For a while, a long while, I let this math blog just sit. I didn’t want to delete it. I spent too much time on it and I knew it was full of great stuff that was still being used. But I wasn’t in love with writing on it.
In my lethargy, the hackers and jerks managed to infiltrate and completely take it down. That was on October 23, 2025.
Today is December 30, 2025. I rescued all the posts and will gradually get all the good ones reposted. But I have to start over, creating the whole website from scratch.
Luckily the wayback machine (internet archive) has a nice snapshot of the images and layout. It’ll take me a while, but I’ll get it all back up. Maybe even with some improvements!
If you are looking for a specific post – something you remember from long ago or something you want to know about – leave it in the comments. I’ll hunt it down and get it posted.
I’m looking forward to having all those great math stories, thoughts and tips live again – I hope you are too.
It inspired me to draw the graphs of Celsius in terms of Fahrenheit and Fahrenheit in terms of Celsius.
The conversion from Celsius to Fahrenheit and back again can be strange. One way to understand it is on a graph. And you can use this to teach some linear algebra too!
Notice these two intersect at (-40, -40). Which means that -40°F is -40°C!
Use it to convert temperatures.
The x values on the red line are Celsius – so find the °C you have and then look at the y-value to convert to °F.
It’s just the opposite on the purple line.
Okay, fine. This isn’t the greatest way to convert – but it’s exciting to see it graphically. And it might be easier to convert this way for someone who’s more visual.
Use it to teach math!
These two lines are inverses of each other. So the coordinates of one are switched to make the other.
Also, they mirror image across that 45° line. I marked the line with dashes and wrote $latex y=x$ on it.
And if you’re into this, their functional composition (both ways) is… x! (not factorial)
Compare and Contrast…
Take a look at the way J.D.Roth did it and then look at the graphs I have. Let your students find the way they like the best. And encourage them to create new ways!
Oh, yeah – and share what happens in the comments!
In order to see what the difference is between motivation and inspiration when teaching math, I’m going to start with a quick story…
You have a dog named Herman. Herman is cute, fuzzy, has a pink nose and loves you unconditionally. You think he’s great. So you want to share him.
You put a bow around his neck, and hand him to your children, Abby and Dirk.
“Here is Herman. He’s cute, lovable, and a perfect pet. Isn’t he fabulous?” you tell them.
Abby looks at Herman and is so excited. She thinks he’s fabulous, wonderful and sees in him everything that you do. Inspiration hits her – she loves him like you do!
Dirk, on the other hand, wants a cat. He’s not sure how to voice this. But since you’re so excited about Herman the dog, he rolls with it.
He wants to please you, so he feigns interest in Herman.
Herman’s not a dog.
Herman is your curiosity. Herman is what you find interesting and inspirational.
And just because Herman is wonderful for you, doesn’t mean Herman is perfect for everyone else.
Abby loves Herman. And Dirk loves Herman, but only because loving Herman pleases you.
We offer Herman, and they take him. Because they want to please us.
Lots of educators these days are talking about helping children connect with math through real life experiences. They want to give children curiosity about math in the real world.
Some children like to build things. Give them a stack of Legos and they’ll work for hours.
There are kids who are outdoor people, always running around and wanting to see what next thing they can find in nature.
Some kids want to be in the kitchen, helping their parents cook dinner.
Some kids are quite happy connecting math just to math.
Some children are gamers, enjoying puzzles, riddles and games just for the fun of it.
And the list goes on…
Grownups take their connection to the real world, their own curiosity, and pass it on to children. We take everything that we find fascinating, our own personal Herman, and hand it to the child.
And they take it. Some because they are excited about it, and some because they want to please us.
Motivation is not inspiration.
The growing thought among educators is that children need to be curious in order to learn math. So we’re creating ways to get children curious.
But are we doing it right?
The child will happily take Herman, your form of curiosity. This could mean they are truly inspired by what you give. And it could mean that they are merely motivated.
Motivation isn’t a bad thing, for sure! But if we mistake motivation for inspiration we are doing the children a disservice.
