Tuesday, March 30, 2021

(x, why?) Mini: Talkin' Baseball

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

That's according to the public address. Honest.

A long way to go for a pun, you say? I don't think 360 feet is that long, but 11220 feet sounds longer when you write it in base four. And base four would be one trip around the bases, right?

And I didn't even mention the diamond!



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Friday, March 26, 2021

(x, why?) Mini: Excited

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Exited iron ion! Exited iron ion! Exited iron ion!

It's sort of a tongue twister, right?



I also write Fiction!


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Wednesday, March 24, 2021

Theory vs. Practice

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

My theory is that this is what'll happen every time I practice!

The mental calculations in the design phase still require the correct flick of the wrist in the application.



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Friday, March 19, 2021

Simplify the Radicals

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Is that because he's evtremely complex, or that he just defies simplification?

One of the problems I have this week every year is coming up with comics for Pi Day and St. Patrick's Day and maybe even recognizing the Ides of March. Another is that I put off ideas I had earlier until after this has all passed. And then I can't remember what that joke I thought of was. Yes, I write lots of stuff down, and sometimes I write it in places where I'll find it again.

Thankfully, I still have the classroom for inspiration! And, yes, this is one of those cases where students may stop working rather than dealing with it and finishing the problem.

There are a few reasons for simplifying radicals, the least of which is because they'll be simplified on state exams. You have to be able to recognize the correct choice when it's written in a different form. More importantly, it's easier to deal with them once they're in simplest form because then they can be combined just like any other like terms.

And happy St. Joseph's Day everyone! Enjoy your pastry!



I also write Fiction!


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Available in softcover or ebook at Amazon.

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Wednesday, March 17, 2021

Happy St. Patrick's Day 2021: Next Wave

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Those adders sure are stubborn, aren't they? Begorah!

The kind of wave is left as an exercise to the reader.

Happy St. Patrick's Day, everyone!



I also write Fiction!


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Monday, March 15, 2021

School Life #20: The Funny Ideas of March

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Funny ideas of March

The after text wasn't supposed to be the title, "tu", but I couldn't think of a better one

We haven't checked in with the students in a while because I haven't discarded the pandemic theme like I thought I would. But I probably will because pandemics are boring and people are looking to escape to something fun. And the masks and gaiters are annoying for facial responses.

For my new readers, Melissa and Vaughn have been together longer than Shawn and Isabel. Kyung, a friend of Isabel's, plays soccer with Shawn. Click on the "School Life" tag for more details.



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Thank you.





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Sunday, March 14, 2021

Pi Day 2021

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

A pithy comic for Pi Day

What else but the Sea could make Two pi arr? Not that they circumnavigate it any time soon.

Advertising note: Since I have ads turned on anyway, I figured I should advertise for myself. I have an ebook of flash fiction available for only $2.00 (not $3.14), and a paperback for $10.00 Check it out.



I also write Fiction!


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Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.





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Friday, March 12, 2021

Up and Down

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Based on a true story. Including the get lower comment.

It's a curiosity of the language that "duck" means to "get down" and that you "get down" from a duck. Or a goose, but let's not speak of that verb.

As for the math on the board, it looks like Mr. Keegan set them up with a problem and started the answer, allowing his students to fill in the missing parts. Keep of like those vague instructions that are given before quests.

Final note: Since I have ads turned on anyway, I figured I should advertise for myself. I have an ebook of flash fiction available for only Two Dollars, and a paperback for $10. Check it out.



I also write Fiction!


Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.





Come back often for more funny math and geeky comics.



Thursday, March 11, 2021

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.


The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.





51. Which expression is equivalent to (7x3)2(x8)1/2?

A 14x10
B 49x10
C 14x7
D 49x7

Answer: B 49x10

(7x3)2(x8)1/2
= (49x6)(x4)
= (49x10)

For powers of powers, multiply. So 3*2 = 6 and 8*1/2 = 4
For the same base multiplied, add the powers. So 6+4 = 10.
The 7 was squared, so it becomes 49.



52. The function y = 3.75 + 1.5(x - 1) can be used to determine the cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

F $1.50 per mile
G $3.75 per mile
H $4.25 per mile
J $5.25 per mile

Answer: F $1.50 per mile
The rate of change is the coefficient of x, which is 1.5, or $1.50.





