G r a d e. 2 M a t h e M a t i c s. statistics and Probability

Transcription

1 G r a d e 2 M a t h e M a t i c s statistics ad Probability

2

3 Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used to aswer questios. essetial Questios: Why do we collect data? how ca data be collected ad recorded? SPecific LeAriG outcome(s): Achievemet idicators: 2.SP.1 Gather ad record data about self ad others to aswer questios. [C, CN, PS, V] 2.SP.2 Costruct ad iterpret cocrete graphs ad pictographs to solve problems. [C, CN, PS, R, V] Formulate a questio that ca be aswered by gatherig iformatio about self ad others. Orgaize data as it is collected usig cocrete objects, tallies, checkmarks, charts, or lists. Aswer questios usig collected data. Determie the commo attributes of cocrete graphs by comparig a set of cocrete graphs. Determie the commo attributes of pictographs by comparig a set of pictographs. Aswer questios pertaiig to a cocrete graph or pictograph. Create a cocrete graph to display a set of data ad draw coclusios. Create a pictograph to represet a set of data usig oe-to-oe correspodece. Solve a problem by costructig ad iterpretig a cocrete graph or pictograph. s t a t i s t i c s a d P r o b a b i l i t y ( d a t a a a l y s i s ) 3

4 Prior Kowledge Studets may have had o formal istructio i statistics. BacKgroud iformatio A pictograph uses uiform, represetative pictures to depict quatities of objects or people. It is used whe the data are discrete (o-cotiuous). The symbols used must be the same size ad shape to avoid misleadig the audiece. Example of a pictograph: Pictographs eed to have a title, labels, ad pictures. Legeds/keys are eeded whe the pictures or symbols are used to represet more tha oe quatity (may-to-oe correspodece). A cocrete graph is made usig the actual objects or people o a graphig mat. Cocrete graphs eed to have a title ad labels. A graphig mat is made from thick plastic sheetig (the type that ca be bought off the roll at a hardware store). Oe side has squares large eough for a perso to stad o. These are made usig maskig tape. There is usually room for three colums ad 10 rows. The secod side has tile-sized squares agai made with maskig tape. There is usually room for five colums ad at least 12 rows. 4 G r a d e 2 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 As childre collect objects, they aturally sort, cout, ad compare. Sortig, coutig, ad comparig are the basis for uderstadig statistics. Childre also aturally ask questios to gather iformatio. Teachers ca use classroom experieces as sources of iformatio to capitalize o childre s iterests ad to help them see that statistics are a part of everyday life. As well, data collectio provides a way to coect mathematics to other subject areas. Good questios are a itegral part of data collectio. Studets eed practice formulatig questios i more tha oe way. By examiig the possible aswers to a set of similar questios, studets ca determie which oe will best provide the desired data. Note: Surveys should be made maageable by obtaiig iformatio from a small populatio (e.g., o larger tha a sigle class), ad by limitig the umber of categories to two or three. Teachers eed to model ad develop the laguage of statistics i oral ad writte formats. mathematical laguage categories match least label more cocrete graph title less pictograph data same amout as compare tallies most survey learig experieces Assessig Prior Kowledge Preset a questio such as, Do you have a pet at home? Ask studets what aswers are possible (yes or o). Ask for suggestios as to how you might gather the iformatio. The suggestios they make should reflect their prior experiece. Complete the survey ad discuss the results. s t a t i s t i c s a d P r o b a b i l i t y ( d a t a a a l y s i s ) 5

6 formulate a questio that ca be aswered by gatherig iformatio about self ad others. orgaize data as it is collected usig cocrete objects, tallies, checkmarks, charts, or lists. Aswer questios usig collected data. suggestios for istructio Read a book such as The Best Vacatio Ever by Stuart J. Murphy or Charlie s Checklist by Rory S. Lerma. Both books have characters that formulate questios ad gather data. Discuss the questios chose ad the methods used to gather ad record the data. Model the formulatio of questios, such as I woder... How ca we fid out? Whom shall we ask? Use everyday occurreces to formulate questios about the childre s eviromet. Sample questios: How do you travel to school? Which kid of pizza did you order? Which author should we read this week? How may times ca you hop o oe foot? What is your favourite aimal? Model questios o the same topic i several ways ad allow the group to choose the best questio for its purpose. This is a importat process of data collectio that they will eed to practise. Examples: How did you travel to school today? Did you walk to school today? How may childre i our class used the school bus today? 6 G r a d e 2 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 Select a survey questio that ca be aswered yes or o. Model ways i which the data ca be collected. Examples: two differet colours of uifix cubes (oe for yes ad the other for o ) tallies a class list ad writig yes or o beside each perso s ame checkmarks Have studets aswer questios about the data. Examples: Which oe has the most/least? How may more? How may less? How may people were surveyed altogether? Math Routie: Questio of the Week Have pairs of studets take turs formulatig a survey questio, collectig the data, represetig it, ad the presetig their fidigs to the class. This ca be used as formative assessmet. Assessig Uderstadig Studets work i pairs. Have each group formulate a survey questio, collect the data, ad summarize the results by makig statemets about the data. s t a t i s t i c s a d P r o b a b i l i t y ( d a t a a a l y s i s ) 7

