G r a d e. 5 M a t h e M a t i c s. Number

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1 G r a d e 5 M a t h e M a t i c s Number

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3 Grade 5: Number (5.N.1) edurig uderstadigs: the positio of a digit i a umber determies its value. each place value positio is 10 times greater tha the place value positio to its right. Geeral outcome: develop umber sese. specific LeArNiNG outcome(s): AchievemeNt indicators: 5.N.1 Represet ad describe whole umbers to [C, CN, T, V] Write a umeral usig proper spacig without commas (e.g., ad ot 934,567). Describe the patter of adjacet place positios movig from right to left. Describe the meaig of each digit i a umeral. Provide examples of large umbers used i prit or electroic media. Express a give umeral i expaded otatio (e.g., = [4 x ] + [5 x 1000] + [3 x 100] + [2 x 10] + [1 x 1] or ). Write the umeral represeted i expaded otatio. Prior Kowledge Studets may have had experiece with the followig: Represetig ad describig whole umbers to pictorially ad symbolically Comparig ad orderig whole umbers to Demostratig a uderstadig of additio of umbers with aswers to Demostratig a uderstadig of subtractio of 3- ad 4-digit umbers N u m b e r 3

4 BacKgroud iformatio For studets to work effectively with large umbers, they eed to have a good uderstadig of the structure of our umeratio system. The Hidu-Arabic, or base-10, umeratio system that we use today origiated i Idia aroud 500 CE, ad was carried to other parts of the world by Arab people. The system gradually replaced the use of Roma umerals ad the abacus i trade ad commerce i Europe ad, by the 16th cetury, was predomiat. The features of the system that led to its acceptace ad the computatioal procedures we use today iclude the followig: 1. It cosists of 10 digits (symbols), 0, 1, 2, 3, 4, 5, 6, 7, 8, ad 9, that are used i combiatio to represet all possible umbers. 2. It has a base umber. I this system, 10 oes are replaced by oe group of 10, 10 tes are replaced by oe hudred, 10 hudreds are replaced by oe thousad, ad so o. The umber of objects grouped together is called the base of the system. Thus, the Hidu-Arabic system is a base-10 system. 3. It has place value. Each place i a umeral has its ow value. For ay place i the system, the ext positio to the left is 10 times greater ad the positio to the right is oe-teth as large. 4. It has a symbol for zero. The symbol has two fuctios. It is a placeholder i umerals like 5027, where it idicates there are o hudreds (or 50 hudreds). It is also the umber that idicates the size of the set that has o objects i it. 5. It is additive ad multiplicative. The value of a umeral is foud by multiplyig each place value by its correspodig digit ad the addig all the resultig products. Expressig a umeral as the sum of its digits times their respective place values is called expaded otatio. For example, the expaded otatio for 8273 is (8 x 1000) + (2 x 100) + (7 x 10) + (3 x 1) or Cosequetly, the focus of the learig experieces that follow is o helpig studets coceptualize the magitude of large umbers ad uderstadig the characteristics of our umeratio system that allow us to read, write, ad iterpret the umerals for these umbers. mathematical laguage Base Digit Expaded otatio Hudred thousad Oe millio Place value Te thousad 4 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

5 learig experieces Assessig Prior Kowledge Materials: BLM 5.N.1.1: Place Value Orgaizatio: Idividual a) Tell studets that i the ext few lessos they will be learig about umbers greater tha , but before they begi you eed to fid out what they already kow about large umbers. b) Ask studets to complete the activity foud o BLM 5.N.1.1. Observatio Checklist Use studets resposes to the questios to determie whether they ca do the followig: compare ad order whole umbers i the thousads write umbers i words idetify the place value positio of the digits i a umeral idetify the value of each digit i a umeral provide examples of large umbers used i prit or electroic media. Materials: A Millio Dots by Adrew Clemets, calculators, stopwatch or timer with a secod had. Orgaizatio: Whole class/small groups a) Ask studets, How may dots do you thik you ca draw i oe miute? If we couted all the dots everyoe i the class makes i oe miute, how may dots do you thik we would have altogether? Do you thik we would have a millio dots? b) Explai that a millio is a big umber ad they are goig to fid out what a millio dots looks like. c) Read A Millio Dots. d) After readig the book, ask studets whether they wat to chage their estimates of the umber of dots that they ca draw i oe miute Have studets draw dots for oe miute. Whe they fiish, have them suggest ways to cout the dots. Ecourage them to thik about makig groups of tes to facilitate the coutig process. N u m b e r 5

