This is the second posting in a series primarily aimed at my students regarding the ACT College and Career Readiness Standards. My goal is encouraging self-assessment so that my students know where their weaknesses might lie, and hopefully getting them thinking about strengthening their skills before the start of school, or the official ACT assessment this upcoming school year.

The second list of topics in this series is Probability, Statistics and Data Analysis.

In our school, students first see probability and statistics in Algebra 2 (though there are many related topics which should be addressed in middle school mathematics). A review of probability comes up in Algebra 2; for students wishing to learn more about these topics Statistics is available as an elective in their Senior year.

For the first example, students need to know which one word in the question? Without knowing this math term, this is an impossible task, with this knowledge the question should be straightforward.

While this is a "higher leveled" question, I believe that it is also one which we should be able to figure out quickly. Notice for a moment the wrong answers. A. We're looking at one of the 12 jelly beans, B. We're looking at 1 of 5 green jelly beans. Can you guess how they arrived at the other two choices?

As mentioned in the first post in this series, our school's average Math ACT score is in the second range. With regard to these topics, this means that our students (on average) cannot find a missing data value or compute simple probabilities (20-23), manipulate data from tables or graphs (24-27) or compute weighted averages.

As I will be teaching both Algebra 2 and Precalculus, I will be working more spiraling of probability & statistics topics into both classes.

If you are one of my students, then I challenge you to review basic probability. I've got a special challenge for you this time. Read through Bear in the Moonlight and then follow it up with James Tanton is the man! Once you've done that, email me to let me know you did it. (mr**&%hills@pre##$%#calc@gmail.com) remove spaces and special characters)

## Thursday, July 31, 2014

## Saturday, July 26, 2014

### ACT college and career readiness standards Mathematics Part 1

I have found that I am rarely surprised by the ACT scores, in mathematics, that my students achieve. "A" students generally score better than most other students, but even these students do not score to their potential on the ACT. I'm sure that nerves and distractions play a part, but I also believe that many students over-estimate their comprehension and ability with using some of the mathematical skills which they've "learned". I'm hoping through a series of blog postings that I can encourage some self-assessment among my students

ACT has prepared a document in which they give score ranges and the skills which they associate with students who can accomplish those skills. I plan on making a series of blog postings to share with my students, especially the Juniors, to help them better understand what they need to get the scores they believe they deserve.

If you look at the matrix, you will find that the skills required for higher scores are far more involved.

The average math ACT score in our school is in the second range. This implies that many of our students, including some of the honors students, can solve "routine" one and two step problems, but once rate, taxes or averages are required the problems become too difficult. (20-23) Solving problems which require planning or converting measurements (24-27) should be well within the skill set of a high school math student. (especially given that ACT problems are written so that one does not require a calculator to solve them).

The answer with the asterisk is the correct answer. Take a moment and work out each one and be sure you understand why the asterisk'ed answer is correct.

If you are one of my students, reading this blog posting as part of our Summer Review Challenge, then I would like you to take a piece of notebook paper and write (or find) 2 examples which would fit into each of the lowest 3 ranges of scores. (so that is how many problems altogether?) Take a picture of them, or scan them and please email them to the email address I send in the previous remind101 messages.

ACT has prepared a document in which they give score ranges and the skills which they associate with students who can accomplish those skills. I plan on making a series of blog postings to share with my students, especially the Juniors, to help them better understand what they need to get the scores they believe they deserve.

If you look at the matrix, you will find that the skills required for higher scores are far more involved.

The average math ACT score in our school is in the second range. This implies that many of our students, including some of the honors students, can solve "routine" one and two step problems, but once rate, taxes or averages are required the problems become too difficult. (20-23) Solving problems which require planning or converting measurements (24-27) should be well within the skill set of a high school math student. (especially given that ACT problems are written so that one does not require a calculator to solve them).

The answer with the asterisk is the correct answer. Take a moment and work out each one and be sure you understand why the asterisk'ed answer is correct.

If you are one of my students, reading this blog posting as part of our Summer Review Challenge, then I would like you to take a piece of notebook paper and write (or find) 2 examples which would fit into each of the lowest 3 ranges of scores. (so that is how many problems altogether?) Take a picture of them, or scan them and please email them to the email address I send in the previous remind101 messages.

## Saturday, July 5, 2014

### Productive Struggle

For my few followers, please excuse my absence. My dad passed within the last 2 weeks of school letting out; and I had to travel across the country and have been dealing with a 'caregiver' committing mass fraud, so much so that my mom nearly was kicked from her nursing facility.

Not what I wanted to post about.....

Letter to my students next year....

Hello....

We are here, together, for the purpose of learning math. But there is a problem with that statement. Anyone care to point out what it is? (all options should be discussed)

I don't seem to be doing any of the learning, at least not observably so. To me this is a problem. How can I expect you to be learners, when it doesn't appear that I am one myself? I promise to put myself in the same position, that of learner, right beside you. I will ask questions I find interesting, and would love suggestions from the class, without knowing the answers. Please do not expect that I will always just explain things, for I don't know everything. My goal is for us to collectively struggle at times.

Learning about math is a struggle. No one ALWAYS finds it easy, not really understanding 100% of it. I learn something new about the content which I teach, every single year. There are things which I will show you, primarily because they important or in a couple cases just cool, but I want more class discussion. To this end I will eventually restrict how much speaking I will do in a class. Students should at times struggle as well as be led.

