2. ESSENTIAL QUESTIONS:
Unit 6 and 7 Essential Question:
How are slope, the tangent ratio, and direct variation interrelated?
Slope, tangent ratio and direct variation are all related to each other. The reason is because all of these concepts have a relationship with ratios and can be used to find out each other. In direct variation, there is a constant ratio (also known as variation constant) as direct variation is the connection between two variable quantities. By looking at an example of direct variation is on page 360 in Integrated Mathematics 1 by McDougal Littell, you can write an equation to show the relationship of direct variation by b=0.75h (b is represented as the base and h is represented as the height). You can see that the equation to find h for this example is an example of direct variation thus there are two variable quantities (base and height) that have a constant ratio. If you were to graph this equation, you should see a straight line passing through the origin and in the first quadrant. You can use the number after 'b' to find out the tangent ratio and slope. The slope and tangent ratio would be 0.75 as the tangent ratio of the acute angle is equal to the leg opposite that angle (7.5) and over the leg adjacent to that angle (10).
(Above this sentence is a picture of a triangle on sample 1 on page 360).
The slope of a line is the ratio of rise to run for any two points on the line. This is related to tangent ratio and direct variation as you can use slope to find out the two concepts and that they are ratios. By referring to the example on page 361, you can see that the base is 10ft and the height is 7.5 ft. For the base, you can say that it is the run and for the height, you can see that it is the rise because the roof rises 7.5 ft across a distance of 10ft. If you set up the ratio of rise to run, you can see that it is 7.5/10 which is 0.75. You can also find out the tangent ratio of this problem as the tangent ratio of the acute angle compares the leg opposite to that angle (7.5) over the leg adjacent to that angle (10) thus the tangent ratio of the acute angle would be 0.75. There is also direct variation in this as there are two variable quantities that have a constant ratio which are the base and height. You can write an equation to show the relationship: y=0.75x (x is the run and y is the rise)Above this sentence is a picture of a triangle on page 361.
The tangent ratio is an example of ratio. The tangent ratio of an acute angle compares the two legs of a right triangle so it is a ratio. By taking a look at the example on page 365, you can see that since an acute angle is shown (angle T), the tangent ratio compares the two legs of a right triangle. You can first find out the value of angle R. Then you can make an equation which is tan (R) = 3/6. You can then do tan-1 (3/6) to find the value of angle R which is about 27 degrees. Now, since tangent ratio is an example of a trigonometric ratio, it is related to direct variation and slope. So to conclude, tangent ratio, direct variation and slope are all connected to each other because they are examples of ratios and that they could be used to find one another.
Above this sentence is a picture of a right-angled triangle on top of page 365.
3. PROJECT:
Unit 6&7 Dilations Project Pictures:
Unit 6&7 Dilations Project Pictures:
My project demonstrates the SLR learning enthusiastically. The reason is because I was always positive in drawing the enlargements and written summary. When I was doing the enlargement of my bulb, everyday I kept on sketched the shape a little bit. I am type of person that likes to be challenged and can be self-motivated. Now, this project really was a tough obstacle for me to come across as I had to put in lots of effort into creating a similar figure. During this whole process, I was always positive about my enlargements and text. I persevered myself into making a 'good and accurate' enlargement with a happy mood. Even though drawing the dots was tough, I really enjoyed this project as it gave me a chance to be educated about something that I'm not familiar with. I wanted to apply the skills I have into the drawing with a good mood. Another reason is because of my written summary. In my written summary, I took all of the activities and lessons from the previous math classes and attempted to use my logical sense and answer the questions carefully. As I said before, I enjoy learning new subjects and topics and in my written summary, I managed to put my thinking into words with a positive attitude. And so to conclude, my project demonstrates learning enthusiastically.
4. REFLECTION:
My MAP scores changed in mathematics as when I did it the second time, I had improved all of my areas in math. Before, my weakness was statistics & probability and it was in the 241-250 range. Now, my weakness is algebra concepts and it is in the 251-260 range. Before, 4 math areas were in the 261+ range but now, 5 math areas are in the 261+ range. By comparing my past MAP score and the recent one, I can say that I have made a lot of improvement in increasing all of the scores. Some steps that I took from August to January to improve are continuing my regular math tuition, taking a look at my notes from class and studying math concepts from other websites. I feel like by reviewing previous math areas and making sure I understand them is a key step for me to improve my MAP scores. Improving on my algebraic concepts will be a new goal. I will achieve it by taking a look at some website that Ms. Lemos had shown in Moodle. This will help me understand from my mistakes and make me gain new knowledge thus will improve on my MAP score if I continue to follow this step. So in conclusion, my MAP score taken from January shown some improvements than the first test.
My MAP scores changed in mathematics as when I did it the second time, I had improved all of my areas in math. Before, my weakness was statistics & probability and it was in the 241-250 range. Now, my weakness is algebra concepts and it is in the 251-260 range. Before, 4 math areas were in the 261+ range but now, 5 math areas are in the 261+ range. By comparing my past MAP score and the recent one, I can say that I have made a lot of improvement in increasing all of the scores. Some steps that I took from August to January to improve are continuing my regular math tuition, taking a look at my notes from class and studying math concepts from other websites. I feel like by reviewing previous math areas and making sure I understand them is a key step for me to improve my MAP scores. Improving on my algebraic concepts will be a new goal. I will achieve it by taking a look at some website that Ms. Lemos had shown in Moodle. This will help me understand from my mistakes and make me gain new knowledge thus will improve on my MAP score if I continue to follow this step. So in conclusion, my MAP score taken from January shown some improvements than the first test.