6 e) Have studets use the total umber of dots that they make i oe miute to determie how log it would take oe perso to make a millio dots the class to make a millio dots f) Have each group decide what else they could do to show how big a millio is. Help them devise ad carry out a pla for showig the magitude of the umber. For example, studets could determie the legth of 1 millio looies laid ed to ed the umber of pages a telephoe book would eed to have to list 1 millio people the umber of boxes of toothpicks they would eed to make a millio g) Have each group share their plas ad what they foud out about 1 millio with the other members of the class. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: make reasoable estimates solve computatioal problems with ad without usig techology develop ad carry out a pla for solvig a problem idicate that they have a sese of the magitude of 1 millio describe the patter of adjacet place positios movig from right to left. Materials: Blak Hudred Square (BLM 5 8.6), scissors, tape, or stapler. Orgaizatio: Small groups a) Write the umbers 600 ad 60 o the board or o a overhead. Ask studets, Would you rather have 600 peies or 60 peies? Have studets explai their reasoig. b) Explai that the place of a digit withi a umber is importat because it tells us the value of the digit, ad today they will be learig more about place value. 6 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

7 c) Poit to each digit i the umeral 600 ad ask studets, What is the place value positio of this digit? Write studets resposes o the board or overhead, ad show studets that the oes ca be represeted with a square, the tes with a strip of 10 squares, ad hudreds with a grid of 100 squares. d) Ask studets, What place value positio comes ext? How ca we use the hudred squares to show 1000? Let studets explore differet ways to arrage the hudred squares to make Each studet should the make a 1000-strip by tapig or staplig te of the hudred squares together. e) Ask studets questios about the relatioship betwee the differet place value positios. For example: How may hudreds i oe thousad? How may times larger is oe thousad tha oe hudred? How may tes are i oe hudred? How may times larger is oe hudred tha te? How may tes are i oe thousad? How may times larger is oe thousad tha te? f) Ask studets, What place value positio comes ext? How much larger tha the thousads positio should the ew place value positio be? Why do you thik this? How ca we use the 1000-strips to show the ext place value positio? Have groups of 10 studets staple or tape their 1000 strips together. Whe studets fiish makig their square strips, ask them questios about the relatioship betwee the differet place value positios similar to the oes i part (e). g) Have studets i each group work together to aswer these questios: What place value positio comes ext? What is the relatioship of this positio to the other place value positios? What would a model of this place value positio look like? Have each group share its aswers with the other members of the class. Ecourage studets to explai their reasoig. h) Repeat part (g) to itroduce studets to the millios positio. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: recogize that each place is 10 times greater tha the place to its right describe the various relatioships amog the place value positios (e.g., is 100 times greater tha 100 ad 1000 times greater tha 10) describe place value positios to the millios N u m b e r 7

8 Write a umeral usig proper spacig without commas. Materials: Paper ad pecils, overhead copy of place value chart whole umbers (BLM 5 8.7) Orgaizatio: Whole class/pairs a) Write a umber o the board or overhead (e.g., ), ad ask studets, How do you read the umber? How do place value patters help us read umbers? b) Show studets a place value chart. Explai that whe we read ad write large umbers, we group the digits ito threes. Each group of three forms a family. Each family has a differet last ame ad is separated from the other families by a space. The family o the far right is the oes. The family to its immediate left is the thousads. The ext family o the left is the millios. I each family, there is a place for oes, tes, ad hudreds. c) Tell studets that, for the remaiig time, they will be focusig o umbers i the thousads family. Record a umber i the place value chart (e.g., ), ad explai how to read the umber ad what each digit i the umber meas. Do three or four more examples. d) Have studets work with their parter. Studets eed to sit so oe perso i a pair ca see the board ad the other oe caot. Write a umber o the board (e.g., ). Studets facig the board read the umber to their parter. Their parter writes the umber dow. Studets the compare the umber they wrote dow with the umber o the board. Repeat the activity several times, givig each studet a opportuity to be both the reader ad the writer. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: read a umber correctly write a umeral correctly with proper spacig 8 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

