327: Sensible or Not? Sampling

Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position.

1. For a high school project, I conducted a census to determine the average rate that teenagers charge for babysitting. 
2. Even though the study used a convenience sample, the results may be meaningful. 
3. The study must have been biased, because it concluded that the 75% of Americans are more than 6 feet tall. 
4. We obtained a simple random sample of milk-producing cows in Jefferson County by drawing the names of 50 dairy farms from a hat and asking the owners of those farms to select three cows for us to study. 
5. A good strategy for stratified sampling involves first using simple random sampling to choose 500 people, then randomly dividing them into ten groups of 50 to represent the 10 strata. 
6. Although the study was conducted with a representative sample and careful analysis, the conclusions still reflect the researcher's anti-death penalty bias. 

ch1.2

326: ASN - Quadrilaterals

source

an image from there:

325: ASN - Another Algebra Set

Always True, Sometimes True, Never True?

Once again ... The why is the important part.

source, with lesson plans and materials.

324: ASN - Algebra

Always True, Sometimes True, or Never True?

Cut out the cards and have students sort them into one of the three categories.
In each case, students need to say WHY its always true or NEVER true, or give an example and a counterexample for when it is SOMETIMES true.

source: lesson plan and handouts.

323: Sensible or Not? Study structure.

Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position.

1. When the IRS decided to determine how many people were cheating on their taxes, they did a study in which the sample consisted of every adult in the United States.
2. My professor conducted a study in which he was unable to measure any sample statistics, but he succeeded in determining the population parameters with a very small margin of error.
3. A poll conducted two weeks before the election found that Smith would get 70% of the vote, with a margin of error of 3%, but he ended up losing anyway.
4. The goal of a new startup company is to compete with Nielsen Media Research in compiling television ratings. They intend to succeed by providing data with a larger margin of error than Nielsen's while charging television stations the same price for their service.
5. The goal of the research is to learn about depression among people who have suffered through a family tragedy, so the population of interest is everyone who has been sick in the past month.
6. We know for certain that a majority of Americans support the President's position on this issue because an opinion poll found support from 65% of Americans, with a margin of error of 5%.

ch1.1

322: Sensible or Not? distribution

Distribution Statements: Sensible or Not?
Defend your answer! Here's your claim ... what's your warrant?

1. Because this data has two modes, it cannot be symmetrical. 
2. This distribution is left-skewed because it has outliers to the left. 
3. Josh works at a veterinary clinic and weighs the dogs. He claims there is less variation in the weights of 10 Rottweilers than in the weights of 10 dogs of different breeds. 
4. Josh combines the weights of 10 toy poodles, 10 Rottweilers and 10 St. Bernards into one big group. He says the distribution has one mode. 
5. Jean concludes that the mean of her symmetric distribution is greater than the median. 

ch4.2

321: Sensible or Not? central measures

Measures of Central Tendency Statements: Sensible or Not?
Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position 

1. A data set should be discarded if the mean exceeds the mode. 
2. A student with an average of 65 computes her new average after earning a 70 on the last exam. Her new average is 72. 
3. Observing that the mean weight of a group of patients is 154 pounds and the median weight is 145 pounds, the doctor concludes that there must be an outlier on the heavy side. 
4. Noting that there are three modes in his data set, Rob assumes there was an error in his data gathering. 
5. The two means in the data lie at 102 and 201
6. The two medians in the data set lie at 23 and 28. 
7. The two modes in the data set lie at 45 and 100. 

ch4.1

320: Sensible or Not? percent

Percent Statements: Sensible or Not?
Defend your answer! Here's your claim ... what's your warrant?

1. The percentage of households with more than four children decreased by 100,000 households
2. Brent makes 120% less than Bill each month 
3. Ann is 10% taller than Brenda, so Brenda is 10% shorter than Ann
4. Fifty percent of the people in the room are men and 50% of the people in the room are single. Therefore, 25% of the people in the room are single men.
5. Pete’s prices are 10% more than Paul’s prices, so Pete’s prices are 110% of Paul’s prices.
6. The interest rate at the bank increased by 100% 

ch2.3

319: Sensible or Not? error

Error Statements: Sensible or Not?
Defend your answer! Here's your claim ... what's your warrant?

1. There are 138,232 species of butterflies and moths on the Earth. 
2. The measurement taken by an electronic timer must be more accurate than that taken by stopwatch. 
3. The relative error that a microbiologist makes in measuring a cell must be less than the relative error that an astronomer makes in measuring the width of a galaxy, because cells are smaller than galaxies. 
4. The bank teller claims that his errors are random even though they are always to his advantage. 
5. The 6 billionth person on Earth was born on October 12th 1999, in Bosnia 
6. I would rather be shortchanged by $1 than by 1% 

ch2.2

318: Exponential Function

Is this enough information to find the equation?

317: Church

How many different math concepts can you use this church as an example for?

316: Intersections

Which one is better?
Which one is easier to solve?

315: Pizza Maker

 

Talk about the rate at which pizza sauce is being pumped out through the tube ...

