12-5A. Equivalent Fractions and Decimals. 1 Daily Common Core Review. Common Core. Lesson. Lesson Overview. Math Background

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1 Lesso -A Equivalet Fractios ad Decimals Commo Core Lesso Overview Domai Number ad Operatios Fractios Cluster Uderstad decimal otatio for fractios, ad compare decimal fractios. Stadards.NF. Use decimal otatio for fractios with deomiators or. Also.NF. Objective Studets will uderstad how to use equivalet fractios to write fractios as decimals. Essetial Uderstadig Every fractio ca be represeted by a ifiite umber of equivalet fractios, but each fractio is represeted by the same decimal or a equivalet form. Vocabulary Materials Decimal models (Teachig Tool ) PROFESSIONAL DEVELOPMENT Mathematical Practices Make sese of problems ad persevere i solvig them. Reaso abstractly ad quatitatively. Costruct viable argumets ad critique the reasoig of others. Model with mathematics. Use appropriate tools strategically. Atted to precisio. Look for ad make use of structure. Look for ad express regularity i repeated reasoig. Math Backgroud Today calculators ad computers are so accessible that decimals have become preferred over fractios for reportig ad calculatig. However, studets ofte fid themselves usig fractios because they are writig ratios the umber of parts cosidered to the umber of parts i all. Therefore, it is importat that studets are able to pass back ad forth betwee fractio ad decimal represetatios. I the previous lesso, studets wrote decimals equivalet to fractios with powers of as deomiators ad vice versa. I this lesso, studets will write decimals equivalet to Daily Commo Core Review fractios with other deomiators. Some fractios ca be simplified to fractios with deomiators that are factors of a power of. Oce a fractio has bee simplified, a fractio equivalet to it ca be writte with a deomiator that is a power of. Fially, this fractio ca easily be writte as a decimal. Studets will also ecouter fractios that have deomiators that are multiples of or, that ca be chaged to become equivalet fractios with a power of as their deomiators. The these fractios ca be writte as decimals. Daily Commo Core Review ot available for this lesso. Cosider usig additioal practice foud i the Studet Editio as review. A

2 Develop the Cocept: Iteractive mi Problem-Based Iteractive Learig Overview Studets will use equivalet fractios to write fractios with deomiators other tha or as decimals. Focus How ca you use equivalet fractios to chage a fractio to a decimal? Materials Decimal models (Teachig Tool ) Set the Purpose You have leared to write fractios with deomiators of ad as decimals. Today, you will lear how to write more fractios as decimals. Coect What does it mea to write a fractio i simplest form? [The umerator ad deomiator have o commo factor other tha.] Commuicate Whe studets share their thikig with the class, they commuicate the thought process they used to write a fractio as a decimal. Pose the Problem Three fourths of the studets i Mr. Brow s class have a youger brother or sister. How would you write _ as a decimal? Give studets time to work i pairs to solve this problem. The have them share their thikig. Whole-Class Discussio Draw three large cogruet squares o the board. Use the secod square to show teths ad the third square to show a hudredths grid. How could you use the first square to show _? [Divide the square ito equal parts ad shade parts.] Divide the square ito fourths usig a horizotal lie ad a vertical lie. Shade fourths. Poit to the secod square. Is it possible to shade some teths to show the same amout shaded as i the first square? [] Poit to the third square. Is it possible to shade some hudredths to show the same amout? [] Shade of the hudredths grid. What fractio tells how may hudredths are shaded? [ _ 7 ] Write _ 7 o the board. What decimal tells how may hudredths are shaded? [0.7] Write _ o the board. Suppose you did ot have models to use. How could you have writte _ as a equivalet fractio with a deomiator of? [Multiply ad by to get 7 ad.] Could you have writte _ as a equivalet fractio with a deomiator of? Explai. [; You ca t multiply by a whole umber to get.] Martise Name Teachig Tool _ _ = 7 7 = Small-Group Iteractio Work with your parter. Write as a decimal. [0.] Write _ as a decimal. Show your thikig. [ _ 00 _ 00 0.] etools Fractios B

