As I was preparing for Wednesday’s Homeschool Math Club Games & Activities meeting, I remembered my old math calendars and thought, that would be a fun activity to offer. So I pulled up the files and discovered that the days of the week matched perfectly. What a cool coincidence!
So in case you missed the math calendars last year, or in case it’s been long enough that your children have forgotten, here are the “new” versions:
Umm Ahmad created an easier version for young students:
[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
[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!
[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.
[Photo by internets_dairy.]
Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest. Let’s start the mathematical fun with an arithmetic card game in honor of our 24th edition and a few number puzzles:
[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: one deck of playing cards (face cards and jokers removed), pencils and scratch paper, timer (optional)
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.
I thought I knew math fairly well.
I thought arithmetic was boring.
I thought the reason other nations beat America in international math tests was that their students worked harder than ours.
I thought all sorts of silly things before I read Liping Ma’s Knowing and Teaching Elementary Mathematics. Now this must-read book is coming out in a new edition, due in bookstores next week.
I can hardly wait!
In American elementary mathematics education, arithmetic is viewed as negligible, sometimes even with pity and disdain—like Cinderella in her stepmother’s house. Many people seem to believe that arithmetic is only composed of a multitude of “math facts” and a handful of algorithms. . . Who would expect that the intellectual demand for learning such a subject actually is challenging and exciting?
— Liping Ma
Arithmetic in American Mathematics Education: An Abandoned Arena?
[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.
[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!
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.]
[Photo by armigeress.]
In 4th grade, math problems take a large step up on the difficulty scale. Students are more mature and can read and follow more complex stories. Multi-step word problems become the new norm, and proportional relationships (like “three times as many”) show up frequently. As the year progresses, fractions grow to be a dominant theme.
As a math teacher, one of my top goals is that my students learn to solve word problems. Arithmetic is (relatively) easy, but many children struggle in applying it to “real world” situations.
In previous posts, I introduced the problem-solving tools of word algebra and bar diagrams, either of which can help students organize the information in a word problem and translate it into a mathematical calculation. The earlier posts in this series are:
In this installment, I will continue to demonstrate the problem-solving tool of bar diagrams through a series of ten 4th grade problems based on the Singapore Primary Math series, level 4A. For your reading pleasure, I have translated the problems into the universe of a family-favorite story by C. S. Lewis, The Lion, the Witch and the Wardrobe.
UPDATE: Problems have been genericized to avoid copyright issues.
Continue reading Narnia Math: Elementary Problem Solving 4th Grade
