But in the first half, it WAS close. The other team, the San Antonio Spurs were actually ahead for a while. Then Philadelphia scored and went ahead, but San Antonio went on a run themselves and retook the lead. In the end the Sixers pulled ahead because that one guy Embiid went crazy and scored 70 which hasn’t been done in a long, long time. You get the picture.

Let’s say your team was the Sixers and the score at one point is 14 to 10 with the Sixers ahead. Subtract those two numbers, 14 – 10 and you get 4. But what if the Spurs score 5 straight points with the Sixers scoring any.

If you think about it, does the actual score make any difference? What matters is who’s ahead.

So what happens to your team’s lead of 4 points if the OTHER team scores 5 straight points? Well, pretty clearly your team is not ahead any more. The other team scored enough not just to TIE, but to go AHEAD and take the lead. It would be 4 + -5 = -1.

Obviously, you could still just add the 5 to the Spurs 10 when it was 14 to 10, and get 15 for them so it was now 14 to 15. And you can see again THIS way your team is indeed down by a point.

By the way, most fans will say the higher number first, like 15 to 14 or even just 15-14, but then say who’s ahead. So 14-10 Sixers, but wait now it’s 15-14 Spurs.

If we’re down a point remember that’s like -1. What if we score a 3-pointer? We’ve gone from down one to being ahead – but by how much? One of the three points from the 3-pointer brought us from down one to being tied, but there’s two more points left from the 3 pointer. 3 – 1 = 2. So now we’re ahead by 2.

But what if when we were down by one the OTHER team scored a 3-pointer? We can’t be ahead after THAT. How do you do that?

Because we were already down, and then you could say went down some MORE – because the other team scored – we could just add the two deficits together, the one point down and the three pointer. 1 + 3 = 4.

So the answer is positive 4? Nope, NEGATIVE 4. You CAN just rearrange the signs and move the numbers around just like that, putting the negative on the 4 because you know it has to be.

Now what if the numbers are bigger? Same thing.

Recently the Charlotte Hornets, one of the worst teams in the league I might add, was losing to the Minnesota Timberwolves, one of the best teams in the league – by 18. The score was 107-89. The Hornets finished the game strong, outscoring the Timberwolves by 21.

So did they come back and win? Yes, they did. They were down 18 and scored MORE than 18 to take the lead. The problem would be -18 + 21 = 3.

If you ignore the signs for a second and just look at the numbers without the signs – what math teachers call the number’s absolute value, by the way – you see easily that 21 is greater than 18. And you will know the answer is – like the 21 – positive. So +3 is the answer, and the final difference in the score of the game.

But what if the Hornets comeback fell just short? What if it was -18 + 17? They would’ve been down 18 and outscored the Wolves by 17 to finish the game – BUT it wouldn’t have been enough. The Hornets would’ve still lost, by just one point. Why? Because -18 + 17 = -1.

Now I did say the Hornets were one of the worst teams in the league so what if – like too many of the rest of their games this season – they were down by 18 and for the rest of the game got outscored by another 12 points? That would be -18 + -12 = -30.

OK, that’s it for now. If you made it this far, I salute you. Keep in mind that listening to or reading “math talk” like this will make your brain stronger even if you don’t fully get it yet.

So keep going and don't give up, don't ever give up!

Remember, every problem you try, every blog you read, is building YOUR strength in numbers.

Thanks for learning.

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Letters.

Letters started to replace numbers! I know you asked, Why are there letters in math???

Great question. Let’s look at an example. Yes, one with a letter in it. Grab a pencil and paper. Pause here if you need to, but come back. It’s important that you participate. As I like to say, math is not a spectator sport.

OK, write down this short equation:

A quick note before I continue: most math teachers would agree starting with numbers, looking for patterns and then writing equations like this is the best way to approach teaching.

So why am I starting with an equation with a letter in it??

Because this is the problem you face in math. The letters are thrown at you and POW you’re confused. I am going to show you how to make sense of those stubborn little equations with letters. Then the next time you see one you’ll know what to do.

