Ch 6 Math PPT
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Transcript of Ch 6 Math PPT
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Problem Types
Problem-involves a situation in which thesolution route is not immediately obvious
Exercise-a situation in which the solution route isobvious
R outine problem-the application of amathematical procedure in the same way it waslearned
Non-routine problem-the choice of mathematicalprocedures is not obvious
Which terms are synonyms?
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Suppose students have been multiplying
whole numbers.
56 77 48 287 793
x2 x4 x5 x7 x8
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Are these problems?
15 rows of stamps.
8 stamps in each row.
How many stamps?
24 packs of baseball cards.
8 cards in a package.
How many baseball cards?
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Try this. Is this a problem for you?
Use the numerals 0,1,2,3,4,5,6,7,8 to form a
3 by 3 square. The sum of the numbers in
every row is 12. The sum of the numbers inevery column is 12.
___ ___ ___
___ ___ ___ ___ ___ ___
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Use 1,2,3,4,5,6,7,8,9
___ ___ ___
+ ___ ___ ___
_________________
___+___+___= 18
Try this. Is this a problem for you?
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Signposts for Teaching
Mathematics Through
Problem Solving
Signpost 1: Allow Mathematics to Be
Problematic for S
tudents
Signpost 2: Focus on the Methods Used toSolve Problems
Signpost 3: Tell the Right Things at the RightTime
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Factors for Success in
Problem Solving
Instruction should build on what children
already know.
Engaging children in problem solving should
not be postponed until after they have
³mastered´ computational skills.
Children should be taught a variety of problem-solving strategies to draw from.
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Factors for Success in Problem
Solving Children¶s problem-solving achievements are
related to their developmental level. Thus, they
need problems at appropriate levels of difficulty.
Factors which contribute to children¶s
difficulties with problem solving include
knowledge, beliefs and affects, control, and
sociocultural factors.
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Choosing Appropriate Problems
Consider including problems that:
± Ask students to represent a mathematical
idea in various ways.
± Ask students to investigate a numeric or
geometric concept.
± R equire students to estimate, or to decide onthe degree of accuracy required, or to apply
mathematics to practical situations.
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Choosing Appropriate Problems
Consider including problems that:
± Ask students to conceptualize very large or
very small numbers.± Ask students to use logic, to reason, to test
conjectures, or to gauge the reasonableness of information.
± Ask students to perform multiple steps, or usemore than one strategy.
± Are open ended.
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Polya¶s Model of Problem Solving
1. Understand the problem.
2. Devise a plan for solving it.
3. Carry out your plan.
4. Look back to examine your solution.
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Problem-Solving StrategiesAct It Out
Make a Drawing or Diagram
Look for a Pattern
Construct a Table
Guess and Check
Work Backword
Solve a Simpler or Similar Problem
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The Horse Problem
A man buys a horse for $60, sells it for
$70, buys it back for $80, and sells it for
$90. How much does the man make or
lose in the horse trading business?
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Interviewer, "Paco had 13 cookies. He ate 6 of them.
How many cookies does Paco have left?³
Meredith: Fifth Month of Kindergarten
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Interviewer, "Carla has 7 candies. How many more
candies does she need so that she will have 11 candies toshare with her friends?³
Allan: Fifth Month of First Grade
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Interviewer, "Nineteen children are going to the circus.
Five children can ride in each car. How many cars will be
needed to get all 19 children to the circus?"
Clint: Fifth Month of Second Grade
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Interviewer, "R obin has 3 packages of gum. There are 6
pieces of gum in each package. How many pieces of gumdoes R obin have altogether?³
Bill: Third Month of Third Grade
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Interviewer, "Tad had 15 guppies. He put 3 guppies in
each jar. How many jars did Tad put guppies in?³
Darla: Third Month of Third Grade
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Interviewer, "Tad had 15 guppies. He put 3 guppies in
each jar. How many jars did Tad put guppies in?³
Ellen: Third Month of Third Grade
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Interviewer, "Nineteen children are taking a mini-bus to
the zoo. They will have to sit either 2 or 3 to a seat. Thebus has 7 seats. How many children will have to sit three
to a seat, and how many can sit two to a seat?³
Allison: Fifth Month of Fourth Grade