Writing to Learn Math: Research prompts help students view math as a human endeavor.
Do you want your children to develop the ability to reason creatively and figure out things on their own?
Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.
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.
And so it begins: Charlotte Mason’s Living Math is LIVE on Kickstarter!
⭐ Don’t delay! ⭐
To have a successful campaign, we need plenty of people to back the project early. The more supporters we get in these early days, the more likely the Kickstarter platform folks will help spread the news for us.
Continue reading Charlotte Mason’s Living Math Launched: Order Your Copy Today
I’m finishing up my plans for the new Charlotte Mason’s Living Math Kickstarter project and pledge levels, which launches early in March.
And I’d really appreciate your help.
Could you please take a few minutes to look over the project page and give me some feedback?
Having new eyes on the page helps make sure everything makes sense.
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.)
The farther we go in math, the more division disappears. It ceases to exist as a separate concept.
Instead, we learn to see division as:
Each of these perspectives offers us a new way to think about and make sense of our calculations.
The methods in last week’s Advanced Multiplication post only work for certain numbers, but we have another, more powerful multiplication tool: We can always use a ratio table to make sense of any multiplication.
Ratios are the beginning of proportional thinking. We can systematically alter the numbers in a ratio to reach any quantity required by our problem.
Students begin working with ratios in story problems that help them visualize and make sense of a proportional relationship.
Continue reading Mental Math: Advanced Multiplication, Part 2
Mental math is the key to algebra because the same principles underlie them both.
As our children learn to do calculations in their heads, they make sense of how numbers work together and build a strong foundation of understanding.
Remember that while mental math is always done WITH the mind, reasoning our way to the answer, it doesn’t have to be only IN the mind. Make sure your students have scratch paper or a whiteboard handy to jot down intermediate steps as needed.
Besides, math is always more fun when kids get to use colorful markers on a whiteboard.
Continue reading Mental Math: Advanced Multiplication, Part 1
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
Denise Gaskins' Let's Play Math 