I’ve written before about supplementing your children’s experience of math by playing games and reading good books.
But as I’m working on my new book, I wanted to add another valuable supplement that we often overlook. So here’s a preview excerpt from Charlotte Mason’s Living Math…
One of the stretch goals for my Charlotte Mason’s Living Math Kickstarter campaign is to add a math journaling prompt to the end of each chapter. So, I’ve been playing around with ideas to get readers writing.
Since the book’s all about how to build mathematical reasoning, I’m looking for ways to prompt creative thinking and flexibility in math calculations.
I found some fun ideas in Guy Gattegno and Martin Hoffman’s Handbook of Activities for the Teaching of Mathematics (which you can download here), including the following riff off a puzzle created by Lewis Carroll.
Once upon a time, when my kids and I were young…
Later the same year, not too long after our discussion of the Bill Gates proportions, I stumbled on some more data. I discovered that the median American family’s net worth was $93,100 in 2004, most of that being home equity.
This gave me another chance to play around with proportions. And since I was preparing a workshop for our regional homeschooling conference, I wrote a sample problem:
The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?
In the last post, I explained that a proportion sets two ratios equal to each other, like equivalent fractions. Each ratio must compare similar thing to similar thing in the same order.
In this case, we are interested in the ratio “Expense compared to Net Worth.”
Continue reading Homeschool Memories: Bill Gates Proportions II
Once upon a time…
We were getting ready for the annual homeschool co-op speech contest, and a friend emailed me for help.
“Can you help us figure out how to figure out this problem?
“This is related to C’s speech. I think we have all the information we need, but I’m not sure:
“The average household income in the United States is $60,000/year. And a man’s annual income is $56 billion.
“Is there a way to figure out what this man’s value of a million dollars would be, compared to the person who earns $60,000/year? In other words, I would like to say—$1,000,000 to us is like 10 cents to Bill Gates.”
We found out later that her son’s numbers weren’t exactly right. He hadn’t understood the difference between income and net worth, so he made Gates sound richer than reality.
But the basic math principles never change, and it’s fun to play with big numbers.
Continue reading Homeschool Memories: Putting Bill Gates in Proportion
There’s a new math journaling prompt this week.
Have your kids tried it yet?
This week’s prompt features one of my explain-your-reasoning to get kids thinking (and writing) about math while avoiding the formality that turns so many students away from geometry proofs. Or you might prefer last week’s prompt, featuring a classic math brainteaser and encouraging students to create their own related puzzles.
Or, if you’re reading this post later and missed those, there’s another great new prompt this week for you to explore.
Check it out:
There’s a new Math Game Monday this week.
Have your kids tried it yet?
This week’s game is one of my favorites for upper-elementary and middle school students, offering plenty of practice doing estimation and mental math with fractions. Or you might prefer last week’s game, featuring a classic two-player logic puzzle that develops strategic reasoning.
Or, if you’re reading this post later and missed those, there’s another great new game this week for you to play.
Check it out:
Ever since the school year started, I’ve been getting questions about how to use my new Math Journaling Adventures logbooks.
[SIDE NOTE: These logbooks are included in this month’s Thanksgiving Sale! You’ll get an automatic 10% discount off all print books, applied at checkout, no special code required.]
“I love the way your math books get my children thinking.
“Finally, they are having fun with math!
“But sometimes I have no idea what the journaling prompt is all about or how to teach it. Where can I buy a solutions manual?”
Um, that’s not how math journals work.
The cool thing about journaling prompts is that they have no “right” answer. They are explorations into different parts of the world of math, nature walks in the land of numbers, shapes, and patterns. Springboards into whatever our children want to investigate, whatever sparks their interest.
A few of the problem-solving prompts may have specific answers, but it really doesn’t matter if our kids find the exact solution a math professional might give. If they write what makes sense to them, they’ve accomplished the goal.
If later, they think of something they hadn’t noticed, or they want to change their answer — well, that is mathematical thinking, too.
I’ve been updating my old book files to a new publishing program, and in the process discovering anew how often websites change and disappear. So frustrating!
Thankfully, the Internet Archive keeps some things that we can look back at. It doesn’t always work, but today it came to the rescue and let me recover the wonderful workbook from the Metropolitan Museum of Art, Islamic Art And Geometric Design, plus some of the pattern pages at the old School of Islamic Geometric Design.
I reference these pages in my Geometric Coloring Designs series (available at my Playful Math Store), so I was glad to find they weren’t lost forever.
Math Art = a great way to spark energy when your students hit the mathematical doldrums.
Here are a couple of fun foldable projects to try with your kids.
Both of the projects below start with squares of paper. Do you know how to convert any piece of paper into a square? Here are two methods.
No peeking! This post is for those of you who have given the trisection proof a good workout on your own.
If you have a question about the proof or a solution you would like to share, please post a comment here.
But if you haven’t yet worked at the puzzle, go back and give it a try.
When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.