If they’re motivated, they’ll only do what’s next to get praise. It’s about you, the grown-up, and how much they can please you.
If they’re inspired, they’ll want to take their learning to the next level – even when you’re not around. They’ll want to see and do things to enhance their understanding without needing your praise and attention. It’s about them.
And when things are about them, they own it. They succeed because they can, not just because we want them to.
What’s your Herman?
And have you passed him along? Was he inspirational or motivational? Share your thoughts in the comments!
This is a guest article by Caroline Mukisa who publishes Maths Insider.
Does your middle- or high-schooler know their times tables? If the answer is a resounding “Yes” then, great, have a great day, and read the other great tips here at MathFour.
I also have some great tips and advice on how to guide your child to maths success on my Maths Insider site.
If not, then it’s time to help your teen develop their own times tables boot camp.
Why are times tables important at all?
Well it’s used loads in algebra, and those geometry questions usually need a fair bit of multiplication or division. It’s also great for those grown-up things that they’re going to be doing in the years to come, working out payment plans, home remodelling, calculating sale prices and just plain making sure that they’re not ripped off in life.
Of course we’ve got computers and calculators, but who wants to be fiddling about to open a smartphone app, just to work out the price of a pair of jeans. And if they press the wrong buttons, how will they know the answer is wrong?
Yep, they’re important!
Why are times tables a problem for older learners?
It’s like spending years trying to pass a driving test. Or still not being able to conjugate Spanish verbs after studying them for ages. Or trying to lose those last few pounds of weight. It sucks, and it gets to the point where it’s easier to develop a work-around: catch the train everywhere, just get by with a few Spanish phrases, or buy bigger clothes.
Of course, your teen can “get by” and may even do rather well at maths without knowing their times tables. But before you give up, try some of the following strategies to help your teen make their own times tables bootcamp to fix those essential times tables facts in their heads. It’s never too late!
Times tables boot camp strategies
1) Figure out what they know, and what they don’t know. Are they fine with their 2’s, 3’s and 4’s and 5’s but shaky after that? Then focus on quickly reviewing the easy tables before some concentrated repetition of the harder tables.
2) Use incremental steps. Make sure the 5’s are solid before moving on to the 6’s and the 6’s are fast before moving onto the 7’s.
3) Give your teen a fixed target. It’s completely possible to learn the times tables from 2-9 in a month with just 5-10 minutes of daily study.
4) Let them choose their own activities. Worksheets won’t be a popular option – iphone apps, You Tube videos, online games are all things that teens are more likely to tolerate.
5) Be encouraging – don’t say, “That’s easy, you should know it” instead say, “I can see you’re working hard on this, keep it up.”
Use these strategies to help your child plan their own successful times tables boot camp, so they won’t have to just “get by” in maths any longer.
Caroline Mukisa is a homeschooling mom of 4, who publishes at Maths Insider.
This past Monday we had a great #mathchat via Twitter. The topic was: “If you could clear one misconception about mathematics and/or teaching it, what would it be?”
I was getting a bit frustrated that a couple of people kept bringing up the misconception that girls aren’t good at math. Even to the point of creating their own hashtag #girlsaregoodatmath2.
In my life, I’ve never heard anyone say this – in any other form than somebody complaining that people say it.
So here’s my response to everyone who keeps saying to me, “I wish people would stop saying, ‘Girls aren’t good at math.’”
What do you think? What will you say from here on out?
I was at my dad’s house the other day and decided to pull out my new Math’d Potatoes game to see how my super-gaming family liked it.
The kids in the house were too young to play, so my sister and I asked Aunt Linda and our stepmom to play with us.
They quickly claimed they were “math Neanderthals” but agreed to play anyway. My dad, an engineer, was asleep.
The game has simple rules.
You play Math’d Potatoes by drawing a card, rolling five dice and making an expression that “satisfies” the card.
The card requests various types of “answers”:
Even or odd
Equal to a certain number
Between two numbers
Less than/greater than a certain number
Everybody got into it.
