*A Mathematical Problem is...*-when you can't get the answer immediately

-unclear about what strategy to use or how to work through a method

**A problem should be....**interesting

motivates the need to solve it

context that interests them

uses their name if possible

at the appropriate level

provides a challenge but allows success

__Big Ideas__**Work systematically**

- organising systematically supports logical and systematic approach to math. Teachers need to model and remind students often about this.

**Look at solved problems**

Some problems can be solved in similar ways. Comparison of strategy use rather than context.

**Solve a simpler Problem**

use smaller numbers to demonstrate the strategy then scaffold to larger numbers

**Find a pattern**

- patterns in math can be easy or complicated. Looking for them is problem solving

**Work Backwards**

- justify your answer if you know it.

__Strategies to teach__**Guess and Check**-

*simplest strategy however develops complexity when justifying the pattern*

**guess is a conjecture, checks are called proofs, a guess that has been checked becomes a theorem**- gain better understanding of problem

- might know the answer

- systematically try possible answers

- our choices have been narrowed down by other strategies

- no other obvious strategy to try

**Guess and Improve**

*- students use initial guess to improve their next one*

**Act It Out**-

*great for demonstrating to class*

- problem is about doing things

- aids understanding

Use equipment -

*should be used by all students of all ages*

-may be difficult to keep track of the solution.

-encourage students to keep a record of what they are doing

- supports logical thinking and sequence of events to solve a problem

**Make a Table**-

*vary in form*

- efficient way of finding number patterns

**Make an organised list**

- should be in natural order

-categorised under headings

Draw a diagram

*- anything that is not a picture, more symbolic dots for animals etc*

**some frequently used diagrams have names - tree diagram**- geometric figures or measurements involved

- gain understanding

- need a visual representation

**Draw a Picture**-

*only drawing enough detail to explain thinking to solve problem*

**Questioning -**

*scaffolds, creates ownership, directs thinking, empowers the learner, maintains momentum of the learning, encourage ideas,*

**Getting Started***-*What are the important things in this problem?

- What is the problem asking you to find out?

- What information has been given?

- Can you guess what the answer might be?

-Has anyone seen a problem like this before?

-What strategy might you use to get started?

**While working on the Problem***-*Tell me what you are doing.

- Why did you think of that?

-Why are you doing this?

-What will you do with the result when you've got it?

-Why is this idea better than this one?

-Can you think of another way to find the answer?

-Can you justify this step?

**At the End***-*Have you answered the question?

-Have you checked your answer?

- Does the answer look reasonable?

- Is there another answer?

-Can you explain your answer to the class?

-Is there another way to solve this problem?

-Can you make the problem harder /trickier?

-What if....

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