Adding Mixed Numbers. Write each improper fraction as a mixed number in simplest form

Transcription

1 - - Plan What You ll Learn OJETIVE OJETIVE OJETIVE To a xe numbers To a xe numbers with renang n Why To fin total istances, as in Example heck kills You ll Nee For help, go to Lesson - Write each improper fraction as a xe number in simplest form 0 0 Explain how to simplify Explanations may vary ample: Divie by The quotient is the integer of the xe number The remainer is the numerator, an is the enonator: Reuce to Interactive lesson inclues instant self-check, tutorials, an activities Investigation: Using Mixe Numbers ut string into lengths of inches, inches, inches, inches, an inches Place two of the pieces en to en a Estimation Estimate the total length of the two pieces b Fin the actual length by aing heck your sum by measuring the total length of the two pieces heck stuent s work Repeat for several ifferent pairs of pieces Lesson Preview heck kills You ll Nee Writing Fractions as Mixe Numbers Lesson -: Example Extra Practice p Lesson Resources Teaching Resources Practice, Reteaching, Enrichment Reaching ll tuents Practice Workbook - panish practice Workbook - Guie Problem olving - Hans-On ctivities Presentation ssistant Plus! Transparencies heck kills You ll Nee - Problem of the Day - itional Examples - tuent Eition nswers - Lesson Quiz - PH Presentation Pro D-ROM - You can fin the sum of xe numbers by aing the whole number an fraction parts separately Then combine the two parts to fin the total omputer Test Generator D nswers may vary ample: It oesn t matter because aition is commutative heck Unerstaning EXMPLE Mentally Mental Math Fin = the whole numbers + = the fractions + = ombine the two parts Reasoning In Example, oes it matter whether you a the whole numbers or the fractions first to get the correct answer? Explain ee above left - Technology Resource Pro D-ROM omputer Test Generator D PH Presentation Pro D-ROM wwwphchoolcom tuent ite Teacher Web oe: aak-00 elf-graing Lesson Quiz PH uccessnet Teacher enter Lesson Planner Resources Plus INTNT HEK YTEM Ongoing ssessment an Intervention efore the Lesson Diagnose prerequisite skills using: heck kills You ll Nee During the Lesson Monitor progress using: heck Unerstaning itional Examples Test Prep fter the Lesson ssess knowlege using: Lesson Quiz omputer Test Generator D

2 Teach Math ackgroun ing xe numbers involves fining a common enonator for the fraction parts, aing the fractions, an then aing the whole numbers separately If the fraction portion of the sum is an improper fraction, you nee to change it to a xe number an a it to the whole number portion of the sum Teaching Notes Error Prevention! Watch for stuents who confuse LD (Least ommon Denonator), LM (Least ommon Multiple), an GF (Greatest ommon Factor) Inclusion You may nee to review how to fin the LD of two fractions EXMPLE Visual Learners Write or circle the enonators, using the same color to emphasize that they nee to be the same itional Examples Use mental math to fin Tyler juggle for hr uring the school week He juggle for hr over the weeken How many hours i he juggle in all that week? hr Fin 0 0 mother cat weighs lb Her kitten weighs lb How much o they weigh together? lb losure The top spee of a giant tortoise is about le per hour OJETIVE nimals giant tortoise travele yars an stoppe Then it travele yars Fin the total istance the giant tortoise travele Fin + Estimate + < + = The giant tortoise travele a total of With Renang EXMPLE Real-Worl Problem olving yars heck for Reasonableness The answer is close to the estimate of heck Unerstaning a ome stuents spent hours on Friay an hours on aturay working on a science project How long i the stuents work? h b Estimation Use estimation to check the reasonableness of your sum N, or Reaing Math You can rea the xe number as an The sum of the fraction parts may be an improper fraction If so, rename it as a xe number Then write the answer in simplest form EXMPLE Fin + The LD is Write the fractions with the same enonator the whole numbers Then a the fractions Rename as the whole numbers implify Fin each sum a b c heck Unerstaning The LD is Write as the whole numbers Then a the fractions How o you a xe numbers? the fraction parts, fining a common enonator, if neee Then a the whole numbers What o you nee to o if the sum of xe numbers inclues an improper fraction? hange the improper fraction to a xe number an a the whole numbers hapter ing an ubtracting Fractions Reaching ll tuents elow Level Give stuents xe number sums to rewrite with the LD hange to tenths: hange to eighths: vance Learners Match up,,, an D to the igits,,, an to solve this mystery problem D,,, D Inclusion ee note on page Visual Learners ee note on page

