Balancing Teddies

The Problem:

(Click on the photographs to enlarge them)

If one yellow teddy balances with two green teddies...




And one green teddy and one yellow teddy together, balances with six red teddies...





Then what balances with two red teddies?

The Solution:

Well if one yellow teddy equals two green teddies; and one green teddy and one yellow teddy together equals six red teddies, then you can replace the yellow teddy with two green teddies. So when you add these two green teddies to the one green teddy that is already on the balance pan, then three green teddies must equal six red teddies.




Once the teddies are put in this arrangement, then it is easy to see that one green teddy is the same as two red teddies.



So what balances with two red teddies?


One green teddy!

What did I learn from doing this activity?

I learnt that to solve this problem, I had to apply algebraic thinking in that I had to figure our how the two facts presented in the problem related to each other - I had to identify the relationship between the two rules. Once I saw the connection, I saw that the yellow teddy on the scale could be replaced with two green teddies, the rest of it was easy to solve visually. From this activity I learnt that algebraic thinking is not limited to manipulating numbers and abstract symbols, but that in some instances visual and even concrete representations can present easier solutions. This activity taught me that using visual and concrete reprentations does not necessitate a trial and error strategy or approach. I also learnt that being able to reflect on the process of how I reached my solution, explain my thinking processes to someone else, then documenting it visually (in a way that made sense) were all difficult to do because it required a much deeper appreciation of the mathematical reasoning in order to justify my solution.

If I were to provide opportunities for children to investigate this activity, I would provide the relevant materials and set the scales up similar to the picture above. I would also allow time for the children to manipulate the material, contemplate their own reasoning before asking them to share how they got their solution and justify their processes.