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Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

Everyone can Start

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Consider the problem above. You may have seen posts like this on social media challenging your mathematical thinking. Where do you even start?

Everyone can start! Here are strategies to productively work through any problem.

Get a grasp on the question

You must be clear what the question is asking. 

What are the diagrams telling you?

The diagrams are representing a scale or an equivalence of weight.

What equivalencies are stated?

  1. one diamond and one square weigh the same as two diamonds and one circle
  2. two squares weight the same as three circles

What are you looking for?

The equivalent weight of 3 diamonds.

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Now can you relate this back to mathematical topics that you have learned?

For example, does this remind you of equations?

If x, y, and z represents the weight of a square, a diamond, and a circle respectively, then

I can rewrite the equivalencies

  1. x + y = 2x + z
  2. 2x = 3z

Ask yourself these critical questions:

  • What do I KNOW?
  • What do you want to FIND?
  • What can I USE?

STUCK?

Try creating different equations? 

Can you find an equation for one square, x? One circle, y? One diamond, z?

What about three or four of the same shape? 

What are the restrictions?

Can you put four shapes on one side of the scale?

What happens if you remove an object?

Does it stay balanced? Which side is heavier as a result?

Can you replace or rearrange shapes on one side or both? Try a few options, to see what balances and what does not.

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You do not need to know the answer to these questions! The ones you don't know may help you clarify what you can and cannot do.

What can I do?

Are we starting to see some equivalencies that will help us solve the problem?

The question asks for the weight of 3 diamonds, can I solve it if I can find the weight of one diamond? What about two diamonds?

Am I able to find the weight of one or two diamonds?

What answer(s) are possible? Does it have to be one answer?

STUCK!

Whenever you realize that you are stuck, write down STUCK! This will help you to proceed, by encouraging you to write down why you are stuck. For example:

  • I do not understand …
  • I do not know what to do about …
  • I cannot see how to …
  • I cannot see why …
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AHA!

Whenever an idea comes to you or you think you see something, write it down. That way you will know later what the idea was. Very often people have a good idea, but lose it subsequently and cannot recall it. In any case, it feels good to write down AHA! Follow it with

  • Try …
  • Maybe …
  • But why …

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  • Check any calculations or reasoning immediately.
  • Check any insight on some examples (specializing).
  • Check that you resolution does in fact resolve the original question.

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When you have done all that you can or wish to, take time to reflect on what happened. Even if you do not feel that you got very far, it helps to write up what you have done so that you can return to it freshly and efficiently at some later date. It is also the case that the act of summarizing often releases the blockage. There are several things worth noting particularly:

  • Write down the key ideas;
  • Write down the key moments that stand out in your memory;
  • Consider positively what you can learn from this experience.

Summary

Ask yourself these questions:

  • What approach can I take to solve the question?
  • What is another approach for solving?
  • Are you stuck?
  • Check the solution.
  • Reflect on key ideas and key moments
  • Extend problem to another context
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