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Different Problem Solving Strategies 3rd – 5th Grade

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Different Problem Solving Strategies 3rd 5th Grade Russell Larson Elementary Math Coordinator Pflugerville ISD Why problem solving is so important for students? – PowerPoint PPT presentation

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Title: Different Problem Solving Strategies 3rd – 5th Grade


1
Different Problem Solving Strategies 3rd
5th Grade
  • Russell Larson
  • Elementary Math Coordinator
  • Pflugerville ISD

Why problem solving is so important for students?
2
What Peppermint Patty would say about problem
solving!
We must help students realize that there is
MORE to problem solving than just numbers and
answers!
3
Examples of Student Problem Solving without
guidance
4
Why teach Problem Solving Skills
  • 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

5
What Research Says About Problem Solving
Strategies
  • 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

6
Effective Instruction Matters!
  • 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 provide with the opportunity to
    think aloud, talk through decisions, and get
    immediate feedback
  • National Math Panel Report 2008

7
Chocolate Math
  • 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
  • Add 5
  • 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.
  • Why????

8
7-9-11
  • 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

Why is math talk so important?
9
What to say instead of I dont
know!
  • 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?

10
Importance on Vocabulary in Problem Solving
  • 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
  • Geometry
  • Measurement
  • NCTM, 1999

11
Graphic Organizer for vocabulary development
Vocabulary Word
Student definition after table discussion
Teacher definition after table discussion
Picture
Picture
List Real World examples of vocabulary word
Picture
Picture
12
2 x 2 Writing Grids !
Students write a total of 6 sentences from the
grid. 2 words from the row (2 sentences) 2
words from the column (2 sentences) 2 words on
the diagonal (2 sentences)
13
3 Components of Mathematical Thinking
  • Making meaning from mystery
  • Making sense of symbols
  • Sorting and classifying unorganized data

14
What to do with word problems
  • 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.

15
Keywords can lead to misunderstanding
  • 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?

Typical answer 45 baseball cards. Why? 71 26
45 cards LEFT
16
2009 TAKS example
G is correct answer 82 BUT13 pick F. Why
17
Solving the Two-step problem issue
  • Take a one step problem to ask a question
    about the answer without giving the answer.

It took 3 hours for the Jones family to drive 195
miles to Washington DC.
Tony bought three dozen eggs for 89 cents a
dozen. (How much was the bill?) How much change
did Tony get back from 5?
Now, think about the answer, and give another
question that uses the answer to solve another
part of a question.
If they drove for 7 more hours the next day at
the same rate, how many miles did the Jones
family travel the second day?
18
2009 TAKS questions Two Steps
19
Two-Step Problem Solving
  • With a partner, write a grade level appropriate
    question that would involve 2 steps.
  • Write the question in parts
  • Part 1 answer
  • Part 2 new question that is the ACTUAL question.

20
Why teach Problem Solving strategies?
  • We want the students to
  • Understand the problem
  • Choose a strategy
  • Solve it
  • Look back

21
Different Strategies that will be introduced
  • 4 cell matrix
  • QTIPS
  • Detective Problem Solving
  • See-Plan-Do-Reflect
  • Group Approach to word problems

22
Analyze Math Word Problems4 cell matrix approach
Do I know the vocabulary?
What are the skills required?
What prior knowledge do I need?
Are there any distracters?
23
Lets Practice!
  • 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.

24
QTIPS approach
  • Question
  • Thought
  • Information
  • Plan
  • Solution

25
Lets practice!
Q T I P S
John could type 20 words per minute. He saw a job
advertisement that required 80 words per minute.
He had 5 weeks before he was going to apply for
the job. How many words per minute did he need to
improve each week to meet the job requirement?
26
Problem Solving Detectives Approach
  • 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

27
Lets Practice!
  • Get in groups of 3
  • One will be the witness, one will be the
    detective, one the by-stander (silent partner)
  • Each get a the correct card for your part
  • Listen for directions
  • Witness and By-Stander will be the only ones to
    read the next slide.

28
Witness Read this information and be ready to
answer questions from the detective.
  • 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?

29
Detective Ask all the questions you need. Write
down the responses from the Witness. By-stander
can take it all in.
  • 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.

30
Sentence Stems to debrief/review
  • Complete this sentence on an index card..
  • I think the Detective strategy was _________
    because it will allow _______________.

31
SEE PLAN DO - REFLECT
PLAN Reflect on the
problem Select an appropriate strategy simplify,
draw, patterns, guess/check modeling, act,
organize, work backward
REFLECT Reread the problem for
reasonable solution Check your solution Justify
your solution Explain your process
SEE Read the problem
carefully Identify the unknown Draw pictures or
diagrams Consider relationship of the
problem Restate the problem in kid words
DO Implement a strategy Solve
the problem Check each step Answer the question
32
Thinking Blocks approach to problem solving
  • Students work with proportional rods, Cuisenaire
    rods, or unifix/snapping cubes for problem
    solving models
  • THINKING BLOCKS
  • www.thinkingblocks.com/tryit.html
  • Different problems each time there is a link
    off each grade level web page

33
Group Approach to word problems
  • Different steps to understand word problems
  • Everyone in the group reads the problem
  • Everyone in the group must share a thought about
    the problem
  • Everyone in the group must ask a question about
    the problem
  • Work as a group to solve the problem together

34
Lets try it out together!
35
Balanced Classroom with Problem Solving
36
Why Different Problem Solving Strategies
  • Make it Happen
  • Make it Work
  • Have the students Explore MANY options!
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