Grade 11 Performance Task

Transcription

1 Thermmeter Crickets 1. Classrm Activity 2. Student Task 3. Task Specificatins 4. Scring Rubric

2 Classrm Activity Nte: Since perfrmance tasks span different parts f the assessment system (summative, interim, and as part f the digital library f resurces), here are sme suggestins fr turning Thermmeter Crickets int a rich, classrm-based learning task: Use available nline resurces t explre crickets chirping (e.g., cunting chirps in sund clips r using apps designed t perfrm the calculatins). Ask students t determine hw changing t Celsius wuld affect the interpretatins. Cllect all f the different frmulas available fr predicting temperature based n the number f cricket chirps. Discuss similarities and differences. Fr which values f the independent variable are the different frmulas mre and less discrepant? (assumes the same variables and measurement units) Seek glbal understanding f why data can lead t different frmulas fr the same phenmenn. Setting the Cntext Teacher: Have yu ever heard crickets chirping? When d yu tend t hear this? What des it sund like? [Let students respnd and share infrmatin.] Teacher: "Interestingly, the speed at which crickets chirp has been fund t be related t the temperature. In fact, a number f different peple have develped frmulas ver the years t predict the temperature based n hw fast crickets are chirping. In this activity, yu will learn mre abut this relatinship." Teacher: Yu will be wrking in small grups t learn sme backgrund infrmatin abut crickets. Each grup will be given a cricket fun facts sheet and a slip f paper with ne questin abut crickets. Yur grup will have apprximately 5 minutes t review the cricket fun facts sheet and t answer yur questin. Please be prepared t share yur findings with the rest f the class. [As an interim task, students shuld research the answers t the questins themselves. As a summative task, this infrmatin wuld be cntained in a cricket fun facts sheet.]

3 Building Backgrund Knwledge abut Crickets Questins in bld fr small grups Only male crickets chirp. Why d they chirp? [Answers belw] t attract females t act as a warning t ther male crickets t stay ut f their territry t warn ther male crickets t stay away frm their females Crickets chirp primarily at night. Why? [Answers belw] Crickets are ncturnal insects. They smetimes eat in the daytime. Male crickets rub their wings, nt their legs, t chirp. Hw d crickets make sunds with their wings? [Answers belw] The underside f a male cricket's wing is rugh and the tp side is cntured differently. When rubbed tgether, they make a chirping sund. Crickets will nt chirp if the temperature is belw 40 degrees Fahrenheit ( F) r abve 100 degrees Fahrenheit ( F). Why? [Answers belw] Crickets d nt survive in temperatures belw 40 F. Crickets cannt live in temperatures abve 100 F. Data Cllectin [Teacher: Shw Number f Chirps Data t students.] Teacher: Lk at the table f data that represents the chirping f a snwy tree cricket in tw different cnditins. In the first sectin f the table, a male cricket was recrded in a rm that had a warm temperature. The same cricket was recrded in a much cler rm, as shwn in the secnd sectin f the table. Each f the cricket recrdings shwn here lasted 20 secnds.

4 Teacher: Using scratch paper, calculate the average number f chirps in ne minute fr each cnditin, using the data in the table shwn. Remember that each recrding lasted 20 secnds. Teacher [after 3 minutes, say]: Okay time is up, here is the crrect respnse. [Shw this table n the verhead prjectr.] Teacher: What d yu ntice abut the cnsistency f the data acrss the different recrdings?" [Students shuld ntice that under a specific cnditin, the data are similar but nt identical.] "And what d yu ntice abut the chirping rates f the snwy tree cricket in the tw different temperature cnditins? Teacher: These kinds f patterns have encuraged many peple t try t develp ways f predicting the temperature by measuring the speed f crickets chirping. Nw yu will wrk by yurself n an assessment task that allws yu t explre the relatinship between cricket chirps and temperature in greater detail.

5 Student Task THERMOMETER CRICKETS PERFORMANCE TASK In this task, yu will rganize and analyze data t mdel the relatinship between temperature and the chirping rates f snwy tree crickets. Yu will develp an equatin t describe the relatinship, and yu will cmpare yur mathematical mdel t anther frmula. Data Set This table shws data abut snwy tree crickets. Each data pint in the table represents the average number f chirps per minute at a specific temperature.

