math550macc2012 [licensed for non-commercial use only] (2024)

Teaching With Tasks

TIMSS video: http://timssvideo.com/timss-video-study

See Japanese geometry lesson and maybe American lesson

There are many good mathematical tasks online. These can be found on Dan Meyer’s page, many of the lesson links provided on our wiki, and many other resources such as NCTM and Math Olympiad.

Below are a sampling of problems/tasks from a variety of online resources. Each group needs to solve their problem and present (with style and the use of ipad or other technology??) to the class:

1. The problem
2. Its solution and at least 2 different ways to determine it
3. What you liked about the problem (what makes it a good task)
4. Suggestions for improving the task or its use in class

You will have 90 minutes to complete your task and prepare your presentation. Many of you will finish before that time has expired. If so, please use the remaining time to explore other tasks and to identify potential lessons for your classroom and possibly for your summer project.

1. The Ball Problem (Japanese) http://www.japanese-online.com/lessons/Mem_JML.htm

How many 'C' balls does it take to balance one 'A' ball?

You would have 2 minutes to finish this problem if you were a Japanese 12 year old.

2. The Hose Problem (Japanese) http://www.japanese-online.com/lessons/Mem_JML.htm

Hose A takes 45 minutes to fill the bucket with water. Hose B can do the same in 30 minutes.

If you use both hoses, how long will it take to fill the bucket?

3. Math Tug of War: Acrobats, Grandmas, and Ivan From Marilyn Burns

Source: 50 Problem Solving Lessons (grades 1-6), M. Burns; 1996, Math Solutions Publications

Use the information below to decide who will win the third round in the tug of war:

Round 1: On one side are four acrobats, each of equal strength. On the other side are five feisty neighborhood grandmas, each also of equal strength. The result is dead even.

Round 2: On one side is Ivan, a neighborhood dog. Ivan is pitted against two grandmas and one acrobat. Again, the result is a draw.

Round 3: Ivan and three grandmas are on one side; four acrobats are on the other.

Who will win the third round in the tug of war?

4. Best Size Can from MAP: http://map.mathshell.org.uk/materials/download.php?fileid=820

See connected resources like rubric and student work. HS expert.

1. Functions from MAP: http://map.mathshell.org.uk/materials/download.php?fileid=762

See connected resources like rubric and student work. HS apprentice.

1. Lottery from MAP: http://map.mathshell.org.uk/materials/download.php?fileid=1160

See connected resources like rubric and student work. MS Expert.

1. Buying Chips and Candy from MAP: http://map.mathshell.org.uk/materials/download.php?fileid=1074 MS Apprentice

1. Proving patterns from NCSM: http://www.mathedleadership.org/docs/ccss/GreatTasksHandout2012.pdf

1. Arcavi Geometry problem from NCTM: http://www.nctm.org/uploadedFiles/Lessons_and_Resources/Core_Math_Tools/Arcavi-06122012.pdf See if you can produce this in Geogebra or Desmos and show to group.

10. Computer Passwords from ISBE assessment tasks: http://map.mathshell.org.uk/materials/download.php?fileid=1074

Includes student work.

11. Sorting Functions from MARS (Inside Mathematics): http://www.insidemathematics.org/pdfs/algebra/sorting-functions/task.pdf

Note all the resources available at http://www.insidemathematics.org/index.php/tools-for-teachers/course-1-algebra/mars-tasks-scoring-rubrics-a-analysis

12. Snail Invasion from Illustrative Mathematics: (See Below) http://www.illustrativemathematics.org/standards/hs HS functions

13. Fishing Adventures 2 from Illustrative Mathematics: (See Below) http://www.illustrativemathematics.org/standards/k8 7^th grade expressions and equations

Snail Invasion:

In 1966, a Miami boy smuggled three Giant African Land Snails into the country. His grandmother eventually released them into the garden, and in seven years there were approximately 18,000 of them. The snails are very destructive and had to be eradicated. According to the USDA, it took 10 years and cost $1 million to eradicate them.

1. Assuming the population of snails grew exponentially, write an expression for the number P(t) of snails in the population (where t is measured in years since their release in 1966.)
2. Using your formula for P(t), find out how long it took for the population of snails to double.
3. Assuming the cost of removing the snails is proportional to the number of snails, how much would it have cost to eradicate them if they had started the eradication program a year earlier?
4. Assuming the cost of removing the snails is proportional to the number of snails, how much would it have cost to eradicate them if the population had grown unchecked for another year?

Fishing Adventures:

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can only carry 1200 pounds of people and gear for safety reasons. Assume the average weight of a person is 150 pounds. Each group will require 200 lbs of gear for the boat plus 10 lbs of gear for each person.

1. Create an inequality describing the restrictions on the number of people possible in a rented boat. Graph the solution set.
2. Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5 people. Group 3 has 8 people. Which of the groups, if any, can safely rent a boat? What is the maximum number of people that may rent a boat?

Other Potential Resources:

Dan Meyer and 3-act tasks (with video)

Teaching Channel

Hunt Institute

Old ISAT

NAEP test bank

TIMSS test bank

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