3 Develop the Cocept: Visual Equivalet Fractios ad Decimals How ca you use equivalet fractios to chage a fractio to a decimal? A pa of corbread was divided ito equal of the pieces, ad out of pieces or corbread remais. Write a fractio equivalet, ad the chage the fractio to a decimal. to _ I simplest form is. Fid a equivalet fractio with a deomiator of. What are equivalet fractios? [Fractios that represet the same amout] How ca you write equivalet fractios? [Multiply or divide the umerator ad deomiator by the same umber.] times what umber equals? _ _ is five teths, or 0.. So, 0. of the corbread remais. Lesso -A Set the Purpose Call studets attetio to the Visual Learig Bridge at the top of the page. I this lesso, you will lear how to use equivalet fractios to write fractios as decimals. Commo Core.NF. Use decimal otatio for fractios with deomiators or. Also.NF. Other Examples as a decimal. Write _ Write 0. as a fractio i simplest form. I simplest form _ is. 0. is eight teths, or _. Fid a equivalet fractio with a deomiator of. Simplify the fractio _. ad are multiples of what umber? times what umber equals? Explai It Reaso Quatitatively Poit out to studets that, whe a problem cotais a fractio ad a decimal, it is helpful to chage oe umber so that it is i the same form as the other. How could you chage _ to a decimal with the same umber of decimal places as 0.? [Fid a fractio equivalet to with a deomiator of.] How could you chage 0. to a fractio? [Write it as a fractio with a deomiator of.] How ca you use equivalet fractios to chage a fractio to a decimal? A pa of corbread was divided ito equal of the pieces, ad out of pieces or _ corbread remais. Write a fractio equivalet, ad the chage the fractio to a decimal. to _ Other Examples Look at the first example. What questio could you ask yourself to decide if you first eed to chage to simplest form? [Ca I multiply by a umber to get or?] What is the aswer to your questio? [] Could you fid a fractio equivalet to _ that has a deomiator of? Explai. [; There is o whole umber I ca multiply the deomiator by to get a deomiator of.] Equivalet Fractios ad Decimals _ is twety-five hudredths, or 0.. So, _ is eight teths, or. So, 0. Explai It. Reaso Why is the fractio ot writte as 0.? See margi. as a. What steps would you take to reame equivalet fractio with a deomiator of? See margi.. S ample aswer: 0. ad _ 0. is ot equivalet to 0. MTH_SE0_CCTK_TPC_L0A.idd. Sample aswer: First I would fid what umber to multiply by to get i the deomiator. That umber is. The I would multiply the umerator ad deomiator by : 0 ad. So 0. 7// MT :

4 Write _ as a decimal. How do you simplify to _? [Divide both ad by.] How do you kow that _ is i simplest form? [The oly whole umber that you ca divide ad by is.] Multiply to fid a equivalet fractio with a deomiator of. times what umber equals? _ _ 7 _ _ 7 7 _ is sevety-five hudredths, or 0.7. I simplest form _ is. Fid a equivalet fractio with a deomiator of. times what umber equals? Write as a decimal. times what umber equals? 7 _ 7 _ is five teths, or 0.. Guided Practice Do you kow HOW? Do you UNDERSTAND? For through, write each fractio as a decimal _ Write a fractio ad a equivalet decimal to show the part of the corbread that has bee eate. _ or 0.. Writig to Explai Whe you write a fractio as a decimal, why do you eed to reame the fractio as a equivalet fractio with a deomiator of or? _ 7 _... _ 7. _. _ _ 0. or , 0. 0., 0.. _, 0., 0.., _, 0., 0... _, 0.0, _., 0.0, , 0.0 Exercise Error Itervetio If studets multiply oly the umerator or deomiator of the fractio by, the review with them how to fid equivalet fractios. Remember, you must multiply the umerator ad the deomiator by the same umber to write a fractio that has the same value. Reteachig Work together with studets to write ad as decimals. Idepedet Practice For Exercises 0, remid studets that whe decidig if umbers are equivalet, it is helpful to have both umbers writte i the same form. Ecourage studets to write the fractios as decimals. However, keep i mid that some studets may choose to write the decimals as fractios I through 0, tell whether each pair shows equivalet umbers. Remid studets that whe chagig a fractio to a decimal, they should first ask themselves if they ca multiply the deomiator of the fractio to get or. If ot, ecourage them to try simplifyig the fractio. I through, write each fractio as a decimal. 