Build a Foundation for
Powerful Problem Solvers
Dr. John W. Staley,
Director Mathematics, Baltimore County Public Schools
President NCSM, National Council of Supervisors of Mathematics
[email protected]
@jstaley06
Take a quick minute and greet each person at your
table.
If there were 10 people at your table, how many
greetings -“handshakes” were there?
How many of your students love
solving ________ problems?
Word
Real-world
Application
Modeling
What tools do you give your students?
Today we will unpack a framework & strategies
that help students develop their problem-solving
toolkit.
Students will use a problem-solving model that
incorporates…
•
•
•
•
•
analyzing given information,
formulating a plan or strategy,
determining a solution,
justifying the solution, and
evaluating the problem-solving process and the
reasonableness of the solution.
1. Make sense of problems and
persevere in solving them.
6. Attend to precision
Standards for Mathematical Practice
2. Reason abstractly and quantitatively
3. Construct viable arguments and
critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in
repeated reasoning
Overarching habits of mind of a
productive mathematical thinker
Reasoning and
Explaining
Modeling and
Using Tools
Seeing Structure
and Generalizing
STAAR-G5-2014Test-math
Problem Solving Process
 Read
- Understanding the Problem
 Plan - Devising a Plan
 Do - Carrying out the Plan
 Look Back - Looking Back
Thinking Behind the Process
 Study the Problem
 Organize the Facts
 Line up a Plan
 Verify your Plan with Action
 Examine your Answer
READ - Understand the Problem
Study the Problem
Highlight the question.
Answer the question
“What is the problem asking
me to find?”
STAAR-G5-2014Test-math
READ
The max number of golf balls he can put in each
box.
Ezekiel can put _____ golf balls in each box.
READ - Understand the Problem
Organize the Facts
Identify each fact.
Eliminate unnecessary facts.
List all necessary facts.
STAAR-G5-2014Test-math
433 golf balls
11 boxes
Same number in each box
READ
READ
2 PLAN - Devise a Plan
Line up a Plan
Identify operation(s) and/or a problem
solving strategy.
Write out the plan in words or as a diagram
according to the strategy selected.
PLAN: Problem Solving Strategies
 Guess, Check, Revise
 Write an Equation
 Use Reasoning
 Work Backwards
 Solve a Simpler Problem
Act it Out
Draw a Picture
Make a List
Make a Table/Graph
Look for a Pattern
Multiple Representations
Verbal
Representation
Graphic
Representation
Numeric
Representation
Algebraic
Representation
STAAR-G5-2014Test-math
433 golf balls
11 boxes
Same number in each box
PLAN
Divide number of
balls by boxes
STAAR-G7-2014Test-math
PLAN
3 DO - Carry Out the Plan
Verify your Plan with Action
Make an estimate.
Carry out your plan.
STAAR-G5-2014Test-math
433 golf balls
11 boxes
Same number in each box
Divide number of
balls by boxes
DO
40 golf balls
STAAR-G5-2014Test-math
DO
40 golf balls
DO
4 LOOK BACK
Examine your Answer
Does your answer make sense?
Is your answer reasonable?
Is your answer accurate?
Write your answer in a complete sentence.
STAAR-G5-2014Test-math
LOOK
BACK
40
golf balls
MS
R
A
Ezekiel can put 39 golf
balls in each box.
LOOK
BACK
Problem Solving…Modeling
READ
PLAN
LOOK
BACK
DO
CCSSI_MathStandards.pdf
Problem Solving


Read - Understanding the Problem

Study the Problem

Organize the Facts
Plan - Devising a Plan


Do - Carrying out the Plan


Line up a Plan
Verify your Plan with Action
Look Back - Looking Back

Examine your Answer
Communication
Communicating to
 Organize your thoughts and
explore
 Ask questions
 Tell your point of view
 Tell what happened
 Explain
 Justify
CH 2

Culture of communication

Building Student
Independence

Using Communication to get
Unstuck
SOLVE
http://www.ntnmath.com
http://ntnmath.com/video%20index/SOLVE/SOLVE.html
Implement tasks that Promote Reasoning and Problem Solving
Teacher Actions

Opportunities for exploring and solving problems that build on and
extend their current mathematical understanding

Selecting tasks that have multiple entry points through the use of
varied tools

Posing tasks on a regular basis

Support without taking over

Encourage varied approaches and strategies
http://www.mathedleadership.org
Research Recommendations
Assisting Students Struggling with Mathematics: Response to
Intervention (RtI) for Elementary and Middle Schools
 Recommendation 3. Instruction during the intervention
should be explicit and systematic. This includes providing
models of proficient problem solving, verbalization of
thought processes, guided practice, corrective feedback, and
frequent cumulative review.
WHAT WORKS CLEARINGHOUSE, April 2009
http://www.rti4success.org/sites/default/files/rti_math_pg_042109.pdf
Research Recommendations
Improving Mathematical Problem Solving in
Grades 4 Through 8
 Recommendation 2. Assist students in monitoring and
reflecting on the problem-solving process.
 Recommendation 3. Teach students how to use visual
representations.
WHAT WORKS CLEARINGHOUSE, May 2012
http://ies.ed.gov/ncee/wwc/pdf/practice_guides/mps_pg_052212.pdf
http://ies.ed.gov/ncee/wwc/practiceguide.aspx?sid=16 (supporting videos)
Build a Foundation for
Powerful Problem Solvers
Dr. John W. Staley,
Director Mathematics, Baltimore County Public Schools
President NCSM, National Council of Supervisors of Mathematics
[email protected]
@jstaley06
Problem Solving
(Polya’s Principles – S.O.L.V.E. Thought Process)
READ
Study the Problem
Highlight the question.
Answer the question,
“What is the problem asking me to find?”
Organize the Facts
Identify each fact.
Eliminate unnecessary facts.
List all necessary facts.
Plan
Line up a Plan
Choose an operation and/or strategy.
Tell in words how you are going to solve the
problem.
Do not use numbers in this step.
Do
Verify your Plan with Action
Estimate your answer.
Carry out your plan.
Look Back
Examine your Answer
Does your answer make sense?
Is your answer reasonable?
Is your answer accurate?
Write your answer in a complete sentence.
Baltimore County Public Schools, Office of Mathematics PreK-12
Adapted from Algebraic Thinking, National Training Network
Write the problem
Read: Study the problem
Plan: Line up a plan
What is the problem asking me to find?
Check the strategy(ies)
I will use.
Read: Organize the facts
List the facts I need to solve the problem.
 Act it out
 Draw a Picture
 Make a List
 Make a Table/Graph
 Look for a Pattern
 Try, Check, Revise
 Write an Equation
 Use Reasoning
 Work Backwards
 Solve a Simpler Problem
Check the operation(s) I
will use.
 Addition
 Subtraction
 Multiplication
 Division
Do: Verify the solution
Look Back: Evalute
Find the solution to the problem by showing all steps.
Check to see if my
solution is…
Reasonable
Accurate
Baltimore County Public Schools, Office of Mathematics PreK-12
Adapted from Algebraic Thinking, National Training Network
Problem Solving PreK-12
READ
PreK -K
1-2
3-5
6-8
Listen to the
story
Visualize
Visualize
Retell
Retell
Think
Represent
Line up a
Plan
Formulate
Compute
Interpret &
Validate
Study the
Problem
Organize the Facts
PLAN
Tell the story in
own words
DO
Solve the
problem
Solve
Solve
Verify your
Plan with
Action
Look
Back
Show your
solution
Share your
strategies
Check and Justify
Examine
your Answer
9 - 12
Understand
the Problem
Updated: June 3, 2016
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