1. Problem Solving
What’s the problem?
Introduce ourselves

2. “If it can be solved using a procedure or an algorithm, it is not a problem. It’s an exercise.”
What is a problem at one time to one child, may be an exercise to another.
Ex. Sharing cookies to a student in grade 1 could be a problem but to a child in grade 4…it’s very likely an exercise.
What do you think about this quote? Discuss.

3. Why teach through problem solving?
The math makes more sense.
Provides the teacher with more understanding of the student’s mathematical thinking.
A challenge can be very motivating
Problem Solving builds perseverance

4. Builds confidence, maximises the potential for understanding, allows for differences in learning styles and approaches
Practice with concepts and skills
Provides students with a stronger understanding of what math is about
Students needs to practise problem solving

5. I took a handful of M&Ms. 1/3 of them were red. Draw the handful.
Before
I took a handful of M&Ms. 1/3 of them were red. Draw the handful.
During
You have ¾ of the pizza left. If you give 1/3 of the left over pizza to your brother. How much of the whole pizza will your brother get?
After
Pay attention to how you solved the problem & share your ideas.
Taking you through a typical 3-part lesson using problem solving as a focus.

6. What is it?
To teach through problem solving, the teacher provides a context or a reason for the learning by beginning the lesson with a problem to be solved and later drawing out any necessary procedures. This approach contrasts with the more traditional approach of presenting a new procedure and only then offering a few problems for students to solve.
(P.38 Making Math Meaningful, Marian Small)
Simply read. Discuss.

7. Things have changed…. Now Step 1: Begin the lesson with a problem
Step 2: Draw out the procedures used
Then
Step 1: Teach the procedure
Step 2: Provide problems that use that procedure

8. Think about the questions you just worked through.
What do you think that lesson would have looked like “then”?

9. A Good Problem: is a question that cannot be answered immediately
is challenging to the learner
holds the learners interest
might have several answers
might have 1 answer but many different approaches
is often connected to real life

10. 3-part Lesson Before Get students mentally ready to work on the task,
(Getting Ready)-20 minutes
Get students mentally ready to work on the task,
Be sure all expectations for products are clear;
During
(Students Work) – 20 minutes
Let go!
Listen carefully,
Provide hints,
Observe and assess;
After
(Class Discourse) – 20 minutes
Accept student solutions without evaluation,
Conduct discussion as students justify and evaluate results and methods (reflection).
(Adapted from Elementary and MiddleSchool Mathematics:Teaching Developmentally   4th Ed., John Van de Walle)
Talk about the lesson that just happened & discuss this though that lens

11. I picked up a handful of M&Ms. One third of them where red
I picked up a handful of M&Ms. One third of them where red. What might the drawing of the M&Ms look like?
Page 27, #4
Examples of resources to find good questions

12. During #5
Resources

13. A Problem Solving teacher:
Encourages risk taking
Provides enough time to students
Respects and encourages respect for each others thinking
Provides opportunity for discussion and challenge solutions
Values perseverance

14. How to teach problem solving?
Begin with the problem
Teach students the Three Read Strategy
Allow students to work on the problem
Draw out the different strategies used
Three-read strategy
1st Read
→Visualise
→ set the context
→ get a general impression
2nd Read
→ listen for details
→ gather the facts
→ determine what question is being asked
3rd Read
→Check the facts
→ check the understanding of the question
Solve!

15. → gather the facts and decide what you’re being asked to find
Three-read strategy
1st Read
→Visualise the context
(ask students general questions)
2nd Read
→ gather the facts and decide what you’re being asked to find -
3rd Read
→verify your facts, clarify what you have to find.
Solve!
1st Read General Questions: about pizza & fractions & brothers
2nd Read: ask students to records these things; when hands shoot up glace at their paper & see if they’ve done this first…nothing get answer til then

16. Problem Solving with Grade 5s

17. Making Math Meaningful Marian Small

18. Making Math Meaningful Marian Small

19. FERMI Questions
Ex. How many piano tuners are there in Toronto?
People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be?
How many hairs are there on a human head?

20. Some problem solving resources
Making Math Meaningful Marian Small
Roads to Reasoning
Puddle Questions
NCTM website
Math Makes Sense texts

21. Taken from Puddle Questions Grade 3 Joan Westley