Thursday, February 24, 2011

Problem 10

Today we solved a problem - draw on a geoboard paper a polygon with four dots on the sides of the polygon. Many gave quadrilaterals. Students were encouraged to draw figures other than quadrilaterals.

After finding the area of a few figures, a conjecture was made - figures with fours dots on the sides and none inside has an area of one.

This led to a discussion on instructional model for teaching problem solving.

Wednesday, February 23, 2011

Growing Plants

The groups did the planning on Day 2. On Day 3, they put into action their plan. And see the results next Monday.

This was a partial discssion of a problem solve din class today - a problem with insufficient (and useless) information.

Alice, Bob and Cheryl form a line to buy tickets.
The shortest is not first an the tallest is not last.
The boy is not the oldest and the youngest is a girl.
The oldest is not first in the line.

What are their positions in the line?

If there is no definite answer, are you able to work out all the possibilities?

Make-Up Work for Lesson 2

If you are absent for part of or the entire of Lesson 2, please complete Lesson 1 Reflection and submit it asap.

Also submit the solutions to the five problems done in class. make a list of problem-solving heuristics and illustrate three of them with examples. Submit this together with your Final Assignment.

One of the five problems is: Fold a square piece of paper in any way you like. With just one straight-line cut create each of the pieces shown in the second photo. The first photo shows your classmates solving the problem in class.

Shake Hands

Allan, Bella, Cheryl, David, Ernie and Farid shook hands with each other. Each person shook hands with everyone else once. Use three different methods to find the number of handshakes in the group.

Tuesday, February 22, 2011

Shake Hands, Say Good Evening and Other Problems

Three sticks are used to make a triangle this size. You need to make 4 such triangles - same size and also equilateral. How many sticks do you need? Can you use only six sticks?

There are five of you. Each says Good Evening to everyone else - once. How many Good Evenings are uttered?

What if instead of Good Evenings, each shake hands with everyone else once. How many handshakes are there?

What about if we do this with the whole class - 46 of us?

Did you like the Sound of Numbers Problem? One containers has 2 objects. The other one has an unknown number of objects. Shale both containers and listen to the sound. How many objects are there in the second container?


Use no more than 10 straws to build the tallest structure possible. It must be able to stand on its own. You cannot cut the straw. You can use masking tape if you wish.


Make a container using newspaper to hold exactly one cup of green beans.

Friday, February 18, 2011

Problem Solving 1

Photo Source: Jalan Besar PCF Kindergarten, Singapore

Problem: Cut the bread (square) in half. In the photograph, the students have 2 triangles and 2 rectangles. Are there other ways to do this?

Further Question: Do you get more jam on the triangle or the rectangle bread?

Today is the first day of lesson and the focus is on experiencing problem solving in mathematics and other domains so that we can arrive at a definition of problem and hence problem solving.

Tuesday, February 15, 2011

Welcome to MAT150 Developing Problem-Solving Skills

Welcome to the course.

It is one week before the course starts. The course is about, well, what the title says - developing problem-solving skills.

More about the course later when we meet in class from 22nd Feb onwards.

First thing first - you have some preliminary reading and writing assignment to get you ready for the course. Please refer to your Course Outline.

There is no prescribed books you need to read but the one suggested is Frameworks for Thinking. It is available online. You can read any other books or even what people write on the internet. The product is My Dictionary of Problem-Solving Terms.

You are expected to submit during the first meeting this booklet that you compiled based on your reading. The idea is that you are familiar with terms common in talking about teaching thinking. Please submit one copy to me and have your own copy for reference. You are likely to edit your entries during the course when you get new insights in the problem-solving process.

Enjoy your reading and see you in class with a sharp pencil ... and mind.