Grade 8 POTW #13 Question:
Grade 7 POTW #13 Question:
Grade 7 POTW #13 Answer:
Grade 8 POTW #13 Answer:
Thursday, December 1, 2016
POTW #13 - Multi-Strand Questions
It is important to notice that the POTW each week contains a variety of different strands of math. We shouldn't learn units or strands in isolation as they are all interrelated (as we recently found out with Spatial Sense connected to multiplying negative values, i.e. Number Sense). Please see the latest POTW below:
Grade 8 POTW #13 Question:
Grade 7 POTW #13 Question:
Grade 7 POTW #13 Answer:
Grade 8 POTW #13 Answer:
Grade 8 POTW #13 Question:
Grade 7 POTW #13 Question:
Grade 7 POTW #13 Answer:
Grade 8 POTW #13 Answer:
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This is how I solved the Grade Seven Potw. I knew that a full circle around would be 360 degrees. Each sector would be 20 degrees, and 360/20 is 18, so there are 18 sides, which answers a). For B, I found out about a formula to find out the total of the interior angles for regular polygons, which was the amount of sides subscracted by 2 multiplied by 180. So, 18-2*180 is 2880. So, the sum of the interior angles of the shape is 2880 degrees.
ReplyDeleteThat is how I solved the Grade Seven Potw
Richard, I have something to add to your formula. You think you need a pair of brackets between 18-2, so the new formula would be (18-2)*180. If you don't have a bracket, then you would do the multiplication first, which gives you -342.
DeleteGrade 7 POTW:
ReplyDeleteThis question not very hard to me. All I needed to know was that a full circle is 360 degrees. Since each side is 20, I divide 360/20 and get 18 sides. There would be 18 sides. To figure out the angle sum, I have a formula which is to subtract the number of sides by 2 and then multiply by 180. This would be (18-2)*180. This equals to 2880 degrees. Therefore, the sum of the angles is 2880 degrees.
-Alan
For the Grade 7 POTW, my answer was 18 sides for A. How i knew this is because a circle has 360 degrees, while since it says the triangles are put every 20 degrees, we do 360/20 and we get 18. For part B, I know that each triangle has to equal 180 degrees, and since there are 16 triangles, all I have to do is 180*16 which would equal to 2880 degrees. Therefore, my answers are 16 sides, and 2880 degrees.
ReplyDeleteI solved this problem by simply multiplying sector angle/360 x circumference for arc length, which was 2Ï€. A Khan Academy video helped me in solving this.
ReplyDeleteArc length = n/360 x πr2
However, 2r can also be 2n, or the angle length as it is essentially also the radius as long as we add pi as well.
Multiplying everythingl
The sector angle is 360/n according to the question, so 360/n / 360 x 2n x π
(360/n x 1/360) x 2n
canceling 360 out:
1/n x 2n x π
2Ï€.
Perimeter is 2n + 2Ï€
Using the arc length and perimeter, I obtained the answer that only the numbersn = 8, n = 9, n = 10, and n = 11 can work.
Good work!
DeleteFor A), the number of sides in the polygon is 18. To find the answer, I knew that a circle has 360 degrees. In this question, I found that they would make a triangle for every 20 degrees. Therefore, you would have to do 360/20, giving you 18 sides. Another way you can find the number of sides is to just count the number of vertices on the polygon, which also gives you 18 sides.
ReplyDeleteFor B), I found a formula to accurately solve the answer to this question. So you would subtract the amount of sides, which is 18 by 2, which gives you 16. After to find the sum of all the angles, I knew that a triangle must have an angle of 180 degrees. Since there are 16 triangles, then you would do (18-2)*180, which gives you 2880 degrees.
Apparently you guys and girls didn't think this Q was too tough, as everyone seemed to get the correct answer.
