Angelo's Scribe of Test Number One

On part one of the math test, we were given eight algebraic equations. Half were written out in numeric form, the other half, as written in words. For the numeric equations, we had to write down the correct word form for that equation. For example, the numerical equation would be 7x + 5x, and then we'd have to write it as seven times a number increased by 5 times a number. Like this:

When we were dealing with the written form, the equation would be like, nine centimeters less than 3/4 of length x. Then we'd have to write it into a numeric equation, which would be 3/4x - 9. Like this:

These type of questions ended the first part.

For Part Two, we were to complete a graph. We were given a graph and the first 3 figures of a pattern. The first 3 figures of the pattern were these:

The graph looked like this :
You had to fill three sides of the graph with the appropriate title.
We also had to create a T - Table showing our understanding of the pattern. It kind of looked like this :

After we completed the chart, and had it all filled out, we had to come up with an algebraic equation on how you would get from x to y. This was the equation needed:

You need to have the x equal the figure number and the y equal the number of squares. In our test these were what we needed to get the questions correct:


This ends the test, hope you guys learned a lot!!!

Angelo's B.O.B

This blog is about the steps to find the surface area and the volume for a cube and a rectangular prism. When doing work for a cube or a rectangular prism you need to include the 3D diagram and their net.

This is the 3D version of a cube :


This is the cube's net :


This is an example of a rectangular prism :


This is it's net :


There are several ways to find a surface area for both of the shapes. One way for the cube is this :

It is clear that if you get the areas of each square in the cube you already can solve the surface area of the cube. You can solve the area of each side by multiplying the two different measurements that make the side. For example, if one side is made up by 2 lengths and 2 widths, you multiply the width and length together to get the area. So if you already have all the areas, just add all six sides together and get the Surface Area.

There are two steps used to solve both of the shapes. I used one of them on the cube.


All you have to do is find the base and multiply that answer with the height. To find the "base" of a shape, all you have to do is multiply it's length with the width.

Now moving on to the rectangular prism. The step I used for this shape can also be used on a cube.

This step take more time. If you multiply length and width, you are finding the area for the Top or the Bottom parts of the shape. If you multiply length and height, you are finding the area for the Front or Back. And if you multiply width and height, you obviously get the area for one of the two sides. Since there are six sides. Once you find the area for one side of the shape, times it by two to get the other side. For example, if you find the area for the Top, just multiply it by two so you can get the area for the Bottom also.
Yes, these steps on finding the volume of a rectangular prism can also be used to find the volume of a cube :

This explanation is quite simple. If you multiply the length and width, find the answer and multiply that to the height. Once your done that, you have solved the volume.

Now...you guys should know how to find the Surface Area and the Volume of a Cube and also a Rectangular Prism.

Angelo's Pythagoras Growing Post

Part1:
A Pythagorean Theorem is when the legs of a right triangle ( a & b ) and the hypotenuse obey the following relationship " a2 + b2 = C2."

A Pythagorean Triple is a right triangle that uses a set of numbers (1,2,3,etc...) that satisfy a2 + b2 = C2. The set of numbers can't have any decimals For example, 3squared + 4squared = 5squared.Another way to say that is, 9 + 16 = 25.

I had to figure out another Pythagorean Triple using only the Perfect Squares up to ten. The perfect squares are:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
The next Pythagorean Theorem after 3 squared + 4 squared = 5 squared is, 6 squared + 8 squared = 10 squared. I proved it in three different visual ways.
The first one I used the right triangle. It is clear that the legs will add up to the hypotenuse.

The second way, i proved it in squares. It is clear that 36 squares (6 squared) + 64 squares (8 squared) will equal 100 squares (10 squared).

The third way, I showed it in squares again. You could see that the a2 and b2 fits in c2 perfectly.


Part 2:
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For the missing hypotenuse, I first wrote down what i knew then began the Pythagorean Theorem. In using the squares, 10 was my Whole Number because it is the the closest perfect square before the number 117. I then got my Denominator by subtracting the two perfect squares from eachother. I got the numeratoe by subtracting the main number and the smaller perfect square. I couldn't end my answer with a Mixed fraction so I divided 17 to 21 to came up with a decimal form.

For the missing leg B I did the similar steps like the missing hypotenuse, but it changed when it came to the subtracting part. To get "B" you had to subtract A from C. After those steps you were back to the normal "missing side" steps.

For the missing leg A it was the same as Missing side B. The square is just in a different position during the subtracting steps.

Part 3:




Before I could do the Pythagorean Theorem, I first had to write down what I knew. The height of the frog from the tongue is 70 cm ( there is 100 cm in a m). The height of the door was 2m. And the distance from Lefrog and the door was 1.5 m. But I couldn't make a triangle just with that information. I had to find out what the height of the door is starting from the height of the tongue. So I had to subtract 70 from 200 which made 130cm or 1.3m. From there, I had my A (1.3) and my B (1.5). That's when I could use those numbers and the Pythagorean Theorem to solve the answer.


