Black Swamp Math Teacher Circle Funding
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October 15, 2015
Funding through the Improving Teacher Quality Grant, Ohio Board of
Regents
Black Swamp Math Teacher
Circle
o
Increase the confidence of math teachers in
problem solving.
o
Deepen teachers' content knowledge
through exploring mathematically rich
problems and develop an arsenal of
techniques to solving unfamiliar and
challenging problems.
o
Form long-term professional relationships
among teachers and mathematicians,
through regular, highly interactive meetings.
o
Provide support for teachers who want to
bring richer mathematical experiences to their
students.
What is a Math Teacher Circle
o
Divide the space between the circles into a section for each member of
your group
o
Write your name outside your section
o
In your section, write something that is unique to you.
o
Once everyone has identified a unique item, find a common trait –
besides being math teachers – and place it in the center of the circles.
o
Continue unique and common things until time is called.
Concentric Circles
https://www.youtube.com/watch?v=5_MoNu9Mkm4
Start at 2:43
Jugs Problem
Suppose that Jug A contains 8 gallons of water.
Suppose Jug B has a capacity of 5 gallons and
Jug C has a capacity of 3 gallons.
By pouring back and forth, find a way to get 4
gallons in one jug.
Keep in mind that there are no measuring lines on
the jugs, so you can empty one jug into another
or pour from one until the other is full.
Your Problem:
Is there another way to achieve the 4 gallons
in one jug?
When you have found a solution, is it the way
with the least number of steps or is there a
shorter way? How do you know?
What amounts of water can you measure in
addition to 4 gallons?
Questions to consider/discuss:
Time to share/discuss
New task:
Each group will have 3 sets of jug
amounts to examine for which amounts
of water can be measured using those
three jugs.
Keep track of your results.
Time to share/discuss
The
BLUE
numbers:
Which measures were you able to pour?
The
PINK
numbers:
Which measures were you able to pour?
The
GREEN
numbers:
Which measures were you able to pour?
Suppose this triangle has height of 8 units, so the height of each small triangle inside is
1 unit. Consider a point inside the triangle. Let its distance from the base of the
triangle stand for the amount of water in the 8-gallon jug, the distance from the
3-gallon line to be the amount in the 3-gallon jug and the distance from the 5-gallon
line for the amount of water in the 5-gallon jug.
Extensions:
http://www.math.washington.edu/nwmi/materials/3jugs.pdf
http://www.mathteacherscircle.org/assets/session-
materials/EJohnstonThe%20Jug%20Band.pdf
Engage with the Black Swamp Math Teacher Circle program funded through the Improving Teacher Quality Grant by the Ohio Board of Regents to enhance math teaching skills and foster a collaborative learning environment. Join us on October 15, 2015, for an enriching educational experience with like-minded educators dedicated to improving math education in Ohio.
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Presentation Transcript
Black Swamp Math Teacher Circle October 15, 2015 Funding through the Improving Teacher Quality Grant, Ohio Board of Regents
What is a Math Teacher Circle o Increase the confidence of math teachers in problem solving. Black Swamp o Deepen teachers' content knowledge through exploring mathematically rich problems and develop an arsenal of techniques to solving unfamiliar and challenging problems. Ohio Circles Glass City? Columbus o Form long-term professional relationships among teachers and mathematicians, through regular, highly interactive meetings. Southeast Ohio Cincy o Provide support for teachers who want to bring richer mathematical experiences to their students.
Concentric Circles o Divide the space between the circles into a section for each member of your group o Write your name outside your section o In your section, write something that is unique to you. o Once everyone has identified a unique item, find a common trait besides being math teachers and place it in the center of the circles. o Continue unique and common things until time is called.
Jugs Problem https://www.youtube.com/watch?v=5_MoNu9Mkm4 Start at 2:43
Your Problem: Suppose that Jug A contains 8 gallons of water. Suppose Jug B has a capacity of 5 gallons and Jug C has a capacity of 3 gallons. By pouring back and forth, find a way to get 4 gallons in one jug. Keep in mind that there are no measuring lines on the jugs, so you can empty one jug into another or pour from one until the other is full.
Questions to consider/discuss: Is there another way to achieve the 4 gallons in one jug? When you have found a solution, is it the way with the least number of steps or is there a shorter way? How do you know? What amounts of water can you measure in addition to 4 gallons?
New task: Each group will have 3 sets of jug amounts to examine for which amounts of water can be measured using those three jugs. Keep track of your results.
The BLUE numbers: Which measures were you able to pour?
The PINK numbers: Which measures were you able to pour?
The GREEN numbers: Which measures were you able to pour?
Suppose this triangle has height of 8 units, so the height of each small triangle inside is 1 unit. Consider a point inside the triangle. Let its distance from the base of the triangle stand for the amount of water in the 8-gallon jug, the distance from the 3-gallon line to be the amount in the 3-gallon jug and the distance from the 5-gallon line for the amount of water in the 5-gallon jug.
Extensions: http://www.math.washington.edu/nwmi/materials/3jugs.pdf http://www.mathteacherscircle.org/assets/session- materials/EJohnstonThe%20Jug%20Band.pdf
