Problem solving
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Problem Solving. The Problem Solving Plan & Problem Solving Strategies. The Problem Solving Plan. Read and Understand the Problem Make a Plan: Choose a Strategy Estimate Carry out the Plan: Apply the Strategy Estimate for Reasonableness: Does it make sense?. Problem Solving Strategies.

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Problem Solving

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Problem solving

Problem Solving

The Problem Solving Plan

&

Problem Solving Strategies


The problem solving plan

The Problem Solving Plan

  • Read and Understand the Problem

  • Make a Plan: Choose a Strategy

  • Estimate

  • Carry out the Plan: Apply the Strategy

  • Estimate for Reasonableness: Does it make sense?


Problem solving strategies

Problem Solving Strategies

  • Draw a picture.

  • Look for a pattern.

  • Guess and Check.

  • Make an organized list.

  • Make a table.

  • Make it simpler.

  • Work backwards.

  • Brainstorm.

  • Use logical reasoning.

  • Act it out or use objects.


Draw a picture

Draw a Picture

  • There are many types of problems where it helps to draw a picture.

  • Work this problem with your group:

    If Kyle wants to cut a board into 6 pieces, how many cuts will he need to make?


Kyle had to make 5 cuts or 3 cuts

Kyle had to make 5 cuts or 3 cuts.


Look for a pattern

Look for a pattern.

  • Solve this problem with your group:

  • Find the pattern to solve.

    The first four triangular numbers are 1, 3, 6, and 10.

    What is the sixth triangular number?


The sixth triangular number is 21

The sixth triangular number is 21.


Guess and check

Guess and Check

  • Sometimes the only way to solve a problem is to guess and check until you find an answer that makes sense.

  • Solve this problem with your group:

    Jerry has a total of $0.48. He has twice as many pennies as nickels and twice as many nickels as dimes. What coins does Jerry have?


Jerry has

Jerry has:

  • 8 pennies = $0.08

  • 4 nickels = $0.20

  • 2 dimes = $0.20

  • The total is $0.48.


Make an organized list

Make an Organized List

  • Lists are a great way to solve some problems! But, make sure you organize your list so that you don’t get confused or leave something out.

  • Solve this problem with your group:

    Sara looked in her closet to find something to wear. She had a blue or red shirt to choose from, a skirt, shorts, or blue jeans to choose from, and sneakers or flip flops to choose from. How many different outfits does Sara have to choose from?


Sara has 12 outfits to choose from

Sara has 12 outfits to choose from.

  • Blue shirt, skirt, sneakers

  • Blue shirt, skirt, flip flops

  • Blue shirt, shorts, sneakers

  • Blue shirt, shorts, flip flops

  • Blue shirt, jeans, sneakers

  • Blue shirt, jeans, flip flops

  • Red shirt, skirt, sneakers

  • Red shirt, skirt, flip flops

  • Red shirt, shorts, sneakers

  • Red shirt, shorts, flip flops

  • Red shirt, jeans, sneakers

  • Red shirt, jeans, flip flops


Make a table

Make a Table

  • My favorite table is a T Chart!

  • Use a T Chart to solve this problem with your group:

    Lydia works in the cafeteria. On Monday, she served 300 students. She served 325 students on Tuesday and 350 on Wednesday. If this pattern continues, how many students will Lydia serve on Friday?


Lydia will serve 400 students on friday

Lydia will serve 400 students on Friday.


Make it simpler

Make it Simpler

  • Solving a Simpler Problem means to break down a bigger problem into smaller ones so it is easier to solve.

  • Solve this problem with your group:

    The houses on Main Street are numbered from 1 to 100. How many house numbers contain at least one digit 7?


19 houses on main street contain the digit 7 at lease once

19 houses on Main Street contain the digit 7 at lease once.

  • First, simplify the problem by figuring out how many house numbers have the digit seven in the ones place:

    7, 17, 27, 37, 47, 57, 67, 77, 87, 97

  • Then, consider how many house numbers have the digit 7 in the tens place (don’t repeat 77!):

    70, 71, 72, 73, 74, 75, 76, 78, 79


Work backwards

Work Backwards

  • Sometimes working a problem backwards helps you find the solution.

  • Solve this problem with your group:

    Sara uses half of a book of stamps to mail her Christmas cards. Her mom uses 8 of the remaining stamps to send off the bills. Finally, Sara’s dad uses half of the stamps that are left. There are 5 stamps left. How many stamps were in the original book of stamps?


There were 36 stamps in the book of stamps

There were 36 stamps in the book of stamps.

  • Start with 5.

  • Since Sara’s dad took half of the stamps, multiply by 2: 5 x 2 = 10

  • Since Sara’s mom took 8 stamps, add 8 stamps: 10 + 8 = 18

  • Since Sara took half of the stamps, multiply by 2: 18 x 2 = 36


Brainstorm

Brainstorm

  • The Brainstorm strategy is often used when all else fails! Brainstorming means looking at a problem in new and inventive ways. Use your imagination, be creative, and by all means, be flexible in your thinking! Eventually the light bulb will go on and you will find a solution!


Use logical reasoning

Use Logical Reasoning

  • Logical reasoning is when you use clues to help you solve a problem.

  • Solve this problem with your group.

    Philip entered his Dalmatian in a dog show along with Mary's poodle and Courtney's collie. Philip, Mary, and Courtney all won prizes. One person won first, one won second, and one won third. Use these clues to solve the problem: Both girls' dogs placed higher than Philip's dog and Mary's dog did not win first place. Tell who won 1st, 2nd, and 3rd place.


Solution

Solution


Act it out or use objects

Act It Out or Use Objects

  • This strategy allows you to use visual images of the information in the problem to solve the problem.

  • Acting or moving around objects can help you remember the process you should use to solve the problem.


Act it out or use objects1

Act It Out or Use Objects

  • Solve this problem with your group. Act it out and use the interlocking cubes to help you solve.

    If you have 16 cookies that you want to share with 3 friends including yourself, how many cookies will each of you get?


You each will get 4 cookies

You each will get 4 cookies.

You used division by sharing the cookies.


The end

The End!

  • Don’t forget to use the Problem Solving Plan when solving problems.

  • Don’t forget about all of the WONDERFUL strategies you can use!


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