Carnival of Homeschooling is hosted at Sprittibee's. this one is the "yearbook edition"... beautifully done.
Selasa, 30 Oktober 2007
Carnival time
Carnival of Homeschooling is hosted at Sprittibee's. this one is the "yearbook edition"... beautifully done.
Sabtu, 27 Oktober 2007
Speed versus accuracy in math
Just go read this very interesting story at Ragamuffin Studies blog: Taming the speed demon.
Up for some challenge in math? Try contests!
Could a nice math contest spark up some interest and motivation in your student(s)?
I really like the idea of math contests and problems of the week. When my kids get a little older, I'll probably use some problem of the week contest from the Internet.
Typically with problem of the week contests you simply do the problems at home and send the solution over the Internet. You, as the teacher, can be in control of time and additional resources used.
The contest problems are more challenging than standard textbook problems. They "stretch their brain", perhaps even strech mom's brain! But that's all for good. We must not let our students live under the impression that all word problems are solved by the method just studied in the lesson.
I've written about the need for challenging and open-ended problems before. You might want to check those posts out as well.
Some contests publish the names of those who solved it right and some simply publish the right solution. Either way, kids can feel a sense of accomplishment if they get the problem right.
Problem of the week contests are excellent for finding challenging problems and for motivation. There exist several:
And, talking of contests, right now there is a great opportunity to take part in a math contest called Math Kangaroo. It is open for all kinds of students, homeschooled or not. Math Kangaroo is probably the most popular math contest in the world with some 3 million students participating worldwide.
This one is not handled over the Internet, though. The contest is held in dozens of locations across USA and many more around the world. The next competition is held on March 27, 2008, and registration is open at MathKangaroo.org.
All children participating in Math Kangaroo will get a certificate of participation, a Math Kangaroo in USA T-shirt and some other souvenirs. The top winners get a certificate of excellence and prizes.
So this sounds like an excellent opportunity for students to experience mathematics in a little different way. The website has past problems that you can use for practicing up for the contest — or just use them for additional challenging word problems.
I really like the idea of math contests and problems of the week. When my kids get a little older, I'll probably use some problem of the week contest from the Internet.
Typically with problem of the week contests you simply do the problems at home and send the solution over the Internet. You, as the teacher, can be in control of time and additional resources used.
The contest problems are more challenging than standard textbook problems. They "stretch their brain", perhaps even strech mom's brain! But that's all for good. We must not let our students live under the impression that all word problems are solved by the method just studied in the lesson.
I've written about the need for challenging and open-ended problems before. You might want to check those posts out as well.
Some contests publish the names of those who solved it right and some simply publish the right solution. Either way, kids can feel a sense of accomplishment if they get the problem right.
Problem of the week contests are excellent for finding challenging problems and for motivation. There exist several:
- Math Forum: Problem of the Week
Five weekly problem projects for various levels of math. Mentoring available. - Math Contest at Columbus State University
Elementary, middle, algebra, and "general" levels. - Aunty Math
Math challenges in a form of short stories for K-5 learners posted bi-weekly. Parent/Teacher Tips for the current challenge explains what kind of reasoning the problem requires and how to possibly help children solve it. - Education Place Brain Teasers
Has a separate one for for grades 3-4, grades 5-6, and grades 7-8. - Grace Church School's ABACUS International Math Challenge
This is open to any child in three different age groups.
Math Kangaroo
And, talking of contests, right now there is a great opportunity to take part in a math contest called Math Kangaroo. It is open for all kinds of students, homeschooled or not. Math Kangaroo is probably the most popular math contest in the world with some 3 million students participating worldwide.This one is not handled over the Internet, though. The contest is held in dozens of locations across USA and many more around the world. The next competition is held on March 27, 2008, and registration is open at MathKangaroo.org.
All children participating in Math Kangaroo will get a certificate of participation, a Math Kangaroo in USA T-shirt and some other souvenirs. The top winners get a certificate of excellence and prizes.
So this sounds like an excellent opportunity for students to experience mathematics in a little different way. The website has past problems that you can use for practicing up for the contest — or just use them for additional challenging word problems.
Selasa, 23 Oktober 2007
Multiplying in parts and the standard algorithm
I haven't blogged for a while but I've been thinking about this topic for a little while now. It is your multiplication algorithm, also called long multiplication, or multiplying in columns. I also happen to be writing a lesson about it for my upcoming LightBlue series 4th grade book.