53. Which graph best represents a function with a range of all real numbers greater than or equal to -6?



Answer: C
The range is the y-values. You want a graph where the minimum value for y is -6. Nothing can go below that.
Graphs B and D go down to negative infinity, below -6.
Graph A does not include values for -6 < y < 0



54. What is the value of x in the solution to this system of equations?

y + 2x = -1
y = 1/2 x + 4


F 6/5
G -2
H -10/3
J 3

Answer: G -2

y + 2x = -1
y = 1/2 x + 4
so 1/2x + 4 + 2x = -1
2 1/2 x + 4 = -1
2 1/2 x = -5
x = -2

Checking the answer:
y = 1/2 (-2) + 4 = -1 + 4 = 3

(3) + 2(-2) = -1
3 - 4 = -1
-1 = -1 (check)



END OF EXAM.





More problems to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction!


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Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.



Tuesday, March 09, 2021

(x, why?) Mini: Solutions

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Some days we'll all be trivia answers. Hear that, Jeopardy? I could be a trivial answer!

I guess there isn't anything preventing me from using these guys more. I haven't done an episode of "The 0'Factor" in quite a while.



I also write Fiction!


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Thank you.





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Monday, March 08, 2021

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.


The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.





46. The graph of a quadratic function is shown on the grid

Which equation best represents the axis of symmetry

F y = 6
G x = 2
H y = 4
J x = 0

Answer: G x = 2
The Axis of Symmetry is the vertical line that would run down the middle of the parabola through the vertex, the turning point. That occurs when x = 2.



47. If p(x) = 5(x2 + 1) + 16, what is the values of p(11)

A 690
B 736
C 622
D 626

Answer: D 626


p(11) = 5(112 + 1) + 16
= 5(121 + 1) + 16
= 5(122) + 16
= 610 + 16
= 626





58. The graphs of lines k1 and k2 are shown on the grid.


Which system of equations is best represented by this graph?

F 3x - y = 2 ; 4x + 9y = 36
G 3x - y = 6 ; 4x + 9y = 4
H x - 3y = -18 ; 9x + 4y = 9
J x y + = 10 ; 9x + 4y = 13

Answer: F 3x - y = 2 ; 4x + 9y = 36
Line k1 has a positive slope. It has y-intercept of -2 and x-intercept of less than 1. There is another point at (1,1). It's slope is +3 (three units rise, 1 unit run).
Line k2 has a negative slope. It has y-intercept of 4 and x-intercept of 9. It's slope is -4/9.

In Choices H and J, the slope of the second line is -9/4, not -4/9. Eliminate these.

In Choice F, 3(0) - (-2) = 2 and 3(1) - 1 = 2.
Additionally, 4(0) + 9(4) = 36 and 4(9) + 9(0) = 36.
Choice F is the correct answer.

Choice G has the same left hand sides as F, but the right hand sides are too small. This can be eliminated.



49. Which statement about the graph of y = (1/3)(2/3)x is true?
Which inequality best represents the domain of the part shown?

A The graph has a vertical asymptote.
B The graph crosses the y-axis at (0, 2/9 ).
C The graph has an asymptote at y = 1/3.
D The graph decreases from left to right.

Answer: D The graph decreases from left to right.
Exponential functions do not have vertical asymptotes. Eliminate Choice A.

When x = 0, y = 1/3, not 2/9. When x = 1, y = 2/9. Eliminate Choice B.

When x = 0, y = 1/3, so y = 1/3 is NOT an asymptote.

The rate is less than one, so the graph will decrease from left to right: 1/3, 2/9, 4/27, etc.



50. The table represents some points on the graph of a linear function.


Which equation represents the same relationship?

F y + 268 = 1/12(x + 20)
G y + 20 = 1/12(x + 268)
H y + 268 = 12(x + 20)
J y + 20 = 12(x + 268)

Answer: H y + 268 = 12(x + 20)
(-20, -268) is a point on the line, with 20 being the x coordinate. So eliminate Choices G and J.

It comes down to whether the slope is 12 or 1/12.

m = (-40 - -124) / (-8 - -1)
= 84 / 7
= 12
Which is Choice H.





More to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction!


Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.



Saturday, March 06, 2021

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.


I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.





