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Using topographic maps to find the best bike route.For high school (Algebra 1) students, 9th grade.

The students will work in groups using a topographic map and actual measurements todetermine the slopes of three routes to school. Students will measure on the map, and scale toactual measurements. Students will create a profile for each of the three routes, and calculate

the average and intermediate slopes from the river to our school using hand graphing andspreadsheet graphing. Students will describe and explain their preferred route of travel bybicycle.Sources: Topographic maphttp://www.topoquest.com/map-detail.php?usgs_cell_id=17996 Topographic map collectionfrom Ryan Nemi (2008-2009)http://www.michigan.gov/dnr/1,1607,7-153-10371_14793-31331--,00.html Department of Natural Resources, Michigan topographic maps (State of Michigan 2001-2012)math reference:Discovering Algebra (second edition), Murdock, Kamischke & Kamischke, Key Curriculum Press(2007) pp. 122 (scaling), 215 (slope).Common Core standards http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice/The SmarterBalanced Consortium (2010)

 At the end of this lesson, students will be able to create a profile from a topographic math,scale from a map measurement to actual measurement, and calculate slope of a line and partof a line.

Common core standards (Mathematics) addressed:N.Q.1, 2, 3 Reason quantitatively and use units to solve problemsG.MG.1, 2, 3 apply geometric concepts in modeling situationsS.ID.7, 8, 9 interpret linear models

We also use the eight mathematical practices from the common core standards:1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

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Classroom activities (2 days):

1) Students will receive a topographic map each, and a set of instructions. If the weather isnice, students will go outside and measure the length of map references (the block length of the school) using a trundle wheel. Otherwise, students will be provided withreference lengths.

2) Students will form groups of 1, 2 or 3.3) Students will create a map scale.4) Students will create a set of data points of measurements from the river to each contour

line as it crosses the road along the 3 routes of Fulton/Prospect, Fountain, and Lyonstreet (end day 1)

5) Students will create a graph or graphs displaying the horizontal and vertical distances of interest from the data (profile), choosing and labeling appropriate axes.

6) Students will determine the overall slope of each of the lines, and determineintermediate slopes of interest.

7) Students will enter the data into Excel, and create an x-y graph (profile) on thecomputer, choosing appropriate axes

8) Students will use Excel to find appropriate slopes.9) Students will write a one-paragraph summary describing the best route for cycling to

school, with reasons based on the information generated. 

Lesson assessment: rubric provided in the handout (next 3 pages). The points distributionreflects the time/effort needed to complete the section.

 Assessment is based on the materials turned in, as well as observation of student participation,and student participation self-assessment.Struggling students will be advised to complete the Excel graph first, because it willautomatically produce axes. Students will have the most difficult time with creating uniform

axes for graphs, followed by changing scales, and then measurements, so teachers need to beprepared to assist students with these topics.The teacher needs to be prepared with some actual distances as measured – the length of theCentral block on each side and the length of the school might be useful references.Students will need pencils, rulers with centimeters, calculators and computers with Excel andWord (with equation editor enabled).Students should be encouraged to write their math in Word, which will be needed in CommonCore assessments.

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Find the best route to school from downtown, by bike.

There are 3 routes to school from downtown: Fulton to Prospect, or Pearl/Fountain, or Lyon. You have to cycle up the sidewalk on Lyon because the traffic is one way against you.

 You are provided with a topographic map. The contour lines represent points of the same

height above sea level. You will see a heavy line labeled 700, so the next line down will be 690ft, and the next line up will be 710ft.

The map does not have a scale, so you will need to measure a distance on the map (I woulduse the cm scale and decimals) and a distance in real life, and create a ratio.

 You will measure distance from the river or from Division Avenue, along each one of the routes,and create a set of data where x is the distance travelled, in feet, from the river, and y is theheight, in feet, from the contour lines.

 You will create an x-y graph (called a profile) by hand for each route, using your data points. You must label the axes correctly. You will find the average slope using the beginning andending points for each route. You will also calculate at least 3 important slopes along the route,for each route.

