Coming Soon! In March, I’ll be launching my newest book, Charlotte Mason’s Living Math: How to Apply the Principles of Education to Help Children Develop Mathematical Reasoning.
And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:
(If you back the campaign on launch day, that encourages the Kickstarter folks to share it with more people.)
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 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:
The question came up on a homeschool math forum:
“My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’
“He wrote down 10 – 2 × 3 + 1.
“When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.
“How can I help him understand order of operations?”
[If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]
Order of operations doesn’t matter in this instance. What matters is communication.
The mother didn’t know how to read what her son wrote.
He could help her understand by putting parentheses around the part he wanted her to read first.
He doesn’t need to know abstract rules for arbitrary calculations, or all the different ways we might possibly misunderstand each other. He just needs to know how to say what is in his mind.
I’ve been getting questions about my Math Journaling Adventures books:
“I’m so excited to try math journaling! We bought your Logbook Alpha, and my 11-year-old math-averse son is trying to be a math rebel at every turn.
“But I feel uncomfortable with the idea of rebellion. Doesn’t he need to learn how to solve math problems the right way?”
One of my favorite things about math is that there really is no “right” way to solve math problems.
As I pointed out in my ongoing Mental Math series, even a problem as basic as 6+8 can be approached from many directions. So perhaps I should say, the “right” way is however the student wants to make sense of the problem.
In math, sense-making and reasoning are always the most important things.
Over the course of this series, we’ve seen how mental math relies on a child’s own creative ways of thinking. In mental math, children develop understanding of how numbers interact with each other in many ways.
In this way, they learn the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.
And the principles that underlie mental calculation are also fundamental to algebra, so that flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.
But as we went through the various example problems, did you find the written-out calculations hard to follow?
Don’t force your children to write down their mental math. It looks dreary when I write the calculations out step by step, but that’s not how it works in a child’s mind. With regular practice, this sort of thinking becomes second nature.
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.
“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.
“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.
“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”
—James Tanton
James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.
But his wonderful, old-fashioned site full of great insights and interesting problems is gone.
😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.
Most of us were never taught how to teach. And we certainly weren’t taught what to do when NOTHING is working.
My friend Sonya Post is offering a free orientation course that will help you rethink how learning actually works, how you can stop second-guessing yourself and start seeing real growth.
I’ve taken the earlier iterations of her course, and I’d recommend it to all parents.
Truly wonderful insights!
The NWD Orientation Course is an introduction to the Notice, Wonder, Discover framework and the underlying habits that develop the underlying thinking skill necessary for learning. Rather than focusing on curriculum tricks or information delivery, the course helps parents understand how attention, observation, curiosity, reasoning, and response shape the learning process itself.
Inside the course, parents will explore how children develop understanding through guided discovery, pattern recognition, conversation, and relationship.
You’ll learn how to create a calmer and more connected learning environment, how to recognize common teaching habits that unintentionally shut down thinking, and how to support the development of flexible, confident thinking across every subjects.
You’ll also learn how all subjects are connected.
The Orientation Course changes the way you see teaching, learning, and formation at home. It lays the foundation for the rest of Sonya’s community and courses by helping parents develop a shared language and vision for learning rooted in attention, wonder, meaning, and formation.
You may have heard me mention Sonya before. She created The Best Math Game Ever, and she teaches the math course I wish my kids and I could have taken:
“I don’t just build these resources — I use them. I’ve walked the road of frustration, math tears, and feeling lost about how to teach well. This course exists because I don’t want you to walk that road alone. This is the framework I wish I’d had years ago, and I can’t wait to share it with you.”
—Sonya Post
I really can’t praise Sonya’s work enough. If you’re struggling at all with your teaching or family life, she’ll turn you around and give you new perspective on how to move forward with grace.
Check out her free course:
Get the Notice, Wonder, Discover Orientation Course
(affiliate link)
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Featured image above copyright © Sonya Post.
Denise Gaskins' Let's Play Math 