Middle school – Page 11 – Denise Gaskins' Let's Play Math

Do Your Students Understand Division?

Posted on September 29, 2009September 9, 2023 by Denise Gaskins

[I couldn’t find a good picture illustrating “division.” Niner came to my rescue and took this photo of her breakfast.]

I found an interesting question at Mathematics Education Research Blog. In the spirit of Liping Ma’s Knowing and Teaching Elementary Mathematics, Finnish researchers gave this problem to high school students and pre-service teachers:

We know that:
$498 \div 6 = 83$
How could you use this relationship (without using long-division) to discover the answer to:
$491\div6=?$
[No calculators allowed!]

The Finnish researchers concluded that “division seems not to be fully understood.” No surprise there!

Check out the pdf report for detailed analysis.

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How to Solve Math Problems

Posted on September 25, 2009September 12, 2023 by Denise Gaskins

[Photo by Aaron Escobar. This post is a revision and update of How to Solve Math Problems from October, 2007.]

What can you do when you are stumped by a math problem? Not just any old homework exercise, but one of those tricky word problems that can so easily confuse anyone?

The difference between an “exercise” and a “problem” will vary from one person to another, even within a single class. Even so, this easy to remember, 4-step approach can help students at any grade level. In my math classes, I give each child a copy to keep handy:

How To Solve a Tough Math Problem

[Note: Page 1 is the best for quick reference, especially with elementary to middle school children. Page 2 lists the steps in more detail, for the teacher or for older students.]

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Happy Square Root Day!

Posted on March 3, 2009May 13, 2022 by Denise Gaskins

[Photo by arsheffield.]

Check it out:

Celebrating Square Root Day

Have a rootin’ tootin’ Square Root Day

Prime, Composite, and Square Numbers activity

Free, printable Square Roots Worksheets

About the Pythagorean Theorem

Pythagorean Puzzle — a lesson plan prototype

81 proofs of the Pythagorean Theorem

And coming soon: Pi Day.

Edited to add: Jonathan‘s class enjoyed extending the concept to include other products. Using the m/d/yy format (not the 4-digit year), how many times in your life has it been true that $month \times day = year$ ?

MathNotations Contest for Middle-High School

Posted on January 19, 2009May 13, 2022 by Denise Gaskins

$math-team-edit$
[Photo by ccarlstead.]

Can you can put together a team of 2-6 middle or high school students for an afternoon of mathematical play? If so, then Dave at MathNotations is running a math competition you just have to check out.

Teachers register by email on or before Thursday, January 29, and will receive the six thought-provoking contest problems and official answer form by return email. Hold the contest at your convenience on Tuesday, February 3, allowing your team up to 90 minutes to complete and electronically submit their answers.

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Free Online Math for Middle School and Up

Posted on January 16, 2009May 21, 2022 by Denise Gaskins

The Art of Problem Solving people recently announced their new Alcumus program, which provides online lessons on assorted math topics, including probability and combinatorics, which most math textbooks do not cover well, if at all.

Update October 2011:

Alcumus currently complements our Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra textbooks, as well as our Algebra 1, Algebra 2, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra 1 online courses. We expect to continue to expand topics in Alcumus.

— AoPS Alcumus information page

I am signing up all my MathCounts students. If you’re a homeschooler, we would love to have you join us!

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2009 Mathematics Game

Posted on January 1, 2009May 13, 2022 by Denise Gaskins

[Photo by Amanda M Hatfield.]

Have you made a resolution to exercise your mental muscles this year? Then please join us for the 2009 Mathematics Game. Here are the rules:

Use the digits in the year 2009 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

All four digits must be used in each expression.

Only the digits 2, 0, 0, 9 may be used.

The decimal point may be used, as in .9, .02, etc.

Multi-digit numbers such as 29 or 902 may be used, but preference is given to solutions that avoid them.

By definition: $0! = 1$ .
[See Dr. Math’s Why does 0 factorial equal 1?]

For this game we will accept: ${0}^{0} = 1$ .
[See the Dr. Math FAQ 0 to the 0 power.]

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MathCounts — Ready or Not, Here It Comes

Posted on December 17, 2008May 13, 2022 by Denise Gaskins

[Feature photo above “You’re a mean one, Mr. Grinch” from CheezBurger.com.]

Okay, kids, I know you’re on break, but Mr. Grinch would tell you that’s no excuse to laze around playing games and eating cookies. There is only a month until our school MathCounts competition, which doesn’t give you much time to prepare. I’ve collected several resources to build up your mental muscle-power before the test…

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More Free Math Resources

Posted on October 23, 2008May 13, 2022 by Denise Gaskins

[Photo by One Laptop Per Child.]

Once again, I am adding to my Free (Mostly) Math Resources page. Here are a handful of helpful websites for teaching math…

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Math Club: Counting 101

Posted on October 13, 2008June 22, 2021 by Denise Gaskins

[Fature photo above by ThunderChild tm.]

The last couple of weeks, in Math Club, we’ve been learning to count. My new set of MathCounts students have never heard of combinatorics, so we started at the very beginning:

Counting and Probability I by Keone Hon

Counting and Probability by Jason Batterson

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30+ Things to Do with a Hundred Chart

Posted on September 22, 2008December 30, 2024 by Denise Gaskins

[Photo by geishaboy500 via Flickr (CC BY 2.0).]

Are you looking for creative ways to help your children study math? Even without a workbook or teacher’s manual, your kids can learn a lot about numbers. Just spend an afternoon playing around with a hundred chart (also called a hundred board or hundred grid).

My free 50-page PDF Hundred Charts Galore! printables file features 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more. Everything you need to play the activities below and those in my new 70+ Things to Do with a Hundred Chart book.