Inquiry Learning: Exploring Quality

Tasks and Creating Quality TasksDiane Leighty

November 5, 2013

Colonial Heights, VAEmail: mthmtcs@verizon.netWebsite: http://mthmtcs.net

Case Study on Teaching a Math Class

• 30 minutes to explore 3 problems Jerome Robinson uses in his classroom.

Discussion of the problems

• 20 minutes - Read the Case Study – Jerome Robinson

• 10 minutes – Discussion of the Case Study

A

B

C

4 7 n

Three squares are placed next to each other as shown. The vertices A, B, and C are collinear. Find the dimension n.

Replace the lengths 4 and 7 by m and k, respectively. Express k in terms of m and n.

3 Squares Problem

•What is the mathematics?

•Where could you use the problem?

•What standards are incorporated? Or can be incorporated?

Exploring Paired Data

YearTotal Reported Cases in USA

Total Deaths

2000 21 22001 66 102002 4153 2842003 9862 2642004 2539 1002005 3000 1192006 4269 1772007 3630 1242008 1356 442009 720 322010 1021 57

West Nile Virus Data

Graph

Total Reported Cases in USA

Total Deaths

21 266 10

4153 2849862 2642539 1003000 1194269 1773630 1241356 44720 321021 57

Reported Cases vs. Deaths

0 2000 4000 6000 8000 10000 120000

50

100

150

200

250

300

West Nile Virus in the USA

Reported Cases in USA

To

tal

De

ath

s

Explore RatioDeaths to Total

Illnesses0.100.150.070.030.040.040.040.030.030.040.06

Statistics Used to Explore Singular Data

•Measures of Central Tendency

•Box-and-Whiskers Plot

•Normal Distribution

•Histogram (if there is enough data)

•Regression Analysis (including Piece-wise)

Suggested Problems:

• Flight Data

• Algebra 1 and/or Algebra 2

• FlightAware website to gather data

• http://flightaware.com/live/findflight/KRIC/KATL/

• Braking Distances

• Algebra 1 and/or Algebra 2

• http://forensicdynamics.com/stopping-distance-calculator

• http://www.stoppingdistances.org.uk/

•Midge Problem• Perfect for Algebra 2 or Pre-Calculus

• Sidewalk Stones

• Ice-Cream Cones

Creating Open-Ended Problems

• Take textbook problems and eliminate or change some of the information to open the problem up to

• discussion,

• thinking,

• problem-solving,

• multiple solutions.

Original Textbook Problem

•A carpenter is building a handicap ramp to a platform that is nine feet off the ground. The ground is perfectly level, and he begins 16 feet away from the structure. How long will the face of the ramp be?

Revised Textbook Problem

•A carpenter is building a handicap ramp to a platform that is nine feet off the ground. The ground is perfectly level, and he begins 16 feet away from the structure. How long will the face of the ramp be?

Tickets to a concert cost $2.50 for students and $3.75 for adults. Suppose x represents the number of student tickets sold and y represents the number of adult tickets sold. Write an inequality that describes the condition that total receipts must exceed $1500.

Original Textbook Problem

REVISED…..

Tickets to a concert cost $2.50 for students and $3.75 for adults. If the total receipts must exceed $1500 in order to make a profit, and there are only 480 seats in the auditorium, how many of each kind of ticket need to be sold? Try to find several combinations that will work. Can you generalize your solution?

Mailing Costs - OriginalRecently the cost c, in dollars of shipping a FedEx Priority Overnight package weighing 1 lb. or more a distance of 1001 to 1400 miles was given by c = 3.1w + 29.07, where w is the package’s weight, in pounds. Graph the equation and use the graph to estimate the cost of shipping a 6 ½ lb package.

Mailing Costs - RewriteRecently the cost of shipping a FedEx Priority Overnight package weighing 1 lb. to Chicago was $32.17 while a package weighing 2 lbs. shipped to Chicago cost $35.27, and a package weighing 5 lbs. to Chicago cost $44.57. How much will it cost to ship a 6 ½ lb. package to Chicago?

Plant StandYou buy a tall, three-legged plant stand. When you place a plant on the stand, it appears to be unstable under the weight of the plant. The diagram at right shows a coordinate plane superimposed on one pair of the plant stand’s legs. The legs are extended to form OBC. Is OBC an isosceles triangle? Explain why the plant stand may be unstable.

“Rich” Tasks ….. • Are accessible and extendable.

• Allow individuals to make decisions.

• Involve learners in testing, proving, explaining, reflecting and interpreting.

• Promote discussion and communication.

• Encourage originality and invention.

• Encourage “what if?” and “what if not?” questions.

• Are engaging and contain opportunity to surprise.

http://www.theproblemsite.com/problems/mathhs/2009/default.aspFlowers! Flowers!

• There are 3 rivers and after each river lies a grave. So there are 3 rivers and 3 graves. A man wants to leave the SAME amount of flowers at each grave, and be left with none at the end. What happens though is that each time he passes through one of the rivers the number of flowers he has doubles. So he has to start off with what number of flowers, taking into consideration that they double, so that he is left with no flowers whatsoever at the end?

For additional resources….

• Capstone Website:

• https://sites.google.com/site/mathematicscapstonecourseunits/

• Dan Meyer’s Blog:o http://blog.mrmeyer.com/

• Mathematics Assessment Project:

• http://map.mathshell.org/materials/tasks.php

• The Problem Site

• http://www.theproblemsite.com/problems/mathhs/

Exeter Mathematics

• Math 1 – Mostly Algebra 1

• Math 2 – Mostly Geometry (incl. Algebra)

• Math 3 – Mostly Algebra 2/Trig

• Math 4 – Advanced Mathematics/Calculus

• http://www.exeter.edu/academics/72_6539.aspx