~ Combining like terms

When we started our polynomials unit, that was when we first started to use algebra and variables were still very new to me. We started off by using algebra tiles representing constants and coefficients which helped but I was still overwhelmed because of all the new things that I was learning at once. It was hard to keep track of everything but as we progressed, I go the hang of it. Eventually , we were given harder questions like 2x+3-x+5x-2x to the power of 2. I was so confused. This seemed impossible until I was introduced to something that would change algebra forever. This was called, “combining like terms.” All

we did was match the coefficients and constants together. For the coefficients, we matched them based on the variable and exponent. For the constants, well we either added them or subtracted them. Using this method, the question becomes -2x to the power of 2+6x+3. Not only does this make the question look a lot easier, but it’s also simplified and doesn’t take up as much space. This leads me into my next top 5 things that I learned in grade 9 math.

~ Leaving things the way they are.

If we use the example from the last question 2x to the power of 2+6x+3, instead of finding the answer, we can just leave it as is. We have already found the number for each of the coefficients and constants which means we don’t need to go any further Another example is with exponents.

Let’s say we have 2 to the power of 5 multiplied by 2 to the power of 2, we can use the multiplication law making the outcome of the equation, 2 to the power of 7. We are also able to leave it the way it is because even if we actually do 2 to the power of 7 the answer will still be the same because as long as you know the correct base and exponent, you don’t need to actually find the number because it takes longer that just writing the base and exponent. This also applies to linear relations, when we are isolating the variable to find x, if we end up getting a fraction, we can just leave it the way it is because we know what it needs to be divided by which means we still have the right answer. This is one of the many little things I’ve learned in math 9, that played a major role throughout the year.

~ Exponent Laws

Before grade 9, I have done things with exponents but I’ve never gotten a general idea of exponents. In grade 8, my idea of exponents was the same when I was explained in grade 9. The exponent is telling us how many times the base number is being multiplied by itself. There was always tips and tricks to exponents when actually figuring them out but at the end of the day, the question still remains 2 to the power of 9. It seemed almost impossible until I was introduced to the exponent laws.

The fact that we are able to either add, subtract and multiply the exponents without actually making copies of the base was amazing. But like most things in life, there was a catch. The multiplication and division laws only apply to exponents that have the same bases. This was definitely something that helped me throughout grade 9 math, even though the laws had a catch.

~ An exponent with 0

During our exponent unit, another handy trick I learned was if any equation had an exponent beside it and the exponent was 0, then everything in the equation would turn to the number 1. As long as the whole equation was covered in brackets and there is an exponent of 0, then everything in the equation would become 1. This means that the answer would be 1. For example, 2 can’t make 0 copies of itself, therefore turning the equation to 1. This was a very handy tip in math 9 but it also confused me at times.

~ Tug of War

This was a funny analogy used for integers. When I was shown this, I was confused but with some explaining and practice it made sense. The “Tug of War” analogy is something that is used when adding integers. Let’s say we have a question like 9+(-10)-12+6+7+3-11. The first step is to organize the numbers into categories based on their signs. In short, all the negatives would be on one side and the positives would be on the other. In this case after we group them up we would have -10,12 and 11 on one side and positive 9,6,7 and 3 on the other side. Then the next step is to add the integers together with the numbers on their sides. All the negative numbers added up would equal -33 and on the positive side it would be 25. From then our new and simplified question is -33+25 from then we can determine the question without having to deal with all those numbers and using this method our final answer is -8. This was a very handy method that helped me a lot during my year of math 9.

~ Summary

Math 9 with Mrs. Burton was very enjoyable, interesting and fun. I could not have been put in any better math class. With everything thing we’ve learned this year, I started off each different topic knowing nothing, but with explanation of the topic and practice, I caught on in no time. Math 9 very interesting, enjoyable and helpful at the same time and I hope I can learn some new tricks and tips in grade 10 math while having fun!

~ All images were hand drawn and made by me.