DeleteQuestion A is easy as all I need to do is figure out how many 20* fit into 360 which is 18 so there are 18 slides in the polygon. The formula to answer question B is to to n - 2 x 180. N is the number of sides so 18 - 2 x 180. That equals a total of 2880* which is the answer to question B.
ReplyDeleteGrade 7 POTW:
ReplyDeleteA) There are 18 sides because if you have 360 degrees in total, and each time you make a new radius it's 20, then you do 360/20, which equals 18. This means that there is 18 sides of the polygon.
B) To find the total angle of the figure, you take the number of sides, minus 2 and multiply by 180. The equation would be S(number of sides)-2*180. This means the numbers would be (18-2)*180, which m would be 16*180, giving me 2880 degrees. The sum of the angles in the polygon is 2880 degrees.
In order to solve letter A, I decided to calculate the angles of the 6 sides, which are 120 degrees. Since a circle has 360, or 120x3 degrees, the shape must have 18, or 6x3 sides.
ReplyDeleteBy filling in the circle with these sides, I discovered that these sides make 16 triangles. Since each triangle's angles equal 180 degrees, I had to multiply 180 by 16, which equals 2880 degrees.
For A) There are 18 sides to the polygon. Because for a circle it goes around 360 degrees. Then since each slice equals 1 side, you divide 360 by 20. 360/20=18 so that means that the polygon will have 18 sides.
ReplyDeleteB) then the sum of the angles is 2880. This is because you 2 from the number of sides which gives you 16. Then since a triangle has angles equal to 180, you multiply 16 by 180 which gives you 2880.
Grade 7 POTW:
ReplyDeletea)First i actually counted the sides first. But then on the "construction" circle that shows each 20 degrees equaling to 1 point. Since we know that 360 degrees is 1 circle we just do 360 degrees divided by 20 degrees for each section. This gives us 18. Therefore there are 18 sides.
b)So Alan showed me the formula we can use to figure this out.To find the sum of the angles you take the number of sides and subtract 2. In this case giving us 16. Then you multiply it by 180 degrees. This gives us 2,880. So the sum of the polygon is 2,880 degrees.
This problem for some reason was really hard for me, But after an hour of trying to make an equation, I did make one sector angle/360 x arc length, which was 2Ï€. So then I made an equation using the numbers
ReplyDeleteArc length = n/360 x (2xπr).
But, 2r can also be 2n, or the angle length as it is technically also the radius if we add π.
According to the question, The convex sector angle is 360/n therfore:
= 360/n / 360 x 2n x π.
= (360/n x 1/360) x 2n.
= 1/n x 2n x π ( 360 is canceled out )
= 2Ï€. ( n is cancelled out )
Therefore, The formula of the perimeter of the sector is 2n + 2Ï€.
Using the arc length and perimeter, I got the answers which were:
n = 8, n = 9, n = 10, and n = 11.
So after all calculations, The numbers which can be plugged in instead of the variable n are 8, 9, 10, and 11.
(P.S - I HOPE ITS RIGHT!)
Great work Khush! That was a tough question.
DeleteFor question A in the POTW the answer is 18 sides. This is because there are 360 degrees in a circle. An each side is made of 20 degrees of the circle if i divide 360 into 20 parts, it gives me 18 sides in total.
ReplyDeleteFor question B the answer is that the total degrees of the polygon is 2880 degrees. I found this out by using a formula. the polygon consists of 16 triangles. I know that a triangle has a total of 180 degrees. 16*180= 2880.
Here is how I went about solving the Grade 7 POTW:
ReplyDeleteA) I noticed that there was a slight angle between the sides. So I came to me that I could simply count the number of sides and connect the dots to get the total amount of sides. After looking at all of them, I saw that there are 18 sides. In a mathematical sense, a circle is 360 degrees and if each piece is 20 degrees, 360 divided by 20 equals 18.
B) In order to solve the sum of the angles, I subtracted the number of sides by 2. This would be 18 subtracted by 2 and that gives me 16. Since every triangle has to equal 180 degrees, we would multiply 180 by 16 and that gives us a product of 2880. Therefore, the sum of the angles is 2880 degrees.
