Saturday, September 28, 2013
Sunday, September 22, 2013
Warm Up: September 25, 7th Grade
Convert the following into fractions, decimals, or percents.
1. 2/5 2. 12.5%
3. 0.70 4. 2.2
5. 25/5 6. 35%
1. 2/5 2. 12.5%
3. 0.70 4. 2.2
5. 25/5 6. 35%
Warm Up: September 24, 7th Grade
Convert the following percents into both decimals and fractions:
1. 12% 2. 15% 3. 325% 4. 2%
When you're finished get a set of tangrams and try to make this shape:
1. 12% 2. 15% 3. 325% 4. 2%
When you're finished get a set of tangrams and try to make this shape:
Warm Up: September 23, 7th Grade
What is the perimeter of the each of the squares that can be drawn around the following circles: (the labeled measurement is the circumference)
Extra credit: Find the area of both and subtract the circle from the square to find what's left.
Sunday, September 15, 2013
Radicals
Radicals are the inverse operation of exponents. The most common one is the square root, which asks you to find what number multiplies by itself in order to get the number under the radical. Sometimes there won't be a clear answer, and in that case you will have to factor the number down into numbers that are squares and numbers that aren't. Then you can pull the ones that are out by taking their square root and leave the numbers that aren't inside.
Here's a video explanation.
Part 2: Examples
Part 3: Estimating the value of a square root.
Here's a video explanation.
Part 2: Examples
Part 3: Estimating the value of a square root.
Warm Up: September 19th, 8th Grade
Order the following numbers from least to greatest. Use a number line if it will help you.
1. -2.3, -1/4, -14, 3/4, 0, 0.6, 3
2. -30/5, -4, 12/5, 2.6, 0.4, 1/2
1. -2.3, -1/4, -14, 3/4, 0, 0.6, 3
2. -30/5, -4, 12/5, 2.6, 0.4, 1/2
Warm Up: September 18th, 8th Grade
1. 3 * (2-5) + 4 - (-3)
2. (4*6) + (-2*12)/3 - 12
3. (10/4) * (16/8)^2
Saturday, September 14, 2013
Warm Up: September 17th, 7th Grade
Have you ever traded something with a friend? An old toy for a ball, or a tube of mascara for some foundation?
Vegetable and Spice Market at Benares, c.1840
Then you did something called bartering, which is how people exchanged things before money was invented. (Yep, money was invented.)
So with that in mind, I'm going to have Kyle MacDonald tell you a story, and then we'll talk about the math
.
Warm Up: September 19th, 7th Grade
1. Have you ever started a project only to see it not get finished? Describe what happened.
"Unfinished" bridge in b&w by Cretense
Perhaps you didn't give yourself enough time, or perhaps you ran out of materials before the project was done. Perhaps you never had the materials to begin with, so you didn't even get as far as the person or people building this bridge.
2. Does that mean you shouldn't think up ideas like this? Why or why not?
3. What do you think would have helped the bridge builder complete the bridge?
Estimating Area
Here's one way to estimate area.
You will probably be given a problem similar to this on the STAAR. The reason why things like this are useful is for arts and crafts projects where part of an object has something done to it, like part of it is painted and the rest is not, or part of it has glitter on it, etc.
The estimated area tells us something about how much of a cover we need to get, so how many bottles of glittter or buckets of paint would be needed. This way we don't have to make extra trips to the store either to buy more or to return what we had that was too much.
This is not the only example of the use of this concept, but is one of the most clear. Other examples include washing windows on a building that isn't completely covered with them, figuring out how much floor wax to use when buffing a wood or tile floor, figuring out how much grass a sprinkler head would cover. I bet you can think of some others.
You will probably be given a problem similar to this on the STAAR. The reason why things like this are useful is for arts and crafts projects where part of an object has something done to it, like part of it is painted and the rest is not, or part of it has glitter on it, etc.
The estimated area tells us something about how much of a cover we need to get, so how many bottles of glittter or buckets of paint would be needed. This way we don't have to make extra trips to the store either to buy more or to return what we had that was too much.
This is not the only example of the use of this concept, but is one of the most clear. Other examples include washing windows on a building that isn't completely covered with them, figuring out how much floor wax to use when buffing a wood or tile floor, figuring out how much grass a sprinkler head would cover. I bet you can think of some others.
