 No Common denominator? Yes ENRICHMENT SMALL-GROUP Exploring Equivalent Fractions (Math Masters, p. 8) 0 Min PROBLEM SOLVING To extend students understanding of equivalent fractions, have them explore fraction-to-decimal conversions using a calculator. Have students enter _ on their calculators and then locate and press the key that will convert the display to an equivalent decimal. On many calculators, this key is labeled F D. Ask: Will equivalent fractions convert to the same decimal? Explain that in this exploration students will work to support their responses. Have each student write a fraction. Make adjustments so there are no duplicates. Students complete Math Masters, page 8. They use their fractions to make a list of 0 equivalent fractions, use their calculators to convert the fractions to decimals, and summarize their results. Find the least common denominator. No Rename both fractions. Is one denominator a factor of the other denominator? Use the QCD. Math Masters, p. 7 Yes Rename the fraction. Add numerators. Write the solution number sentence. STOP Discuss students summaries. Equivalent fractions name the same amount. They can also be defined as fractions that have the same decimal result when their numerators are divided by their denominators. EXTRA PRACTICE SMALL-GROUP -Minute Math Min To offer students more experience with using a calculator to add fractions, see -Minute Math, pages, 98, 99, and. Name Date Time 8 Teaching Master Exploring Equivalent Fractions Yes. Do equivalent fractions convert to the same decimal?. Complete the fraction column in the table so there are 0 equivalent fractions.. Use your calculator to convert each fraction to a decimal. Write the display in the decimal column. (Don t forget to use a repeat bar, if necessary.) Sample answers: Fractions Decimals 8 9 _ _ 0. Explain your results. Describe the relationship between the equivalent fractions and their decimal form. The equivalent fractions can all be renamed as _, the simplest form. Converted to a decimal, _ is equal to. So all equivalent fractions have the same decimal form. Math Masters, p. 8 Lesson 8