I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

# Tag Archives: arithmetic

### Equations vs. Expressions

This is Day 15 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

“I don’t trust equations. I trust quotes.”
~Khalid Masood

You’ve probably heard (or even said), “Whatever you do to one side, you have to do to the other.”

Or maybe, “Plug it in.”

These phrases are all applicable to specific things – not generic terms that can be used in any math situation.

And the big differentiator is equation vs. expression.

### Like Night and Day

You can separate your world into night and day. There’s a slight bit of iffy-ness when it comes to dawn and dusk, but generally night and day works.

Equations and expressions are like night and day. If you start with the equations, you’re most likely going to continue with the equations. Whereas if you start with expressions, generally you won’t create equations.

And just like dawn and dusk, there is a little bit of overlap.

### Some Definitions

An expression is a collection of symbols. We’re most comfortable with expressions and make some sort of sense. For example, $3+2$ is an expression. So is $99((($, but that’s a little freakish looking.

An equation is an expression with an equal sign. More specifically, an equal sign that actually means two things are equivalent. (You can certainly have $99===((($, but that doesn’t mean much right now. So we’d still call that an expression.)

You may have noticed that all equations are expressions. Much like all squares are rectangles. But like squares and rectangles, we mostly call expressions that are equations just equations. And we leave the word “expression” for non-equations.

### Both Sides

The “sides” are the two sides of an equal sign. So that rule doesn’t apply to expressions. Like these:

$42 = 97-55$
left hand side is $42$, right hand side is $97-55$

$y+3=19$
left hand side is $y+3$, right hand side is $19$.

$8x+3$
no sides (there are terms but not sides… see?)

### Set it Equal to Zero

This only works if you turn an expression into an equation (like to graph it). And then it only works when you’re looking for the x-intercepts.

Me: Check out this expression: $8x+3$
You: Gee, it sure would be swell to see a picture of that.
Me: Okay, graph $y = 8x + 3$
You: If I solve $0 = 8x + 3$, I’ll get the x-intercept.
Me: Fo shizzle! (hashtag-I-wish-I-was-cool)

### Just Plug It In

You can plug random things into the variables in an equation, but it may not make it true.

Me: Check out this equation: $y+3=19$
You: Let’s plug in my favorite number $7$ for $y$.
Me: No prob, but that gives us $10=19$
You: Which means you owe me an ice cream.
Me: Whatever.

But if you plug them into an expression, there’s no truth to it. It just gives out a number. And that’s okay.

Me: Check out this expression: $8x+3$
You: Hey, cram my favorite number $7$ in for $x$.
Me: Okay, that gives $59$.
You: Groovy. Let’s go get ice cream. I’ll buy.

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### Some Ways to Tell When a Math Problem is Wrong

Sometimes it’s easier to see when a math problem is wrong than to see when it’s right. Here are some examples. Continue Reading

### Variations on the Number 4

Here are some variations on the number 4. Some are nice, some are a little freaky. Continue Reading

### 2 Responses to Variations on the Number 3

1. Allen Arnold says:

A 3-sided polygon, a triangle, is the only “rigid” shape. Any polygon with more than 3 sides is not rigid because it can be easily deformed. A triangle, by contrast, is strong because it resists deformation. Therefore, triangles are often used in construction. For example, “trusses” are structures made of steel beams in the form of triangles. Often, many smaller triangles are welded together to form larger triangles for greater strength. Trusses are used wherever strength is needed: bridges and supports of all kinds. The Eiffel Tower is made of trusses consisting of thousands of steel triangle-shaped constructions.

• Bon says:

Very cool, Allen! Reading that gave me goosebumps (circular, but they don’t need to be rigid!)

### Variations on the Number 2

Here are some variations on the number 2, as well as a few facts. Continue Reading

### Variations on Numbers

Do you practice fact families with your children? How about variations on different numbers? This is the first in a video series showing variations on numbers. Check it out! Continue Reading

### Twinkle Twinkle Little Star Math Song

Do you sing Twinkle Twinkle Little Star to your kids? Try this math song with the same tune! Continue Reading

### 4 Responses to Twinkle Twinkle Little Star Math Song

1. Maybe a Pop Goes the Weasel where you use some numbers?
3 times around the mulberry bush,
the monkey chased the weasel,
4 more times they went in the rush
7 to pop the weasel!

Then there’s the already mathy nursery songs:
5 little sausages sizzling in the pan…

• Bon says:

Fun! That’s a classic, too, isn’t it, John? I’ll have to think more on that one.

2. I vote for a follow up video post by the magnificent K8! Thanks for the idea to make math a soothing and enjoyable experience for our little ones.

• Bon says:

Once I can get her to dance like a monkey (on command) I’ll be filming K8 with this! Thanks, Wil!

### 6 Responses to Multiplication Facts – Sevens

1. T. says:

Lovely example of slowing things down to ‘smell the patterns’, so to speak!

• Bon says:

Thanks, T. I’m glad you enjoyed it!

• Bon says:

Of course! I hope you are able to use it!

2. Great material. I tutor first graders and use exercises that are very similar. Thank you for posting.

• Bon says:

First graders are fun – and so curious. Rock on with your tutoring!

### Math iPad App Numerosity Launches!

The latest and coolest in math games helps kids practice order of operations and other algebra plays. Continue Reading

### Distributive Property Gets Destroyed by the Lattice Method

Tricks to do math are only useful if used by their creator. Do your best to refrain from giving tricks to students. Continue Reading

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