Unit 1 Day 7

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.

Commented on Franks blog.

Youtube video. 

Unit 1 day 8

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.

E.C. YouTube video:

Unit 1 day 6

Objective: "Similar triangles; angle-angle"
Example:

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!!!

Commented on Franks blog.

Youtube video:

Day 5 unit 1

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. 

Commented on Franks blog. 

E.C. YouTube video:

Unit 1 day 4

Objective: "Surface arrea of prism, pyramid, cylinder, cone, and sphere."

Quiz:

1. Where would you find surface area of this in real life? Rectangular prism
2. Where would you find surface area of this in real life? Pyramid

3. Where would you find surface area of this in real life? Cylinder

4. Where would you find surface area of this in real life? Cone

5. Where would you find surface area of this in real life? Sphere

Answer key

1. To know how much paint you need for a rectangular wall. Good to know for math class in the future.

2. To know how to make cool sculptures including shapes like pyramids. Also helps to know for a math class in the future.

3. To know how big pole needs to be when putting a building up. Good to know for math class.

4. To see if a party hat will fit on a kids head.:) Good for math classes in future.

5. To know if your hands are big enough to palm a basketball. Good for math classes in the future.

Commented on Jeremy's blog.

Youtube video:

Tips from the pros.

Day 3 unit 1

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 you pi r2 +pi r l.

5. To find the surface area of a cylinder you use the formula 2pi r2 + 2pi r h

Commented on Kyles and Masons blog

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