[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 Arithmetic Fairy
[Photo by trazomfreak.]
Homeschool Freebie of the Day (which introduced me to Number Stories of Long Ago) shares another gem today: an mp3 recording of The Arithmetic Fairy, by E. Nesbit, one of my family’s favorite authors.
Young Edwin is an English schoolboy who deplores his daily math class. He wishes he could easily solve the problems he faces each day…
You can download the entire book of fairy tales from LibriVox:
“The Arithmetic Fairy” is chapter 7. Enjoy!
For Niner: A Bit of Calculus Fun
Students headed into finals week need to blow off some steam, so let’s have a little fun with calculus. Hey, Niner, does this look familiar?…
[10 Steps to Solving a Calculus Problem by hydriapotts.]
Word Problems from Literature
[Photo by Passion of Bilwa.]
I’ve put the word problems from my elementary problem solving series into printable worksheets:
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.
What a Teacher Wants To Hear
I finally get it — you don’t have to worry about memorizing a bunch of formulas if you just understand where they come from. You can always figure them out again.
— unidentified student in Doug’s class
from the comments on Kate’s post Formulas? What Formulas?
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
Game: Target Number (or 24)
[Photo by stevendepolo via Flickr (CC BY 2.0).]
Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: deck of math cards, pencils and scratch paper, timer (optional)
Set Up
All players must agree on a Target Number for the game. Try to choose a number that has several factors, which means there will be a variety of ways to make it. Traditionally, I start my math club students with a target of 24.
Shuffle the deck, and deal four cards face down to each player. (For larger target numbers, such as 48 or 100, deal five or six cards to each player.) The players must leave the cards face down until everyone is ready. Set the remainder of the deck to one side.
Denise Gaskins' Let's Play Math 