9 describe the meaig of each digit i a umeral. Materials: Number cards with the umbers 0 through 9 (BLM 5 8.5) with oe umber per card, ad large strips of paper showig the place value headigs (BLM 5.N.1.2), oe for each group Orgaizatio: Small groups (group size depeds o the size of the umbers) a) Put the place value colum headigs o the walls so they are just above the studets heads. b) Say a umber (e.g., ). Studets i each group must fid the appropriate umber cards, the arrage themselves ito a lie udereath the colum headigs showig the umber you said. Ecourage studets to tell what each digit i the umber meas. Have studets repeat the activity several more times. c) Expad the place value colum headigs to iclude hudred thousads ad have studets form 6-digit umbers. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: idetify the place value positio of each digit i a umber describe the meaig of each digit i a umber N u m b e r 9

10 describe the meaig of each digit i a umeral. Materials: Noe Orgaizatio: Whole class a) Tell studets they will be doig some umber calistheics. Explai that they will be actig out a umber you write o the board or overhead projector. They must act out the umber by doig i sequece: as may hops o their left foot as specified by the value of the digit i the hudred-thousads as may jumpig jacks as the value of the digit i the te-thousads positio as may clap-your-hads as i the value i the thousads positio as may touch-your-toes as the value i the hudreds positio as may hops o their right foot as the value of the digits i the tes place as may figer saps as the value of the digits i the oes positio For example, for the umber , studets would do 2 hops o their left foot 4 jumpig jacks 3 clap-your-hads 1 touch-your-toes 6 hops o their right foot 7 figer saps b) Have studets act out ; ; ad Whe studets are familiar with the movemets for each place value positio, have them act out 3-digit, 4-digit, 5-digit, ad 6-digit umbers. c) Vary the activity by havig studets choose the umbers that they act out. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: idetify the correct place value positio of each digit i the umber idetify the value of each digit i a umber 10 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

11 Write a umeral usig proper spacig without commas. Materials: Paper ad pecils Orgaizatio: Whole class a) Write four or five umbers o the board that use differet arragemets of the same digits. For example: b) Read oe of the umbers (e.g., te thousad five hudred thirty). Ask the studets to tell you which oe you chose. Have studets explai how they kew which umber you read. Ecourage studets to describe what the zeros i each umeral mea. c) Cotiue readig the umbers ad havig studets idetifyig them. Whe they fiish idetifyig all the umbers, have them order the umbers from smallest to largest ad the write the umbers i expaded otatio. d) Repeat the activity usig differet sets of umbers. e) Vary the activity by usig six-digit umbers istead of five-digit umbers. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: describe the meaig of each digit i a umeral describe the patter of place value positios movig from right to left idetify the place value positio of each digit i a umeral express a umeral i expaded otatio N u m b e r 11

12 Write a umeral usig proper spacig without commas. express a give umeral i expaded otatio. Materials: Dice Orgaizatio: Small groups a) Distribute six dice to each group. Tell studets that they will be tossig the dice five times. The first time they roll the dice they should create a six-digit umber with the umbers that they roll. They should record the umber ad the write it i expaded otatio. Next, they should remove oe die ad roll the remaiig five dice to create a five-digit umber. Agai, they should write the umber i both stadard otatio ad expaded otatio. Studets should cotiue removig a die, creatig a umber with the umbers that are rolled, ad recordig the umbers i stadard otatio ad expaded otatio util they have oe die left. b) Have each group share its results with the other members of the class. c) Vary the activity by havig studets write the umber i stadard otatio ad i words. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: write a umeral usig proper spacig without commas express a give umeral i expaded otatio write a umeral i expaded otatio 12 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