Aunt Linda and Louise (my pet name for my stepmom) both agreed that it was a fun math game. This is in spite of the fact that neither one of them like math, and Aunt Linda doesn’t even like to play games at all!
My dad saw the game the next morning.
I had intentionally not waken up my father to play with us the night before. My decision was validated the next morning.
My dad is an engineer, and as such tends to use the phrase “all you have to do is,” and the word “just.” He’s a very smart man, and I’ve learned lots from him through the years. And one of those lessons is: “Keep an engineer away from sensitive math learners.”
Sure enough, when he saw the game, he eagerly said, “What’s this? Are we going to play it?”
When I explained we played the night before he responded with, “Why didn’t you wake me? I totally would’ve won.”
Math learning is slowly build, and quickly destroyed.
When we were playing, Aunt Linda and Louise were both starting to warm to the idea of math. They were enjoying the game. My sister and I were holding back just a little to give them an opportunity to discovery their own skills. (We both experienced the engineer–math–dad super push growing up.)
So by the end of the game that night, they were excited, confident, and enjoying themselves.
Had I woken up my father to play the game, he certainly would have won. He might’ve turned it into a competition, or he might have tried to help a little too much.
Either way they would’ve lost interest. Their confidence would have been destroyed. And two beautiful, smart and happy women would have their, “I’m a math Neanderthal” thoughts validated.
You can use this with your children.
If you or your spouse are in a math related field, or was “always good at math,” be aware of your potential intimidation factor. Hold back. Don’t help. Allow discovery and confidence to come at its own slow and natural pace. Your children will learn math, in their own time.
Don’t force it, or you might destroy it.
Note: They sent me this game for free. This is not a review, per se, but still – you should know how I got it.
It’s part of our DNA to assess the world around us. As soon as a baby sees Mommy different from Daddy (or smells the difference), she starts comparing. When she figures out that there are more than one of something, things get even more interesting.
Give each of two toddlers a ball. Then stand back and watch. If they aren’t exactly the same ball, one of them will want to switch, and the other will say no. It won’t matter which ball is truly superior, only that one child will soon perceive inequity in ball ownership.
If they are given the same color and size ball, you can watch their little brains calculate this and work to discern some difference.
And it doesn’t stop at kids. Women do it all the time. Is my bottom as big as hers? Do we wear the same size shoes (and will she let me borrow hers if we do)? Is my dress more expensive than her dress?
Comparison in math corresponds to comparison in the world.
Some things are really exactly the same.
Your two crystal champagne flutes you bought for your wedding are likely the same. Not only is one interchangeable with the other, but you couldn’t tell the difference if you were to switch them.
This can get a little sticky for math. There is only one number 3.
But when I write 3 = 3, there are really 2 threes running around. (Math friends: I realize two champagne flutes are not the same as two number 3s. But making analogies in the real world is tough if you don’t take a little poetic license.)
Sometimes things have the same value.
Have you ever traded a dollar bill for 4 quarters? Those aren’t exactly the same (you would be able to tell the difference if you replace one with the other) but they have the same value.
If you return a blouse to a department store that your weird uncle Zeno gave you, and get a blouse that fits your style much better, these will have the same value. Monetarily speaking, of course.
If you ship your G7 back to Canon when it’s under warranty, and they return a G10, the value to them was equivalent (while the value to you has increased).
Some things have the same size and shape.
When you replace the transmission in your car, you’re doing so with an equivalent copy that’s better than what you already have. If you replace the engine in your 1969 Mustang with a souped-up model, you’re playing the same game.
In both these situations, the replacement version, although superior in functionality, is the same in size and shape.
Sometimes things are interchangeable.
Like in the example above, with the cars, as long as one thing works equally as well as the other, you can compare them and call them “equal.”
If you reach for a pen from the pen jar on your desk, any pen will work as well as any other.
The two pens may not be exactly the same, have the same value or even be the same size and shape. But you can interchange one for the other when writing a check.
And sometimes equality is merely perceived.