0. See margi. Idepedet Practice. Guided Practice 7 _ is sevety-five hudredths, or 0.7. So, 0. of the corbread remais. 0. Multiply to fid a equivalet fractio with a deomiator of. Could you use the same steps to chage _ to a decimal as you used to chage to a decimal? Explai. [; _ is i simplest form already. Also, the deomiator ca be multiplied by to get the deomiator.] Could you use the same steps to chage to a decimal as you used to chage _ to a decimal? Explai. [; There is o whole umber I ca multiply the deomiator by to get the deomiator or.] Lesso -A 7. Sample aswer: So that the deomiator of the fractio is equivalet to the place value of the decimal. TH_SE0_CCTK_TPC_L0A.idd AM 7 7// : AM 7

5 Develop the Cocept Problem Solvig Studets use uderlyig processes ad mathematical tools for Exercises 0. Remid studets to check for reasoableess whe solvig each problem. Exercise Laguage of Math: Everyday Vocabulary The term battig average may be ew to studets. A battig average tells the umber of hits a player usually gets out of a certai umber of times at bat. The fractio _ tells you that Roger usually gets hits out of times at bat. However, sometimes he may get more or less. Poit out that battig averages are usually writte as a decimal to the earest thousadth without the 0 to the left of the decimal poit. Therefore, the battig average 0. or 0.0 would usually be writte.0. Exercise Use Bar Diagrams What hidde questio do you eed to aswer before you ca solve this problem? [How may days are i week?] How does the bar diagram show the aswer to this questio? [The bar is divided ito 7 parts, ad each part represets oe day.] Exercise Check for Reasoableess Ecourage studets to check the aswer they choose for reasoableess. Visualize _ of a shape shaded. About how much of the shape is shaded: a little less tha half, a little more tha half, or almost the whole shape? [Almost the whole shape] Is the value of the decimal you chose close to whole? [] Early Fiishers Have studets write ad solve a compariso problem similar to Exercise that is about a class of fourth graders. Have studets explai how they ca use equivalet fractios to chage a fractio to a decimal, usig _ ad as examples. Problem Solvig. Roger got hits out of times at bat. What is his battig average as a fractio i simplest form? The write a equivalet decimal. _ ; 0.. Critique Reasoig The model below represets whole. Maura says that the shaded part of the model Is Maura shows that _ correct? Explai why or why ot. See margi. Battig Average Number of hits Number of times at bat. A bad has 0 istrumets. Tyler says that of the istrumets are strig istrumets ad 0. of the istrumets are wid istrumets. Does the bad have the same umber of wid istrumets ad strig istrumets? Explai. See margi.. Gia wrote a -digit umber. She used each of the digits,,, ad 7 oce. How may differet -digit umbers ca Gia write?. Writig to Explai Which is greater, or 0.7? Explai your aswer. is equivalet to 7, ad Reaso The cell phoe was iveted i Swede i 7. How may years ago was the cell phoe iveted? 7. Write a fractio i simplest form ad a equivalet decimal to show what part of a dollar cets represets. (Hit: dollar cets.) _ ; umbers Aswer for 0: years For, use the diagram at the right The umbers are equal.? ewspapers i all. Kwa has 7 customers o his paper route. He delivers ewspapers every day. How may ewspapers does he deliver i oe week? 7 ewspapers. Reasoableess Betty s score o. a -poit quiz was out of, or What is writte as a decimal? Newspapers delivered each day 0. Nie of the studets i the school play are fourth graders. Which decimal represets the part of the studets that are fourth graders? A 0. B 0. A 0. C 0. B 0. D 0. C 0.7 D 0. Joural 7. Maura is ot correct; Sample aswer: The grid shows 70 or 0.7. To show 0.07, oly 7 small squares should be shaded. MTH_SE0_CCTK_TPC_L0A.idd writte as a decimal is 0... N o; Sample aswer: 0. 0., so the bad has fewer strig istrumets tha wid istrumets. 7// MT :

