Ch 6 Math PPT

8/7/2019 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?



Suppose students have been multiplying

whole numbers.

56 77 48 287 793

x2 x4 x5 x7 x8



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?



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.

___ ___ ___

___ ___ ___ ___ ___ ___



Use 1,2,3,4,5,6,7,8,9

___ ___ ___

+ ___ ___ ___

_________________

___+___+___= 18

Try this. Is this a problem for you?



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



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.



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.



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.



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.



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.



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



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?



Interviewer, "Paco had 13 cookies. He ate 6 of them.

How many cookies does Paco have left?³

Meredith: Fifth Month of Kindergarten



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



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



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



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



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



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

Documents

Ch 6 Math PPT