Tuesday, February 25, 2014
Using Probability to Learn Statistics
Probability tests using number cubes or spinners are a good way to create a set of data. The numbers have variance without being overly large, a mode is present, the range is also not very large, and you can relate the mean to probability through the "Law of Averages". You can also bring up the bell curve. The data set created can be used to create circle graphs by showing experimental vs theoretical probability, bar graphs by breaking it down per probability device, histograms and line plots to show frequency of results, scatter plots to show trends between the spinner and the number cube, and box and whisker graphs to show range, median, and quartiles. This will require a bit more care with the data sheet, as carelessness will lead to the initial part failing.
Sunday, February 16, 2014
Graphing Linear Equations
For those of you who are ready, here's the next step from what we were doing with charts:
Graphing Linear Equations!
It actually gets kinda fun once you get the hang of it.
Here's Cool Math's explanation.
Here's a game for solving them.
You may have seen this one before but it is also about graphing linear equations.
Graphing Linear Equations!
It actually gets kinda fun once you get the hang of it.
Here's Cool Math's explanation.
Here's a game for solving them.
You may have seen this one before but it is also about graphing linear equations.
Probability
How to solve probability problems:
Each of the letters in the word
SUPREMACY are on separate cards
face down on the table. If you pick a
card at random, what is the
probability that the letter on it will fall
within the range of "H" and "U" in the
alphabet?
Probability problems are usually about creating ratios, then using them to answer questions related to them. To find the ratio, find out the total things that can happen. This is the SECOND or BOTTOM number of the ratio. Then find the things the problem desires to happen. This is the FIRST or TOP number of the ratio. In this way, the desired outcome is set to the total outcomes. This gives you a fraction. You can then simplify the fraction and/or convert it to percent or decimal depending on what the problem asks. The percent triangle can help you with that.
Let's solve the example problem: The problem says there are cards for each letter in the word. So count them up. Supremacy has 9 letters. This is our second or bottom number.
Then they have defined a range of letters. Any time a problem defines a PART of the set, they are wanting you to create a FRACTION, which is the ratio of part to whole. So Figure out which cards are between H and U, including H and U. We leave out A, C, and E because they are before H and thus out. We leave out Y because it is after U. This leaves us with 5 letters. This is the first or top number.
So our ratio is 5 / 9.
Things to be careful about: In this set of problems, the word "or" usually means add the probabilities together. So if they wanted to know the probability of getting an "S" or getting a "U", you would add those probabilities together: Each is somewhat unlikely though, as getting an "S" has a 1 in 9 chance. The "or" increases that by 1 in 9. So 1/9 + 1/9 = 2/9.
Also, please note that this is just ONE event. If the problem asks for you to draw again, YOU'RE NOT DONE with the math.
The problem would have stated "If you pick a card at random, replace it, and then draw again..." You would multiply the probability of getting the first with the probability of getting the second. So with the "H" to "U", we would have 5/9 * 5/9. This gives us 25/81. Note this number is SMALLER, because the chances of it happening GO DOWN.
Other than that, you need to practice these. Here are some probability games and here are some practice problems.
This description of probability can be displayed in Spanish..
Each of the letters in the word
SUPREMACY are on separate cards
face down on the table. If you pick a
card at random, what is the
probability that the letter on it will fall
within the range of "H" and "U" in the
alphabet?
Probability problems are usually about creating ratios, then using them to answer questions related to them. To find the ratio, find out the total things that can happen. This is the SECOND or BOTTOM number of the ratio. Then find the things the problem desires to happen. This is the FIRST or TOP number of the ratio. In this way, the desired outcome is set to the total outcomes. This gives you a fraction. You can then simplify the fraction and/or convert it to percent or decimal depending on what the problem asks. The percent triangle can help you with that.
Let's solve the example problem: The problem says there are cards for each letter in the word. So count them up. Supremacy has 9 letters. This is our second or bottom number.
Then they have defined a range of letters. Any time a problem defines a PART of the set, they are wanting you to create a FRACTION, which is the ratio of part to whole. So Figure out which cards are between H and U, including H and U. We leave out A, C, and E because they are before H and thus out. We leave out Y because it is after U. This leaves us with 5 letters. This is the first or top number.
So our ratio is 5 / 9.
Things to be careful about: In this set of problems, the word "or" usually means add the probabilities together. So if they wanted to know the probability of getting an "S" or getting a "U", you would add those probabilities together: Each is somewhat unlikely though, as getting an "S" has a 1 in 9 chance. The "or" increases that by 1 in 9. So 1/9 + 1/9 = 2/9.