The standard multiplication algorithm is not awfully difficult to learn. Yet, some books advocate using so-called lattice multiplication instead. I assume it is because the standard method is perceived as being more difficult. But let's look at it in detail.
Before teaching the standard algorithm, consider explaining to the students multiplying in parts, a.k.a. partial products algorithm in detail:
To multiply 7 × 84, break 84 into 80 and 4 (its tens and ones). Then multiply those parts separately, and lastly add.
So we calculate the partial products first: 7 × 80 = 560 and 7 × 4 = 28. Then we add them: 560 + 28 = 588.
If you practice that for one whole lesson before embarking on the actual algorithm, how much better prepared the kids will be!
Next, they will see the standard way of multiplying:
Obviously, the steps here are the same. You multiply the ones first: 7 × 4 = 28, write down 8 of the ones, and carry the 2 of the tens. then you multiply 7 × 8 = 56, add 2 to get 58 and write that down in tens place.
What about this way of writing it down?
It uses a little more space, but the underlying principle of multiplying in parts is more obvious.
It works with two two-digit numbers as well:
Now, the individual multiplications are 7 × 4, then 7 × 80, then 40 × 4 and lastly 40 × 80.
Lastly, I'll touch on lattice multiplication. It uses the same exact principles; however I am not sure if it makes the underlying principle any more obvious to the students than the standard algorithm (and it does take more time and space).
Answer 588.
Check out Lattice Multiplication to learn how it's actually done; it's hard to explain without images.
Either way, you NEED to explain multiplying in parts to the students. In this case it's not enough just to be able to go through the motions of an algorithm, because multiplying in parts is so needful in everyday life, and later in algebra (distributive property).
Consider for example these mental multiplications you might encounter while shopping:
5 × $14.
Just do 5 × $10 = $50 and 5 × $4 = $20, and add those. Answer $70. I'm sure most of us are quite used to doing such simple products mentally.
4 × $3.12. Go 4 × $3 = $12 and 4 × 12 ¢; = 48 ¢, and add. Answer $12.48.
The standard multiplication algorithm is not awfully difficult to learn. Yet, some books advocate using so-called lattice multiplication instead. I assume it is because the standard method is perceived as being more difficult. But let's look at it in detail.
Before teaching the standard algorithm, consider explaining to the students multiplying in parts, a.k.a. partial products algorithm in detail:
To multiply 7 × 84, break 84 into 80 and 4 (its tens and ones). Then multiply those parts separately, and lastly add.
So we calculate the partial products first: 7 × 80 = 560 and 7 × 4 = 28. Then we add them: 560 + 28 = 588.
If you practice that for one whole lesson before embarking on the actual algorithm, how much better prepared the kids will be!
Next, they will see the standard way of multiplying:
2
84
× 7
588
Obviously, the steps here are the same. You multiply the ones first: 7 × 4 = 28, write down 8 of the ones, and carry the 2 of the tens. then you multiply 7 × 8 = 56, add 2 to get 58 and write that down in tens place.
What about this way of writing it down?
84
× 7
28
+ 560
588
It uses a little more space, but the underlying principle of multiplying in parts is more obvious.
It works with two two-digit numbers as well:
84
× 47
28
560
160
3200
3948
Now, the individual multiplications are 7 × 4, then 7 × 80, then 40 × 4 and lastly 40 × 80.
Lastly, I'll touch on lattice multiplication. It uses the same exact principles; however I am not sure if it makes the underlying principle any more obvious to the students than the standard algorithm (and it does take more time and space).
8 4
+---+---+
|5 /|2 /|
| / | / | 7
5 |/ 6|/ 8|
+---+---+
8 8
Answer 588.
Check out Lattice Multiplication to learn how it's actually done; it's hard to explain without images.
Either way, you NEED to explain multiplying in parts to the students. In this case it's not enough just to be able to go through the motions of an algorithm, because multiplying in parts is so needful in everyday life, and later in algebra (distributive property).
Consider for example these mental multiplications you might encounter while shopping:
5 × $14.
Just do 5 × $10 = $50 and 5 × $4 = $20, and add those. Answer $70. I'm sure most of us are quite used to doing such simple products mentally.