Order of Operations
Mr. Khan from Khan Academy explains why we need order of operations, and then links that to PEMDAS.
Video
Hope this helps you understand this concept.
Hope this helps you understand this concept.
Warm Up: September 17, 8th Grade
Colors have opposites based on their intensity. Likewise, math operations have opposites.
In this case, pick your favorite color and write its number down. Then find it's opposite and write its number down.
After that, write the following words:
Addition
Multiplication
Exponents
Then try to figure out their opposites.
Warm Up: September 16, 8th Grade
Place the following numbers on this number line: 1/2, 5%, 2, -3, -10%, -1 3/4, 1.5, -2.3
Warm Up, September 16, 7th Grade
You have 8 beautiful apples.
How would you divide them between 2 friends. What about between 3? 4? 5? 6?
What if each apple was worth 100 beans?
How many beans would you have if you traded all your apples? What about only 4 apples? 3?
How would you divide them between 2 friends. What about between 3? 4? 5? 6?
What if each apple was worth 100 beans?
How many beans would you have if you traded all your apples? What about only 4 apples? 3?
Thursday, September 12, 2013
3D Nets
I intended to put this up earlier. Here's a video explaining nets if you had trouble reading what I wrote. It also explains faces, edges, and vertices.
Monday, September 9, 2013
Surface Area: Pyramids
Now that we've looked at prisms and cylinders, we need to consider the formula for pyramids.
2. Write the formulas
As you can see on the formula chart, this formula is rather different compared to prisms and cylinders. One of the differences is the requirement of lateral height (l). This is the height from the base to the top of the pyramid measured along a face instead of through the middle of the shape. Since the sides are all triangles, they would add up into one big triangle, but would still follow the area formula, so that's where the 1/2 comes from. Also there is only one base.
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (s+s+s) * l + ((1/2) * b * h)
3. Plug in the numbers
S. A. = (1/2) * (5 + 5 + 5) * 7.1 + ((1/2) * 5 * 4.3)
4. Solve
That looks like alot, so let's break it down by using order of operations. The perimeter is easy with 15, and half that is 7.5.
S. A. = 7.5 * 7.1 + ((1/2) * 5 * 4.3)
Next, half of 5 is 2.5. S. A. = 7.5 * 7.1 + (5 * 4.3)
S. A. = 53.25 + 21.5
S. A. = 74.75 square feet
Let's try another.
1. What shape is it?
This is a rectangular or square pyramid.
2. Write the formulas
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (2b + 2h) * l + (b * h)
3. Plug in the numbers
S. A. = (1/2) * (2 * 9 + 2 * 9) * 9.2 + (9 * 9)
4. Solve
S. A. = (18) * 9.2 + (81)
S. A. = 165.6 + 81
S. A. = 246.6 square centimeters
1. What shape is it?
There are no rectangular faces, so this is a triangular pyramid.
As you can see on the formula chart, this formula is rather different compared to prisms and cylinders. One of the differences is the requirement of lateral height (l). This is the height from the base to the top of the pyramid measured along a face instead of through the middle of the shape. Since the sides are all triangles, they would add up into one big triangle, but would still follow the area formula, so that's where the 1/2 comes from. Also there is only one base.
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (s+s+s) * l + ((1/2) * b * h)
3. Plug in the numbers
S. A. = (1/2) * (5 + 5 + 5) * 7.1 + ((1/2) * 5 * 4.3)
4. Solve
That looks like alot, so let's break it down by using order of operations. The perimeter is easy with 15, and half that is 7.5.
S. A. = 7.5 * 7.1 + ((1/2) * 5 * 4.3)
Next, half of 5 is 2.5. S. A. = 7.5 * 7.1 + (5 * 4.3)
S. A. = 53.25 + 21.5
S. A. = 74.75 square feet
Let's try another.
This is a rectangular or square pyramid.
2. Write the formulas
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (2b + 2h) * l + (b * h)
3. Plug in the numbers
S. A. = (1/2) * (2 * 9 + 2 * 9) * 9.2 + (9 * 9)
4. Solve
S. A. = (18) * 9.2 + (81)
S. A. = 165.6 + 81
S. A. = 246.6 square centimeters
Sunday, September 8, 2013
Surface Area
So, now let's talk about surface area. It's exactly that, the area of the surface of a 3D shape. So if you understand how the 3D Net works of that shape, the surface area makes sense.
