Math Games

7th Grade:

Solving 1 step equations involving addition & subtraction.
http://www.harcourtschool.com/activity/elab2004/gr5/19.html

Solving 1 step equations involving multiplication and division.
http://www.harcourtschool.com/activity/elab2004/gr6/12.html

Using a model to solve 2 step equations.
http://www.mathplayground.com/AlgebraEquations.html

Keeping the balance
http://www.topmarks.co.uk/Flash.aspx?f=CalcBalancev5

Solving Equations
http://www.mathplayground.com/shuttle_mission_math/shuttle_mission_math_game.html

8th Grade:

Solving 1 step equations involving addition & subtraction.
http://www.harcourtschool.com/activity/elab2004/gr5/19.html

Solving 1 step equations involving multiplication and division.
http://www.harcourtschool.com/activity/elab2004/gr6/12.html

Solving Equations
http://www.mathplayground.com/shuttle_mission_math/shuttle_mission_math_game.html

Learning about linear equations.
http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html

Math Anxiety

http://math.about.com/od/reference/a/anxiety.htm

Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math. When one tries to memorize procedures, rules and routines without much understanding, the math is quickly forgotten and panic soons sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverses. In other words, 'It's not yours to reason why, just invert and multiply'. Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone every use pizzas or math manipulatives to show you why it works? If not, you simply memorized the procedure and that was that. Think of math as memorizing all the procedures - what if you forget a few? Therefore, with this type of strategy, a good memory will help, but, what if you dont' have a good memory. Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome."

When Students Fail...

I just read this article about when students fail math.  It was very insightful.

http://www.slate.com/articles/health_and_science/science/2013/04/math_teacher_explains_math_anxiety_and_defensiveness_it_hurts_to_feel_stupid.html

What I'd Tell My Teenage Self

I saw this on TED and wanted to share it with you.

http://blog.ted.com/2013/11/13/what-id-tell-my-teenage-self-life-and-career-advice-from-the-ted-staff/

As for me? I'm not sure what I would say.  Probably, "Don't put too much stock in what others think of you.  In a few years, you won't be around them anyway."

Someone forgot his Pythagorean Triple

Watch this...

And become SMARTER THAN HALF THE AUDIENCE!

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Algebra Dougie

One more, this time to Teach Me How to Dougie.

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Repeat It (Algebra)

MJ's classic Beat It with different lyrics that apply to what we're learning.

Have a little fun!

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Something Funny...

And now for something completely different!

Brought to you from the deep dark recesses of youtube:  Hint: Stick with it and you'll hear Thrift Shop.

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Graphing Linear Equations

Most of you know what a linear equation is.  You've not heard it called this, but you know what it is.  All the sequences we've had so far form linear equations.  So what are some things you can take away from what we've done with sequences?

1.  All linear equations have a constant rate of change.  As in, when x goes up by 1, y goes up by the same number each time, whether it's up by 2, 3, 5, etc.

We call this rate of change m.  In equation form, it's the number that is multiplied by x (remember inverses mean that it could be the number you're dividing by, too!).

These equations also have a constant number where x crosses the y-axis, called the y-intercept.  You find this by setting x to zero.  Then when you multiply by the change, the change falls out, leaving the intercept.  This intercept is called b.

A linear equation has a few different forms, but the most workable form is called the slope-intercept form.  This means we are solving for y by doing stuff to x.  So y = m * x + b

We can then graph the line on a coordinate plane based on using a process table for y = m * x + b.

You can see that demonstrated here:

Properties of Equality

The properties of equality are basic algebraic facts that help us solve equations.  We are already using these, we just haven't put names to them yet.  So in this video this teacher puts the name with the concept.  You will cover this again in 9th grade and refresh it in 10th and 11th grade.  So you might as well learn it now so that it's faster in 9th grade and an old concept in 11th grade.

To see this concept in more detail, watch this video.

The major takeaway are the properties of equality for the operations.  Used in conjunction with the additive and multiplicative identities and inverses, we can solve for variables.

Here is the list of properties:

Additive identity: a + 0 = a (or 4 + 0 = 4, etc)

Multiplicative identity:  a * 1 = a  (or 4 * 1 = 4, etc)

Additive inverse: a + -a = 0 (or 4 + -4 = 0, etc)

Multiplicative inverse a * 1/a = 1 (or 4 * 1/4 = 1, etc)

Addition property of equality: if a = b, then a + c = b + c  (if 4 = 4, then 4 + 2 = 4 + 2)

Subtraction property of equality: if a = b, then a - c = b - c (if 4 = 4, then 4 - 2 =  4 - 2)

Multiplication property of equality: if a = b, then a * c = b * c (if 4 = 4, then 4 * 2 = 4 * 2)

Division property of equality: if a = b, then a / c = b / c (if 4 = 4, then 4 / 2 = 4 / 2)

Using these properties, we can solve any equation with 1 variable.  We can simplify any equation with 2 variables.  Understanding these properties will help you write equations for word problems, or pick the correct equation out of a list.