41. Which expression is a factor of 18x2 - 15x + 2?

A 3x - 2
B 9x - 1
C x - 2
D 2x - 1

Answer: A 3x - 2
We can factor the trinomial, using "borrow & payback". Multiply (18)(2) = 36. What are two factors of +36 that add up to -15? They both have to be negative numbers.
Check them all: -1 and -36, no; -2 and -18, no; -3 and -12, bingo! (You can stop now)

18x2 - 15x + 2
18x2 - 12x - 3x + 2
Group the terms
(18x2 - 12x) - (3x - 2)
Now find the GCF of each pair
6x(3x - 2) - 1(3x - 2)
(6x - 1)(3x - 2) are the factors

The answer is A.



42 The graph of linear function g is shown on the grid.

What is the zero of g?
Record your answer and fill in the bubbles on your answer document.

Answer: -6
The zero is where the line crosses the x-axis, which is -6.





43. Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?

A y = 3/4 (x + 3)2 + 7
B y = -3/4 (x + 3)2 - 7
C y = 3/4 (x - 3)2 + 7
D y = -3/4 (x - 3)2 - 7

Answer: D y = -3/4 (x - 3)2 - 7
The point (1, -10) is unnecessary information and no calculation is needed.
You are given the vertex and the four choices are in vertex form.
Choice D is the only possible answer as A, B, and C do not have vertices at (3, -7).

The one thing that (1, -10) tells you is that the parabola must open downward because -10 is below -7, so the number in the front must be negative.



44. The graph of part of linear function g is shown on the grid.


Which inequality best represents the domain of the part shown?

F -9 < x ≤ 2
G -9 ≤ x < 2
H -6 < g(x) ≤ 3
J -6 ≤ g(x) < 3

Answer: F -9 < x ≤ 2
The domain is the possible x values, and the range is the possible g(x) values. Eliminate Choices H and J.
There is an open circle at x = -9 that indicates it is not part of the solution, and a closed circle at x = 2 that indicates it is part of the solution. This means Choice F.



45. A student graphed f(x) = x and g(x) = f(x) + 3 on the same coordinate grid. Which statement describes how the graphs of f and g are related?

A The graph of f is shifted 3 units up to create the graph of g.
B The graph of f is steeper than the graph of g.
C The graph of f is shifted 3 units down to create the graph of g.
D The graph of f is less steep than the graph of g.

Answer: A The graph of f is shifted 3 units up to create the graph of g.
Whatever answer you would get for f(x), g(x) will always be 3 more than that. Since f(x) and g9x) are measured on the y-axis, adding through will move the points upward.
Adding or subtracting to a function will not affect its steepness. You would need to multiply.





More to come. Comments and questions welcome.

More STAAR problems.

I also write Fiction!


Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.



Friday, March 05, 2021

Tuna

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Coming to D&DTV!

I heard the pun. I figured as long as I could illustrate it, it was a fair catch.

Be glad they didn't come out at night -- it could've been a Tuna Luna Luna.

The fact that today is a Friday during Lent is totally co-incidental. Mostly.

This reminds me that I haven't called the guy to tune my piano since before the pandemic.



I also write Fiction!


Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Thank you.





Come back often for more funny math and geeky comics.



Wednesday, March 03, 2021

Apparent Magnitude

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

You know that there are people for whom that was obvious.

I did want to show students in this one, but I realized that I wanted the whiteboard head on for perspective.



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STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.


I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.





36. What is the equation of the line that passes through the point (-2, 7) and has a slope of zero?

F x = 7
G y = -2
H x = -2
J y = 7

Answer: J y = 7
A line with a slope of 0 is a horizontal line in the form y = b. Since the point (-2, 7) is on the line, b must be 7.



37 Which ordered pair is in the solution set of y ≥ 1/3 x + 4?

A (-6, 1)
B (-1, 6)
C (6, -1)
D (1, -6)

Answer: B (-1, 6)
You don't need the provided graph, so I didn't include it in the answer. You could graph the inequality and check to see which point lies in the shaded region.
It would be quicker to just check the choices.
Is 1 ≥ 1/3 (-6) + 4?
1 ≥ -2 + 4
1 ≥ 2, X, not true, eliminate Choice A

Is 6 ≥ 1/3 (-1) + 4?
6 ≥ -1/3 + 4
6 ≥ 3 + 2/3, true. Choice B is the answer.





38. Which table does NOT show y as a function of x?


Answer: H
The only restriction on a function is that every imput has only one output.
In choice H, the value -0.2 repeats for the x value (input) but has two different y values (outputs) associated with it. This is not allowed in a function.
Consider a function to be like a function key on a calculator. You input a number and press the function key, you expect the same output every time you enter the same input. It can't be 5 sometimes and 8 other times.



