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Problem Solving Strategies

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Strategies for Problem Solving

Aug 25, 2014

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Strategies for Problem Solving. Math 7 and 8 Ms. Stewart. Problem Solving: A Four Step Process. Step 1: Read the Problem 3 Times On the first read, get a general sense of what the problem is about On the second, figure out what information is given and what you need to find

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Strategies for Problem Solving Math 7 and 8 Ms. Stewart

Problem Solving: A Four Step Process Step 1: Read the Problem 3 Times • On the first read, get a general sense of what the problem is about • On the second, figure out what information is given and what you need to find • On the third reading, underline/highlight the information you will need to solve the problem

Problem Solving: A Four Step Process Step 2: Select a strategy or several strategies for solving the problem • Think about other problems you have solved. Is this problem like one of them? Can you use a similar strategy? • Plan how to use the strategy and what tools you will need like a ruler, calculator, graph paper, number line, etc.

Problem Solving: A Four Step Process Step 2: Select a strategy or several strategies for solving the problem • Possible strategies to choose from: • Make a model or diagram • Act it out • Work backward • Look for a pattern • Make an assumption • Trial/Error • Choose an appropriate formula • Make an organized list, table or chart • Set up an equation and solve • Solve a simpler problem to shed light on a more difficult one • Find hidden or missing information

Problem Solving: A Four Step Process Step 3: Solve the problem by carrying out your plan • Use mental math to estimate a possible answer • Do the calculations • Record each step you are doing • Explain and justify your thinking

Problem Solving: A Four Step Process Step 4: Check your answer. Does it make sense? • Is your answer close to your estimate? • Does your answer fit the facts given in the problem? • Is the answer reasonable? If not, make a new plan. Try a different strategy. • Consider solving the problem a different way. Do you get the same answer? • Compare your method with other students

Grade 7 Word Problems

What strategies could solve these problems? Problem 2: Rani is paid $7 per hour to baby-sit the neighbour's two children. Rani is saving for a new bike. How many hours does he need to baby-sit to earn enough money for the bike? Problem 1: Honi has 100 m of fencing. She uses it to fence off a rectangular field for her horse to graze in. The length of the field is 30 m. How wide is the field? Problem 3: The corner store has five flavours of ice cream: orange fizz, strawberry, bubble gum, chocolate and rocky road. How many different two-scoop cones are possible? Problem 4: Marja would like to go glow in the dark bowling for her birthday. The alley charges $10 for one lane plus $6 per person. This includes bowling shoe rentals. Marja’s mother can afford $40. How many friends can Marja invite?

Problem 1 Solutions

Problem 2 Solutions

Problem 3 Solutions

Problem 4 Solutions

Grade 8 Word Problems

What strategies could solve these problems? Problem 1: Dina’s family owns and operates a small restaurant. They have many small square tables and folding chairs. What is the greatest number of people that can be seated when 10 tables are put together? Problem 2: A road crew is repainting the solid yellow line down the center of the road from Halifax to Truro. 1L of the paint covers 4m2. How many litres of paint does the crew need? Problem 3: Raj and his friend Matt live in a neighborhood where the streets form a regular grid pattern. How many different routes are there from Raj’s house to Matt’s? Assume that Raj does not retrace his steps and always takes the shortest route. Problem 4: Amy’s mother bought a basket of strawberries. Ben came and ate half of them. Steve came home next and ate half of the remaining berries. Dora returned and ate half the number that remained. Amy came home last. She ate half of the remaining strawberries and left two whole strawberries for her Mom. How many berries were originally in the basket?

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• Preferences

Different Problem Solving Strategies - PowerPoint PPT Presentation

Different Problem Solving Strategies

Different problem solving strategies russell larson elementary math coordinator pflugerville isd russell.larson_at_pflugervilleisd.net http://www.pflugervilleisd ... – powerpoint ppt presentation.

