Category: Math 10

Colour, In Math- Inquiry Project 2017

kaitlyns2016 on


Inquiry 2017 -1xu7kj0

Main Question: My main inquiry question is “Can Colours Exist in a Mathematical Form?”. I wanted to know if it was possible for colour to be represented by math.

Further Questions: After all of my research and findings, I became really interested in the idea of being able to do what a computer does, in your own brain, mainly towards calculating colours and colour codes. My new question is “How do Computers Calculate the Hex Colour Code of Two Different Colours Added Together?”

Extension: This project was a really cool exploration for me because I learned a lot about the hexadecimal system and colour codes, which is so interesting to see. I found that being able to understand how the computer sees colour was really exciting because a device functions so differently than the human brain. Its very cool to see such a visual concept put into materialistic content, because colour really is something you see and witness. I think that I can go further with my project by elaborating my insight on the hexadecimal system, so one day, i can actually calculate and manipulate colours the way the computer does.

 

Algebra Tiles Review Math 10 H 2017

kaitlyns2016 on

These are examples of how you use algebra tiles to represent an equation. The large squares represent X squared, and had two sides, blue and red, to determine whether it is positive or negative (blue = positive, red = negative). There is also the long rectangles that represent X, with the positive side being green and the negative red. The side length of X is the same side length of X squared, which makes sense because X multiplied by X equals X squared. The smallest square pieces represent the number 1. The colours are yellow for positive and red for negative. These are the basic pieces used in algebra tiles, and the ones that I used today.

In the image above, you see that there are two X tiles and one 1 tile across the top. They are all positive. Down the left side, there is one positive X tile, and two negative 1 tiles. Inside the grid, you see a series of shapes that fill the area. This equals the answer to the original equation. All of the tiles correspond to the side lengths of the shapes outside of the grid. Inside there are two positive X squared tiles, four negative

In this image, the tiles that fill the space are two negative X squared tiles, five positive X tiles, and two negative 1 tiles. To find the tiles that make up this answer, you use the side length of the inner tiles and translate it to the outside, so the X squared tiles would have a side length of an X tile. An X tile would have the side lengths of an X tile and a 1 tile. To determine whether it is either positive or negative, you would just use the rules that two negatives or two positives multiplied together equal positive, and a positive multiplied by a negative equals a negative.

Garibaldi Lake Task

kaitlyns2016 on

Garibaldi Lake Task

Garibaldi Lake is a beautiful alpine lake that is located north of Squamish. It is turquoise in colour because of the meltwater from the glaciers, and is cascaded by many mountains, including Mount garibaldi.

How to Estimate Garibaldi’s Volume

Sources: https://en.wikipedia.org/wiki/Garibaldi_Lake

https://www.google.ca/maps/place/Garibaldi+Lake/@49.9319498,-123.0535502,13z/data=!4m13!1m7!3m6!1s0x54871de627a17cc9:0x913f7329f4571920!2sGaribaldi+Lake!3b1!8m2!3d49.9366437!4d-123.0272101!3m4!1s0x54871de627a17cc9:0x913f7329f4571920!8m2!3d49.9366437!4d-123.0272101?dcr=0

How to Evaluate the Lakes Volume

Sources: https://en.wikipedia.org/wiki/Garibaldi_Lake

The Barrier

The Barrier is a lava dam that holds up Garibaldi Lake. Though it is currently stable, there are many fears that it will one day collapse and let the lake drain down into Squamish, thus creating a a problem for many people below.

What would happen if the Barrier faulted?

Sources: https://en.wikipedia.org/wiki/The_Barrier

http://www.squamishchief.com/news/garibaldi-lake-a-ticking-time-bomb-1.1753732

 

Math 10 Honors Numbers Summary

kaitlyns2016 on

Math 10 Honors Numbers Summary

In the last few weeks, our class has learnt a lot about Numbers and Radicals. Most of the material we went over was familiar, although there were a few things that were brand new to me.

Prime Factorization:

One of those things is how when you use prime factorization, it can help you to determine the prime factors that make up that number. Prime factorization is really helpful because you are breaking down the number to its smallest roots, and that can help you find out a lot about the number.

HOW IT WORKS:

You start with a number you want to prime factorize. You then begin to break it up into whole multiples of itself, and then break those multiples into smaller multiples, and you keep doing this until you end up with numbers that cannot be broken up into whole numbers any longer, otherwise known as Prime Numbers. These last prime numbers are the prime factors of your original number, which means if you multiply them all together, you should end up with the original number.

GCF & LCM:

Another example is how you can use prime factorization to find the LCM and the GCF.

GCF: This is the Greatest Common Factor between two numbers. The easiest way to find a GCF is to prime factorize 2 numbers. Once you have done that, you take out the common factors within both numbers and multiply those together to get the GCF.

LCM: This is the Lowest Common Multiple between two numbers. The easiest way to find a LCM is to prime factorize 2 numbers. Once you have done that, you take out all factors of both numbers, except for the ones common between the two numbers. Then you multiply those together to get het LCM.

Radicals:

I also learned the concept of turning entire radicals into mixed radicals, and vice versa. This is a neat trick for simplifying radicals and making them into easier numbers to understand and work with.

HOW IT WORKS:

Find a number that is not a perfect square, cube, etc. Take out a factor that is a perfect square or cube, etc, depending on the root of the radical. Once you have found a number, root it so it becomes a coefficient. Keep on dividing the number inside the radical until you have a number that is not divisible by the root anymore. You will then be left with a mixed radical.

Converting Mixed to Entire:

To convert a mixed radical into an entire radical, you basically take the coefficient and depending on the root, you square or cube, etc, it and multiply it with the number inside the radical. Then you are left with a larger, “entire” radical.

Those were the highlights for me in this unit. I found these 4 things very helpful and interesting, and I will definitely be using these tricks in the future.