Equivalent Fractions and Decimals

Transcription

1 LESSON 9 Equivalent Fractions and Decimals FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 4NFC5 Express a fraction with a denominator as an equivalent fraction with denominator, and use this technique to add two fractions with respective denominators and Also 4NFC MATHEMATICAL PRACTICES MP Reason abstractly and quantitatively MP4 Model with mathematics MP Attend to precision MP8 Look for and express regularity in repeated reasoning F C R Coherence: Standards Across the Grades Before Grade 4 After NFAa 4NFC5 5NBTAb NFAb F C R Rigor: Level : Understand ConceptsShare and Show ( Checked Items) Level : Procedural Skills and FluencyOn Your Own Level : ApplicationsThink Smarter and Go Deeper Learning Objective Record tenths and hundredths as fractions and decimals Language Objective Students show, and then explain how to record tenths and hundredths as fractions and decimals Materials MathBoard FC R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 49J About the Math Professional Development Teaching for Depth This lesson strengthens student understanding of the relationship between places in the base-ten number system Students have learned with whole numbers that a digit in any place has a value times the value of the same digit one place to its right In the tens place, has a value of, which is ten times the value of in the ones place In this lesson, students write equivalent fractions and decimals by applying the relationship they have learned between tenths and hundredths In the tenths place, has a value of, which is ten times the value of in the hundredths place, Professional Development Videos 57A Chapter 9 Interactive Student Edition Personal Math Trainer Math on the Spot Animated Math Models HMH Mega Math

2 Daily Routines Common Core Problem of the Day 9 The weather reporter on the nightly news said that inch of rain fell in the last 4 hours in the local area What is written as a decimal? Vocabulary equivalent decimals Interactive Student Edition Multimedia Glossary e Vocabulary Builder Materials Word Description (see eteacher Resources) Guess the Meaning Review the meaning of equivalent fractions with students, and use that review as a springboard to discuss the new vocabulary word, equivalent decimals Then have students complete the sections of the Word Description for the word equivalent decimals ENGAGE with the Interactive Student Edition Essential Question How can you record tenths and hundredths as fractions and decimals? Making Connections Ask students to tell what they know about fraction models How can you represent the fraction 4 with a fraction model? Check students models Learning Activity What is the problem the students are trying to solve? Connect the story to the problem Ask the following questions What denominator would you use to represent the decimal 5 as a fraction? Explain Possible answer: because the decimal is five tenths What denominator would you use to represent the decimal as a fraction? Explain Possible answer: because the decimal is twenty-two hundredths Literacy and Mathematics View the lesson opener with the students Then have the class participate in the following activity Tell students to give examples of decimals and fractions that they encounter in their everyday lives Have students describe how they could represent the decimals with place-value charts and the fractions with fraction models Literature Connection From the Grab-and-Go Differentiated Centers Kit Students read the book and learn how fractions and equivalent fractions are used to read music How can you record tenths and hundredths as fractions and decimals? A Melody in Fractions Lesson 9 57B

3 LESSON 9 4NFC5 Express a fraction with a denominator as an equivalent fraction with denominator, and use this technique DO EDIT--Changes must be made through "File to NOT add two fractions with respective denominators info" and CorrectionKey=B EXPLORE Lesson 9 Unlock the Problem Equivalent Fractions and Decimals MATHEMATICAL PRACTICES Have students read and discuss the problem Unlock Unlock the the Problem Problem One Way Daniel spent a day hiking through a wildlife preserve During the first hour of the hike, he drank liter of water How many hundredths of a liter did he drink? MP7 Look for and make use of structure By what number should you multiply the? Explain ; possible denominator of MODEL RECORD = = _ multiply the numerator and denominator by the same =, so it is like multiplying by number Another Way Explain where the tenths place is in the place-value chart one place to the right of the You may use the models in One Way to emphasize that is equivalent to because they name the same amount What do you notice about the shaded area on both of the grids? They are the same size Math Talk Use Math Talk to help students understand that writing a zero to the right of a decimal does not change the value of the decimal How can you use equivalent fractions to write as hundredths? Possible answer: Multiply both the numerator and the write as denominator by to write the equivalent fraction Write as Write as a decimal Think: tenths is the same as tenths hundredths Ones Tenths Hundredths ELL Restate Use decimal models to explain the meaning of equivalent decimals Shade of a tenths model and of a hundredths model MATHEMATICAL PRACTICES Explain how you can write as hundredths Possible explanation: there are hundredths in tenth, so there are hundredths in tenths Chapter 9 57 Meeting Individual Needs 4_MNLESE479_C9Lindd 57 Reteach 9 Differentiated Instruction DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A Lesson 9 Reteach //4 : PM Enrich 9 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A Lesson 9 Enrich Equivalent Fractions and Decimals Matching Fractions and Decimals Match each fraction or decimal in Column A with an equivalent fraction or decimal in Column B Write as an equivalent fraction with a denominator of Column A Column B Step Think: is a common factor of the numerator and the denominator Step Divide the numerator and denominator by So, Lori ran mile Use a place-value chart Step Write as an equivalent decimal Ones Tenths Hundredths Step Think: hundredths is Ones tenths hundredths 9 ; 9 ; 4 4 ; 4 7 ; 7 Chapter Resources 4_MNLEAN44_C9Rindd _ 8 ; Explain how you found the match for Possible answer: I wrote an equivalent fraction by multiplying the numerator and denominator Write the number as tenths in fraction form and decimal form 7 5 Write the number as hundredths in fraction form and decimal form Tenths So, Lori ran mile 7 4 _ 57 Chapter 9 Math Talk Explain why tenths is equivalent to hundredths Using a dime and ten pennies as a comparison, discuss with students how and are equivalent, or equal amounts, but are written differently Possible explanation: is Multiply the numerator tenths or and denominator by to get The equivalent decimal is liter of water, or _ So, Daniel drank _ Lori ran mile How many tenths of a mile did she run? Differentiated Instruction Another Way Image Credits: (cr) Bill Brooks/Alamy the decimal point = Explain where the hundredths place is in the place-value chart two places to the right of as a fraction or a decimal fraction with a denominator of Why do you also multiply the numerator by? To find an equivalent fraction, I need to of decimal point Underline what you need to find How can you represent hundredths? One Way Write as an equivalent explanation: I need to write as a fraction with in the denominator Since =, I multiply by Strategy: Number and Operations Fractions 4NFC5 Also 4NFC MATHEMATICAL PRACTICES MP, MP, MP7 Essential Question How can you record tenths and hundredths as fractions and decimals? 45 by 5 to get I then found the decimal equivalent, 45 5 ; 5 Reteach Chapter Resources 4//4 : PM 4_MNLEAN44_C9Eindd 9- Enrich 4//4 : PM

