Mind-reading and expected value.

I just finished looking at Dan Meyer's blog and saw that part of the most recent posting discussed uses for dice in class.   I have a trick I use with my students, let me tell you about it.

I give out 5-6 sets of three dice.  I have the students roll them and then add up all the numbers which cannot be seen (bottom, middles and middles).  Once they have the sum, they sit back with the dice still stacked and I "read their minds" to get the sum.  I have math on my side, and as long as they add correctly I can get the sum.

Last year I tied this activity into expected value in probability and it was a hit.   I don't want to give too much away, as my students have been following my blog as part of their summer enrichment.  Suffice it to say I can "read" the answer from their thoughts from across the classroom pretty well as there is only 1 piece of information I need.

It's a great mini lesson that is always great for engagement and I like that it's the kind of thing that the students take home and show their families.

ACT Readiness -pt 7- Graphical Representations

The next Standard relates to Graphical Representation.  These problems will either require a student to read information out of a graph, ie slope; or they will require a student to describe what happens to the graph, given a set of numbers or equation.

Upon first glance, I notice that many of the skills listed include an asterisk.  These standards are assessed on the ACT and Plan tests, but not the Explore test. Standards with a dagger are only assessed on the ACT.

The two examples here are higher leveled questions.  The first one requires that you understand how points change when a shape is translated in the coordinate plane.  The second one is interesting as the axes are not labeled with regard to scale, but the instructions tell you the scale is the same which is critically important to answer this question.  Do you understand how the answers were reached?

My students, ask yourself, how good do you understand the skills listed in the matrix?  Do you feel you could do each of these skills if asked?   Let's play taboo again:  Please list 5 more words to be restricted when trying to describe slope, ie rise/run.  Do the same with Parallel, Perpendicular,Vertex and Center (of a circle).  Email these to me, same email address as before.

ACT Readiness -pt 6- Expressions, Equations and Inequalities

If I ask my students, "What is Algebra all about?"  I can guarantee that at least 1/3rd will say solving equations.  I'm not sure this is necessarily bad, after all we do spend much of Algebra dealing with equations.  I hope that one day most of my students will answer that Algebra is all about the processes by which rationally problems are observed, analyzed and then solved.  (or something like that)

Here I present, Expressions, Equations and Inequalities.  Of the three, I would say that the last is most confusing and yet also the most "real-life", and yet the hardest to use in the classroom, without being trivial. Its also one of the hardest things for most students to use.

24-27 is the "meat and potatoes" or "curry and rice" of most Algebra classes.  I spend more time helping students hone these skills than just about anything else.  I know that most years my students have had to practice multiplying binomials (20-23), especially a binomial squared.  Factoring was also a big issue in recent students as well.

What steps do you need to use to solve the previous problem?  Do the decimals with different place values make the problem more difficult, or make it look more difficult?  Below are some more advanced examples:

The score range for each of these problems is the same.  The first problem requires greater literacy skills and the second requires greater computational skills.  We all struggle in different areas, which do you find more difficult?

The next range includes :"write expressions, equations and inequalities for common algebra settings".  We should be better at this.  We will be better at this.

If you are one of my students then the practice provided for this standard includes:  translating expressions and Equations Basketball

ACT Readiness- pt 5- Numbers and their Properties

The next set of standards will be Numbers and their Properties.  I hate to think that this is an area of weakness, but after years of seeing students counting on their fingers and the difficulty which my students have with factors (both prime factorization and factoring standing out as examples) I can't say that it isn't a possible source for student struggling.

Why does this first problem start with y not equal to 0?  Do you agree with the asterisk'ed answer?

How could you "work out" this second problem?  Would a list or table simplify calculating the answer?  How would you set up one of these to do this?

I look at the first column and seeing fractions, even equivalent ones leaves me wondering.  Also, I look at one of the higher columns and I see rules of exponents and complex numbers, and I know these are skills my students can accomplish.  Makes me feel like more and more that I need to know exactly where our students have struggled in the past.

I have a couple of ideas for my lovely students to do on this one.  First off, Beginner , That's COOL! and (if you use IoS, then FactorMan).

One more thing...on paper please list out the numbers 10 - 25.  For each number list out possible ways to multiply two numbers to get that number as an answer and then find the sum of those factors. (you need only do the positive factors and stick with whole numbers)

For example 24:
1*24: (sum) 25
2*12: (sum) 14
3*8: (sum)  11
4*6:  (sum) 10

Please keep the work from these "challenges" until after school starts.  Details will be given as to why before the end of the first week of school...

ACT Readiness- pt 4- Standards Functions

 The next standard is functions. All questions in this standard are applicable ONLY to the ACT, not the Plan or Explore tests.  There are generally not a lot of trigonometric questions on the ACT, but here is where most of them will be found.

There is only 1 example for this standard.  It is, predictably, a trigonometric example.




 I know the temptation is to get a numeric answer, but let me remind you that ACT questions are supposed to be written in a way that they can be solved WITHOUT a calculator (and I don't know the sin,cos or tan of 70 degrees off the top of my head).

For my students, let's first review the Unit Circle and a Real life Trigonometric Function.  Do a web-search for data relating to another real life trigonometric function and copy data which could be graphed to be trigonometric, please send it to me.

ACT Readiness - Pt 3 - Measurement and Plane Figures

This one will be a two-fer as these standards are generally covered in Geometry (rather than Algebra).

 Area and Perimeter of common shapes are usually pretty straightforward for students, unless they confuse the two.  Additionally, at times a formula may be given and being able to identify what each letter in the formula represents may be tricky.

Lots of triangle material here.  Pythagorean Theorem is listed in two of the score ranges, and after the session the Global Math Department had on it a few months ago, even I learned something. I've got to come up with a way to share some of those insights with my students.

For my students, tackle this Activity.  There are 5 parts, try each one and don't give up until you understand the theorem and can apply it to solve problems.