Daily Objective: "similar triangles"
Similar triangles are exactly the same as similar figures. You have to put one length of one triangle over the other length on that same triangle, equal to the length given on the similar triangle.
Quiz:
1. How tall is the tree below?
2. How do you set up a proportion?
3. How do you check if your answer is correct?
Answer key
1. The answer to the problem is that the tree is 20 meters tall. To get this you set up a proportion 2/3 X x/30 and you cross multiply these and get 3/60 and you divide that and end up with an answer of 20 meters tall.
2. To set one up you need to make a cross multiplication table numbers should go on both sides of the division line. ( / X / ) Once you do that you cross it and skip x and keep that number to divide it with the result of your other two numbers.
3. You can check you work by using common sense. All you need to do is look at the previous triangle and if it within a reasonable range your most likely right.
Objective: "Scale factor of sides and scale factor of area"
The scale factor of sides is the same as similar triangles and the same as similar figures. The scale for area is also the same for as far as we are into the math units. This is the same as before, where you have to put one length over the other, and then put it equal to the other similar shape length over x. Then you have to cross multiply and divide by the number next to x.
This is an example of a question on similar lengths/area.
Quiz
1. Find the missing length:
2. Find the missing length
3. Does it matter if the angles are different in the similar shapes?
Answer key
1. The correct answer would be x=4, because you put 6 over 8 is equal to 3 over x, and after cross multiplying, you should end up with 6x=24. Then you divide 24 by 6 and end up with x=4.
2. The right answer for this question is x=10. You should have 5 over 12 equals x over 24. After cross multiplying you should end up with 12x=120, and then divide 120 by 12, and then x=10.
3. The angles do matter, because they are different shapes, although usually they don't give you the angles for the shapes in math so you know they are the same.
Commented on Suzi's blog.
Similar triangles (AA) need to have the same angles to be similar triangles. They can be different sizes but as long as they have the same angles they will be similar triangles.
Quiz:
1. Find if the example above has similar angle-angle triangles.
2. Are these triangles similar (AA)?
3. Can you use a different way to find the angles of a triangle?
Answer key
1. The answer is yes. To find out if these are similar triangles all you need to do is use a protractor correctly to determine the angles of both triangles.
2. The answer is no. Clearly these angles are way off, but if you want to be sure you can double check with a protractor.
3. Yes you can, many times when test taking you wont have access to a protractor so what you can do is use the method using cos, sin, and tan and to remember how to use it just remember SO-CA-TOA!!!
Objective: "Similar figures: what are they and finding missing lengths."
Finding the missing lengths in similar figures is exactly the same as finding scale as we talked about in day 2. You have to put the smaller length from the figure that has two sides that are labeled with numbers. Then you put the length that is larger from the shape that is incomplete as talking about side lengths labled. You put them next to each other and cross multiply to get something that looks like this: #x=#, so a number times x is equal to a number.
Quiz
1. Find the missing length:
2. Does it matter if you put the smaller or larger number over the other?
3. Does this system work for all shapes?
Answer key
1. The missing length would be 21cm. To get this you would have to put 6 over 9 equals 14 over x. After you cross multiply, you should end up with 6x is equal to 126. You then divide 126 by 6, which should give you 21 cm.
2. It does not matter if you put the smaller or larger on top, but you do have to do the same for both. For example, from question 1, it doesn't matter if you did 6 over 9 or 9 over six, as long as you did 14 over x so it matches smaller side over longer side, or x over 14.
3. Yes this system will work for all shapes, except for circles. Circles are a whole different thing.
Objective: "surface area of prism, pyramid, cylinder, cone, and sphere"
How to find surface area of:
Prism:3D figure with rectangle sides. Area of 2 bases plus area of sides
Pyramid: Area=area of base plus area of all sides
Cylinder: 2pi times r2+2pi times r times height
Cone: pi times diameter times height
Sphere: 4 times pi times r2
Quiz:
1. How do you find the surface area of a rectangular prism?
2. How do you find the surface area of a pyramid?
3. What is the equation to find the surface area of a sphere?
4. How do you find the surface area of a cone?
5. How do you find the surface area of a cylinder?
Quiz answers
1. Area of 2 bases plus area of sides
2. Area of base plus area of all sides
3. To find the surface area of a sphere, you multiply pi times 4, then take that and multiply that by radius squared. It is just finding the area of a circle, and multiplying that by 4.
4. To find the surface area of a cone youpi r2 +pi r l.
5. To find the surface area of a cylinder you use the formula 2pi r2 + 2pi r h
Objective: "Area from day 2 and introduce concept of scale."