4 Jasmine collected liter of water in a jar during a rainstorm How many tenths of a liter did she collect? Equivalent decimals are decimals that name the same amount You can write as a decimal that names tenths Share and Show 58 One Way Write as an equivalent decimal Show in the place-value chart Ones Tenths Hundredths Think: There are no hundredths is equivalent to _ tenths Write as _ Another Way Write as a fraction with a denominator of STEP Write as a fraction is _ hundredths hundredths written as a fraction is _ STEP Write as an equivalent fraction with a denominator of Think: is a common factor of the numerator and the denominator _ = = _ So, Jasmine collected _, or _ liter of water Write 4 as hundredths Write 4 MATH BOARD as an equivalent fraction Write 4 as a decimal 4 = 4 = 4 4 Fraction: Ones Tenths Hundredths 4 Decimal: 4 Image Credits: (t) Steve Satushek/Getty Images One Way What digit is in the hundredths place of? Discuss with students that since has a in the hundredths place, an equivalent tenths decimal can be written for it Another Way How do you know what denominator to use when writing as a fraction? Possible answer: means hundredths, so is the denominator of the equivalent fraction Why do you divide by? Possible answer: I divide by because I need to show the answer in tenths, not hundredths Dividing by is the same as dividing by, so it does not change the value MP Construct viable arguments and critique the reasoning of others Suppose Jasmine had collected liter of water Could you answer the question the problem asks? Use equivalent fractions to support your answer Possible answer: no; = ; to write an equivalent fraction with the denominator, you need to divide the numerator and denominator by cannot be evenly divided by EXPLAIN MATH Share and Show MATH BOARD The first problem connects to the learning model Have students use the MathBoard to explain their thinking Advanced Advanced Learners Learners Materials Decimal Models (see eteacher Resources) Students work in pairs One student uses either a tenths or a hundredths decimal model and shades or more columns of the model The student then writes a fraction to represent the shaded part of the model The partner then names the shaded part of the model in three other ways: using an equivalent fraction and by writing two equivalent decimals Partners compare the answers to the model, and then trade roles and repeat the activity as time allows Kinesthetic / Visual Partners,, and COMMON ERRORS Error Students may write a zero in the tenths place rather than the hundredths place when writing an equivalent decimal Example 7 = 7 Springboard to Learning Model 7 and 7 using decimal models to illustrate that they are different decimals Recommend that students continue to use decimal models to either find equivalent decimals or to check their work Lesson 9 58

5 Use the checked exercises for Quick Check Students should show their answers for Quick Check on the MathBoard Math Talk Use Math Talk to reinforce the importance of place value when writing equivalent decimals How many tenths and hundredths are in 5? tenths and 5 hundredths Are 5 hundredths enough to make another tenth? no Write the number as hundredths in fraction form and decimal form 7 7, 7 Write the number as tenths in fraction form and decimal form , 5 7, If Then Quick Check a student misses the checked exercises Rt I Differentiate Instruction with Reteach 9 Personal Math Trainer 4NFC5 RtI Tier Activity (online) On Your Own Practice: Copy and Solve Write the number as hundredths in fraction form and decimal form 8 Math Talk Practice: Copy and Solve Write the number as tenths in fraction form and decimal form 8 8, 8 4, 4 9, 8, 8, 9 9, 9 7 7, 7, No Possible explanation: 5 is tenths 5 hundredths Since 5 hundredths is not enough to make another tenth, you cannot name 5 as only tenths MATHEMATICAL PRACTICES Reason Abstractly Explain whether you can write 5 as tenths, Exercises 4 require students to synthesize what they have learned about mixed numbers and naming equivalent fractions Some students may try to rename the whole-number part of the mixed number Use models to show these students that the whole-number part stays the same and only the fraction part changes when writing equivalent mixed numbers 4 4 Write the number as an equivalent mixed number with hundredths Possible answers are given Chapter 9 Lesson Chapter 9