13 Write a umeral usig proper spacig without commas. express a give umeral i expaded otatio. Write the umeral represeted i expaded otatio. Materials: Calculators, overhead of the excerpt from Which Do You Prefer Chuky or Smooth? (BLM 5.N.1.3) Orgaizatio: Idividual a) Have studets read the excerpt show below. Ask them to rewrite the umber words usig umerals ad rewrite the umerals usig umber words. I additio, have studets write each of the umbers i expaded otatio. I her book called Which Do You Prefer Chuky or Smooth?, Heather Brazier tells us the followig: O a average day i Caada we cosume eighty thousad, eight hudred forty-ie kilograms of peaut better. Of the total, kg are chuky (46) b) Have studets figure out how much smooth peaut better must be eate by Caadias o a average day. Have them write their aswer as a umeral ad i words. c) Throughout the year, have studets brig i examples of large umbers that they fid i ewspapers or magazies. Keep a class chart that shows the umber i umerals, expaded form, ad words. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: write umbers i word form write the umeral for a umber writte i words write a umeral i expaded otatio provide examples of large umbers used i prit or electroic media N u m b e r 13

14 describe the meaig of each digit i a umeral. Materials: Calculators Orgaizatio: Whole class Procedures: a) Ask studets to show o their calculators. Tell them that their goal is to chage the 2 to 0 (zero it) by subtractig oe umber. Whe studets fiish, ask them the followig: What umber do you have o your calculator ow? What umber did you subtract to wipe out the 2? Why did you subtract that umber? b) Cotiue askig studets to show five-digit ad six-digit umbers o their calculators. After you ame a umber for them to show o their calculators, ask them to zero a digit i oe of the place value positios. Ecourage studets to describe what they did ad why they did it to zero a digit. c) Ask studets to add a umber to wipe out a digit (e.g., addig 4 ca wipe out the 6 i 506). d) Vary the activity by tellig studets that they ca use either additio or subtractio to wipe out a digit. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: idetify the place value positio of each digit i a umeral idetify the value of each digit i a umeral use techology to compute sums ad differeces 14 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

15 Materials: Number cards (BLM 5 8.5) (oe set per studet) Orgaizatio: Groups of three or four a) Tell studets that they will be playig a place value game. Explai how to play the game. 1. Had each studet a complete set of cards. Oce studets are i the group, all cards should be combied together. 2. Shuffle the cards ad lay them face dow i the playig area. 3. Players take turs drawig five cards from the deck. 4. Players arrage the cards i their hads so that they have the largest possible umber. 5. Oe player says, Let s see the umbers ad everyoe lays their cards face up i frot of them. A card caot be moved after it has bee placed face-up o the playig surface. 6. Players take turs readig the umber that they created. The player who has the largest umber ad reads the umber correctly wis a poit. 7. The wier is the perso with the most poits after five rouds of the game. b) Demostrate how to play the game ad aswer ay questios that studets may have. Have studets play the game. c) Vary the game by havig studets draw six cards istead of five create the smallest possible umber with their cards Observatio Checklist Observe studets resposes to determie whether they ca do the followig: read 5-digit ad 6-digit umbers correctly use place value cocepts to determie which of two or more umbers is the largest use place value cocepts to determie which of two or more umbers is the smallest N u m b e r 15

16 Write a umeral usig proper spacig without commas. describe the meaig of each digit i a umeral. Materials: Calculators, paper ad pecils Orgaizatio: Pairs a) Tell studets that they will be playig a game called Give ad Take. Explai how to play the game. 1. Players write dow a six-digit umber cotaiig o zeros ad o idetical digits. Players keep their umbers hidde from each other throughout the game. 2. Players take turs beig the giver ad the taker. Each player tries to icrease his or her umber by takig digits from the other player. 3. A tur begis whe the asker says: Give me your x s, where x ca be ay digit from 1 through 9. (e.g., Give me your 7s. ). 4. If that digit is i the giver s umber, the giver aouces its place value (e.g., You get 700. If the digit is ot i the giver s umber, the giver aouces this by sayig, You get zero. ). Note that the value of a digit that is asked for depeds o its positio i the giver s umber. If 7 is asked for ad the umber is , the the giver says, You get 700. If the giver s umber is , the the giver says you get As soo as the giver respods with the umber, the asker adds that amout to his or her umber (e.g., + 700) ad the giver subtracts that amout from his or her umber (e.g., 700). 6. Players umbers chage with each ew additio or subtractio. Players always use the most recet form of their umbers whe addig, subtractig, or aoucig the place value of a digit. Players keep track of their chagig umber by addig ad subtractig from their origial umber ad its successors. For example: = = If the same digit appears two or more times i a giver s umber durig play, the giver ca say either of its values (e.g., for 845, 218, the giver ca say 8 ad ot metio the ). 8. The game eds after each player has had five turs as asker. Players check each other s additio ad subtractios. The player with the largest umber is the wier. 16 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