4 × $3.12. Go 4 × $3 = $12 and 4 × 12 ¢; = 48 ¢, and add. Answer $12.48.
Jumat, 19 Oktober 2007
Denise's fraction quiz
I want to point out to you a post by Denise at Let's Play Math. She has a quiz concerning fraction rules: can you explain to your children why this way or why that way, as concerning fractions?
Quiz: Those frustrating fractions
QUOTE:
Maybe you can explain why, maybe you can't. But don't worry. She's going to continue the topic and explain all of these, on her blog. Don't miss that.
Quiz: Those frustrating fractions
QUOTE:
Question #1
If you need a common denominator to add or subtract fractions, why don’t you need a common denominator when you multiply?
Maybe you can explain why, maybe you can't. But don't worry. She's going to continue the topic and explain all of these, on her blog. Don't miss that.
Rabu, 17 Oktober 2007
From the mouth of a child
Background: my daughter has been learning about 3-digit numbers and she's pretty confident with numbers that have hundreds now. She's also heard us adults mention some bigger numbers.
Today she said that she knows how the numbers go:
"Hundred, thousand, million, googol, and gamazon."
What's a "gamazon"??
It's a new number she made up, which "comes after googol and nine hundred ninety-nine."
I guess she's learned something anyway.
Today she said that she knows how the numbers go:
"Hundred, thousand, million, googol, and gamazon."
What's a "gamazon"??
It's a new number she made up, which "comes after googol and nine hundred ninety-nine."
I guess she's learned something anyway.
Selasa, 09 Oktober 2007
Archimedes knew more than we thought
This story is fascinating; they found a long-lost works of Archimedes under the text of a prayer book, and used modern technology to "see" under the prayer text.
After the text was recovered, it was discovered that Archimedes actually found some of the principles of calculus, and used them to figure out volumes and areas. He dealt with "actual" and "potential" infinity, which is exactly what calculus is about.
And he lived thousands of years before Newton!
A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.
After the text was recovered, it was discovered that Archimedes actually found some of the principles of calculus, and used them to figure out volumes and areas. He dealt with "actual" and "potential" infinity, which is exactly what calculus is about.
And he lived thousands of years before Newton!
A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.
Jumat, 05 Oktober 2007
Word problems in Singapore math and bar diagrams
If you're interested in Singapore math's word problems, and how their bar diagrams work, check out this blog entry by Denise at Let's Play Math:
Pre-algebra problem solving: 3rd grade
She goes through a bunch of word problems from Singapore Math 3-A book, and explains both a solution based on algebraic thinking, and a solution with bar diagrams.
It's good reading for all of us who teach, actually.
Pre-algebra problem solving: 3rd grade
She goes through a bunch of word problems from Singapore Math 3-A book, and explains both a solution based on algebraic thinking, and a solution with bar diagrams.
It's good reading for all of us who teach, actually.
Rabu, 03 Oktober 2007
Math card game for all four operations (elementary)
I'm sure youngsters will like this card "game"! I'm going to try it with mine.
Actually it's not really a game, but a fun way for kids to write some of their own math problems using a deck of cards. She even provides a free printout:
Little Blue School: Math Card Game for Addition, Subtraction, Multiplication, Division
HT: This week's Carnival of Homeschooling
Actually it's not really a game, but a fun way for kids to write some of their own math problems using a deck of cards. She even provides a free printout:
Little Blue School: Math Card Game for Addition, Subtraction, Multiplication, Division
HT: This week's Carnival of Homeschooling
Selasa, 02 Oktober 2007
Factoring worksheets
I took time yesterday to make a new worksheet generator. I always enjoy building those; I like simple programming like that and the math in it.
But while doing it, I almost felt I should have been answering emails or doing some of the other projects I have...
Anyway, here it is:
Generate free factoring worksheets - factorize numbers to their primer factors.
But while doing it, I almost felt I should have been answering emails or doing some of the other projects I have...
Anyway, here it is:
Generate free factoring worksheets - factorize numbers to their primer factors.
Senin, 01 Oktober 2007
Math Mammoth and other curricula
I wrote some thoughts concerning the comparison between Math Mammoth Lightblue series and other homeschool math curricula.
It's not complete, and I'd appreciate your thoughts, as well, to add to the page.
It's not complete, and I'd appreciate your thoughts, as well, to add to the page.