6 MATHEMATICAL PRACTICES M 7 Carter says that 8 is equivalent to 8 Describe and correct Carter s error Inland Water How many lakes and rivers does your state have? The US Geological Survey defines inland water as water that is surrounded by land The Atlantic Ocean, the Pacific Ocean, and the Great Lakes are not considered inland water 9 WRITE Math Just over of the entire United States is inland water Write as a decimal About 7 of the area of Rhode Island is inland water Write 7 as a fraction 7 5 Possible answer: 8 is tenths 8 hundredths, which is the same as 8 hundredths Write 8 hundredths as 8 MATHEMATICAL PRACTICE Can you write as tenths? Explain No Possible explanation: is hundredths You need hundredths to make a tenth DIFFERENTIATED INSTRUCTION 8 For numbers 8a 8e, choose True or False for the statement 8a is equivalent to True False 8b is equivalent to True False 8c 4 4 True False 8d 4 is equivalent to 4 True False 8e 5 is equivalent to 5 True False WRITE Math Show Your Work DEEPER Louisiana s lakes and rivers cover about of the state Write as hundredths in words, fraction form, and decimal form ten hundredths,, INDEPENDENT ACTIVITIES Image Credits: (cr) Gene Ahrens/Alamy 4 ELABORATE Problem Solving Applications MATHEMATICAL PRACTICES Exercise 7 requires students to correct an error using the relationship between equivalent fractions and equivalent decimals Math on the Spot Video Tutor Use this video to help students model and solve this type of Think Smarter problem Math on the Spot videos are in the Interactive Student Edition and at wwwthinkcentralcom Exercise 8 assesses a student s ability to determine the equivalence of fractions and decimals Students who answer True to all parts of the question may only have noticed that the digit in both forms of the number is the same These students may not understand how to use tenths and hundredths to compare the values of the numbers Students who answer 8b, 8c, and 8e as False may not realize how to rename tenths as hundredths to compare Connect to Science MP Attend to precision For Exercise, discuss with students why the fraction must have a denominator of Activities What s My Place? Students complete orange Activity Card by writing the decimal and the fraction that is represented by a group of base-ten blocks Differentiated Centers Kit Literature A Melody in Fractions Students read the book and learn how fractions and equivalent fractions are used to read music Games Fraction Action Students practice matching fractions with pictorial models 5 EVALUATE Formative Assessment Essential Question Using the Language Objective Reflect Have students show, and then explain to answer the Essential Question How can you record tenths and hundredths as fractions and decimals? Possible answer: I can write equivalent fractions and decimals using models or place value Math Journal WRITE Math Write 5 in three equivalent forms Lesson 9 5

7 Practice and Homework Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving Use the Write Math section to determine student s understanding of content for this lesson Encourage students to use their Math Journals to record their answers Equivalent Fractions and Decimals COMMON CORE STANDARD 4NFC5 Understand decimal notation for fractions, Write the number as hundredths in fraction form and and compare decimal fractions decimal form _ Think: 5 tenths is the same as 5 tenths and hundredths Write ; ; 9 ; Practice and Homework Lesson 9 8 ; 8 Write the number as tenths in fraction form and decimal form ; 4 ; ; Problem Solving 8 Billy walks mile to school each day Write as hundredths in fraction form and in decimal form ; 9 WRITE Math Write 5 in three equivalent forms Check students work Chapter Chapter 9

8 Lesson Check (4NFC5) The fourth-grade students at Harvest School make up of all students at the school What fraction is equivalent to? Kyle and his brother have a marble set Of the marbles, are blue This represents 5 of all the marbles What decimal is equivalent to 5? 5 Continue concepts and skills practice with Lesson Check Use Spiral Review to engage students in previously taught concepts and to promote content retention Common Core standards are correlated to each section Spiral Review (4OAC5, 4NFA, 4NFB4c, 4NFC) Jesse won his race by 45 seconds What is this number written as a decimal? 4 Marge cut pieces of tape for mounting pictures on poster board Each piece of tape was _ 8 inch long How much tape did Marge use? 45 inches 5 Of Katie s pattern blocks, 9 are triangles A number pattern has 75 as its first term What is 9 in simplest form? The rule for the pattern is subtract What is the sixth term? 5 _ 4 45 FOR MORE PRACTICE GO TO THE Personal Math Trainer Lesson 9 5