The skills of mathematics, especially Algebra are important. List them: (I'm thinking properties of equality, distribution and composition) Anyone, play soccer or baseball or football? Make me a list of the rules of each of these games - who knows I might need one in time. Do you like the game? --if you're going to do this, don't read ahead yet -- (************************************************************************************************************************************************************************************************************************************************** Are the rules the game? What purpose do the rules have? What SHOULD happen when someone breaks the rules?

A mistake that many smart people make is not looking for the creativity in math. It is undefinable that there is math in art Donald in Math Magic Land . Soon enough I will show you that there is wonderful art in math. (I've got 2-3 art projects in functions)

Lastly, I have a challenge to you. (Commence with Bionic Bee.)

((I have a great problem which I know 5th graders can solve in about 5-10 minutes, high school students, alg2 and above, usually take at least the class period and benefit from completing it as homework, and the one time I gave it to college calculus students I had phone calls begging for help....it might make a good task here))

The Bionic Bee (I play a clip from Wild,Wild West with Will Smith)

(my apologies, I can't really draw it out here and honestly drawing it out is important)

Two trains have managed to find themselves, though unaware, on the same track-heading towards each other. You're a spy, and while you cannot stop the trains, you do have one trick up your sleeve. The Bionic Bee! You launch it down the track, speeding toward the other train.

It is capable of travelling 560 miles per hour, in a straight line, and also capable of instantaneously changing its direction 180 degrees (I do give the high school-ers and college students the angle as pi if I'm feeling mischievous). It has a full array of sensors, but it also has a programming flaw - once it does a 180 it will continue making that same degree change.

The two trains are 980 miles apart (I've thrown Km in from time to time, but only on the 5th graders and guess what? It doesn't hurt their time....) One train is a new, green-energy steam train. It cruises along at 170 mph. The older diesel train barely manages 110 mph. Neither train knows the destiny that fate has in store for them.

It is now 2:15 pm. What questions do you have at this point? (I normally just ask at what time do the trains collide and how far will each have traveled to get there?).

--------------------------------------------------------------------------------------------------------

Sadly, though this isn't a lesson which I don't already know. I'm thinking for the 1st week of precalc it might make a good challenge. I just need to be on the lookout for content and level (to borrow from mostly every video game) appropriate, and definitely nontrivial.

Not what I wanted to post about.....

Letter to my students next year....

Hello....

We are here, together, for the purpose of learning math. But there is a problem with that statement. Anyone care to point out what it is? (all options should be discussed)

I don't seem to be doing any of the learning, at least not observably so. To me this is a problem. How can I expect you to be learners, when it doesn't appear that I am one myself? I promise to put myself in the same position, that of learner, right beside you. I will ask questions I find interesting, and would love suggestions from the class, without knowing the answers. Please do not expect that I will always just explain things, for I don't know everything. My goal is for us to collectively struggle at times.

Learning about math is a struggle. No one ALWAYS finds it easy, not really understanding 100% of it. I learn something new about the content which I teach, every single year. There are things which I will show you, primarily because they important or in a couple cases just cool, but I want more class discussion. To this end I will eventually restrict how much speaking I will do in a class. Students should at times struggle as well as be led.

The skills of mathematics, especially Algebra are important. List them: (I'm thinking properties of equality, distribution and composition) Anyone, play soccer or baseball or football? Make me a list of the rules of each of these games - who knows I might need one in time. Do you like the game? --if you're going to do this, don't read ahead yet -- (************************************************************************************************************************************************************************************************************************************************** Are the rules the game? What purpose do the rules have? What SHOULD happen when someone breaks the rules?

A mistake that many smart people make is not looking for the creativity in math. It is undefinable that there is math in art Donald in Math Magic Land . Soon enough I will show you that there is wonderful art in math. (I've got 2-3 art projects in functions)

Lastly, I have a challenge to you. (Commence with Bionic Bee.)

((I have a great problem which I know 5th graders can solve in about 5-10 minutes, high school students, alg2 and above, usually take at least the class period and benefit from completing it as homework, and the one time I gave it to college calculus students I had phone calls begging for help....it might make a good task here))

The Bionic Bee (I play a clip from Wild,Wild West with Will Smith)

(my apologies, I can't really draw it out here and honestly drawing it out is important)

Two trains have managed to find themselves, though unaware, on the same track-heading towards each other. You're a spy, and while you cannot stop the trains, you do have one trick up your sleeve. The Bionic Bee! You launch it down the track, speeding toward the other train.

It is capable of travelling 560 miles per hour, in a straight line, and also capable of instantaneously changing its direction 180 degrees (I do give the high school-ers and college students the angle as pi if I'm feeling mischievous). It has a full array of sensors, but it also has a programming flaw - once it does a 180 it will continue making that same degree change.

The two trains are 980 miles apart (I've thrown Km in from time to time, but only on the 5th graders and guess what? It doesn't hurt their time....) One train is a new, green-energy steam train. It cruises along at 170 mph. The older diesel train barely manages 110 mph. Neither train knows the destiny that fate has in store for them.

It is now 2:15 pm. What questions do you have at this point? (I normally just ask at what time do the trains collide and how far will each have traveled to get there?).

--------------------------------------------------------------------------------------------------------

Sadly, though this isn't a lesson which I don't already know. I'm thinking for the 1st week of precalc it might make a good challenge. I just need to be on the lookout for content and level (to borrow from mostly every video game) appropriate, and definitely nontrivial.

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