1. 5th Grade Problem Solving
with
8 Mathematical Practices
Laura Chambless
St. Clair RESA Consultant
www.protopage.com/lchambess
2. Pre & Post Teacher Survey
Complete the left side
“Before Attending
Mathematical Practices
Workshop”
3. Write Your Own Story
Problem
1. Think of a story problem you
would use with your students.
2. Write it down on a 3x5 card.
3. Place the card under your name
tag.
4. Learning Target
I can integrate the Mathematical
Practices in my teaching to
develop deeper mathematical
knowledge within my students.
5. 8 Mathematical Practices
CCSS for Mathematical
Student-friendly Language
Practice
Make sense and persevere in I don’t mind trying many times to understand and
solving problems. solve a math problem.
Reason abstractly and
I can think about the math problem in my head, first.
quantitatively.
Construct viable arguments and I can make a plan, called a strategy, to solve the
critique the reasoning of others. problem and discuss other students’ strategies too.
I can use pictures, objects, math symbols, and
Model with mathematics.
numbers to show how to solve a problem.
Use appropriate tools I can choose the best math tool like calculators,
strategically. rulers, pictures, or objects to solve the problem.
I can check to see if my strategy and calculations are
Attend to precision.
correct. I use clear mathematical language.
Look for and make use of I can use what I already know about math to solve
structure. the problem.
Look for and express regularity I can use different strategies or find a pattern from a
in repeated reasoning. similar problem to solve a new math problem.
From: Teaching Children Mathematics, March 2012, Getting Started in K – Grade 2, pg. 440-445.
www.protopage.com/lchambless
7. Solve and Discuss Structure
• Some children go to board and solve
a problem
• Other children solve the problem at
their desk.
• Teacher asks two children at the
board to explain their method.
8. Solve and Discuss Structure
The explaining student:
• Relates solution to a math drawing
• Asks if there are any questions
• Responds to the questions
The listening student:
• Asks questions
• Suggests edits to the explanation or
solution
9. Solve and Discuss Structure
• The Solve and Discuss Structure is
actually a
Solve, Explain, Question, and Justify
structure
• Aspire to make your classroom a
place where all children listen to
understand each other, not just being
quiet while someone else is talking.
10. Content Focus
5.NF.6
5.OA.6 Standard:
Solve real world problems involving
multiplication of fractions and mixed
numbers
11. How Does MP Look in Action
Your Story Problem
Liz put 2/5 of her money in the
bank and spent ½ of the
remainder. If she had $30
left, how much money did Liz have
at first? Write an equation.
3 min. by yourself
15 min. with a small group (2 or 3)
Report out 2 min per group
12. Mathematical Practice
Rubric
3 min. Review Rubric
(from: Institute for Advanced Study)
http://www.ocf.berkeley.edu/~mimiyang/misc/rubric.pdf
Pair Share
1. Look at Math Practice #1 and #2
2. Discuss where your story problem fell
on the rubric.
3. Group Discussion
13. Remodeling Tasks
Original Problem
Liz had $100. She put 2/5 in the bank and spends ½
of what is left. How much did she spend? Write an
equation.
How did I make it more
intellectually challenging?
*** Review Level of Cognitive Demand Handout
14. Analysis of My Task
Part 1: Selecting and Setting up a Mathematical Task
Goals: 5.NF. 6 Standard
Solve real world problems involving multiplication of fractions
All Task Answers: $100 should see different representations
Representations Used: array drawings, fraction bars, comparison
bars, …
Record and Report work:
Independently- 5 min. using whiteboard
Small Group– 5 to 15 min. - adding to each students whiteboard
Whole Group Report: 2 min.
15. Analysis of My Task
Part 2: Supporting Students’ Exploration of the Task
Questions to help get started:
1. Can you tell me what is happening in the story?
2. Is there another ways can write the equation?
3. Can you make a list of all the steps needed to solve the
problem?
4. What representation are you thinking about using?
5. Which operation do you think you need to use?
6. What are you being asked to find?
7. How can you break apart the problem?
Look at Common Errors pg. 126 to help think of questions.
16. Analysis of My Task
Part 3: Sharing and Discussing the Task
What solution paths do you want shared during class
discussion?
*How many steps are in the problem, *Where to start in the
problem,*Once you knew how much she spent, how did you
figure out the missing 2/5s?
Looking for different strategies and representations.
Mathematical Ideas: fractions broken into equal parts
Expand on, debate, and question the solutions
Solve and Discuss: (Solve-Explain-Question it- Justify it)
Evidence
Questions to build mathematical ideas connections
Why did you start where you did? Did anyone else start there?
Can anyone retell what that group just said?
How are _____’s pictures same/different than ____’s pictures?
17. Your Story Problem
1. Get into groups of 4.
2. Everyone reads their story problem
they wrote at beginning of session.
3. The group chooses one to remodel.
4. Each person fills in the Remodeling
a Mathematical Task sheet while
group is collaborating.
5. Groups will give a 2 min. report to
class.
18. 2 Minute Report
Requirements
• Original Problem
• Remodeled Problem
• Mathematical Practice- refer to rubric
• Part 1: Setting up the mathematical
task
• Part 2: Questions to supporting
students’ during task
• Part 3: Questions to use during class
discussion
20. Problem Solving with
Bar Diagrams
1. Understand: Identify what is known and what is
unknown. Draw the bar diagram to promote
comprehension and demonstrates
understanding. (Situation vs. Solution Equation)
2. Plan: Decide how you will solve the problem
(find the unknown). Analyze the bar diagram to
find a solution plan.
3. Solve: Execute the plan. Use the bar diagram to
solve.
4. Evaluate: Assess reasonableness using
estimation or substitution. Substitute the
solution for the unknown in the bar diagram.
21. Bar Diagrams
Watch Introduction Video
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p1/index.html
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p2/index.html