17 Observatio Checklist Observe studets resposes to determie whether they ca do the followig: idetify the correct place value positio of each digit idetify the value of each digit i a umber use calculators correctly to determie sums ad differeces write a umeral with the proper spacig with o commas N u m b e r 17

18 N o t e s 18 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

19 Grade 5: Number (5.N.2) edurig uderstadigs: computatioal estimatios produce approximate aswers. Geeral outcome: develop umber sese. specific LeArNiNG outcome(s): AchievemeNt indicators: 5.N.2 Apply estimatio strategies, icludig frot-ed roudig compesatio compatible umbers i problem-solvig cotexts. [C, CN, ME, PS, R, V] Provide a cotext for whe estimatio is used to make predictios check reasoableess of a aswer determie approximate aswers Describe cotexts i which overestimatig is importat. Determie the approximate solutio to a problem ot requirig a exact aswer. Estimate a sum or product usig compatible umbers. Estimate the solutio to a problem usig compesatio, ad explai the reaso for compesatio. Select ad use a estimatio strategy to solve a problem. Apply frot-ed roudig to estimate sums (e.g., is more tha = 800) differeces (e.g., is close to = 700) products (e.g., the product of 23 x 24 is greater tha 20 x 20 or 400 ad less tha 25 x 25 or 625) quotiets (e.g., the quotiet of is greater tha or 200) N u m b e r 19

20 Prior Kowledge Studets may have had experiece with the followig: Addig whole umbers with sums less tha Subtractig whole umbers with differeces less tha Usig differet strategies to estimate sums ad differeces Multiplyig a 1-digit whole umber times a 2-digit or 3-digit whole umber Usig a persoal strategy to estimate a product Dividig a 2-digit whole umber divided by a 1-digit whole umber divisor Usig a persoal strategy to estimate a quotiet related Kowledge Studets should be itroduced to the followig: Demostratig a uderstadig of multiplicatio (1- ad 2-digit multipliers ad up to 4-digit multiplicads) Demostratig a uderstadig of divisio (1- ad 2-digit divisors ad up to 4-digit divideds) BacKgroud iformatio Computatioal estimatio is the process of determiig approximate aswers to computatioal problems. Studets who are skillful estimators have a good grasp of basic facts, place value, ad the operatios of additio, subtractio, multiplicatio, ad divisio. They are also adept at metal mathematics ad flexible i their use of estimatio strategies, such as the oes described below. Frot-Ed Estimatio: Frot-ed roudig ivolves idetifyig the most sigificat (left-most) digits i a questio, performig the appropriate operatio, ad determiig the place value of the digits. For example: is more tha 1700 sice = 17 (ad aex the zeros) (or sice = 1700) is approximately 300 sice 5 2 = 3 (ad aex the zeros) (or sice = 300) 4 x 728 is more tha 2800 sice 4 x 7 = 28 (ad aex the zeros) (or sice 4 x 700 = 2800) is more tha 300 sice 9 3 = 3 (ad aex the zeros) (or sice = 300) 20 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

21 Note: It is importat for teachers to emphasize estimatio skills. Discourage studets from calculatig first, the estimatig (e.g., I kow is 7.2, so I will estimate it is close to 7. ). Although frot-ed roudig ca be used with ay operatio, it is most powerful whe addig ad multiplyig. With these two operatios, the computatio is always uderestimated. Compatible Numbers: This strategy ivolves searchig for pairs of umbers that are easy to compute. Whe usig this strategy, studets look at all the umbers i a problem, ad chage or roud the umbers so they ca be paired usefully with aother umber. It is particularly effective for divisio. For example, i the questio , roudig the divided to 2300 (the closest hudred) or 2000 (the closest 1000) does ot facilitate the estimatio process. However, roudig it to 2400 (a compatible umber because it is divisible by 6) makes estimatig the quotiet easier. This strategy is also useful for additio. For example, whe addig several umbers, studets look for umbers that ca be paired or grouped together to make multiples of 10. about about 100 about Therefore, the sum of is about 200 or about 100 Compesatio: Compesatio ivolves refiig, or adjustig, a origial estimate that was obtaied with aother strategy. For example, the frot-ed estimatio of 220 for the sum ca be adjusted to 240, sice ad (the umbers i the oes positio) are both close to 10. Similarly, the frot-ed estimatio of 2400 for 43 x 62 ca be adjusted to 2600 sice (3 x 60) + (2 x 40) would be greater tha 200. Also, for 44 x 54, for example, you ca roud oe umber up ad oe umber dow ad compute 50 x 50 for a estimate of 2500, rather tha frot-ed roudig for a estimate of I may istaces, differet strategies ca be applied to the same problem. The choice of strategies depeds o the studets, the umbers, ad the operatios ivolved. Teachers eed to help studets become aware of the various strategies ad help them develop cofidece i their ability to estimate. To do this, they eed to egage studets i discussios about the strategies they used to estimate the solutio to a computatioal problem (Sharig strategies ca lead to the developmet ad use of ew strategies.) accept a rage of estimates i order to help studets uderstad that there is o oe right estimate ecourage studets to idetify real-world situatios that ivolve estimatios N u m b e r 21