The general formula for surface area for prisms is as follows:
The perimeter of the base times the height, plus the area of the base times two. So, let's look at a few examples for more information.
3. Plug in the numbers
diameter not radius was given S.A. = (2 * 3.14 * 10) * 5 + 2 * (3.14 * 10^2)
10^2 = 100 S.A. = (62.8) * 5 + 2 * (314)
S.A. = 314 + 628
S.A. = 942 square inches.
Last example for now:
The general formula for surface area for prisms is as follows:
The perimeter of the base times the height, plus the area of the base times two. So, let's look at a few examples for more information.
Here is a triangular prism. It's 3D net is similar to this:
The large rectangle in the middle has a base equal to the height of the shape, and a height equal to the perimeter of the base.
So let's follow the same steps we use for Volume and work this out.
1. What shape is it? Already identified.
2. Write our formula.
General S.A. = P * h + 2 * B
Specific S.A. = (s+s+s) * h + 2 * (0.5 * b * h)
Remember that the height in the general formula refers to the height of the prism. Also remember to follow order of operations. The area of the base is still the area of a triangle formula, just like with volume.
3. Plug in the numbers
S.A. = (9+8+7) * 5 + 2 (0.5 * 9 * 6)
That looks like a lot, but with practice, it will get easier.
4. Solve
S.A. = (24) * 5 + 2 (27)
S.A. = 120 + 54
S.A. = 174 square miles
Since it's area, it won't be cubic miles. We're measuring the covering on the outside of the shape, not how much space is contained inside it. Let's try another.
1. What shape is it?
This is a cylinder. It's net looks like:
2. Write the formula
Same general formula: S.A. = P * h + 2 * B
Different specific formula: S.A. = (2 * pi * r) * h + 2 * (pi * r^2)
Since we're dealing with circles, we use circumference for perimeter and area of a circle for our base.
diameter not radius was given S.A. = (2 * 3.14 * 10) * 5 + 2 * (3.14 * 10^2)
10^2 = 100 S.A. = (62.8) * 5 + 2 * (314)
S.A. = 314 + 628
S.A. = 942 square inches.
Last example for now:
1. What shape is it?
This is a rectangular prism. Never mind the slant, it's still a rectangular prism.
Pick bases: I'm picking the 3 x 5 sides, as they'll be easy to use.
2. Write formulas:
Same general formula: S.A. = P * h + 2 * B
Specific formula: S.A. = (b+b+h+h) * h + 2 * (b * h)
Again, note that the h outside parenthesis refers to the height of the prism.
3. Plug in the numbers
S.A. = (3+3+5+5) * 12 + 2 * (3 * 5)
4. Solve
S.A. = (16) * 12 + 2 * (15)
S.A. = 192 + 30
S.A. = 222 square inches
Test Thursday
I pushed off the Test to this Thursday, but if I push it back further, it will be just as tough because even more information would be on it. So click on the review tab, as information on scale factor, volume, and 3D Nets will be on the test. You should look over these topics before the test. I know these topics are challenging to some of you, but that's why I decided to hit them first in the year. We will revisit them a few times later on. After the beginning of October, we'll start hitting some of the easier things.
3D Nets
We'll work on 3D Nets on Tuesday. Here are some examples:
The only word that's strange is cuboid, which we call a rectangular prism. I will go over each of these in detail.
For more interactivity, click here.
This shape has 5 faces, 1 base which is square and 4 triangle sides.
This shape is a triangular prism. Note that it also has 5 faces, however 3 are rectangles and 2 are triangles. As with every prism, there are 2 bases. The faces that are bases are the triangles.
This shape is a triangular pyramid. The quadrilateral shapes on the edges are not included in the pyramid, those are tabs in case you printed out the shape and attempted to glue it together. You notice that it has 4 faces, all of which are triangles. If they're all equivalent, any of those triangles could be the base.
This shape is the net of a cone. The quarter circle is exactly that, a quarter circle with the height of the cone as the radius.
This is the net of a cylinder. The long rectangle has a base equal to the circumference of the circle, and the height is equal to the height of the cylinder.
Finally, a net of a rectangular prism. As you can see, there are 6 faces, just like a cube. The bases are any two equal and opposite rectangles. The easiest ones to identify are the ones on the left and right sides.