OK, so

Maybe you’ve seen that before. Perhaps it was last week or 20 years ago, who knows. I can almost hear you groaning. And that um, yearning, you feel for actual numbers is good. Use that. In fact, write these other equations directly below the first equation.

2 + 0 = 2

10 + 0 = 10

57 + 0 = 57

OK, that’s enough. If you didn’t align them one directly under another, take a minute and do it again. Don’t bother erasing.

I think we can all agree these numerical equations are pretty obvious. I mean if you have $10 and you earn $0 you have $10.

But we come back to the big question: why replace the numbers with

Because that one little letter,

I like to say that the variable is “able to vary”.

Get it? Variable… “able to vary”.

So why is a simple equation like even a thing? It’s so obvious. What’s the point? It turns out that little equations like that are tremendously important in more complex math like algebra and even calculus.

What is the one number you can add to ANY number and the result is the same as what you started with? You guessed it – ZERO!

So we could add ZERO to anything and not change its value. In math class you will hear the word identity; identity means value.

An equation like

But here’s the thing. If you only subtract 7 from 23 your equation would be

You should subtract 7 from the left-hand side of the equation as well, which gives you x + 7 – 7.

But of course 7 – 7 = 0 so the equation would be

And in this case x = 16. And you have solved the equation.

There you have it, the first episode of Strength in Numbers.

You learned what a variable is and how they represent any number.

You explored that in an example you will definitely see in math class.

Finally, if you didn’t follow everything here that’s OK. Be encouraged. Your brain is powerful! Listening to this even once will help you make new connections whether or not you fully master it. And that helps you develop understanding and build confidence.

Now YOU have Strength in Numbers.

Thanks for learning.

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It's a rite of passage that all teenagers ask

Quick poll for adults: raise your hand if you've used the Quadratic Formula anytime in the last 10 years.

(If you did, please tell your story in the comments below.)

As a high school math teacher I field**The Question** all the time. As a rule, I have three (yes, 3) short answers and one long answer.

Short Answer #1: One of my best students ever, Duy, gave the following answer when someone in his class posed**The Question:** "Friday. You'll use this on the test Friday."

Sure enough, there's logic in that snarky, snappy answer. You need to pass your math classes to graduate, and to do that you need to pass your tests.

Short Answer #2: Never. You're right, you are not going to use the Quadratic Formula unless you're teaching math. OK, yes, an engineer may employ the concept but certainly they are using software to handle the calculations.

Before I share Short Answer #3, let's look at the long answer.

While you won't likely use the Quadratic Formula in everyday life, you will encounter problems in any job or business that require you to slog through really__boring__ __tediousness__ of your work. Allow me to expand on that ... in two parts. (Didn't I mention this would be long?)

The first part of my long answer I give my students in response to**The Question**: there may come a day when you suffer __boredom__ in a job or in whatever business you run, so if you can find a way to slog through the __monotony__ and understand something admittedly kinda boring like the Quadratic Formula and *in the process *develop __perseverance,__ then you will be better prepared to do the boring things you'll have to do as an adult.*

The 2nd part of my long answer I give my students in response to**The Question**: there may come a day when you suffer __tediousness__ in a job or in whatever business you run, so if you can find a way to slog through the __details__ and understand something admittedly pretty tedious like the Quadratic Formula and *in the process *develop __intelligence,__ then you will be better prepared to do the tedious tasks you'll have to do as an adult.**

Now (finally) Short Answer #3 to**The Question**, *When am I ever going to use this?*

Short Answer #3: Everyday of your life.

You see, you WILL use__perseverance__ and __intelligence__ everyday of your life. Yep, even as you learn the Quadratic Formula, you are learning and developing both __perseverance__ and __intelligence,__ even if you don't use the formula ever again in real life.

Now you might be thinking*well, I'm just not a math person - I just don't get it.*

And that, my friends, leads us to the next BIG QUESTION ...**What if I don't get it?**

(If you did, please tell your story in the comments below.)

