Reader Input on Slope Post

A longtime reader of Turtle Talk, Jeff LeMieux, of Oak Harbor, WA, sent in a suggestion based on today’s post on positive and negative slope. Jeff found a way to help students remember not only positive and negative slope, but also the infinite slope of vertical lines, and the 0 slope of horizontal lines … all using the letter “N.”

This is clearly a situation where the picture speaks more loudly than words, so I’ll just let Jeff’s submitted picture do the talking. By the way, to see this image even better, just double click it!

Slope Memory Trick

Thanks for putting this together and sharing it, Jeff!

Remember the Difference in LOOK between Positive and Negative Slope

Some ideas just slap you in the face.

I got slapped this morning as I was flying home from LA to Albuquerque. Those little cocktail napkins they hand out with “beverage service” often give me the urge to write. So this morning, nerdily enough, as I sipped my orange juice at 30,000 feet above the Salton Sea, I worked on figuring out a better way to help students grasp the difference in look between positive and negative slope.

That’s when I got “slapped.”

First, you must realize that I use the three-letter abbreviations of POS and NEG for positive and negative. Do some of you use these as well? I mention this because those abbreviations hold the key. You have to use the first letter of the NEG abbreviation and the last letter of the POS abbreviation.

Let’s start with NEG.

The first letter of NEG is, of course, “N.” But look what I noticed …

Visual Clue for Negative Slope

The trick for POS is a tad more complicated. But I’m hopeful it will work.

Visual Clue for Positive Slope

So what do you think? Will this work for your students?

If you test it out, please let me know what you find. I’m interested to know. Thanks!

SAT and ACT Preparation

Every once in a while I get a call like this:

“Hi, this is ____. My son is taking the SAT on Saturday. Can you, like, help him get ready for the test so he can score real high?”

“Real high.” That’s what I wonder if the parent is.

I’ve been tutoring students to prepare them for the SAT and the ACT for many years now, and there’s one thing I’ve found to be true:  there is no shortcut to doing well.

While there are steps students can take to do better on these tests — including a few time-tested test-taking strategies — there is nothing I can do as a tutor (or a test-prep coach) that substitutes for solid academics over a student’s entire school career, and a longterm approach to the high-stakes tests.

What I’d like to do in this post, then, is to sketch out a road map that will help parents take a longterm approach to the SAT or the ACT.

1st)  Simply ensure that your child has solid academics from 1st grade through 12th grade.

2nd)  Encourage your children to read a great deal. Read yourself to model the importance of reading.

3rd)  Have a lot of discussions with your children. Talk about intellectual issues, politics, science, math, literature, the news, etc.

4th)  Starting in 8th grade or around that time, find a list of 1,000 or so words that are on the SAT and the ACT and help your child learn 5 words a week. Use the words during discussions. Encourage your child to use his newly learned vocabulary. Help your child learn the nuances of the words. The best way to learn vocabulary is through hearing the words spoken correctly, and trying to use them yourself.

5th)  Starting in late 9th grade or early 10th grade, get your child a book on the ACT or on the SAT. Have your child start to take short practice tests. Help your child get familiarized with the tests.

6th)  Talk with your kids about the importance of these tests. Discuss how much good scores on the SAT or the ACT can open up doors to the best colleges and universities. Discuss the importance of scholarships and correlate high test scores with scholarship opportunities.

7th)  Toward the end of 10th grade, start to look for a good test-prep program. Or look for a tutor who can help your child start getting ready for these tests.

8th)  After your child has had experience taking some practice tests, sit down with your child and together set some goals for test scores. Make clear that the goals are being set just to give your child something to aim toward.

If you take these steps, your child will have a big head start toward doing well on the SAT or on the ACT. And you will never find yourself in the position of thinking that a couple of sessions before the test will “do the trick.”

 

Why the LCM trick works

This video explains why the trick for finding the LCM works. Some people asked to explain the math behind the trick, so here it is.

Divisibility by 2, 5 and 10

Here are the tricks for divisibility by 2, 5 and 10.

Find the LCM — FAST!

Here’s a video that goes with a blog entry that many people have found helpful: Find the LCM — FAST! This trick can be a real time-saver, so feel free to pass this around.

How to Find the LCM for Three Numbers

Several readers have said they like my trick for finding the LCM described in the post “How to Find the LCM — FAST!” but wonder how to use the trick for finding the LCM for THREE numbers. Here is how you do that.

Essentially it involves using the same LCM trick three separate times. Here’s how it’s done.

Suppose the numbers for which you need to find the LCM are 6, 8, and 14.

Step 1)  Find the LCM for the any two of those. Using 6 and 8, we find that their LCM = 24.

Step 2)  Find the LCM for another pair from the three numbers. Using 8 and 14, we find that their LCM = 56.

Step 3)  Find the LCM of the two LCMs, meaning that we find the LCM for 24 and 56. The LCM for those two numbers = 168.

And that, my good friends, is the LCM for the three original numbers.

So, to summarize. Find the LCM for two different pairs. Then find the LCM of the two LCMs. The answer you get is the LCM for the three numbers.

Here are a few problems that give you a chance to practice this technique.

Find the LCM for each trio of numbers.

a)  10, 25, 30

b)  16, 28, 40

c)  14, 32, 40

Answers:

The LCMs for each trio are:

a)  150

b)  560

c)  1,120

The “Ladder of Primes”

Remember the best teachers you had? Remember how they made their classes come alive? How one of the ways they made things exciting was by using analogies — little stories that connected new concepts to things you already knew and understood?

Educational researchers today are studying what makes analogies such an effective teaching tool. They have found that the use of analogies is one of the best techniques for making concepts “stick.” By relating that which students need to know to that which they already do know, teachers create bridges in understanding, and those bridges give students a way to grasp a new and difficult concepts.

The same holds true in math class. If we teachers use powerful analogies that make concepts more memorable, students are more likely to enjoy the lesson, and as a result, they’ll be more likely to remember what was taught.

I would like to present a quick-and-easy analogy that helps students learn about our number system, on the one hand, and which also helps students work with fractions, on the other hand.

The analogy is to something I call the “Ladder of Primes.”

Summertime Geometry Scavenger Hunt

Here’s a nice summer-days math project …

I just happened to be looking at the NM Highway signs page online a couple of days ago when I saw this nice little list of signs, just below:

NM Highway Signs

I couldn’t help but notice that there are quite a few recognizable geometric figures on this page, and I thought, “This would be a cool thing to show to kids who either have studied, or are studying geometry.”

My suggestion: Show this to your children and ask them how many geometric figures they can recognize.

Monday the 13th

Today is Monday, the 13th.

So what, right?

Well, maybe not so fast …

If you have a mathematical/logical bent of mind, you might find that interesting.

Friday the 13th is generally considered a bad luck day. So if that is the case, you might wonder if Monday the 13th would be the logical opposite to Friday the 13th, a good luck day. Afterall, Friday is the end of the workweek, and Monday is the beginning of the workweek.

So in that sense, can it be said that Monday and Friday are opposites? And what might that imply.

So here is the challenge. Compose a logical argument as to whether or not Monday the 13th should be considered a lucky day.

That is the challenge for Monday, the 13th of June 2011.

HINT:  You may want to include information about the “truth value” (truthiness, as Steven Colbert likes to say) of statements and their converses.

REWARD:  The first person who presents a compelling logical argument, one way or the other, wins a $10 gift certificate toward the purchase of any Singing Turtle Press products. All comments must be posted by 1 a.m. on Tuesday, the 14th of June, this year.