Source 1
Source 2
Source 3
The only word that's strange is cuboid, which we call a rectangular prism. I will go over each of these in detail.
For more interactivity, click here.
This shape has 5 faces, 1 base which is square and 4 triangle sides.
This shape is a triangular prism. Note that it also has 5 faces, however 3 are rectangles and 2 are triangles. As with every prism, there are 2 bases. The faces that are bases are the triangles.
This shape is the net of a cone. The quarter circle is exactly that, a quarter circle with the height of the cone as the radius.
Finally, a net of a rectangular prism. As you can see, there are 6 faces, just like a cube. The bases are any two equal and opposite rectangles. The easiest ones to identify are the ones on the left and right sides.
Source 1
Source 2
Source 3
Pyramids and Cones
The formula for Pyramids and Cones is almost exactly like the formula for Prisms and Cylinders. One of the major differences is the 1/3. It's an important difference because in coming to a point for the height, it limits the volume compared to a similar prism or cylinder. Here are some examples.
Again the base is a diameter (16), so radius is 8. V = (1/3) * (3.14 * 8^2) * 16
4. Solve
8^2 = 64. 64 * 3.14 = 200.96 V = (1/3) * (200.96) * 16
V = (1/3) * 3215.36
V = 1071.79 cubic meters
The same four steps apply to these shapes.
1. What shape is it?
It's a cone. The base is a circle, so we'll need area for that.
2. Write the formulas.
The general formula for cones and pyramids is V=(1/3)B*h
V = (1/3) * B * h
specific to cones V = (1/3) * (pi * r^2) * h
3. Plug the numbers in:
The base lists a diameter 2, not a radius, so that radius is 1 (2/2=1). Height is 3.
V = (1/3) * (3.14 * 1^2) * 3
4. Solve
3 divided by 3 is 1. 1^2 is 1. V = 1 * 3.14 * 1
V = 3.14 cubic feet.
Let's try one that's more difficult.
1. What shape is it?
Cone, same as the first.
2. Write the formulas.
V = (1/3) * B * h
Same as the first. V = (1/3) * (pi * r^2) * h
3. Plug the numbers in.
Again the base is a diameter (16), so radius is 8. V = (1/3) * (3.14 * 8^2) * 16
4. Solve
8^2 = 64. 64 * 3.14 = 200.96 V = (1/3) * (200.96) * 16
V = (1/3) * 3215.36
V = 1071.79 cubic meters
Let's try this one.
1. What shape is it?
Pyramid with a square base. I know it's square because of the 7x7. The height is defined by the line in the middle. It could also be listed outside the diagram as a separate line. In this case, it's 6.
2. Write the formulas
general formula V = (1/3) * B * h
specific formula V = (1/3) * (b * h) * h
3. Plug the numbers in
V = (1/3) * (7 * 7) * 6
4. Solve
V = (1/3) * (49) * 6
6 divided by 3 is 2. V = 49 * 2
V = 98 cubic meters.
1. What shape is it?
Another square (rectangular) pyramid.
2. Write the formulas.
general formula V = (1/3) * B * h
specific formula V = (1/3) * (b * h) * h
3. Plug the numbers in
V = (1/3) * (6 * 6) * 8
4. Solve
V = (1/3) * (36) * 8
V = 12 * 8
V = 96 cubic yards
1. What shape is it?
This one's a triangular pyramid. There are no rectangles or squares on the shape. The base has a right triangle, so its base and height are 4 and 3. The height of the pyramid is the line through the middle, and is 4.
2. Write the formulas
general formula V = (1/3) * B * h
specific formula V = (1/3) *(0.5 * b * h) * h
3. Plug the numbers in
V = (1/3) * (0.5 * 3 * 4) * 4
4. Solve
V = (1/3) * (6) * 4
V = 2 * 4
V = 8 cubic meters
Warm Up, Monday, Sept. 9
Source
According to bmigaming.com, this claw machine has dimensions of Height: 76", Width: 31", Depth: 36"
If we were going to try to use a shoe box that has dimensions of Height: 11.5", Width: 7", and Depth: 3.75", Define the ratio of each dimension. Then figure out what the correct ratio is that all 3 dimensions can fit inside the shoe box dimensions. This means that when you multiply the ratio by the other dimensions, they are less than or equal to the dimensions of the shoe box.
