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Math week 4

This week in math we finished up our trigonometry unit and started up our polynomial unit. In this weeks blog post I am going to focus on how to solve word questions in trigonometry. Word questions aren’t always easy but you have to look for clues throughout the question to make it easier. In this post I will show you what clues you should be looking for and then I will solve step by step a word question.

Clue 1: Ladder, string, guy wire is always going to be the side on a triangle that’s the angled side.

Clue 2: Tree, building, pole is always going to be the vertical side of the triangle and if you think about it, it makes sense because all those things are vertical objects that stands straight up and down.

Clue 3: Shadow, ground is always going to be the horizontal line of the triangle.

Clue 4: The angle of elevation is the angle from the horizontal line upwards and the angle it creates is the angle of elevation.

Clue 5: The angle of depression is the angle from the top of the triangle but it is on the outside of the triangle.

Word  question:

Step 1: First we need to take the clues the question gives us and draw a diagram. I first notice in the question, they say that the building stands 1063ft high, which I know is referring to the vertical line. I then see they give us the angle of elevation which is 34.1 degrees. Then they ask us to find the length of the shadow, which I know is going to be the horizontal line.

After analyzing this information I can now make a diagram of the information they gave me.

Step 2: Now that  have a diagram drown I can solve this just like any other question.

The most important thing while solving word questions is drawing the right diagram. I recommend that you have the diagram drawn above, at the top of the blog to help identify the clues the questions are giving you. And once you draw your diagram it is very easy, you just solve it like any other question!

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Math week 3 – Blog post

This week in Math 10 we started our Trigonometry unit. In this blog post I will be showing how you find the angle of a triangle using trigonometry. To find the angle it only takes a few simple steps, but you need to be sure that you show your work and how you found your answer.

In my example I will be using this right triangle.

Step 1: First you need to label the sides of the triangle using the terms opposite, adjacent and hypotenuse. I recommend that you find the hypotenuse first by looking for the longest side of the triangle and note it is always across from the 90-degree angle. Next, I find the adjacent because I know it’s the side in between the angle you are looking for and the 90-degree angle. And finally, you have the opposite which is always across from the angle you are looking for.

Step 2: Next you need to identify if you are going to be using cosine, tangent, or sine. To easily find which one you are going to use the acronym “SOHCAHTOA”. In this case I can easily identify that I have to use my hypotenuse and my opposite side in this equation. So, I can go back and look at my acronym and see that “SOH” matches up with my sides because the “O” in it stands for “opposite” and the “H” stand for “hypotenuse.

Step 3: Now you are going to start your equation. You are going to start with “sin x” equals opposite divided by hypotenuse and how you know that is going back to “SOH” you can see “O” comes before “H” that is how you know which one is on top and what is on the bottom.

Step 4: Because you are finding the angle you are going to use inverse sine, which means when you write it out you put -1 above sin. In this step you are showing that inverse sin is being multiplies by 24/40.

Step 5: Now you are ready to put this equation in your calculator. You will put it in your calculator the same way it is on the paper. Because it is inverse sine you need to push shift and then put in your equation. (It is different on all calculators so identify what you need to do on yours)

Step 6: When you press equal on your calculator it is going to give you a number with a lot of decimals. Because you are finding an angle it is going to ask you to find the nearest degree. How you do that is look at the first number after the decimal, if it is 5 or bigger round up and if it is 4 or smaller round down.

(This photo wouldn’t go the right way but the decimal was 36.86989765)

Step 7: So because the decimal is 36.8 we are going to take that and round up to 37 degrees and that is your final answer.

Here is another example without breaking it down.

And just like that you can easily find the missing on every right triangle. Remember to write “SOHCAHTOA” on the top of your paper to help you out and remember to show your work!

Posted on No Comments on Week 2 – Math 10

Week 2 – Math 10

This week in math we learnt how to deal with negative exponents. When dealing with a negative exponent you need to move it to the other side of the fraction line. Remember every number is over 1. I will first explain the simple way to do it and then explain how to deal with a negative exponent while solving a bigger problem.

