Transcript December 14th In

Bridges in Mathematics &
Best Practices
John Madden
Math Coordinator
Shelburne Community School
[email protected]
Copyright VMI
Problem Solving Steps:
1.
Identify the problem.
2.
Gather the information needed to solve it.
3.
Calculate or solve it.
4. Verify that your answer is reasonable and solves the
problem from step 1.
The idea is that in general these types of questions do not
engage higher levels of thinking:
Verification questions, the answers to which are already known by you or your
student:
What is the name of . . .?
How many times did you . . .?
Closed questions, which can be answered "yes", "no", or "I can":
Do you remember . . .?
Can you state the formula for . . . ?
Rhetorical questions in which the answer is given within the question:
In what year was the War of 1812?
How long did the Seven Year War last?
Defensive questions, which lead to justification, resistance, and self-protection:
Why didn’t you complete your homework?
Why would you do a thing like that?
Agreement questions, the intent of which is to invite others to agree with an opinion
or answer:
This is really the best solution, isn’t it?
Let’s do it my way, okay?
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What do you predict will happen next?
How did you figure it out?
Does anyone have a different way to solve this
problem?
Con you convince us?
Can you prove that?
How do you know? (show evidence)
What part do you agree or disagree with? Why?
What do you think?
Do you see any patterns? Can you extend them?
What might come next?
What did you notice about…?
What if…? (conjecture)
Does anyone have a different answer?
Here are a smattering of problems ranging from
Kindergarten through fifth grade. (5 minutes)
Can you identify the theme that is building?
What is your justification?
Work on the first two pages (back-to-back)
Work on the next page (back-to-back)
Using a Picture to See Multiplication: 13 x 12
First, students use the rectangle to
multiply the ones and tens in each
number and then add them to find the
product.
Then, they see how these numbers can
lead to a computational algorithm,
which they practice first with pictures
and numbers and then with numbers
alone.
Work on the next page (back-to-back)
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May & June Problems #3
Pose a question and solve and solve it on
another sheet of paper (5 minutes).
Find a partner and have them solve it.
Get them to solve it another way by
questioning them. Use genuine questions
only… this is the tricky part. Don‘t impose
your thinking…
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Private think time – solve the problem. Show
and justify all of your thinking.
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Can you solve it another way?
Structured math talk
Plenary discussion and sharing
Vi Hart - Math Doodling