Thursday, September 5, 2013
Scale Factor Game
Here's a math game that is a mix of platformer and ratio finder.
http://www.mathplayground.com/ScaleFactorX/GameLoader.html
Hope you have fun!
http://www.mathplayground.com/ScaleFactorX/GameLoader.html
Hope you have fun!
Volume: Cylinders and Prisms Examples
More examples as follows:
1. What shape is it?
This is a box, so it's a rectangular prism. On rectangular prisms, I need to pick 2 opposite sides as my bases. I am going to choose the top of the shape, and the bottom of the shape. This means that my base is square because the dimensions are 6x6.
2. Write the formulas
general V=Bh
specific to rectangular prisms V=(b * h) * h
3. Plug the numbers in:
I get the 6x6 from my base, then the only different number is 3. If it was a cube, the numbers would all be 6.
V=(6 * 6) * 3
4. Solve
Pretty clear here:
36*3 = 108
108 mi^3
1. What shape is it?
This is a ramp, so it's a triangular prism.
2. Write the formulas
general V=Bh
specific to triangular prisms V=(0.5 * b * h) * h
3. Plug the numbers in:
The two bases are triangles, so I need to be looking for that right angle. It's in the bottom corner, so my dimensions for my triangle are 8*6. It looks like the dimensions for each rectangle are 10*8, 6*8, and 8*8, so that means my height is 8.
V=(0.5 * 8 * 6) * 8
8 * 6= 48
48 * 0.5 = 24
24 * 8 = 192
192 in^3
1. What shape is it?
This is a can, so it's a cylinder.
2. Write formulas
general V=Bh
specific to cylinders V=(pi * r^2) * h
3. Plug the numbers in:
20 cm is for the whole way across the circular base. That means I need half that for radius, so 10. The only other number on here is 9.
V=(3.14 * 10^2) * 9
10^2 = 100.
100 * 3.14 = 314
13
314
* 9
____
2826
2826 cm^3
We'll do pyramids and cones later.
1. What shape is it?
This is a box, so it's a rectangular prism. On rectangular prisms, I need to pick 2 opposite sides as my bases. I am going to choose the top of the shape, and the bottom of the shape. This means that my base is square because the dimensions are 6x6.
2. Write the formulas
general V=Bh
specific to rectangular prisms V=(b * h) * h
3. Plug the numbers in:
I get the 6x6 from my base, then the only different number is 3. If it was a cube, the numbers would all be 6.
V=(6 * 6) * 3
4. Solve
Pretty clear here:
36*3 = 108
108 mi^3
1. What shape is it?
This is a ramp, so it's a triangular prism.
2. Write the formulas
general V=Bh
specific to triangular prisms V=(0.5 * b * h) * h
3. Plug the numbers in:
The two bases are triangles, so I need to be looking for that right angle. It's in the bottom corner, so my dimensions for my triangle are 8*6. It looks like the dimensions for each rectangle are 10*8, 6*8, and 8*8, so that means my height is 8.
V=(0.5 * 8 * 6) * 8
8 * 6= 48
48 * 0.5 = 24
24 * 8 = 192
192 in^3
This is a can, so it's a cylinder.
2. Write formulas
general V=Bh
specific to cylinders V=(pi * r^2) * h
3. Plug the numbers in:
20 cm is for the whole way across the circular base. That means I need half that for radius, so 10. The only other number on here is 9.
V=(3.14 * 10^2) * 9
10^2 = 100.
100 * 3.14 = 314
13
314
* 9
____
2826
2826 cm^3
We'll do pyramids and cones later.
Volume By The Numbers
Here's the list in order to find volume:
1. What shape is it?
Answering this question helps you decide which formulas to write down.
2. Write formulas
Mr. V counts it wrong if you don't write formulas.
3. Plug in the numbers.
This part can be a little tricky if you see extra numbers. If you get tripped up by this, I'll explain in detail.
4. Solve.
Finish doing the math. Some of you are doing these steps so fast you're making mistakes. Others are having difficulty with step 3 because they have trouble identifying the base.
Let's try some problems:
As you can see this problem has a lot of information on it. But by following the steps you can eliminate some of the confusion.
Step 1. What shape is it?