Also, please note that this is just ONE event. If the problem asks for you to draw again, YOU'RE NOT DONE with the math.
The problem would have stated "If you pick a card at random, replace it, and then draw again..." You would multiply the probability of getting the first with the probability of getting the second. So with the "H" to "U", we would have 5/9 * 5/9. This gives us 25/81. Note this number is SMALLER, because the chances of it happening GO DOWN.
Other than that, you need to practice these. Here are some probability games and here are some practice problems.
This description of probability can be displayed in Spanish..
Sunday, February 9, 2014
Decimals Games
Scooter Quest
Identify the correct place value.
Bubble Burst
This game deals with adding decimals.
Multiply and Divide by 10s
Practice this one before doing decimal division.
Decimal Division
This is practice for dividing decimals.
Snake Math: Basic Advanced
This is a classic game with math about fractions and decimals added to it. Advanced is faster than basic.
City Defense
This game involves adding, subtracting and multiplying decimals.
Sunday, February 2, 2014
Making Mistakes
You’re afraid of making mistakes. Don’t be. Mistakes can be profited by. Man, when I was young I shoved my ignorance in people’s faces. They beat me with sticks. By the time I was forty my blunt instrument had been honed to a fine cutting point for me. If you hide your ignorance, no one will hit you and you’ll never learn.- Ray Bradbury
Keep It Cloud It Junk It (Math Version)
A few weeks ago, Mrs. Parker demonstrated a reading strategy for us. I've been thinking about a way to change it into a math strategy and I think I've come up with it.
Her strategy was a focus question, then ideas would be set into 3 categories, 1 lead to group discussion, 1 was certain, and the other was extraneous information. So Cloud It, Keep It, Junk It. I think this might be applied to word problems like so: Solve It, Use It, Junk It.
Word problems typically have details about the problem and extra information in them just like reading a passage for a purpose.
So for example, look at the following question:
6. You can win $10 if you can successfully do one of the following given one shot:
I Roll a 6 on a single number cube
II Roll a sum of seven on two number cubes
III Roll a number greater than 4 on a single number cube
Which of these three choices should you have the best chance of getting the $10?
(note, I am not making this offer)
F. I only
G. II and III
H. III only
J. I, II, and III
There's a lot of information here. Let's split up these things into Solve It, Use It, Junk It.
Solve It Use It Junk It
P(6) best $10
P(sum 7) number cube win
P(5 & 6) one shot
sum
greater than
Remember that P(6) is shorthand for the probability of getting a 6. As you can see 3 things are in the solve it category.
The $10 is extra information and doesn't help you solve the problem, so is junked.
Then in Use It, we see that we want to compare the probabilities from the word "best", that they all involve number cubes because no other probability device was used, and that they are not multiple events (one shot). We also see the word sum (which means add) and greater than. These are details that modify the probability needed.
After that we solve it by creating ratios. P(6) = 1/6. P(sum 7) = 6/36 and P(5 & 6) = 1/3.
Might need to think about this some more.
Her strategy was a focus question, then ideas would be set into 3 categories, 1 lead to group discussion, 1 was certain, and the other was extraneous information. So Cloud It, Keep It, Junk It. I think this might be applied to word problems like so: Solve It, Use It, Junk It.
Word problems typically have details about the problem and extra information in them just like reading a passage for a purpose.
So for example, look at the following question:
6. You can win $10 if you can successfully do one of the following given one shot:
I Roll a 6 on a single number cube
II Roll a sum of seven on two number cubes
III Roll a number greater than 4 on a single number cube
Which of these three choices should you have the best chance of getting the $10?
(note, I am not making this offer)
F. I only
G. II and III
H. III only
J. I, II, and III
There's a lot of information here. Let's split up these things into Solve It, Use It, Junk It.
Solve It Use It Junk It
P(6) best $10
P(sum 7) number cube win
P(5 & 6) one shot
sum
greater than
Remember that P(6) is shorthand for the probability of getting a 6. As you can see 3 things are in the solve it category.
The $10 is extra information and doesn't help you solve the problem, so is junked.
Then in Use It, we see that we want to compare the probabilities from the word "best", that they all involve number cubes because no other probability device was used, and that they are not multiple events (one shot). We also see the word sum (which means add) and greater than. These are details that modify the probability needed.
After that we solve it by creating ratios. P(6) = 1/6. P(sum 7) = 6/36 and P(5 & 6) = 1/3.
Might need to think about this some more.
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