Part 4:

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Just in case you guys can't read the question. It says, " Mary had a dream to dunk. So one day she attempted. She stood at the free throw line, which was 20 feet away from the net. The basketball net's height is 10 feet tall. Mary is 4 feet tall for her feet to her arms. Her arms has a reach of 1 feet. How far and high does she have to jump to SLAM DUNK???

Answer:
First you had to write down what you knew. After that you had to make the triangle with the starting lengths. I subtracted 4 from 10 to get the starting height(A). I subtracted 1 from 20 to get the starting distance(B). Once I got those facts, I could finally do the Pythagorean Theorem. After I get the number for C², I could use the squares and get the Mixed Fraction. After that, I would just have to divide the Numerator to the Denominator, and add the answer to the Whole Number.

Angelo's Scribe

Mr. Jerema is teaching us , and he introduced "Pythagoras" to us. We learned that a triangle can also be a right angle.
We first learned about the three basic angles. He showed us that a circle has a 360º angle. If we cut the circle in half it will be 360 divided by 2 and it will turn into a 180º angle, also known as a straight angle. If we cut the semi - circle in half, it will be 180 divided by 2 and it will turn into a 90º angle, also known as a "right angle."



So if we make a right angle and then add the extra line to make it a triangle, it will make a "right angle triangle." In a right angle triangle, there are two legs and a hypotenuse. The legs are the two lines to make a right angle, and the hypotenuse is the longest line.The legs can also be labeled "a" and "b." The hypotenuse will always be a "c."


To find the area of a rectangle, you would have to multiply the length (a) and width (b) together. But if you want to find half of the area, it has to be Length(a) times Width(b) divided by two. If you want, you could also cut the rectangle in a triangular way (it will be the same thing).

Angelo's scribe

Today, Mr Harbeck was away (AWWWWWWWWWWW) so we just did fraction word problems.
I'll show you how I did three of them:



Explanation1: I needed to find out 3/8 of 24, so i first divided 8 to 24. The answer was 3, and that meant 3 is 1/8 of 24. So, to get 3/8 i had to times 1/8 three times. That's why i did 3 times 3.



Explanation2: I needed to find out 3/5 of 125, so i first divided 5 into 125. The answer was 25, and that meant 25 is 1/5 of 125. So, to get 3/5 i had to times 1/5 three times. That's why i did 25 times 3.



Explanation3: I needed to find 7/8 of 160, so i first divided 8 into 160. The answer was 20, and that meant 20 is 1/8 of 160. So, to get 7/8 i had to times 1/8 seven times. That's why i did 20 times 7.

This is how I did my questions. Hope you guys agree!

Angelo's Scribe

Today in class we learned different strategies to solve addition fractions. The three startegies were using clocks, money, and double number line ( also called Common Denominators).

We first startegy we did was clocks. We found out that the magic number for clocks was 60 minutes. After that, we figured out the numbers that would divide evenly into 60. They were 2, 3, 4, 5, 6, 10 , 12, 15, 20, 30, and 60. We did an exmaple question and this is how I solved it.



1/3 is 20 mintues on a clock. 1/12 is 5 minutes on a clock, but since it's 5/12 we just have to multiply 5 minutes, 5 times. This will get us 25 minutes. Add it together and get 45 minutes over 60 minutes. You could reduce it to 9/12. Reduce it one more time and get the final answer, 3/4

The second startegy we did was money. We found out the magic number for money and it was 100. After that , we figured out that 2, 4, 5, 10, 20, 25, 50 and 100 were the numbers that divide into 100 evenly. We did an example qeustion and this is how I
solved it.



The first number 3/10 was easy to solve , because the denominator, 10, meant that it was in dimes. SO all we had to do was multiply 3 by 10 and it equaled 30 cents over 100. The second number was easy to solve, because the denominator, 20, meant that it was in nickels. So all we had to do was multiply 9 by 5 and it equaled 45 cents over 100. Add that together and get 75 cents over 100. You might see it kind of looks like three quarters. So the final answer is 3/4.

The last strategy we did was double number lines. We found out that any number can go into it. We did an example question and this is how i did it.



Since 5/8 equals 55/88, by just multiplying 5 and 8 with 11.
3/11 equals 24/88, by just multiplying 3 and 11 by 8.
the number line was up to 88 since that was the denominator. we first did 3/11 (24/88) and added 5/8 ( 55/88) which equalled to 79/88.

This ends todays math class! Remember to finish your math homework.

Clock:
1/2 + 3/10
4/5 + 1/12
1/3 + 11/20

Money:
5/20 + 1/10
2/4 + 10/25
17/50 + 2/5

Double Number Line:
6/13 + 2/5
1/4 + 6/8
12/19 + 1/3