This is a triangular prism. I know this because it has 2 faces that are triangles, and any pyramid must have at least 4 triangles. Prisms also have rectangular faces. Everyone see that the rectangular faces are 6 by 12 and 6 by 4? This means that the height of my prism is 6.
Step 2. Write Formulas
My general formula for prisms is: V=Bh
My specific formula for triangular prisms is: V=(0.5*b*h) * h
The height for my base always forms a right angle with the base. So 3.9 is the height of the triangular base and 12 is the base of the triangular base. (sorry for the word confusion, but those are the labels Texas wants us to use.). I already saw that the height of the prism is 6, because that's the same for all the rectangular faces.
Step 3. Plug in the Numbers.
I described alot above. The numbers are: V=(0.5*12*3.9)*6
Step 4. Solve.
12 * 0.5 = 6 (always find an even number to divide by 2 first when dealing with triangular shapes)
5
3.9
* 6
___
23.4
1 2
23.4
* 6
____
130.4
V = 130.4
1. What shape is it?
Answering this question helps you decide which formulas to write down.
2. Write formulas
Mr. V counts it wrong if you don't write formulas.
3. Plug in the numbers.
This part can be a little tricky if you see extra numbers. If you get tripped up by this, I'll explain in detail.
4. Solve.
Finish doing the math. Some of you are doing these steps so fast you're making mistakes. Others are having difficulty with step 3 because they have trouble identifying the base.
Let's try some problems:
Step 1. What shape is it?
This is a triangular prism. I know this because it has 2 faces that are triangles, and any pyramid must have at least 4 triangles. Prisms also have rectangular faces. Everyone see that the rectangular faces are 6 by 12 and 6 by 4? This means that the height of my prism is 6.
Step 2. Write Formulas
My general formula for prisms is: V=Bh
My specific formula for triangular prisms is: V=(0.5*b*h) * h
The height for my base always forms a right angle with the base. So 3.9 is the height of the triangular base and 12 is the base of the triangular base. (sorry for the word confusion, but those are the labels Texas wants us to use.). I already saw that the height of the prism is 6, because that's the same for all the rectangular faces.
Step 3. Plug in the Numbers.
I described alot above. The numbers are: V=(0.5*12*3.9)*6
Step 4. Solve.
12 * 0.5 = 6 (always find an even number to divide by 2 first when dealing with triangular shapes)
5
3.9
* 6
___
23.4
1 2
23.4
* 6
____
130.4
V = 130.4
Tuesday, September 3, 2013
Changes
Hello everyone, just wanted to update you with some changes I made. Sorry they came fairly late tonight. I updated the Assignments, Review, and Project pages, so if that applies to you, be sure to check them out. I noticed only one person so far had seen the video on scale factor today. I should have made that more clear.
Scale Factor
Much of our modern world would not be possible without diagrams that are to scale. The best way to think about this is to think about where you live or the school, and then think about how much paper it would take if the architect who designed it didn't use a scale. If that doesn't prove why it's useful consider this. If you're interested in the history of scale drawings, it's here.
Now you'll notice that ratios are in use. If you need a refresher on ratios, you can look here. You may also have some scale factor problems that are missing side problems. If you need a refresher on that, you can check this video out.
Here's a great explanation of scale factor:
So our goal for understanding is to learn the scale factor formula, and then learn how to apply it.
So in the video, let's take the original image of Mr. Simpson and enlarge it by using a scale factor of 5. Remember, this creates a ratio of 5:1 with the scale diagram being on top. What would the new dimensions of the enlargement be? Make sure to write this and the formula down in your math journal or a piece of paper so it can be recorded in your warm-up spiral.
Now you'll notice that ratios are in use. If you need a refresher on ratios, you can look here. You may also have some scale factor problems that are missing side problems. If you need a refresher on that, you can check this video out.
Here's a great explanation of scale factor:
So our goal for understanding is to learn the scale factor formula, and then learn how to apply it.
So in the video, let's take the original image of Mr. Simpson and enlarge it by using a scale factor of 5. Remember, this creates a ratio of 5:1 with the scale diagram being on top. What would the new dimensions of the enlargement be? Make sure to write this and the formula down in your math journal or a piece of paper so it can be recorded in your warm-up spiral.