As a high school math teacher I field

Short Answer #1: One of my best students ever, Duy, gave the following answer when someone in his class posed

Sure enough, there's logic in that snarky, snappy answer. You need to pass your math classes to graduate, and to do that you need to pass your tests.

Short Answer #2: Never. You're right, you are not going to use the Quadratic Formula unless you're teaching math. OK, yes, an engineer may employ the concept but certainly they are using software to handle the calculations.

Before I share Short Answer #3, let's look at the long answer.

While you won't likely use the Quadratic Formula in everyday life, you will encounter problems in any job or business that require you to slog through really

The first part of my long answer I give my students in response to

The 2nd part of my long answer I give my students in response to

Now (finally) Short Answer #3 to

Short Answer #3: Everyday of your life.

You see, you WILL use

Now you might be thinking

And that, my friends, leads us to the next BIG QUESTION ...

My Mom made me run cross country at Cary High School. I wasn't the fastest but I'm so glad she made me do it. Thanks, Mom. Junior year I enjoyed running so much I ran track too. I still love running to this day and have even run a few half marathons and one full (not recommended). I also love running since there are no ridiculous obstacles like hurdles to block my path, just the open trail and the track ahead. Never understood hurdles. Running not hard enough for ya? Hurdlers say Let's add an obstacle every 10 yards! I guess they need a challenge? Or maybe they see the hurdle as an athletically poetic metaphor for life? |

While I don't love hurdles on the track, I see the hurdle as a nice metaphor for goal setting.

If you ever ever tried hurdling, how low would you want the hurdle to be on your first try? Pretty low, I'd guess. And maybe after a few tries, a smidgen higher so there's *some* challenge to it. But why start out as a new hurdler at the standard height? I'd be sure to crash and burn.

See, we all set a goal of some sort this time of year. The question is*How do we set the perfect goal?*

We've all set the standard goals: I am going to do lose weight, read more, or save more. How much success have we had with those?

For 2020 mine was to read 20 books in a year, and to pick them from my stack on the bookshelf. (OK I have another stack on my bedside table. And another on my desk, but anyways.)

See, we all set a goal of some sort this time of year. The question is

We've all set the standard goals: I am going to do lose weight, read more, or save more. How much success have we had with those?

For 2020 mine was to read 20 books in a year, and to pick them from my stack on the bookshelf. (OK I have another stack on my bedside table. And another on my desk, but anyways.)

But if I ask myself, *am I really going to do that?* The honest answer is *No*.

We have to be honest with ourselves. So, I drop my target number. Lower the hurdle! Yes, it's humbling. But it's better.

Now just how low do you go? (Maybe the limbo is another applicable metaphor.)

You offend yourself. Let me explain.

I'll ask myself*C**an I read 2 books in a year?* Geez. Seriously?! Of course I can read 2 books over the course of a whole year. *OK, how about 3?* Definitely. *How about 5 then*? Sure. *8? I think I can do that. 10? *Ummmm... yes. * *

Start from the bottom up, and see what offends you. Then, slowly raise the "hurdle" height - your goal - to a manageable level, then up one more notch. You'll see how you start feeling uncomfortable as the goal gets higher and higher. I ended up reading just 11 out of the 20 I planned to read in 2020 so I learned 20 was too high. And my new goal to read 14 books in 2021 is humbling a bit since I had high hopes last year.

We will set our goal at the perfect "height" or the perfect target number if it's between manageable and a bit of a stretch, but not so high that we're guaranteed to fail.

We have to be honest with ourselves. So, I drop my target number. Lower the hurdle! Yes, it's humbling. But it's better.

Now just how low do you go? (Maybe the limbo is another applicable metaphor.)

You offend yourself. Let me explain.