6 Solve each equatio for z.. z. z. z z z z. z. z. z z z z 7. z. z. z z z z Roud each decimal to the earest teth Fid the sum. Estimate to check if the aswer is reasoable.., 7. 7,,7,, 7. 7,0,7. 7, Reaso Fid each value of w that is ot correct. Write it correctly, ad explai the error.. 0 w 0. w 0. w. w w w w w See margi. Correct See margi. w 7; Divided icorrectly. Number Sese Costruct Argumets Write whether each statemet is true or false. Explai your aswer.. The expressio equals 7. True; or The product of ad is closer to,00 tha,00. False; is about 700,00.. The sum of ad 7 is less tha 00. False; The sum of ad 7 is about , ad The quotiet of 0 divided by is. False; The quotiet of 0 divided by ay ozero umber is always The product of ad is more tha 00. True; Usig metal math, 0 00,, ad 00.. The differece of ad 7 is greater tha 00. True; The differece is greater tha Lesso -A Exercises Reteachig Studets may have difficulty rememberig to work backward to solve the problem. Have them write out the problem i word form ad how to solve the problem i word form. Use Exercise as a example. Studets should say z divided by equals ad ask what divided by equals. Remid them to work backward from there. Ask studets what they eed to do to both sides of the equatio to isolate z. Exercises Studets ca exted previous kowledge about roudig umbers to the tes ad hudreds place whe workig o these exercises. What place value do you use whe roudig a umber to the hudreds place? [Tes] What place value will you use whe roudig a decimal to the teths place? [Hudredths] Exercises Reaso Quatitatively Discuss with studets commo errors they ca make whe solvig equatios. Remid studets to look closely at the operatio i each equatio ad decide if the give value for the variable is correct. Number Sese Exercise 7 Poit out that this exercise is differet from the others because it requires the use of two operatios. Remid studets that the word is separates the two quatities they are checkig for equality. What expressio represets the quatity to the left of is? [ ] What expressio represets the quatity to the right of is? [00 ]. w is icorrect. The correct solutio is w ; Foud the sum of ad 0 istead of the differece.. w is icorrect. The correct solutio is w ; Foud the sum of ad istead of the product.

7 Close/Assess ad Differetiate Close Essetial Uderstadig Every fractio ca be represeted by a ifiite umber of equivalet fractios, but each fractio is represeted by the same decimal or a equivalet form. I this lesso, you leared how to use equivalet fractios to chage a fractio to a decimal. Name Quick Check Master. Which shows as a decimal? A 0.0 B 0. C 0. D 0.. Which shows as a decimal? 0 A 0. B 0. C 0. D 0.0 Formative Assessmet Q A Use the Quick Check to assess studets uderstadig.. Which shows a pair of equivalet umbers? A 0 ; 0. B _ ; 0. C ; 0. D ; 0.7. Which shows a pair of equivalet umbers? A ; 0. B _ ; 0. C 0 ; 0. D _ 0 ; 0.0. Writig to Explai Whe writig as a decimal, why do you first eed to reame the fractio as ad the as? See studet samples to the right. Quick Check -A Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. ASSESSMENT Exercises are worth poit each. Use the rubric to score Exercise. Exercise Writig to Explai Studets should explai why they must first simplify to ad the write a equivalet fractio with a deomiator that is equivalet to a decimal place value. Model Thikig Aloud Help studets verbalize what they are thikig. Say, To chage a fractio to a decimal, I eed a fractio with a deomiator of or. I otice that the deomiator of _ is. Studet Samples -poit aswer The studet correctly explais why he or she must first simplify ad the writes a equivalet fractio with a deomiator that is equivalet to a decimal place value. -poit aswer The studet correctly shows chagig to a decimal but does ot explai why the steps are ecessary. The deomiator of _ is. I ca t multiply by ay whole umber to get, or. So first I eed to write _ I ca multiply the umerator ad deomiator of _ by to get the equivalet fractio. The fractio shows teths, so I ca write as the decimal 0.. _ i simplest form. That s _. = _ = = 0. -poit aswer The studet demostrates little or o uderstadig of how to chage a fractio to a decimal. _ = _ = Prescriptio for Differetiated Istructio Use studet work o the Quick Check to prescribe differetiated istructio. Poits Prescriptio 0 Itervetio O-Level 7 Advaced A

