Problem solving challenges

Why Problem Solve?

Problem Solving teaches flexibility, creativity, cooperation, discovery, confidence.

Step 1: Read and Understand the Problem

· What does it ask for?

· What important information is given?

· Will drawing a diagram or representing it more visually help?

Step 2: Choose a Strategy

· What strategies could be helpful?

· How will you keep track of your ideas?

· Some possible strategies;

                    Guess & check

                    Guess & improve

                    Draw a table (to find a pattern)

Draw a diagram

                    Use algebra

                    Use a model or matrix

                    Use equipment

                    Use smaller cases or easier examples  

Step 3: Solve the Problem

·      Informally explore – play around with ideas

·      Neatly set out your work using the selected strategy

·      Be systematic, follow a logical sequence of steps

·      Apply the mathematical skills you already have

·      Be prepared to change strategies if things don’t work out

Step 4: Look Back

·      Have you solved the problem?

·      Could it be solved in a better way?

·      Is the solution correct? How can you tell?

Here are some class problem solving challenges:

• Can you move a marble uphill with touching it?

• Can you draw the process of making toast?

Coding challenges:

• https://code.org/

• https://www.codesters.com/code/

Other Resources

https://robertkaplinsky.com/lessons/

https://www.edgalaxy.com/journal/2012/5/29/an-excellent-collection-of-fermi-problems-for-your-class.html

Leaning Tower of Pasta

Ping Pong Pickup Challenge

Mathscraft challenges

Tricky problems (you will need to make assumptions and justify them)

How many tonnes of CO2 emissions could be avoided in your lifetime if New Zealand transitions to a completely electric vehicle fleet?

How many rocket launches from Mahia Peninsula would it take to establish a lunar colony?

What is the fastest humanly possible time for the Olympic 100m freestyle event?

If a New Zealand student uploads a video clip that goes viral, how long will it take before 1% of the world’s population has seen it?

If Mount Taranaki erupted, how much would it cost the aviation industry?