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

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Problem Solving What’s the problem? Introduce ourselves

“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.

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

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

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.

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.

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

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

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

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

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

During #5 Resources

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

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!

→ gather the facts and decide what you’re being asked to find

Making Math Meaningful Marian Small

Making Math Meaningful Marian Small

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?

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

Taken from Puddle Questions Grade 3 Joan Westley