Probsolvwebquest

04/12/23 © Judy Campf, Chatsworth School

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Searching for Solutions

Steps for Successful Problem SolvingAn Introduction to the Searching for Solutions WebQuest http://gouchercenter.edu/jcampf/searching_for_solutions.htm


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Problem Solving

• Are you ready to tackle a math problem with confidence?

• Do you have a briefcase filled with problem-solving strategies that help when you encounter a new problem?

• Do you get confused about how to solve problems?


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Strategies for Solving Problems• making a table,

chart or graph• using estimation

• making a list

• acting out the problem

• guess and check

• working backward

• finding a pattern

• solving multi-step problems

• drawing pictures or diagrams

• interpreting remainders

• making and using models

• using formulas• choosing an

operation• solving a simpler

problem• writing a number

sentence or equation


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Problem Solving Steps

• UNDERSTANDUNDERSTAND the problem

• PLANPLAN a solution

• SOLVESOLVE the problem

• LOOK BACKLOOK BACK and check your solution


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UNDERSTANDUNDERSTAND

• Restate the problem

• Highlight or identify important

facts

• Determine the question or problem

to be solved


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PLANPLAN

Choose a strategy• Find a Pattern• Read a Table or Chart• Make an Organized

List• Draw a Diagram

Choose a strategy• Write an Equation• Work Backward• Make a Simpler

Problem• Guess and Check


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SOLVESOLVE

• Identify Needed Facts• Choose an Appropriate Strategy• Pencil and Paper• Calculator• Addition, Subtraction,

Multiplication, Division• Show ALL Work


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LOOK BACKLOOK BACK

• Restate the Question• Check the Answer• Does the Answer Make Sense?• Record the Answer• Add Necessary Units or Labels


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Let’s Try Some Problems

Finding a Pattern

Making a Table or Chart

Making an Organized List

Drawing a Diagram

Using an Equation #1


Working Backward

Make a Simpler Problem

Application of Strategies


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Finding a Pattern

A penny bubble-gum machine contains four colors of gum balls. What is the maximum amount of money needed to get two gum balls of the same color? Explain your reasoning.

Passport to Mathematics Book 1 - Chapter 1 - 1.1 Problem of the Day


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UNDERSTAND the problemWhat are the most important facts in this problem?How many colors? What is the cost per gum ball?

PLAN a solution / SOLVE the problemWhat PATTERN can you create that is similar to

this problem? Make the PATTERN and test it out.1¢ 1st color (red) 2¢ 2nd color (blue)

3¢ 3rd color (green)

What is the question?

LOOK BACK and check the solutionDoes it make sense?

The Answer


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Finding a Pattern - Answer

5 ¢Consider only the worst case - the first four don’t match. The fifth gum ball will match one of the first four.

Solve More ProblemsFinished Solving

Problems


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Making a Table or Chart

Suppose you have 5 compact discs (CDs) and a CD player that holds 3 CDs at a time. How many different sets of 3 CDs can be chosen to load into the CD player?



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UNDERSTAND the problemWhat are the most important facts in this problem?How many CDs do you have?

How many CDs will the player hold?

PLAN a solution / SOLVE the problemMake a TABLE and put the information into it.



The Answer

A, B, CB, C, D

C, D, EA, B, D

A, B, EB, C, E

Etc.


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Making a Table or Chart - Answer

10 combinationsABC ABD ABE BCD BDE CDE ACD ACE CBE ADE


Problems


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Making an Organized List

A “palindromic” number is a number that reads the same forward as backward, such as 3223. Find the smallest palindromic number greater than 7456.



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UNDERSTAND the problemWhat are the most important facts in this problem?

What is a “palindromic” number?

PLAN a solution / SOLVE the problemMake an ORGANIZED LIST of numbers greater

than 7456. Check for palindromic numbers.



The Answer

7457 NO

7458 NO

7459 NO

7460 NO

7461 NO Etc.7456

NO


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Making an Organized List - Answer

7557 is the smallest palindromic number greater than 7456


Problems


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Drawing a Diagram

If each edge measures 3.7 inches, what is the sum of the measure of the edges of a cube?



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What measurements are given? What is a cube? How many edges will be measured?

PLAN a solution / SOLVE the problemWhat DIAGRAM can you draw to solve this

problem?



The Answer

3.7 inches per edge x ? edges = ???


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Drawing a Diagram - Answer

44.4 inches3.7 inches x 12 edges on a cube = 44.4 inches


Problems


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“Echoing” a one-digit number to make it a two-digit number (e.g., making 3 into 33) is the same as multiplying by 11. When a two-digit number is “echoed” in the same way, making it a four-digit number, by what number is it being multiplied?



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UNDERSTAND the problemWhat are the most important facts in this problem?What is echoing? Can you find examples?

PLAN a solution / SOLVE the problemWhat EQUATION can you create that is similar to

this problem? Write other EQUATIONS and look for a pattern.



The Answer

22 2222 57 5757 93 9393


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Using an Equation #1 - Answer

101Using the prior examples:2222 ÷ 22 = 1015757 ÷ 57 = 1019393 ÷ 93 = 101


Problems


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Three times a certain number is between 380 and 390. Four times the same number is between 500 and 510. What is the number?



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What equations are given? What can you predict?

PLAN a solution / SOLVE the problemWhat EQUATION can you create that is similar to

this problem? Write other EQUATIONS and look for a pattern.



The Answer

390 ÷ 3 510 ÷ 4 500 ÷ 4 380 ÷ 3


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Using an Equation #2 - Answer

127Dividing 380 and 390 by 3 showed the answer was between 126 and 130.Dividing 500 and 510 by 4 showed the answer was between 125 and 128.


Problems


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Working Backward

The average of five numbers is 78. Three of the numbers are 65, 83, and 92. The other two numbers are the same. What are the other numbers?



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UNDERSTAND the problemWhat are the most important facts in this problem?What is an average? What numbers are given?

PLAN a solution / SOLVE the problemWORK BACKWARD using the given numbers and

the formula for finding an average.



The Answer

Subtract 65, 83, and 92 78 x 5 Average of 5 numbers = 78


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Working Backward - Answer

75 and 7578 x 5 = 39065 + 83 + 92 = 240390 - 240 = 150150 ÷ 2 = 75


Problems


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Make a Simpler Problem

Use the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Find four numbers in a row whose sum is one half the sum of the other eight numbers.



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UNDERSTAND the problemWhat are the most important facts in this problem?What numbers must be used?

What operations will be needed?

PLAN a solution / SOLVE the problemMAKE A SIMPLER PROBLEM by testing the

process on easier numbers.



The Answer

Sum of 5, 6, 7, 8, 9, 10, 11, 12 = 68 Sum of 1, 2, 3, 4 = 10


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Make a Simpler Problem - Answer

5, 6, 7, 85 + 6 + 7 + 8 = 261 + 2 + 3 + 4 + 9 + 10 +

11 + 12 = 5226 x 2 = 52


Problems


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Application of Strategies

A large store plans to assign a three-letter inventory code to each kind of item it sells. How many different three-letter codes are possible?


The Answer


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Application of Strategies - Answer

26 x 26 x 26 = 17,576


Problems


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Congratulations!

You have lots of skills to add to your problem-solving

suitcase. Now it is time to begin the

Searching for Solutions WebQuest

!

Education

Probsolvwebquest