• Russell Larson
• Elementary Math Coordinator
• Pflugerville ISD
• russell.larson_at_pflugervilleisd.net
• http//www.pflugervilleisd.net/curriculum/math/
• 512-594-0123
• Help students deal with problems creatively and effectively
• Stimulate students and help develop thinking skills and problem solving strategies in both new and unfamiliar situations
• Develop, reinforce, enhance, and extend mathematical concepts and skills in students
• Help students engage in imaginative and creative work arising from mathematical ideas
• Mathematical problem solving skills are critical to successfully function in todays technologically advanced society
• Solving word problems requires understanding the relationships and outcomes of the problem
• You must make connections between the different meanings, interpretations, and relationships to mathematical operations
• Van de Walle, 2004
• Why teach different problem solving strategies?
• Explicit instruction with students who have mathematical difficulties has shown consistent positive effects on performance with word problems and computation
• Student receive extensive practice in use of newly learned strategies and skills
• Students are provided with the opportunity to think aloud, talk through decisions, and get immediate feedback
• National Math Panel Report 2008
• Pick the number of times a week that you would like to have chocolate (more than 1, but less than 10)
• Multiply this number by 2
• Multiply by 50
• If you have already had your birthday this year, add 1756
• If you have not had your birthday this year, add 1755
• Subtract the four digit year that you were born
• You should have a 3 digit number now
• The first digit is your original number.
• Walk 7 steps from where you are anddiscuss why with your partner why you think the Chocolate Math worked.
• Walk 9 steps from where you are anddiscuss the reasons your first partner gave.
• Walk 11 steps from where you are anddiscuss the combination of reasons
• May I please have some more information?
• May I ask a friend for help?
• May I have some to time to think?
• Where could I find that information?
• A students math vocabulary level directly affects his/her conceptual understanding of mathematics, ability to communicate with peers about mathematical problems, and performance on high stakes tests
• Numbers and Operation
• Algebraic Reasoning
• Measurement
• Probability/Statistics
• Making meaning from mystery
• Making sense of symbols
• Sorting and classifying unorganized data
• Focus on the Meaning of the problem, not just the numbers.
• Identify the numbers that are Important.
• Thinking leads to an Estimate of the answer- show reasonableness.
• TALK about all probable/reasonable answers.
• The association of keywords with the mathematical operation is problematic in that reliance on these translations cues can lead to systematic errors
• Misleading suggests the wrong operation
• Some problems dont have key words
• Sends the wrong message that the word problem doesnt have meaning and the structure of the problem is ignored
• Example Jose took the 26 baseball cards he no longer wanted and gave them to Brian. Now Jose has 71 baseball cards left. How many baseball cards did Jose begin with?
• Take a one step problem to ask a question about the answer without giving the answer.
• With a partner
• Each partner writes a basic word problem
• Write the missing question
• You can begin to create a class set of multi-step questions.. Trade with other class
• We want the students to
• Understand the problem
• Choose a strategy
• 4 cell matrix
• Detective Problem Solving
• See-Plan-Do-Reflect
• Group Approach to word problems
• Mrs. Evans wrote clues on the board to describe a mystery geometric shape. The fourth clue was erased. What clue is the most reasonable choice as the fourth clue?
• 1. It is a 3 dimensional object.
• 2. It has 6 faces.
• 3. It has rectangular shaped faces.
• a. None of the sides are equal
• b. It has 12 edges
• c. It has 5 vertices.
• d. It has 1 curved surface.
• Read, Explain, Reflective Reasoning
• 2 3 students in a group
• Witness, Detective, and By Stander
• Witness Sees everything
• Detective Solves the crime
• By Stander Observes all
• Get in groups of 3
• One will be the witness, one will be the detective, one the by-stander (silent partner)
• Each person gets the correct card for their part
• Listen for directions
• Witness and By-Stander will be the only ones to read the next slide.
• Maria and her family drove 1,236 miles on vacation. Monica and her family drove 376 miles on their vacation. What was the total number of miles both families spent driving on their vacations?
• Research says you have to read the problem multiple times in order to get all the details and information.
• Allow the witness to review the problem several times, and the detective needs to write down the facts they learn.
• Complete this sentence
• I think the Detective strategy was _________ because it will allow _______________.
• Different steps to understand word problems
• Everyone in the group reads the problem
• Everyone in the group must share a fact about the problem
• Everyone in the group must ask a question about the problem
• Work as a group to solve the problem together
• Make it Happen
• Make it Work
• Have the students explore MANY options!

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