problem+solving+2.notebook
February 17, 2009
Draw a Picture or Diagram
Get the problem out of your head and onto the paper. After reading a problem, take the data and create a picture or diagram with it. This takes problems that seem complex and makes them simpler.
Pictures should not be works of art. There is no need for colors or details. Use simple shapes to represent complex items from a problem.
Orli is decorating a birthday cake for Jillian. She decorated the top of the circular cake with a ring of 8 roses. In between each rose, she put two candles. How old is Jillian?
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Simplifying Through Pictures
There were five flags flying over the entrance to Great Adventure. Each flag was flying at a different level. The red flag was flying higher than the green one. The yellow flag was lower than the green one. The purple was higher than the green one, but lower than the red one. The blue flag was a little lower than the yellow one. What was the order of the flags from highest to lowest?
The red flag was flying higher than the green one.
Red
Green
The yellow flag was lower than the green one.
Red
Green
Yellow
The purple was higher than the green one, but lower than the red one.
Red
Purple
Green
Yellow
The blue flag was a little lower than the yellow one.
Red
Purple
Green
Yellow
Blue
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
More Complex Problems
The Boy Scouts were planning a breakfast in the school gym. There were 6 round tables and 4 square tables. 6 people can sit at each round table and 4 people can sit at each square table. How many people can sit at all the tables?
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Students often leave space in between data as they record information. So they can add information as the problem progresses.
There were 5 cars in a race. The blue car was in front of the green car. The yellow car was behind the green car. The red car was between the blue and green cars. The orange car was in front of the blue car. What was the order of the cars from first to last?
END
Michelle Allen 5th grade BVE
FRONT
problem+solving+2.notebook
February 17, 2009
James is helping his father fence in part of the yard for the garden. The area they are fencing is 20 feet wide and 16 feet long. They need to put a post in the ground every 4 feet. How many posts will they need?
Try sketching out the fence posts...
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
I have 1 large bag. Inside the large bag are 2 medium bags. Inside each medium bag are 3 small bags. Inside each small bag are 3 tiny bags. Inside each tiny bag is a quarter. How much money is in the bag? I plan to use the money to buy some candy. Each piece of candy costs $0.20. How many pieces of candy can I buy?
Make this your big bag. Sketch out the others. Then solve the candy problem.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
There were 20 kids at the Valentine party. Each child could chose the flavor of sherbert he or she wanted for a snack. 1/2 the kids chose orange sherbert. 1/5 of the remaining children chose lime. Then, 1/4 of the remaining children chose raspberry. The rest of the kids had lemon. How many children had each kind of sherbert?
Try making a pie chart.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Communication About the Strategy
• Why was drawing a picture a good strategy for solving this problem?
• Does a picture need to be detailed to solve a problem? Explain.
• Explain how your diagram helped you solve this problem.
• Can a picture or diagram help you find errors in your thinking? Explain.
• How did a picture help you better understand this problem?
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Guess, Check, and Revise
Beginning with a Guess
If you aren't sure where to begin, take a guess that is reasonable. Put the guess into the problem situation and work back to check if it is correct. Decide whether you need to go up or down before making another guess.
Look for clues in the problem that will help you make an educated guess. For example, if the problem asks for 3 consecutive numbers that have a sum of 33, students shouldn't start with the number 28.
Take the time to justify the reasonableness of an answer. Revising the Guess
This is a critical step to solving the problem. Students will need to recognize whether the guess is too small or too large before revising their answer.
Jared and Chris were playing Monopoly. At the end, Chris had $50 more than Jared. Together they had $430. How much did each person have?
Start with a reasonable guess...Chris had $250 and Jared had $200. That totals $450, which is too high. Go back and start with a smaller number.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
Helpful Tips
• Don't be afraid to talk aloud when figuring out an answer.
• Remember this strategy takes time. You will not get the answer on the first guess.
• Work with a friend to talk out how to best begin the problem.
• Be a risk taker.
• Be patient and persistent as you check and revise each guess.
ex. Caroline's age this year is a multiple of 5. Next year, her age will be a multiple of 4. How old is Caroline now?
Using Guess, Check and Revise with Equations
ex. _____ * 2 + 10 = 26
Michelle Allen 5th grade BVE
February 17, 2009
problem+solving+2.notebook
February 17, 2009
Using More than One Strategy
Taylor and Rosemary are playing a game of darts. Hitting the center circle (bull's eye) is worth 15 points, the next circle is worth 12 points, the next is worth 10 points, and the outer circle is worth 8 points. How might Taylor have scored 40 points in 4 rows?
More Advanced Skills
Jonathan opened his book and saw 2 consecutive page numbers. The sum of the page numbers is 43. What are the numbers?
How can you make this an equation?
x + (x+1) = 43
Michelle Allen 5th grade BVE
problem+solving+2.notebook
Communication About the Strategy
• How did you come up with your first guess?
• Explain why revising is so important.
• How did Guess, Check and Revise help you solve this problem?
• Why did you choose this strategy to help you solve this problem?
• Why is it important to be persistent when solving problems?