3 Hours at Practice Total Monay Tuesay heck Unerstaning EXERIE EXMPLE Real-Worl Problem olving ports Practice sports team practice for hours on Monay an for hours on Tuesay How long i the team practice? Fin The LD is Write as the whole numbers Then a the fractions Rename as the whole numbers The team practice for hours Number ense One recipe uses cups of lk nother recipe uses cups of lk You have cups of lk at home Do you have enough lk to make both recipes? Explain No; you nee c of lk, but you have only c For more practice, see Extra Practice Practice ssignment Guie Objective ore, 0 Extension 0 Objective ore, Extension Test Prep Mixe Review uitory Learners Exercises all on ifferent stuents to name the LD for each pair of xe numbers Practice - omplete to rename each xe number ??? Write each sum in simplest form Practice by Example Example (page ) Example (page ) Examples, (pages, ) Mental Math Fin each sum pples You have pouns of re apples an pouns of golen apples How many pouns of apples o you have? lb Fin each sum Exercise has been starte for you j occer uppose you play nutes uring the first half of a soccer game an nutes uring the secon half How many total nutes o you play? n Estimate the length of rope neee to go am grew three pumpkins for the pumpkin aroun a triangle with sies feet, growing contest The pumpkins weighe feet, an 0 feet pouns, pouns, an pouns Fin about ft the combine total weight of am s pumpkins pouns ompare using R,, or Use benchmarks to help 0 R R R R Reteaching - ome xe numbers can be ae mentally Example : Fin the whole numbers the fractions ombine the two parts Fin each sum 0 0 Or, you can follow these steps Example : Fin 0 Write with a common enonator the whole numbers 0 the fractions Rename as GP Use the Guie Problem olving worksheet with Exercise

4 Error Prevention! Exercises,, Ren stuents to label their answers with the correct units nswers may vary ample: like fractions: ; to the sum of the whole numbers: 0 ometimes; answers may vary ample: xe number: ; whole number: Mental Math ompare using R,,or + j + j 0 R R + j + j a Ties t low tie, the water is feet eep t high tie, the water epth increases by feet How eep is the water at high tie? GP ft b The next ay, the epth is feet at low tie The epth increases the same amount as the ay before What is the water epth at high tie? ft Writing in Math Explain how you can use mental math to fin the sum ee below left 0 Number ense Is the sum of two xe numbers always, sometimes,or never a xe number? Give examples to support your answer ee below left Publishing In a newspaper, an article is inches long nother article is inches long How much space is neee for both articles? in Fin each sum Fabric uppose you nee the amounts of Fabric olors fabric shown in the table to make a flag How olor Length (yars) much total fabric o you nee? y Re a Dogs You walk your og les to your frien s house, les to the park, an White le back to your house How far o lue you walk your og? b uppose a frien claims to walk a og twice as far as you o How far oes your frien walk? Fin each sum 0 0 nswers may vary ample: tretch Your Thinking opy the iagram Write the numbers,,,,, an in the circles so that the sum of the numbers along each sie of the triangle is ee left hapter ing an ubtracting Fractions

5 Test Prep Multiple hoice What is the sum of an? D What is the sum of an? I 0 F 0 G 0 H 0 I Take It to the NET Online lesson quiz at Which two numbers have a sum of? wwwphchoolcom Web oe: aaa-00 an an an D an hort Response Ruth s house is near a park that has a -le rollerblaing path 0 Ruth rollerblaes les from her house to the park he goes once aroun the path an then rollerblaes home a What is the total istance she rollerblaes? a-b ee margin b Explain how you foun your answer Mixe Review Lesson - Lesson - Practice Game Vacation Pero s faly rives 00 les in two ays The secon ay they rive 0 les less than the first ay How many les i they rive the first ay? 0 implify each expression + 0 0,000 How to Play Draw a square game boar an ivie it into smaller squares Write fractions in half of the squares an xe numbers in the other half Player circles any two numbers an then fins their sum The sum is ae to the player s score Player circles two ifferent numbers, fins the sum, an as it to his or her score Players take turns until all numbers have been chosen ny answer may be challenge If the answer is correct, the challenger loses a turn If the challenger corrects the answer, that sum is ae to the challenger s score The other player s turn is over without any change to his or her score The player with the greater total score wins That s ome um! ssess Lesson Quiz - Write each sum 0 0 lternative ssessment Each stuent in a pair writes several problems involving aition of xe numbers tuents exchange papers an write the sums in simplest form You may wish to allow stuents to use fraction bars to help them a the fractional parts of the xe numbers Have partners recor how they foun the sums Test Prep Resources For aitional practice with a variety of test item formats: Test-Prep, p Test-Taking trategies, p 0 Test-Taking trategies With Transparencies Exercises Encourage stuents to estimate before they fin the sum to elinate answer choices Enrichment - ritical Thinking Write the numbers in the boxes so that each row an each column of boxes has the given sum The sum is 0 The sum is ; ; ; ;; ; ; ; ; ; - The sum is [] a b by an appropriate metho such as fining the sum of the istance from her house to the park, istance aroun the lake, [] correct total without an istance back work shown OR home; correct explanation 0 ; OR with a computational with error a correct metho shown ; ; 0 0 ; ; ; 0