Today, I learned about tessellations in math class. Our school’s art teacher came in and showed us some examples of tessellations in art, and then we made some. We first took a piece of paper and cut it in half, in any line we wanted. Then, we taped the two flat edges together and cut it again in a quirky way, and we taped it again. Then, we took a small poster and traced our shape numerous times until the whole poster was full of shapes. Then, we looked and saw a figure in our shape, and colored it in as we deemed appropriate.
Here’s me cutting and taping the shape:
And here’s me drawing the shapes:
And here’s the completed project, my horses:
We just started a chapter devoted to circles in Geometry, and I decided to show you what I’m learning.
A Chord’s endpoints lie in the circle.
A Secant goes straight through the circle.
A Tangent only touches the circle at one point.
The Point of the Tangent is where the tangent touches the circle.
Now, try to classify all of the lines in this problem:
Chords- AB, AC, AD
Point of the Tangent- E
Radii (plural of Radius)- AB, AC, AD
In Geometry, we finished chapter about Spatial Reasoning. Spatial Reasoning is all about using formulas to find the lateral area, surface area, and volume of 3-D figures. First, we had to determine what figure could be made from a net, so I made a few of those problems for you to solve:
For the top one, the answer is a cylinder, because the two circles go on top of the rectangle to make a cylinder.
For to bottom one, the answer is a pentagonal pyramid, because the triangles go up to make a pyramid over the pentagon, which is the base.
One lesson that we learned in Geometry this week is estimating the area of irregular shapes. I made a problem below:
You have to count the squares and the half-squares to make an estimate.
Did you get it yet?
The answer is 37.
For this math blog post, I decided to make a few stories with holes.
1. A man goes to his rabbi and says, “Rabbi, is this bacon kosher?” The rabbi takes one look at it and says, “Yes.” How?
2. Two men walk into a bar. One man goes to the bartender and says, “I’ll have a glass of H2O.” The man next ot him says, “I’ll have some H2O, too.” He drinks it and then dies. Why?
1. The bacon was made out of soy.
2. H2O2 is the chemical combination for hydrogen peroxide. The bartender thought he meant that, so he gave him peroxide.
For this week’s Math Blog Post, I drew a picture of how you can solve the height of a shadow. It doesn’t have to be just used for shadows, however.
Let me explain:
Step 1: Convert the feet into inches by multiplying by 12. Fred is 5 feet, 2 inches, which is 62 inches. The building is 50 feet, 2 inches, which is 602 inches. The building’s shadow is 60 feet, which is 720 inches. Remember that we are solving for Fred’s shadow.
Step 2: Put the inches into a formula:
Fred’s height Building’s height
__________ = _____________
Fred’s shadow Building’s shadow
The above formula is put into effect in the picture above. When you multiply 62 (Fred’s height) by 720 (Building’s shadow), you get 44,640.
Step 3: Divide.
Divide 44,640 by 600, and you get 74.4. But that’s not the answer. You must divide 74.4 by 12 to put it into feet and inches. 74.4 divided by 12 is 6.2, which is rounded to 6 feet, 2.5 inches.
We recently learned about ratios in Geometry class. This is not a new concept, so I learned it pretty easily. I decided to teach you guys about it.
A ratio can be found on a map. You may see on a map a mini-ruler and then text that says 1 in = 2 miles. This means that for every inch you measure on the map, it equals two miles in real life. Now, what would ou do if you wanted to find distance on a map?
Say Spot A is 3.5 inches away from Spot B on the map. Since every inch is equal to two miles, you just have to multiply 3.5 by 2.
3.5 x 2 = 7
So, Spot A is 7 miles away from Spot B!
I decided to solve two Stories With Holes this week as my math blog post. Enjoy!
1. How can half of eight be three?
Answer: The actual digit 8 is made up of two three’s- one forwards and one backwards. Try it on a piece of paper!
7. “This parrot will repeat any words it hears,” said the pet shop owner. A lady bought the bird but brought it back a week later to complain that the bird had not yet spoken a single word. Yet the salesperson had told the truth. Explain.
Answer: The parrot is deaf.
The Triangle Inequality Theorem goes as follows:
“The sum of any two side lengths of a triangle is greater than third side length.”
This means that A and B must be greater than C. If it isn’t greater, then the triangle’s sides don’t match.
For example: A is equal to 4, B is equal to 3, and C is equal to 7.
This WOULD NOT be a complete triangle because 4+3=7.
Let’s try another one: A is equal to 34, B is equal to 21, and C is equal to 50.
This WOULD be a complete triangle because 34+21=55, and 55 is more than 50.
Got it? Good!
Today I will be explaining two geometry theroems- the Isosceles Triangle Theorm and the Equiangular Triangle Theorm.
Isosceles Triangle Theorm– This theorm states, “If two sides of a triangle are congruent, then the angles opposite it are congruent.” This theorm can be used the prove congruence in isosceles triangles.
Equiangular Triangle Theorm– This theorm says, “If a triangle is equilaterial, then it’s also equiangular.” It can be used for algebra problems within geometry.