Quiz
1. How do you find the area of a circle?
2. Find the area of a rectangular table top that is 12 feet long and 3 feet high.
3. Find the area of a triangle that has a base of 10 and a height of 10.
4. What is the equation to find the area of a trapezoid?
5. What is the area of a parallelogram with a base of 5" and a height of 7"?
6. Find the area of a square with the height of 9" and a base of 9"
7. How do you find the area of a polygon?
8. A pole casts a shadow at 10 feet. A person is 7ft tall casts a 5 foot shadow. Find the height of the pole.
Answer key
1. To find the area of a circle, you need to use the equation pi (which is 3.1415......) times the radius of the circle squared. So you would find the diameter of the circle, and divide that by two. That gives you the radius. After that, you times the radius b itself to get radius squared. You take the radius squared and multiply that by pi, and you get the area of a circle.
2. The area would be 120 feet squared. You take the base times the height, and for this problem, you would get 12x10 which equals 120.
3. When finding the area of a triangle, you multiply the base by the height, and then take the answer of that and divide it by two. So for our problem, you would multiply 10 by 10, which equals 100, and divide that by 2, which then gives you 50, which would be a final answer of 50 units squared (units because you were not given a specific unit.
4. The equation to find the area of a trapezoid is probably the most complicated at first. Since a trapezoid has two bases, you have to add them together, then multiply that by HALF of the height. it seems weird, but this is the simplest way for me.
5. The equation to find the area of a parallelogram is the same as the one for a square or rectangle which is base times height. Since the base is 5 inches and the height is 7 inches you would multiply those two together and end up getting 35 square inches.
6. In order to find the area of a square you multiply the base times height. So the base is 9 and the height is 9 so when you multiply the two you end up getting the area of 81 square inches.
7. To find the area of a polygon, you first have to find the perimeter, which is just on side length times however many sides there are. Then you take the apothem, which is halfway into the shape from any side, and divide that y two. So you multiply half of the apothem by the perimeter to find the area.
8. The answer is the 10ft shadowed pole is 14ft tall. The pole is 14 ft tall because in order to find the answer is to set up a proportion. It would be 10 over x equals 5 over 7. Then you cross multiply, and get 5x = 70. After that you divide 70 by 5, which gives you 14 feet.
Daily Objective: "Area of squares, rectangles, triangles, trapezoids, parallelograms, circles, and polygons. Define point, line, plane, line segment, ray, angle, median, altitude, perpendicular."
Definitions:
Area of:
Square: area= base x height.
Rectangle: area= base x height.
Triangles: area= base x height divided by two.
Trapezoids: area= base 1 + base 2 x half of the height.
Parallelograms: Area= base times height.
Circles: Area= pi x radius squared.
Polygons: (apothem is halfway into the shape from any side, so half of the apothem would be 1/4 into the shape from any side) area= 1/2 of apothem x perimeter.
Lines definitions:
Point: A place on a graph, where line can cross or pass through. An example would be: (4,6)
Line: A continuous extent of length, can be straight or curved, to help show data on graphs.
Plane: A plane is a flat thickness that extends forever and has no thickness.
Line Segment: a line that has two end points ad looks like a line, except it doesn't go on forever.
Ray: A line with on end point, but then extends on forever from that end point.
Angle: the space where two lines intersect and it is usually measured in degrees.
Median: The middle of data, when the data is lined up from least to greatest or vis versa, and you cross of the lowest, then the highest, then the next lowest, and then the next highest, until you have one point left. If you end up with two points, you add them together and divide that by two.
Altitude: An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.
Perpendicular: This is when two line intersect, creating a 90 degree angle.
Quiz
1. What is the area of a square when its perimeter is a total of 20?
2. How do you find the area of a rectangle?
3.Whats the difference between finding the area of a triangle and a rectangle?
4. Whats the formula to find the area of a trapezoid?
5. Is the parallelogram formula for area the same as squares and rectangles?
6. How to find area of half a circle?
7. Whats the formula for area of a polygon?
8. What is a point?
9. Can a line be curved?
10. Can a plane have any thickness/height
11. Does a line segment go on forever?
12. How many endpoints does a ray have?
13. Whats the highest angle you can have when two lines intersect without it being one line?
14. Find the median. 14,17,20,21,23,25,70,75,80,85,100
15. Define altitude
16. What angle is a perpendicular angle?
Answer Key
1. The area of the square is 25. 5+5+5+5=20 then base(5) times height(5) = 25
2. To find the area of a rectangle is base times height.
3. Both triangle and rectangle have to multiply base and height, but triangle needs to divide by 2 after.
4. Area for trapezoid is base 1 + base 2 x half of the height.
5. Yes, it is base times height.
6. Its pi r2 divided by 2
7. 1/2 of apothem times perimeter
8. A place on a graph, where line can cross or pass through.
9. Yes, it doesn't have to be straight
10. No, it cant have any thickness at all, it wouldn't make sense
11. No, that would be a regular line.
12. Only one endpoint the other goes on forever!
13. 179 degrees one more and it would be a straight line.