22 icorporate estimatio throughout their istructioal programs (Like problem solvig, estimatio should ot be taught i isolated uits.) mathematical laguage Aex Approximate Compatible umbers Compesatio Estimate Estimatio Frot-ed roudig learig experieces Assessig Prior Kowledge Materials: Noe Orgaizatio: Idividual a) Tell studets you eed to kow what they kow about computatioal estimatio so you ca help them become better estimators. To fid out what they kow, give them some problems to estimate. Tell studets that you will show them several problems, oe at a time, ad they will have a appropriate amout of time (decide this based o idividual studets approximately 30 secods) to estimate the solutio to each problem. They must record their estimate before their time is up. b) Give studets the followig problems: x x c) Have studets share their estimates ad the strategies they used to determie them. 22 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

23 Observatio Checklist Check studets resposes to the problems to determie whether they ca estimate the solutios to additio, subtractio, multiplicatio, ad divisio problems. Use the class discussio to fid out what strategies studets use to make their estimates. provide a cotext for whe estimatio is used. Materials: Markers ad ewspapers/magazies Orgaizatio: Whole class a) Tell studets that they are goig to ivestigate the use of estimated ad exact umbers. b) Give studets copies of differet ewspapers. Ask them to circle the umbers used i the headlies ad articles. Next, have studets review the cotext for the use of each circled umber to determie whether the umbers i the headlies or articles refer to exact or estimated (approximate) values. For example, have studets decide whether these statemets take from a ewspaper refer to exact or estimated values: Oe millio people evacuated from New Orleas The codo resold for $ Last year, tos of scrap metal were recycled c) Egage studets i a discussio about the umbers they foud i the ewspapers. Ecourage them to explai why they thik a give umber is exact or estimated. Have studets discuss why estimated umbers are ofte used i ewspaper articles (e.g., estimated umbers are easier to iterpret ad use). Observatio Checklist Observe studets resposes to determie whether they ca do the followig: idetify real-world examples of estimated umbers distiguish betwee exact ad estimate (approximate) umbers give a reasoable explaatio why a umber is either exact or estimated N u m b e r 23

24 Materials: Situatio Cards (BLM 5.N.2.1) ad idex cards Orgaizatio: Small groups a) Give each group a card with oe of the situatios o it. b) Ask studets to decide whether the situatio o their card requires a estimated aswer or a exact aswer, ad to list the reasos for their respose. c) Have each group read its situatio to the other members of the class, ad explai why they thik the situatio requires a estimated or exact aswer. d) Have each group create a situatio card. Each group should record, o a separate piece of paper, the reasos why they thik the situatio they created requires a estimated or exact aswer. Have the groups exchage cards ad decide whether the ew situatio they were give requires a estimated or exact aswer ad why they thik so. Each group should compare its respose with the respose of the group who created the situatio. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: provide a cotext for whe estimatio is used to approximate a aswer provide a cotext for whe estimatio is used to predict a aswer distiguish betwee situatios that require a exact aswer ad those that require a estimated aswer give reasoable explaatios of why a situatio requires either a exact or estimated aswer 24 G r a d e 5 M a t h e m a t i c s : s u p p o r t d o c u m e t f o r t e a c h e r s

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