Step 1: As you can see it is very simple, take the base and power and move then to the other side of the fraction line; in this case you can’t see a fraction so you have to remember there is always an invisible 1, making it one over x to the third.

Step 2: If you have a coefficient in front of the power and the base it does not move with them. You take the base and the power and move it under the coefficient.

Now for a harder problem:

Step 1:  To start with you need to put the entire problem over 1. Without changing anything in the brackets you change the exponent outside of the bracket to a positive exponent.

Step 2: Next step is to distribute the exponent by following the power law. Multiply the exponents.

 

Step 3: Next you need to take the y^-4 and move it to the top of the fraction to get rid of the negative exponent.

Step 4: You’re going to get rid of the 1 because it doesn’t change anything. And you have simplified it as much as you can.

 

And just like that now you know hoe to deal with negative exponents. Always remember every number is over 1 even if you can’t see it!

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Week 1 – Math 10

This is my first week having math in person in about a year. The adjustment to having to do it online last march was very difficult as we were all preoccupied with what was going on in the world and the uncertainty of it all. As we move back into in person learning I have seen my grades, mental health and overall happiness go up a significant amount.

This week we learnt how to find the Greatest Commun Factor or GCF. When you are finding a GCF you are essentially finding the largest factor that the numbers share. You do. this process in a few different steps. Here is how:

Step 1: Break the two numbers down in factor trees and find all the prime factors. To make a factor tree you need to keep breaking the number down until you get to a prime number (2,3,5,7,11…)

Step 2: Find all the factors of both numbers and right them all down. If you want to check you did it right, all the factors of its respected number, when multiplied together should equal the number.

Step 3: Looking at the list of number in front of you find the common factors. I circle them for a visual. In this case it would be 3.

Step 4: And just like that you have found the GCF. 3 is the largest number that divides into both 18 and 21. Tip: Even if there are 3 common factors always pick the greatest of them.

Now that we have the basics down, we can use some bigger numbers. Using the same steps, we will be able to find the GCF of any number. In this case I first broke down 78 and 112 into factor trees to find its prime factors. I then wrote out the prime factors and was easily able to identify that 2 is the GCF of 78,112.

Tip: When finding the GCF of bigger numbers instead of using a factor tree you could use a factor ladder which will allow you to stay more organized.

And just like that you now know how to find the Greatest Common Factor of any number big or small.

 

 

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ÉVP final reflection

 

 
Name: Makayla Date:

 

 

 

 

How does the artifact you selected demonstrate strengths & growth in the communication competency?

 

In what ways might you further develop your communication competency?

 Self-Reflection

Describe how the artifact you selected shows your strengths & growth in specific core competencies. The prompt questions on the left – or other self-assessment activities you may have done – may guide your reflection process.

 

How has your understanding of your strengths and abilities changed since the beginning of the quarter?

I don’t think they changed I think this class gave me a chance to reflect on my strengths and understand how they can benefit me and how I can use them to my advantage.

 

How have your plans concerning your future shifted, if at all, over the course of the quarter?

My plans haven’t changed but it helps me understand things that I didn’t know before like how much university was or how to make a resume. It helped me become more aware of how close it really is and how I need to start looking into it soon,

Concerning your future, in what areas do you still feel uncertain about? How can you address these areas?

I feel uncertain about what I want to pursue. I know I want to go to university, but I don’t know for exactly what yet. I need to find something I feel passionate about. Because once I do that it will be easier to find a program I want to pursue.

 

 
 

 

 

How does the artifact you selected demonstrate strengths & growth in the thinking competencies?

 

In what ways might you further develop your thinking competencies?
 

 

 

How does the artifact you selected demonstrate strengths & growth in the personal & social competencies?

 

In what ways might you further develop your personal & social competencies?

In this class I am proud of my reflections we did on different things like what kind of learners we are. They took a lot of time and I put a lot of effort in them even when sometimes I didn’t want to.