Donkeys Revenge – Exponent Laws

First blog post of Grade 9! Good to be back. Over the last month I have been working on a Scimatics group project called Exponent Laws. Throughout it we learnt what exponents are, how they’re used, and how to incorporate them into a board game for our final product.

Starting out this project like any other by getting into groups and creating some very basic game rules using exponents to get a sense of what everyone knows. This was milestone 1. This is actually where a lot of big decisions were unknowingly made for the final project. The people I did milestone 1 with was with Judah and Ewan who eventually became our final group. This was also where our decision to have a Shrek themed game was made, these were our game rules:

Ending off the first day of the project with a mind map to gather any questions, information, and ideas for the project, this was mine:

Over the month we were working on math sheets to learn the 6 different exponent laws. These laws help us do different exponent equations and are a requirement to have at least 4 in our final game, we only ended up having 2-3 rules in our game.

Law 1: Product of Power a^2 x a^4 = a^6

  • add exponents when multiplying alike bases

Law 2: Quotient of Powers a5 / a^3 = a^2

  subtract exponents when dividing alike bases

Law 3: Power of a Power (a^3)^5 a^15

– multiply exponents when raising a power by another exponent

Law 4: Distributed Property

– division division (a / b)^2 = a^2 / b^2

  • multiplication (a x b)^8 = a^8 x b^8

Law 5: Zero Power 15^0 = 1

– anything to the power of 0 is 0

Law 6: Negative exponents 7^-2 x 4 = 7 / 7 x 4

  • multiplying a negative number is dividing a positive number vice versa

It then came time for milestone 2, our first draft of game rules. These were very unclear as we hadn’t fully finished the game yet. Over time and through more revision we redefined the rules, this was draft 1:

We are now starting to get to the point where we nee to think about the physical game board and its pieces. After back and forth’s on whether to use coins, dice, what kind of cards, we decided on cards, player pieces, and a game board we would all make ourselves.

Milestone 3 shows up in the form of a Khan Academy quiz. I didn’t do very well on this quiz as I hadn’t memorized the different laws very well. Studying on my part would have easily solved this issue, lets remember that next time.

Immediately onto milestone 4 with our second draft of game rules and our cards. By now we had gotten a good understanding of what we wanted our rules to be. We had a problem which we felt present throughout the entire project which was organizing our rules. If I had to do this project again I would get some other game rule sheets (monopoly, risk) and see how they formatted their rules.

Milestone 5 was an exponent laws test. Unlike the Khan Academy quiz this was on paper which was personally a big relief. I was glad the test showed up at the time it did because the project began to feel too focused on making the game.

The time in between milestone 5 and 6 was used to finalize our game. The rules, pieces, board, cards all to be presented and played by another class in a couple of days. I took care of the game board and player pieces, Ewan finalized the cards and although Judah was ill some of the time he still managed to pull his weight. Here are the final cards and final board:

Here we are with game day, milestone 6. It was really fun to see and play everyones game and ignore the underlying thought that everyone else’s work was more creative than ours. When it came to playing our game it was pretty fun and didn’t seem that challenging to the players. The rules didn’t have to be repeated too many times, it was pretty easy to get a hold of. I did realize that our group focused a little too much on the game aspect, calling back to when I mentioned we only had 2-3 game rules. I think our group just needed examples on where to go for this project. Now next years grade 9s have a lot more examples, you’re welcome.

There were 3 competencies I needed to complete for this project. “Reasoning and Analyzing”, “Communicating and Representing”, and Applying and Innovating”.

I would say we were accomplished in using logic and patterns to solve puzzles and play games. Donkeys Revenge had a logical repeating pattern to get to the end: roll dice, draw card, interact with card, repeat. We had a points system that impacted the game (health and shield points) which portrayed easy win conditions.

When it came to representing mathematical ideas in concrete, pictorial and symbolic forms we were in between developing and accomplished. We had pictorial math with cards to progress through the game. However we only had 2-3 exponent laws in the game so we didn’t represent exponents as best as possible.

The last competency is more individual: Contribute to care for self, others, community, and world through individual collaborative approaches. I was using my time efficiently in class to not fall behind, I’ll say the same about the rest of my group.

Now that the quiz, test, game, and worksheets are finished the only thing I have to answer is this projects driving question, being:

“How does math make games more complex, interesting, and re-playable?”

Math is both probable and certain. Addition and subtraction questions wont change because there is only 1 outcome, for example 4 + 4 will never not = 8. But with things like coin tosses, spin wheels, and multiple choice quizzes there are multiple possibilities you cant control the outcome of. Applying this to the idea of playing a game, if every function in the game only has 1 outcome the game gets boring and stale fast. However with multiple outcomes it becomes more complex and re-playable and variable you cant control games become a lot more interesting.

The project has now come to a close, so what are my thoughts? I really like this project but it was easy to lose sight of what was important. It was by no means boring because we got to make a game, but also easy to lose focus because we got to make a game. Ive actually done another project similar to this last year which you can read here. Adios.

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