Michelle Allen 5th grade BVE
February 17, 2009
problem+solving+2.notebook
February 17, 2009
Use Logical Reasoning
Tips to Success
• Use process of elimination
• Graphic organizers (matrices, Venn Diagrams, etc.)
• Talk it over with a friend
Most problems use some type of logical reasoning to be solved. Sometimes we use logical reasoning as out primary strategy to solve a problem.
Logical reasoning is the process of thinking in an organized way to reach a conclusion. Logic problems are usually filled with a great amount of confusing data. Often, the data is not explicit and you will need to use inferencing skills.
ex. John does not use a bat to play his favorite sport. So, John's favorite sport is not baseball since that uses a bat.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Role of Inferencing
Lindsay has a three­scoop ice cream cone. She has a scoop of chocolate, vanilla, and strawberry ice cream. The chocolate ice cream is the last flavor she will eat. The vanilla scoop is not touching the chocolate. What is the order of the ice cream flavors?
Using a Logic Matrix
Kathy, Lisa, and Dan each have a snack. One has banana, one has a chocolate bar, and one has raisins. Dan does not like candy. Kathy peels her snack. Lisa's snack melts on a hot day. Which snack does each child have?
Banana
Use the magic eraser
to reveal the correct
answer.
Chocolate
Raisins
Kathy
yes x x
Lisa
x yes x
Dan
x x yes
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Using a List to Organize Clues
The Redskins and Eagles played a football game. The Redskins scored 34 points. Use the clues to figure out how many points the Eagles scored.
It is less than 38.
It is more than 27.
It is a multiple of 4.
The two digits add up to 10.
28
29
30
31
32
33
34
35
36
37
The magic eraser will
reveal the correct answer.
28
29
30
31
32
Michelle Allen 5th grade BVE
33
34
35
36
37
problem+solving+2.notebook
February 17, 2009
Using a Venn Diagram to Organize Ideas
The coach brought the 10 players on Robbie's basketball team to the ice cream parlor to celebrate their big win. The palyers could order an ice cream cone, a soft drink, or both. 7 players had ice cream and 6 players had a soft drink.
Ice Cream
Michelle Allen 5th grade BVE
Soft Drink
problem+solving+2.notebook
Communicating About the Strategy
• Explain the strategy you used to solve the problem.
• Explain why you set up the matrix or Venn diagram the way you did.
• Explain how the matrix or Venn diagram helped you solve the problem.
• How did recording and eliminating possibilities help you solve the problem?
• What was difficult about this problem? How did you make it easier?
Michelle Allen 5th grade BVE
February 17, 2009
problem+solving+2.notebook
February 17, 2009
Work Backward
Working backward causes us to reverse our thinking. We do this when we know how a situation ends, but don't know how it started.
It is important to routinely refer back to the answer throughout the process. Otherwise, you may become confused and reverse the operations.
Pay attention to the order the information is presented. Sometimes they mix it up to challenge you.
ex. If it's 2:00 PM and we just spent 15 minutes reviewing our homework, what time did we start reviewing our homework?
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Practice Problems
If I have $4.00 in my pocket after going to the grocery store, and I spent $2.50 at the store, how much money did I have in my pocket to start?
Mrs. Higgins went to Burger Barn. She spent half the money she had on lunch. Then spent $0.75 on dessert. She had $1.00 left. How much money did she have at the start?
Michelle Allen 5th grade BVE
problem+solving+2.notebook
Recognize Familiar Problems
Ask yourself, how is this problem like another problem I have solved before?
Look for signal words like ­ more, same, twice, etc.
Lucy had a bag of gumballs.
She had more yellow than red.
She had the same number red as blue.
She had twice as many blue as green.
She had 4 green gumballs.
How many green gumballs did Lucy have?
Highlight the words that signal an operation.
Michelle Allen 5th grade BVE
February 17, 2009
problem+solving+2.notebook
February 17, 2009
Increasing the Complexity of Problems
Mr. Short had a rectangular garden. The perimeter of his garden was 48 feet. The length of his garden was 15 feet. What was the width of his garden?
Label the garden with the correct measurements.
Caroline waited in line for the rides at the amusement park. She got on the log flume ride in 2/3 the time that it took to wait in line for the coaster. The rapids line was 3/5 of the time it took to wait for the log flume. Caroline waited in line for 3/4 of an hour for the roller coaster. How long was the wait for each ride?
Start with what you know... 3/4 of an hour = 45 min. for roller coaster
Work backwards from there.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Equations
_____ + 3 ­ 1 = 12
Write a problem where you will have to Work Backwards to solve this equation.
Michelle Allen 5th grade BVE
problem+solving+2.notebook
February 17, 2009
Communication About the Strategy
• How did working backward help you solve this problem?
• Explain to a friend, who has never worked with this strategy, how to work backward to solve a problem.
• Why is working backward a good strategy for solving this problem?
• Why is it important to check your work after solving a problem using the Work Backward strategy?
• Write a problem that could be solved by working backward.
Michelle Allen 5th grade BVE