8 Determie the commo attributes of cocrete graphs ad of pictographs by comparig a set of cocrete graphs ad a set of pictographs respectively. Aswer questios pertaiig to a cocrete graph or pictograph. create a cocrete graph to display a set of data ad draw coclusios. create a pictograph to represet a set of data usig oe-to-oe correspodece. Solve a problem by costructig ad iterpretig a cocrete graph or pictograph. suggestios for istructio Model the costructio of a cocrete graph. Have studets formulate a questio ad decide the aswer choices. Make a label for each choice. Decide o a title for the graph ad write it o a strip of paper. Place the labels at the bottom of each colum of the graphig mat ad the title at the top or o the side. Have studets stad i the appropriate colum. Studets eed to be show how to lie up o the Idividual graphig mats ca be made from checkered or striped viyl. graphig mat start at the bottom, oe perso i each square, do ot skip squares. Discuss the results. Demostrate the use of oe-to-oe matchig as a strategy for comparig the data. Have studets hold hads with someoe from the ext colum ad cout studets without parters to determie the differece. Note: Data ca be trasferred to the pictograph usig a small grid ad studet pictures. Cocrete Graph Do You Like Pizza? No Yes Pictograph Note: Although pictographs cosist of uiform pictures, use studet photographs o a similar backgroud to make a class pictograph. 8 G r a d e 2 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 Use coloured cubes, pasta, cereal, or cadies, ad a small graphig mat. From the collectio of objects have studets select oe that represets their favourite colour. Make colour labels ad a title for the graph. Have studets place their object i the correct colum o the graph. Chage the cocrete graph to a pictograph by havig studets substitute a coloured square or circle for the actual object. Discuss the similarities ad differeces betwee the two graph types. Have studets create three differet represetatios of the same set of data. Example: Glue coloured pasta o the first grid. O the secod grid, draw ad color pasta pieces to represet the same iformatio that is o the first oe. Lastly, represet the same data with tallies. Discuss how the three grids are the same ad how they are differet. Costruct two differet cocrete graphs. Have studets compare the graphs ad idetify the commo attributes (title, labels). Costruct two differet pictographs. Have studets compare the graphs ad idetify the commo attributes (title, labels). I preparatio for the iterpretatio of data, lead studets to ask ad aswer questios about the iformatio o graphs. Example: Sample questios: What does the pictograph show? How do you kow? What does this tell about the colours of apples? Which do we like most? least? How may more are there of our most favourite colour tha our least favourite colour? Which do we like more yellow or gree? How do you kow? How may people were surveyed? How do you kow? s t a t i s t i c s a d P r o b a b i l i t y ( d a t a a a l y s i s ) 9

10 Provide meaigful opportuities for studets to collect, represet, ad iterpret data. Examples: vote o a class book to read collect data o the umber of suy, cloudy, raiy, sowy days i a particular moth decide o a game to play for idoor recess The sciece, social studies, ad health curricula provide meaigful cotexts for workig with data. Assessig Uderstadig 1. Show studets a cocrete graph or a pictograph. Have studets describe, orally or i writig, what the graph is showig (iterpret the data). 2. Give studets a set of data. Example: Do you have a cat? Yes No Have studets costruct a cocrete graph or pictograph usig the data. 10 G r a d e 2 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 Puttig the Pieces together Plaig a class celebratio Cotext Tell studets that they are goig to be plaig a class celebratio/special evet. Have them braistorm for thigs they would like to have at the celebratio (food, games, beverage, music, movie, etc.). Have studets work i parters or small groups. Assig each group (or have groups select) a category from the braistormed list. Have each group formulate a questio determie the aswer choices collect the data represet the data i graph form summarize the data i writte form preset the results to the class s t a t i s t i c s a d P r o b a b i l i t y ( d a t a a a l y s i s ) 11

12 N o t e s 12 G r a d e 2 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