Like the toddlers with the balls from above. Different people will put different value judgments on items. So there is the case that equality is in the eye of the holder. Or wanter.
What does equality mean to you?
As we progress through this series, we’ll see how equality and the equals sign in mathematics relate to equality in the real world. And thinking about how equality in the real world works is the first step.
So what do you think of when you think about two things being equal? Share your thoughts in the comments.
My day job colleague told a beautiful story yesterday. He had been washing his car late at night, in the dark, and was approached for assistance. He is generous beyond belief, and apparently he made a real impact.
I was washing my car the other night and really getting after it. I had the scrubbing brush going and was really making progress on getting the car clean. I was totally focused and I felt a tap on my shoulder. It startled me and I turned around to be faced with a large African-American woman who said, “I’m sorry, I don’t mean to interrupt, but we’re having car problems. Is it possible you can help us? I think we need the battery jumped.”
I looked down the street and saw no other people and no car. Within a split second I remembered my latest purchase: a wireless battery charger that needs no people, no cables and no extra car to jump a battery. I got it out of my garage and handed it to her.
“I’m in the middle of washing my car. Why don’t you borrow this? It should help.”
She thanked me and walked away with the charger. I got back to washing my car.
Five minutes later there was another tap on my shoulder. Another African American woman was standing there holding a five dollar bill. She offered it to me.
“Oh my goodness, no,” I said. “I’m not taking your money. I’m just glad I could help.”
Another 5 minutes went by and I saw one of the ladies put the battery charger close to my garage. I was really getting into the car washing at this point – suds everywhere – so I didn’t pay much attention.
When I was returning my carwash supplies to the garage, I saw a crisp new $100 bill on top of the battery charger!
That thing was only $40 – and they just gave me $100 to borrow it!
This is a wonderful and touching story. These ladies were having difficulty finding someone to help them. Not only did my friend help, he also freely gave them something to use and trusted without question that they would return it.
They, too, were moved by his generosity.
The numbers don’t work.
It looks like this:
Battery charger cost: $40
“Rental fees” offered: $5
Shown gratitude: $100
The numbers don’t make sense. And in a way they shouldn’t. The $100 bill wasn’t really money. It was the biggest, fattest, loudest thank you note ever written. There’s no value you can place on someone being free and generous and trusting.
It still goes in as $100 in the eyes of the bank. But what do they know?
Notice the math and share the story.
When you share this story, point out the math. Especially if you tell this in front of (or to) children. Making the connection of generosity and emotion to math will help everyone see how integral math is in our lives.
How about you? Do you have a story of generosity that you’re just now realizing involves math? Share it in the comments!
I mailed out the bulk of the thank you notes for Daughter’s 2nd birthday party gifts. And wouldn’t you know it, it involved algebra!
I have so many stamps from the last 20 years, in every denomination you can imagine. I’m trying to use them up because I only save full sheets of stamps. (I’m a bit of a stamp collecting snob.)
Rule #1: No more than the required postage on any letter.
It has to be exact.
As of this writing, postage in the US is $.44 per letter.
I have $.33 stamps, $.37 stamps, $.41 stamps, etc. And I’ve purchased $.01, $.02, $.03, and on up to supplement and make my postage exact.
Rule #2: No more than 2 stamps of the same kind on a letter.
I like variety.
With these requirements, here are some of the combinations that I’ve come up with:
So how is this algebra?
Here is an algebra equation from the stamps in the picture:
10x + 17y = 44
The equation means x number of 10 cent stamps plus y number of 17 cent stamps will give me the exact total of 44 cents! So x=1 and y=2.
And here’s another:
10x + 24y = 44
The equation means x number of 10 cent stamps plus y number of 24 cent stamps will give me the exact total of 44 cents! So x=2 and y=1.
It would make it a better set of algebra problems if I allowed more than two types of stamps. But I’m sticking with my variety rule. 😀
How about it – will it make writing thank you notes with your kids more fun? More challenging? More annoying? Share your thoughts in the comments!
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