39. A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t), at different times.


Based on the table, which function can best be used to model this situation?

A h(t) = 99t2 + 858
B h(t) = -4.9t2 + 295t + 0.6
C h(t) = -4.9t2 + 295t + 2
D h(t) = 99t2 + 1,470.3

Answer: B h(t) = -4.9t2 + 295t + 0.6
It's a projectile, so it is going to have negative acceleration. That is to say, it will be an upside-down parabola. You should also be aware that the leading coefficient is problems of these types is likely to be -16, -5, or -4.9, depending on if the question uses imperial units, and if they decide to round the numbers.
You can see that the height peaks at 30 and declines again. This means that the leading coefficient is negative. Choices A and D can be eliminated.
You can graph the other two in a graphing calculator and check the table of values, or you can do a quadratic regression in your calculator.
My graphing calculator lines out with 0.6 as the y-intercept, so +2 would be farther away.

Honestly, this is an odd problem in that B and C are so close together given the size of the values. The margin of error between them is miniscule.



40. Which value of x makes the equation 0.75(x + 20) = 2 + 0.5(x - 2) true?

F 64
G -64
H 56
J -56

Answer: J -56

0.75(x + 20) = 2 + 0.5(x - 2)
0.75x + 15 = 2 + 0.5x - 1
0.25x = -14
x = -56

I assume the "64" answers come from mathematical errors giving you either 16 or -16.





More to come. Comments and questions welcome.

More STAAR problems.

Tuesday, March 02, 2021

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2017, cont.


I had to put these on hold for a while. They're back now.

The State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2018.

More STAAR problems.

Administered May 2017

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.





31. A student used f(x) = 5.00(1.012)x to show how the balance in a savings account will increase over time. What does the 5.00 represent?

A The interest the savings account earned for the first year
B The annual interest rate of the savings account
C The number of years the savings account has earned interest
D The starting balance of the savings account

Answer: D The starting balance of the savings account
I hope the student was using a spreadsheet and showing what happens over many, many years, because $5.00 at 1.2% interest won't accrue to much of anything. And in the real world, banking fees would eat up that money, leaving the student owing money.
But as far as the test is concerned, 5.00 is the Principal, the starting money.



32. The graph of a function is shown on the grid.


Which ordered pair best represents the location of the y-intercept?

F (1/3, 0)
G (0, -2)
H (0, 1/3)
J (-2, 0)

Answer: G (0, -2)
At the y-intercept, the value of x is 0, so Choice F and Choice J are eliminated.
It's also below the x-axis, so the value of y is negative, making G the only Choice.
(1/3, 0) is a good approximation for the x-intercept.





33. Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day.

Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?

A t(x) = 450 - 0.06x
B t(x) = -0.06(x + 450)
C t(x) = 450 + 0.06x
D t(x) = 0.06(x + 450)

Answer: A t(x) = 450 - 0.06x
The thickness of 450 is the initial value (the y-intercept) and doesn't take a variable. The 0.06 is a daily decrease, so it gets subtracted every day for x days.
Choice C is no good because that shows the ice increasing in size, not decreasing.



34. What is the positive solution to the equation 0 = (1/3)x2 - 3?

Record your answer and fill in the bubbles on your answer document.

Answer: 3

0 = (1/3)x2 - 3
0 = x2 - 9
9 = x2
x = 3 (positive solution)

You could also have factored the Difference of Squares and continued from there, getting the same result.



35. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards.

Which function models the amount of fertilizer in cubic yards left after w weeks?

A f(w) = 0.97(78,000)w
B f(w) = 1.03(78,000)w
C f(w) = 78,000(0.97)w
D f(w) = 78,000(1.03)w

Answer: C f(w) = 78,000(0.97)w
Eliminate the first two immediately. The number 78,000 represents the original amount that the decay rate will be applied to. Since it is decreasing (decaying) the rate has to be less than 1.00, so Choice D is eliminated.
A 3% decrease means subtract 1.00 - 0.03 = 0.97, which is the rate in Choice C.





More to come. Comments and questions welcome.

More STAAR problems.

Plan Delta

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

There's a good chance that Ken is pulling Michele's leg here. They are married after all.

Delta can become a buzzword (or part of one) in education, which is probably what inspired this.

That, and trying to get any kid to unmute or turn their camera on, for even a few seconds.



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