314: Stats Starter 2

Following on from yesterday's question, we have a puzzle from the same source.

Which of those central tendency statistics are necessary in order to find the missing numbers? (Necessary meaning that you can't find a particular number without it.) In order words, do we really need all five statistics?

Source.

313: Stats Starter 1c

Here is that same list of numbers.

You create a new problem this time ...
Can you create a solvable problem with just two hints?
Or do we need three?


Original source.

312: Stats Starter 1b

Here is a list of numbers.

You create the problem ...
What are some different statistics that you could give to a classmate (other than the ones below) yet still keep this a solvable problem, with the same answers as the original problem?


Original source.

Original problem:
mean = 76; range = 32; IQR = 21

311: Stats Starter 1a

Here is a list of numbers.

What information would you NEED in order to determine the missing numbers?



Source.

If you want to solve the original problem yourself, you can go there and look for the rest of the problem and a discussion on finding the answers, but here is the set of numbers provided:
mean = 76; range = 32; IQR = 21

310: Missing Area

What things do we know?
What lines do we need to construct?
What unknowns do we need to plop a variable on?

Is this a problem best given to a Geometry class, an Algebra class, or Pre-Calculus class?

Source, For the Nguyen!

309: Rational Cube Routes

Imagine a cube, 2 inches on a side ...

Actually, don't bother, I'll put one over there on the right side. ==>>

Now imagine if you were sitting on a vertex. How far is it (straight line distance) to the other vertices?

How many of those paths would be rational number distances?

What if you were on the midpoint of an edge and considering the paths to the vertices again. How many of those paths would have rational lengths distances?

And, no, I won't apologize for the pun. Pfft!

source:

Edge of a cube has length 2, P is the midpoint of an edge. Show that the greatest distance from P to a vertex is 3.
- David Marain (@dmarain) October 28, 2014

308: Congruent Lines?

Can two lines of infinite length be considered congruent?

Student question that sparked a good debate: are all lines congruent? Not segments, but whole lines. Thoughts?
— Justin (@JustinAion) October 20, 2014

307: Expected Value vs Psychology

Which would you press ... and why?

306: Factorials and Perfect Squares

Let's examine the function g(n):

g(n) = smallest integer such that g(n)*n! is a perfect square.

How should we go about finding if there's a pattern in that?

Plot of log(g(n)) versus n @jamestanton g(n) = smallest integer such that g(n)*n! is a perfect square. pic.twitter.com/tUvhiR0LjI
— Republic of Math (@republicofmath) October 18, 2014

305: Space and the Atmosphere

What kind of approach might give us the thickness of the atmosphere in the video?

304: Speed Reading

What's a good problem you can make based on this video?

Reading at 500 words a minute? Maybe it's all in the delivery. — Ed Southall (@solvemymaths) October 18, 2014

303: Reworking Pythagoras

Pythagorean theorem:  a² + b² = c².

“In a right triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two legs.”

Here is the problem: does the figure whose areas we compare, drawn on the triangle's legs, have to be square?

Can there be other shapes – triangles, rhombuses, regular pentagons, etc. – that make the Pythagorean Theorem more generally true?


Source: Grant Wiggins, "The Problem of So-Called Problems - unpublished paper 2013"

332: Which values of x do we choose? Polynomials

For the following functions, think about "How to graph like a math teacher." Math teachers want to sketch graphs quickly and efficiently and choose values of x that work "nicely" in the equation and  generate integer values of y, thus making it easier to graph.

• Which points are best found by inspection?
• Which points are best found by substitution?
• Which points are best found by symmetry?

$y = (x-2)^2(x+2)$

$y = (x-1)^3$

$y = x^3-8$

$y=x^3+3x^2$

$y=(x-3)^2(x+3)^2$

What are your favorite examples of this?

302: Systems of a Sort 8

Where should we start this shape substitution puzzle?

Where should we start this shape substitution puzzle?

Source: Mimi! (I Hope This Old Train Breaks Down...)

301: Systems of a Sort 7

What's the best way to proceed here?

300: Systems of a Sort 6

Your teacher (me) is thinking about buying a new car. Presently, the cost of gas is $3.60 per gallon and he knows that he is going to commute to work each day and drive errands on the weekend ... about 300 miles per week.

He wonders whether or not to buy a Corolla or a Prius. Currently, he drives a Ford Ranger pickup truck, which is paid off but is starting to have some expensive repair bills. If he averages those costs, it's about $200 per month.

Option 1: The Corolla costs $16,800 (about $400/month) and gets roughly 36 mpg.
Option 2: The Prius costs $24,200 (about $570/month) and gets roughly 49 mpg.
Option 3: The Ranger is paid off but has repairs (about $200/month) and gets 21 mpg.
What should he do?

Prius:

Corolla:

299: Systems of a Sort 5

Is there an easy way to tell if those lines will have one solution, no solution, or an infinite number of solutions?

298: Systems of a Sort 4

This system of equations has a peculiar characteristic ... I think it is easier to solve it by analytical means than by using Desmos or a TI-84. 

Do you agree?

What about it makes a graphical solution difficult?