## Saturday, March 31, 2012

### If a hen and a half can lay...

Share your teaching methods for the classic problem in the title:

If a hen and a half can lay an egg and a half in a day and a half, how many eggs can 3 hens lay in 3 days?

Would you ask students for an immediate intuitive guess and expect many to say 3?
The answer is 6 so the purpose of this post is reflection on sharing instructional strategies.

What are the BIG IDEAS here? Do you use one basic strategy in teaching all ratio problems?  Does dimensional analysis work for middle schoolers?  Should students always reduce everything to a single unit ratio like 1 hen per day? How many ways could your students devise if we tell them the answer is not 3?

Not much sharing going on like in the old days of this blog but maybe it's time..

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Shameless self-promotion!
Consider buying my Challenge Math Problem book designed for standardized tests, Problems of the Day, etc. Go to top of right sidebar for more info.

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## Tuesday, March 27, 2012

### State Testing Review Time In Your District=?UTF-8?B?Pw==?=

This is that special time of the year when some districts, particularly in elementary grades, hand out practice materials for the test and teachers are expected to devote the majority of class time to it.

Here's my question...
Does anyone out there feel that these materials seem to be somewhat different and of a higher level of difficulty than regular classroom materials/tests?  If this is the case then what are the implications for the child, the teacher and the district?  I do have strong feelings about this but I'll wait for your comments first. WHAT ARE YOUR THOUGHTS?

Also I have to repeat a tweet I just saw from the brilliant Timandra Harkness from the UK. She made my day...

"I'm decorating my bathroom with those new fractal tiles. I think it's going to take forever."

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## Sunday, March 25, 2012

### PerCent "More" - Applying RATIOS DEEPLY

PROBLEM
Two thin cylindrical steel  disks have diameters of 35 in and 25 in. The area of the base of the larger is what % more than the smaller?

We would hope juniors in Alg 2 or Precalc would know the basic setup for % more, % increase/decrease or % change types, particularly since this is a middle school concept. Of course we know this is often not the case!

After having students work in small groups for a few minutes and watching them pushing calculator buttons you have someone come up and explain, asking questions and reviewing basics. As is typical, some students will use the diameters instead of the radii and get the right answer anyway. What are the "BIG IDEAS" here?

Write on the board (35/25)^2 = 49/25, then 24/25 = 96%.  No explanation. You give students in small groups 2 minutes to make sense of this and have 2 groups take turns explaining it to the class.A mental calculation?

Before you kneejerk reflexively react to this with " Even some of my honors students would struggle with that", I would like my readers to reflect on our obligation to stretch their minds and promote conceptual understanding.

IN NO WAY AM I SUGGESTING THAT IS THE METHOD MOST STUDENTS SHOULD USE!

SO WHAT ARE THE KEY MATH CONCEPTS USED IN MY EXPLANATION?

Of cou

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## Saturday, March 24, 2012

### Investigation for "Squares"

In square ABCD of side 1, E is the point on diagonal AC such that AE=1.

(a) Explain without numerical calculation why
√2 < BE + DE < 2
(b) Show that BE+DE = 2(√(2-√2)) ≈ 1.531 without using Law of Cosines
(c)  Be a math researcher! How might you generalize this?

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## Saturday, March 10, 2012

### NEW MATH CHALLENGE QUIZ/PROBLEM BOOK AVAILABLE

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back. Suitable for SAT I, SAT Math I/II, Math Contest practice or daily/weekly Problems of the Day. Questions include multiple choice, cases I/II/III type and constructed response. Price is \$9.95 and secured pdf will be emailed when purchase is verified. DON'T FORGET TO SEND ME AN EMAIL FIRST SO THAT I CAN SEND THE ATTACHMENT! (dmarain "at" "geemail dot com")

## Friday, March 2, 2012

My beloved wife of 42 yrs passed away on 2-28-12 after battling pancreatic cancer over 8 months. She gave tirelessly to those in need all of her life and never asked for anything for herself. She can finally have the rest she has earned. I, her 7 children, 4 grandchildren and all those whose lives she touched feel a gaping hole in our hearts...