8 Differetiated Istructio Itervetio O-Level Advaced Par ter Par ter Talk Equivalet Fractios ad Decimals Sh 70 0 Remid studets that oe way to write a equivalet fractio is to multiply the umerator ad deomiator by the same umber. You ca write a fractio with a deomiator of as a decimal. What deomiators ca be multiplied by a umber to get a equivalet fractio with a deomiator of? [, ] Make a list as studets ame the deomiators. Work together to chage to to 0.. Get Started or Oe Whole Oe Whole Take turs. Say ay fractio that has i the deomiator. Your parter explais how to show that fractio o the grid ad says a equivalet decimal i hudredths. If you have more time Ceter Activity H -A Repeat for hudredths. Have studets ame a few deomiators for hudredths. k. are wor your t hikig while you Pick a umber tile to fid a decimal. Say that decimal. Explai how to show that decimal o the whole grid with parts. Explai how to fid a equivalet fractio. Cover the equivalet fractio with your umber tile. Display each 0 tile exactly oce. If you have a parter, take turs. 0 0 Sh k. are wor your t hikig while you Pick a umber tile to fid a fractio. Say the fractio. Explai how to show that fractio o the whole grid with parts. Explai how to fid the equivalet decimal. Cover the equivalet decimal with your umber tile. Display each 0 tile exactly oce. If you have a parter, take turs. Get Started or mi Talk If you have more time Try agai. This time say the equivalet fractio i the grid ad aother equivalet fractio for each decimal. Ceter Activity HH -A Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. MTH_ANC_TRM_CA-0a.idd 7// :7 PM Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. MTH_ANC_TRM_CA-0a.idd 7// : PM : Parter Talk Liste for ames of equivalet decimals. For example, a studet might say, Two teths is equivalet to twety hudredths because there are te hudredths i every teth. Leveled Homework Reteachig Master Practice Master Reteachig Name Name -A Equivalet Fractios ad Decimals equals?. _ 0 0. ; 0.. ;. _ _ 0.. Which decimal is equivalet? to _ 0. _ 7. _ _ 0 0. Tell whether each pair shows equivalet umbers. ; 0... _ ; 0.. ; 0. R A Write a fractio i simplest form ad a decimal for the shaded part of each shape.. _ A 0.0 C 0. B 0. D 0. ; 0.. _ ; Kevi has 0 words to lear for his spellig test o Friday. He has leared of the words. of the So, he has leared _ 0 i simplest form, words. Write _ 0 ad fid a equivalet decimal. 0. Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. 7// :7 PM etools Fractios MTH_ANC_TRM_P-0a.idd ; 0. ; 0. ; 0. _.. is greater. Gia wrote that tha 0.7. Is Gia correct? Explai why or why ot. ; 0. ; ad ; 0. > 0.7. P a.. Shade some parts of each shape below. Write a fractio i simplest form ad a decimal to represet the shaded part of the shape. 7. as. Sample aswer: I reamed _ Next, I multiplied the umerator ad deomiator by :. 0., 0.. so _ 0 ; 0. ; 0.. _.. 0. Look at Exercise. Explai how you decided whether the umbers are equivalet. 7 ; 0.. _. Nie out of, or _, of the people at the skatig rik brought their ow. skates. Write a equivalet decimal for _ MTH_ANC_TRM_R-0a.idd 0. ; Write each fractio as a decimal.. 0. A rock bad has members, of the members play ad strig istrumets. Also, 0. of the members sig. Does the bad have the same umber of strig istrumet players as sigers? Explai ; _. _ I through, tell whether each pair shows equivalet umbers. I through, fid the missig umbers. The write each fractio as a decimal.. _. _ 0. Step Reame the fractio Step Write the decimal. usig a deomiator of, _ is five teths., or,000. _ = 0. Thik: What = _ umber times So, _ = 0. _ =.. _. -A Visualize Fractios ad Decimals I through, write each fractio as a decimal. Write _ as a decimal. Erichmet Name -a Equivalet Fractios ad Decimals A fractio ad a decimal ca both be used to represet the same value. Step Write the fractio i simplest form. Erichmet Master Practice. Aswers may vary. Check studets Aswers may vary. Check studets work. work. E A Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. 7// :0 PM etools Fractios MTH_ANC_TRM_E-0a.idd Copyright Pearso Educatio, Ic., or its affiliates. All Rights Reserved. 7// : PM etools Fractios B