Properties of Arithmetic

I'm sure some of you have wondered "how does Mr. V. know all these tricks?"  One reason is because I have learned this set of arithmetic properties here:

http://www.coolmath.com/prealgebra/06-properties/

Many of you are already using these without knowing it.  The multiplicative inverse property is used in solving proportions through butterfly method.

The additive inverse property is used to solve for x in linear relationships when y is constant.

I just like the way the concepts are presented at coolmath. I hope you do too.

Oh, and if you don't learn them now, you will continue to struggle and will probably have trouble in the rest of your math career through high school and possibly beyond.

Scientific Notation Flow Chart

This flow chart should help you figure out how to write scientific notation and convert it back to standard notation.

Pythagorean Triplets

Here are some more examples of Pythagorean Theorem problems.

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Linear Patterns

Here's a video explaining how to find a pattern based on a sequence.

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Most of you are fairly accomplished at this method.  What you have been having trouble at is understanding how to write the rule.  Mr. Khan shows a way to understand the rule in this video.

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Here's a more complicated example that actually gets Mr. Khan going into Algebra 1!

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Here's one more example.

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Hope these help you prepare.

Spaghetti and Meatballs For All

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Pythagorean Theorem

Here is a video explaining the Pythagorean Theorem.

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Dixit

How to play Dixit:  Also watch Wil Wheaton, Beth Riesgraf, Leo Chu, and Casey McKinnon.  A bit of bad language but not much.

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How to Think Big

Thinking about Infinity.

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Similar Figures

Sal Khan explains similar triangles much in the way I do.

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Proportions

I know I direct taught alot about proportions, but here's Sal Khan discussing proportions, so if you feel like you didn't understand, that's okay.  Just watch this video a few times to try to get it.

Watch this video first about why ratios are proportional:

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Video 2

Hope this helps you.

Ratios

Sal Khan explains ratios much like I would:

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Warm Up: October 7th

Times Table Time.

If you already have this down, that's fine, it'll be useful to have it as reference today.  If you don't have this down, you need the practice.

Take your half grid paper and start working.

Vocabulary Word:  Congruent: Having the same size or shape

In a sentence: Two volleyballs are congruent if they're made by the same company and have the same model number.

In a math context:  Two triangles are congruent if their angles and sides are equal.

When you're finished with times tables, write two of your own sentences with congruent.

How to Improve your Listening

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Warm Up, September 25, 8th Grade

Warm Up, September 24, 8th Grade

When you're finished, try to make this tangram pattern.

Warm Up, September 23, 8th Grade

Comedian and Juggler Puts Hand Percussionists to Shame

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Warm Up: October 1

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%

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:

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.

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.

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Part 2: Examples

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Part 3: Estimating the value of a square root.

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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

Warm Up: September 18th, 8th Grade

Order matters.  Sometimes it seems like it is chaotic, but if you don't follow the order, it won't turn out correctly.  Math is the same way.  This is why I can get two or more answers that have their calculations right and still be wrong.  So if you don't follow PEMDAS, you're going to get wrong answers and be unhappy about it.

1.  3 * (2-5) + 4 - (-3)

2. (4*6) + (-2*12)/3 - 12

3. (10/4) * (16/8)^2

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

.

Video

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.

Order of Operations

Mr. Khan from Khan Academy explains why we need order of operations, and then links that to PEMDAS.

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Hope this helps you understand this concept.

Ordering Numbers

Sal Khan shows us how to order numbers here:

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Hope this helps.

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?

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.

Surface Area: Pyramids

Now that we've looked at prisms and cylinders, we need to consider the formula for pyramids.

1. What shape is it?

There are no rectangular faces, so this is a triangular pyramid.

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

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.

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.

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:

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
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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.

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.

Warm Up

Pick a logo from the following image and expand it to fit a full piece of paper.  Remember to keep the length to width ratio the same.

Source


Then on the back of that piece of paper, write the original dimensions, the new dimensions and the scale factor.

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!

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.

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

Gear Ratio

Here's a fairly clear explanation for one reason why ratios are important in modern life.

Video

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.