14. 25. You place in numerical order and then cross lowest then highest out, continuing that process until you have one number in the middle.
15. An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.
Objective: "Students will be able to write an equation of a line given data points"
When you have a x-y table you find the equation and graph the line.
Quiz
1. Write an equation of a line given these data points. (4,10) (8,50)
2. Write an equation of a line given these data points. (3,-9) (5,-13)
3. Write an equation of a line thats parallel to y=2x and goes through the point (4,4)
Answer key
1. y=2.5x + 0
You would do the same as in the answer for question two, with the y2-y1 over x2-x1, and after plugging in the data points into the equation, you should be getting the linear equation of y=2.5x.
2. y=-2x
you have to use the equation y2-y1 over x2-x1. You should get -13 - -9 over 5 - 3. After doing the math, you should have -4 over 2, which is equal to -2, and that would be the slope of the linear equation.
3. y=2x-4
To get the answer, you have to plug the points into the equation. You take y=2x, and plug in (4,4). you would then get 4=2(4), which is equal to 4=8. Then you do 4 minus 8, and get -4, which would be the y intercept.
commented on Ryan's blog today.
Youtube video help to explain:
Objective: "Students will graph linear inequalities"
Linear inequalities are same as y=mx+b without the equal sign, and instead, you have these >,<, <, >
Ex. Because y is greater you shade to the left(The greater side).
Quiz
1. Graph the inequality 2x-y<2
2. What do you do if the line is horizontal?
3. What do you do if the line is vertical?
Answer key
1.
2. Shade either above or below the line based on the equation.
3. Shade either left or right of the line depending on the equation.
Objective: Students will define the y-intercept in math as well as translate it to a real world meaning.
The y-intercept is where the line crosses the vertical axis/y-axis.
The real world meaning is where the price starts for example is how much the cost to start an installation or something along those lines.
Example: The line intercepts the y axis at the point (0,2), making the y-intercept 2.
Quiz:
1. Can the y-intercept be in the negatives?
2. Does the y-intercept have to be a whole number?
3. Does the y-intercept have to start at 0?
Answer key
1. Yes, the y-intercept can be in the negatives and it can pass through the negative y axis.
2. No, the y-intercept does not have to be a whole number.
3. No, the y-intercept can pass through any point on the y-axis
Objective: "Students will write the linear equation of a line using data from a line of best fit, or given 2 points."
This is the equation for lines:
To find the eqaution of a line when givin two points, it is actually quite simple if you know what you are doing.
First you need to know this equation: ( y2 - y1 )
( x2 - x1 )
This means that when you have two data points such as (2,6) and (4,8) for example, you take the 8, since it is the second y point and 6 is the first y point, and the you minus 6 from 8. You then do the same for the bottom, so you would have 4 minus 2. After you do the subtracting, you should end up with a y value over an x value, so from our example you should have 2/2 (or 1). This would be the rise over run in our linear equation, so our equation would look like this so far: y = x. to find the y intercept, you need to plug in one of the two data points t into your eqation. I am going to choose the point (4,8). I would get 8 = 1(4), which would be 8 = 4. After you have this, you take the number to the left of your equal sign, and you subtract the number on the right from the number on the left. so our final equation would look like this: y = x +4.
Quiz:
1. Write the equation used for lines.
2. Find the slope of a line passing through these points. (6,8) and (-5,-3)
3. What does the "b" represent in the equation?
Answer Key
1. The equation used for lines is y = mx + b.
2. The correct slope is y = x, or one.
3. The "b" in the linear equation represents the "y" intercept.
My name is Jesse Espinoza. I am a freshmen at Loveland high school. I am 15 years young. I'm athletic and like most sports and usually like playing a variety of them. My favorite sport is football and my favorite team is the San Diego super Chargers! I also like school because of the friends, and the opportunity to do well in life. I'm a creative funny guy who likes pizza and long romantic walks on the beach<3 Just kidding! I'm a hard worker and accomplish whatever I put my mind to. Thats about it! Thanks for reading my blog!
What I've learned
Geometry in Construction has taught me many things like how to work together, divide work, and to not be afraid to ask questions. It will help me in the future weather its working on my future house or doing taxes which applies to the math. It may even help if I take interest in a career involving hands on skills. It may be very hard but it ends up being very worth it as I know I can apply many of these skills in my life years to come.
Letter
Dear Robert and Carrie,
Thank you so much for all the help on the house its helped us making the house a whole lot. You guys are really nice and cool and I hope your house is great and works fine! I really hope to see you guys again. I couldn't have thought of anyone else id rather help work on this house for. Thanks for everything and letting us work on your house. You guys must have a lot of trust in us!!:)