 You will enter your data into Excel, and create an x-y graph as above. Choose your axes andlabel them correctly. Use Excel to find the average slope, and at least 3 important slopes alongthe route, for each route.

 You will use your information about slopes, and your profiles, and write a paragraph whichdescribes the best bike route to school, and your reasons why. If there is disagreement in your

group, you may submit more than one paragraph.

 Your group should hand in: Your scale measurement, reference measurement and scale ratio (6 points) Your three sets of raw measurement data (6 points) Your 3 sets of data in feet (6 points) Your 3 hand drawn graphs including axes (20 points) Your 3 Excel graphs including axes – may be submitted electronically(E) (12 points) Your calculated slopes (4) for each of the three graphs, showing calculations (E) (20 points) Your one paragraph describing the best route to school (E) (10 points) Your group participation paper – no grade without this paper!!

Total grade is out of 100.Scores will be adjusted based on participation.

Extra credit:(a) Calculate the actual surface distance from the river to Central High school(b) Use Topomaps to find another place that interests you, and create a profile. Explain how orif you would walk this profile, and why (a 20% slope is considered steep for walking).

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Self-assessment rubricStudents in the group:P:__________________________ 

Q:____________________________ 

R:____________________________ 

Please answer honestly about how many items you personally completed:

 Activity P Q R 

I measured a reference length on the map.

I measured a reference length outside.

I found the scaling ratio, with units.

I measured data points (give number of points that you

measured).

I created graphs by hand ( give number of graphs that youmade).

I created graphs on Excel (give number of graphs that youmade).

I calculated slopes (give number of slopes that you calculated).

I contributed to the paragraph.

I wrote the paragraph.

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Encuentre que la mejor ruta para educar del centro, por la bicicleta.

Hay 3 rutas de educar del centro: Fulton para Prospectar, o la Pearl/Fuente, o Lyon. Tiene queir en bicicleta arriba la banqueta en Lyon porque el tráfico es de un solo sentido contra usted.Es proporcionado con un mapa topográfico. Las curvas de nivel representan los puntos de la

misma altura sobre el nivel del mar. Verá una línea pesada marcada 700, así que la próximalínea será abajo 690 p, y el próximo forman fila será 710 p.El mapa no tiene una escala, así que deberá medir una distancia en el mapa (utilizaría la cmescala y los decimales) y una distancia en la vida diaria, y crearía una proporción.Medirá distancia del río o de la Avenida de División, por cada uno de las rutas, y creará unconjunto de los datos donde X es la distancia viajada, en pies, del río, y Y es la altura, en pies,de las curvas de nivel.Creará un gráfico X-Y (llamó un perfil) a mano para cada ruta, utilizando sus puntos de datos.Debe marcar las hachas correctamente. Encontrará la cuesta media que utiliza el principio yterminar los puntos para cada ruta. Usted también calculará por lo menos 3 cuestasimportantes por la ruta, para cada ruta.Entrará sus datos en Excel, y creará un gráfico X-Y como arriba. Escoja sus hachas y márqueloscorrectamente. Utilice Excel para encontrar la cuesta media, y por lo menos 3 cuestasimportantes por la ruta, para cada ruta.Utilizará su información sobre cuestas, y sobre sus perfiles, y escribirá un párrafo que describela mejor ruta de la bicicleta para educar, y sus razones por qué. Si hay desacuerdo en su grupo,puede someterse más de un párrafo.

Su grupo debe entregar:Su medida de la escala, medida de referencia y escala proporción (6 puntos)Sus tres conjuntos de datos crudos de medida (6 puntos) Sus 3 conjuntos de datos en pies (6

puntos)3 la mano gráficos dibujados inclusive hachas (20 puntos)Sus 3 gráficos de Excel inclusive hachas – puede ser sometido electrónicamente (E) (12 puntos)Sus cuestas calculados (4) para cada uno de los tres gráficos, mostrando cálculos (E) (20puntos)Su un párrafo que describe el mejor ¡La ruta para educar (E) (10 puntos)Su papel de participación de grupo – no grado sin este papel!!El grado total es fuera de 100.Las cuentas serán ajustadas basadas en la participación.

Translation by freetranslation.com I apologise in advance.