6 Develping and Analyzing a Mdel 1. A. Using the data table, create a scatter plt f the temperature and number f chirps per minute fr snwy tree crickets. [Nte: The nline delivery and respnse frmat fr these types f questins is still being evaluated.] B. Explain the patterns yu bserve n the graph. 2. A. Estimate the line f best fit fr the data pints n the graph, and graph this line. B. Write an equatin t represent the line. C. Write an interpretatin f the slpe f yur equatin (mathematical mdel) in terms f the cntext f chirping rates and temperature. 3. Describe hw well yur mathematical mdel fits the given bservatin data n cricket chirps and temperature, using crrelatin cefficient, R 2, and/r plts f residuals. Cmparing a Mdel Ams Dlbear develped an equatin in 1897 called Dlbear s law. He arrived at the relatinship between number f chirps per minute f a snwy tree cricket and temperature. Yu can use this law t apprximate the temperature, in degrees Fahrenheit, based n the number f chirps heard in ne minute. Dlbear's law: where T = temperature ( Fahrenheit) N = number f chirps per minute 4. A. Plt the line that represents Dlbear s Law n the same graph as yur line f best fit. B. What are the differences between this mdel and the ne yu develped earlier? (Include a discussin f their slpes and y-intercepts in yur answer.) Interpret what these differences mean in the cntext f chirping rates and temperature. 5. Explain the differences between the results f Dlbear s frmula and what yu see in the bservatin data fr determining the temperature depending n the number f times a cricket chirps. Supprt yur cnclusin using fur data pints. Why d yu think these differences culd ccur?

7 Task Specificatins Sample Item Id: MAT.HS.CRICKETS.PT Title: Thermmeter Crickets Cntent Dmain(s): Mdeling; Algebra; Functins; Statistics and Prbability Assessment Target(S): Claim 2, Target A: Apply mathematics t slve prblems arising in everyday life, sciety, and the wrkplace. Claim 2, Target C: Interpret results in the cntext f a situatin. Claim 2, Target D: Identify imprtant quantities in a practical situatin and map their relatinships (e.g., using diagrams, tw-way tables, graphs, flwcharts, r frmulas). Claim 3, Target C: State lgical assumptins being used. Claim 3, Target F: Base arguments n cncrete referents such as bjects, drawings, diagrams, and actins. Claim 4, Target D: Interpret results in the cntext f a situatin. Claim 4, Target E: Analyze the adequacy f and make imprvements t an existing mdel r develp a mathematical mdel f a real phenmenn. Scre Pints: See Scring Rubric Task Purpse: The purpse f this task is t assess students ability t use new data t challenge the assumptins f an existing mathematical frmula.

8 Scring Rubric Scring Criteria fr Thermmeter Crickets Task Scrable Parts Pints Claims 1. A. Using the data table, create a scatter plt f the temperature and number f chirps per minute fr snwy tree crickets. 0 2 Pints Full credit fr crrectly pltting data pints. Students might nte a pssible linear relatinship between the tw variables. Accept ther valid respnses. Cntributes evidence t Claim 2, Prblem-slving B. Explain the patterns yu bserve n the graph. 2. A. Estimate the line f best fit fr the data pints n the graph, and graph this line. B. Write an equatin t represent the line. C. Write an interpretatin f the slpe f yur equatin (mathematical mdel) in terms f the cntext f chirping rates and temperature. 3. Describe hw well yur mathematical mdel fits the given bservatin data n cricket chirps and temperature, using crrelatin cefficient, R 2, and/r plts f residuals. 0 3 Pints Full credit fr prviding a line f best f fit apprximating y = 0.23x + 31, depending n tls used. Pssible interpretatin f slpe wuld be that fr every ne unit increase in the rate f chirping, there is an average increase f 0.23 degrees in temperature ( F). Accept ther valid respnses. See sample graph n last page f this dcument. 0 3 Pints Full credit fr reprting n Pearsn crrelatin cefficient, apprximately r = 0.85, indicating a strng psitive assciatin. Infrmal residual analysis supprts the apprpriateness f linear mdel. Accept ther valid respnses. Cntributes evidence t Claim 4, Mdeling Cntributes evidence t Claim 4, Mdeling

9 4. A. Plt the line that represents Dlbear s Law n the same graph as yur line f best fit. B. What are the differences between this mdel and the ne yu develped earlier? (Include a discussin f their slpes and y-intercepts in yur answer.) Interpret what these differences mean in the cntext f chirping rates and temperature. 0 4 Pints Full credit fr nting that the bth Dlbear s frmula and the cnstructed mdel have psitive slpes, but differ slightly (0.25 and 0.23). One interpretatin f this culd be that cmpared t Dlbear s frmula predictins, the bserved crickets in the data table seemed t have a slightly slwer rate f temperature change fr every unit change in number f chirps. Respnses als nte that y-intercepts fr the tw mdels als differ, 40 and 31. Accept ther valid respnses. Cntributes evidence t Claim 4, Mdeling, and t Claim 3, Cmmunicating Reasning 5. Explain the differences between the results f Dlbear s frmula and what yu see in the bservatin data fr determining the temperature depending n the number f times a cricket chirps. Supprt yur cnclusin using fur data pints. Why d yu think these differences culd ccur? 0 2 Pints Full credit is given fr nting that in all but ne case, Dlbear s frmula verestimated the temperature f the bserved crickets in the data table. Respnses shuld include the calculating f fur data pints using Dlbear s frmula t supprt explanatin. (Students may speculate abut the discrepancy in Dlbear s frmula and the data cllected in terms f measurement errr, pssible different species f crickets, ther envirnmental variables [e.g., humidity], prximity t mating seasn, ther valid respnse.) Cntributes evidence t Claim 3, Cmmunicating Reasning

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