Caine's Arcade: Shoebox Version
For our first project of the year, we will be creating shoebox versions of arcade games. Our goal for this project is to create scale models of the arcade games so that we have prototypes (first versions) that are easily tested and shared. Also a shoebox is more portable than the constructs we will be making for the Global Day of Play.
Thus, everyone should watch at least the first video of Caine's Arcade in order to know what we're talking about. When you're done, come back here for the list of things needed.
Original Arcade Game Dimensions: You need to specify a height, a width, and a length. They need to be in inches, so you need to convert yards and feet to inches. If the game has different geometry in places, divide the game into simpler geometry. So if I was miniaturizing a skee-ball game, I would have the track as one shape, and then the scoring area as another.
Once I have the basic shapes, I would need to do some research (asking google is a good place to start) about the dimensions of the game. If you use the word "dimensions" you should get clearer options.
Once you've done that, you also need Original Shoebox Dimensions, again in inches. This will give you an idea of if your dimensions match, or if you need to make the shoebox arcade game dimensions smaller than the shoebox. Trying to make your shoebox fit the arcade is a bad idea and will probably lead to a lot of extra work. That said, I won't penalize anyone who does this, provided their scale factor is correct.
Finally, you need to prove that all your dimensions have the same scale factor. If you don't know what that math term is, don't worry, I'll be explaining it before you have to turn this project in.
So to list it out, the things I'm expecting are:
Shoebox Arcade Game
A piece of paper with the following written on it:
Your heading, Shoebox Arcade Game as the title,
Name of Arcade Game picked,
Original Dimensions of the Arcade Game you picked,
Original Dimensions of the Shoebox,
Dimensions of the Game that fit on/in the shoebox,
Scale factor between the original and small game,
Additional materials used listed.
If you want to create a totally new game, see me and we'll discuss similar arcade games to use as dimensions.
Thus, everyone should watch at least the first video of Caine's Arcade in order to know what we're talking about. When you're done, come back here for the list of things needed.
Original Arcade Game Dimensions: You need to specify a height, a width, and a length. They need to be in inches, so you need to convert yards and feet to inches. If the game has different geometry in places, divide the game into simpler geometry. So if I was miniaturizing a skee-ball game, I would have the track as one shape, and then the scoring area as another.
Once I have the basic shapes, I would need to do some research (asking google is a good place to start) about the dimensions of the game. If you use the word "dimensions" you should get clearer options.
Once you've done that, you also need Original Shoebox Dimensions, again in inches. This will give you an idea of if your dimensions match, or if you need to make the shoebox arcade game dimensions smaller than the shoebox. Trying to make your shoebox fit the arcade is a bad idea and will probably lead to a lot of extra work. That said, I won't penalize anyone who does this, provided their scale factor is correct.
Finally, you need to prove that all your dimensions have the same scale factor. If you don't know what that math term is, don't worry, I'll be explaining it before you have to turn this project in.
So to list it out, the things I'm expecting are:
Shoebox Arcade Game
A piece of paper with the following written on it:
Your heading, Shoebox Arcade Game as the title,
Name of Arcade Game picked,
Original Dimensions of the Arcade Game you picked,
Original Dimensions of the Shoebox,
Dimensions of the Game that fit on/in the shoebox,
Scale factor between the original and small game,
Additional materials used listed.
If you want to create a totally new game, see me and we'll discuss similar arcade games to use as dimensions.
Monday, September 2, 2013
Review of Area's Relationship to Volume
In case you weren't here for math class the day we talked about the formula sheet, here is another example of a Venn Diagram that explains how the formulas for area and volume are related.
As you can see, all the volume formulas contain the area formulas for their base. This is why the general formula for volume includes the capital B. This can create confusion because of the two heights, so be careful when you pick sides. We'll practice this in class some too.
Pyramids and cones have an additional modifier to the formula due to their shape. It actually takes 3 pyramids to create a prism of the same base.
video
The short video above shows visually why the volume is different even though the area of both bases are the same. Disregard the yellow food coloring. :-P
Hopefully this helps you later if you forget.
Pyramids and cones have an additional modifier to the formula due to their shape. It actually takes 3 pyramids to create a prism of the same base.
The short video above shows visually why the volume is different even though the area of both bases are the same. Disregard the yellow food coloring. :-P
Hopefully this helps you later if you forget.
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