For part A, i knew that there were two ways we could do it. The first way was simply counting how many vertices the shape has. The other one involves a bit of math. We know that a full circle is 360 degrees. We also know that one triangle is 20 degrees. So we can do 360/20 and we get would get 18 both ways.
ReplyDeleteFor part B, i have to find out the total sum of all the angles. First i figured out the total number of degrees in 1 triangle. Since i knew that every triangle is the same. So whatever number pops out we need to multiply it by 16 (16 triangles would fill up the polygon). So i know that in order for a triangle to be an actual triangle, all the degrees should have a sum of 180. This means that, each of the triangle has 108 total degrees. Now we multiply that by 16 and get 2880.
a) The polygon has 18 sides. I know that there are 360 degrees in a circle and every triangle is 20 degrees. If I divide the circle by each of these parts of it, I would get 18 triangles. Because of this, I know that there are 18 sides.
ReplyDeleteThe polygon has 18 sides.
b) From background knowledge I know that the formula to find the interior angles in a polygon is
(the number of sides of the polygon - 2) * 180.
If I insert my numbers into this formula, I will get the sum of the angles in the polygon.
(18 - 2) * 180
= 16 * 180
= 2880
The sum of the angles in the polygon is 2880 degrees.
Here is how I solved it:
ReplyDeleteSo to find the parameter of the sector you would have to add the sides ( n) and the arc length:
2n + arc length
To get the arc length, this is the formula:
AL = Ark length
n = side length AND radius as both are the same in this case
AL/2Ï€n = 360/n / 360
AL/ 2Ï€n = 1/n
AL = 2Ï€n/n
AL = 2Ï€
Formula to find the perimeter of the sector:
2n + 2Ï€
And now we plug in numbers!
The range of the numbers that n can be is 7-11 including the numbers
So 7, 8, 9, 10, 11
For the question for Grade 8s, I tried my best with momentary hep from my Mom and Brother. I did not fully understand the question, but based off what I got, the answer is that 3 possibilities ( that is if sector MON can also equal 20 or 30 as well as in between) of 20, 24 and 30. I completed this in my math notebook.
ReplyDeleteSo, I guess you can say I did mine on paper, with help.
ReplyDeleteFor a), I know the circle has 360o degrees, and the triangle point has 20 so if I divide 360 by 20, it equals 20. So the number of sides is 18.
For b), I learned the formula (S-2)*180=
I replace S with the number of sides and when I evaluate it:
(18-2)*180=
16*180=
2880o
The sum of the angles is 2880 degrees.
1.It has 18 sides as 360 divided by 20 is 18.
ReplyDelete2. From the center of the circle, triangles form. 180-20=160. 160*18= 2880
Therefore, the polygon has 2880 degrees of angles in it.
A) To find the number of sides I did 360 / 20 which gave me 18. The number 360 is a whole circle and 20 is the angle. Therefore, there are 18 sides. Another simpler way to find out how many sides there are is to just count them. xD
ReplyDeleteB) For B, I wasn't quite sure how to do this but thankfully Derek and Richard explained it to me. So using the formula for angles,(number of sides - 2) * 180, I inputted the number of sides. Therefore, (18-2) * 180 = 2880 degrees.
I accidentally closed the tab on myself through the solving explanation (it was long). Basically I got the answers of: n = 7, n = 8, n = 9, n = 10, and n = 11
ReplyDeleteA) I found out that the number of sides on the polygon is 18. Since a circle has 360 degrees and each triangle in the circle is 20 degrees, I did 360 / 20 which equals 18.
ReplyDeleteB) Since each triangle has a 180 degree angle and there are 2 sides on each of these interior parts of the triangle, we do 18-2 to get 16. Since all triangles must have 180 degrees, you do 180*16 to get 2880 degrees.