[Photo by pfala.]
Thanks to John Cook’s article about factorials in the recent Mathematics and Multimedia Carnival, we’re adding new rules to the 2010 Mathematics Game.
Let’s play with multifactorials!
Brighten Up Your Monday with Puzzles
Mondays come every week. Bleh! Here are some puzzles I found this weekend, to brighten up your day…
[Update + Forgetful Waiter Puzzle from singingbanana.]
Introduction to Probability
[Photo by Ella’s Dad.]
Throughout history, around the world, people in every culture have enjoyed playing games of chance. Strangely, mathematicians did not begin to study chance and probability until the 17th century.
Rate Puzzle: How Fast Does She Read?
[Photo by Arwen Abendstern.]
If a girl and a half
can read a book and a half
in a day and a half,
then how many books can one girl read in the month of June?
Kitten reads voraciously, but she decided to skip our library’s summer reading program this year. The Border’s Double-Dog Dare Program was a lot less hassle and had a better prize: a free book! Of course, it didn’t take her all summer to finish 10 books.
How fast does Kitten read?
Hobbit Math: Elementary Problem Solving 5th Grade
[Photo by OliBac. Visit OliBac’s photostream for more.]
The elementary grades 1-4 laid the foundations, the basics of arithmetic: addition, subtraction, multiplication, division, and fractions. In grade 5, students are expected to master most aspects of fraction math and begin working with the rest of the Math Monsters: decimals, ratios, and percents (all of which are specialized fractions).
Word problems grow ever more complex as well, and learning to explain (justify) multi-step solutions becomes a first step toward writing proofs.
This installment of my elementary problem solving series is based on the Singapore Primary Mathematics, Level 5A. For your reading pleasure, I have translated the problems into the world of J.R.R. Tolkien’s classic, The Hobbit.
UPDATE: Problems have been genericized to avoid copyright issues.
Continue reading Hobbit Math: Elementary Problem Solving 5th Grade
The Cookie Factory Guide to Long Division
[Photo by scubadive67.]
Help! My son was doing fine in math until he started long division, but now he’s completely lost! I always got confused with all those steps myself. How can I explain it to him?
Long division. It’s one of the scariest of the Math Monsters, those tough topics of upper-elementary and middle school mathematics. Of all the topics that come up on homeschool math forums, perhaps only one (“How can I get my child to learn the math facts?”) causes parents more anxiety.
Most of the “helpful advice” I’ve seen focuses on mnemonics (“Dad/Mother/Sister/Brother” to remember the steps: Divide, Multiply, Subtract, Bring down) or drafting (turn your notebook paper sideways and use the lines to keep your columns straight).
I worry that parents are too focused on their child mastering the algorithm, learning to follow the procedure, rather than on truly understanding what is happening in long division.
An algorithm is simply a step-by-step recipe for doing a mathematical calculation. But WHY does the algorithm work? If our students could understand the reason for the steps, they wouldn’t have to work so hard on memory tricks.
Review: Math Mammoth
When Maria of Homeschool Math Blog asked if I would review her Math Mammoth curriculum, I jumped at the chance. I’ve always enjoyed her blog posts, and I liked the worksheets I had seen on her website. (Maria gives away more than 300 pages absolutely free!)
She sent me her then-new 4th grade worktexts, and Kitten and I dug in.
Well, that was longer ago than I care to admit. But of course, it takes quite a bit of daily use before one can be absolutely sure of one’s opinion about a homeschool program — or at least, it does for me. Too many times a homeschool resource will look great in the catalog, and we’ll start it with high hopes only to bog down in the day-to-day grind and abandon it after a few weeks or months. So I wanted to give Math Mammoth a thorough workout before I wrote this review.
And all excuses aside, I really am a pro at crastinating…
My aim is to help parents and teachers teach math so our children and students can really understand what is going on. I’ve strived to explain the concepts so that both the teacher and the student can “get it” by reading the explanations in the books.
— Maria Miller
author of Math Mammoth worktexts
and Homeschool Math Blog
Prime Numbers Are like Monkeys
[Photo by mape_s.]
I’m afraid that Math Club may have fallen victim to the economy, which is worse in our town than in the nation in general. Homeschooling families have tight budgets even in the best of times, and now they seem to be cutting back all non-essentials. I assumed that last semester’s students would return, but I should have asked for an RSVP.
Still, Kitten and I had a fun time together. We played four rounds of Tens Concentration, since I had spread out cards on the tables in the library meeting room before we realized that no one was coming. Had to pick up the cards one way or another, so we figured we might as well enjoy them! She won the first two rounds, which put her in a good mood for our lesson.
I had written “Prime numbers are like monkeys!” on the whiteboard, and Kitten asked me what that meant. That was all the encouragement I needed to launch into my planned lesson, despite the frustrating dearth of students. The idea is taken from Danica McKellar’s book Math Doesn’t Suck.
2010 Mathematics Game
[Photo by pfala.]
Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the 2010 Mathematics Game!
Here are the rules:
Use the digits in the year 2010 to write mathematical expressions for the counting numbers 1 through 100.
- All four digits must be used in each expression. You may not use any other numbers except 2, 0, 1, and 0.
- You may use the arithmetic operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial). You may also use parentheses, brackets, or other grouping symbols.
- You may use a decimal point to create numbers such as .1, .02, etc.
- Multi-digit numbers such as 20 or 102 may be used, but preference is given to solutions that avoid them.
Bonus Rule
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.[Note to teachers: This rule is not part of the Math Forum guidelines. It makes a significant difference in the number of possible solutions, however, and it should not be too difficult for high school students or advanced middle schoolers.]
Algebra: A Problem in Translation
[Photo by *Irish.]
In my post Elementary Problem Solving: The Tools, I introduced word algebra as a way to help students think their way through a story problem. In the next two posts, I showed how the tool worked with simple word problems.
Now, before I move on to focus exclusively on bar diagrams, I would like to show how word algebra can help a student solve a typical first-year algebra puzzle.
A homeschooling friend who avoided algebra in high school, trying to help her son cope with a subject she never understood, posted: “Help! Our answer is different from the book’s.” Here is the homework problem:
Josh earned $72 less than his sister who earned $93 more than her mom. If they earned a total of $504, how much did Josh earn?
Denise Gaskins' Let's Play Math 