I'll ask myself

Start from the bottom up, and see what offends you. Then, slowly raise the "hurdle" height - your goal - to a manageable level, then up one more notch. You'll see how you start feeling uncomfortable as the goal gets higher and higher. I ended up reading just 11 out of the 20 I planned to read in 2020 so I learned 20 was too high. And my new goal to read 14 books in 2021 is humbling a bit since I had high hopes last year.

We will set our goal at the perfect "height" or the perfect target number if it's between manageable and a bit of a stretch, but not so high that we're guaranteed to fail.

In the classic movie White Christmas, Bing Crosby makes extravagant plans for a big holiday show and says "Wow" when told the price tag. Overhearing this exchange, his partner Danny Kaye asks despairingly, "How much is 'Wow'"? __Crosby responds__, "It's right in between 'ouch' and 'boing'".

Exactly. Our goals should be a little "Ouch" or a little humbling since we perhaps haven't achieved this new level before. But it should be below "Boing" too, not bouncing too far beyond what we can achieve.

Now it's your turn to offend yourself. As you raise the bar, you'll start to fee uncomfortable, and you're close at that point. You'll find that perfect target. Think of this skill of offending yourself and adjusting your goal as a newfound strength in*manipulating *numbers. Then go out and run over that hurdle.

Next post: Remember the Why! Keeping at the forefront of your mind the*reason *for having a goal in the first place is tantamount to achieving it.

P.S. Consider giving yourself a__head start__ as you consider your next goal.

Mark B. Anderson

Tutor & Founder, Strength in Numbers Tutoring

]]>Exactly. Our goals should be a little "Ouch" or a little humbling since we perhaps haven't achieved this new level before. But it should be below "Boing" too, not bouncing too far beyond what we can achieve.

Now it's your turn to offend yourself. As you raise the bar, you'll start to fee uncomfortable, and you're close at that point. You'll find that perfect target. Think of this skill of offending yourself and adjusting your goal as a newfound strength in

Next post: Remember the Why! Keeping at the forefront of your mind the

P.S. Consider giving yourself a

Mark B. Anderson

Tutor & Founder, Strength in Numbers Tutoring

It was March 2014 and I had pretty much oozed into my chair at work. Hadn't worked out much if at all. Whatever New Year's resolutions I had set for improving fitness had faded away a couple months earlier.

So I decided to climb Mount Everest.

One of the wellness guys in my office said that the simple act of taking the stairs was a great way to get your heart rate up and improve fitness. But there was a problem. Starting up a habit like taking the stairs - to the 10th floor - wasn't just going to happen like a big bang.

Nope, I wasn't internally motivated to do it just because it was healthy. Maybe you can relate.

I needed to shape a goal that was fun and memorable and even inspiring. Technically speaking, I needed to quantify my goal. That's the "M" in S.M.A.R.T. goal setting. I needed to make my stair-stepping goal Measurable.

When you have to measure something what do you turn to? A ruler, of course. So I grabbed my ruler and measured one step in the stairwell. After a few calculations I figured I would need to climb 49,764 stairs to say I climbed Mount Everest.

OK, the equivalent of Mount Everest... without the snow... and without deadly freezing temperatures. The point is this: I found something that motivated me, and who cares if it's silly.

On Dec 31, 2014 I reached the summit - the locked door of the 13th-floor roof access inside an endless stairwell, echoing my gasps for air. But I did it.

So I decided to climb Mount Everest.

One of the wellness guys in my office said that the simple act of taking the stairs was a great way to get your heart rate up and improve fitness. But there was a problem. Starting up a habit like taking the stairs - to the 10th floor - wasn't just going to happen like a big bang.

Nope, I wasn't internally motivated to do it just because it was healthy. Maybe you can relate.

I needed to shape a goal that was fun and memorable and even inspiring. Technically speaking, I needed to quantify my goal. That's the "M" in S.M.A.R.T. goal setting. I needed to make my stair-stepping goal Measurable.

When you have to measure something what do you turn to? A ruler, of course. So I grabbed my ruler and measured one step in the stairwell. After a few calculations I figured I would need to climb 49,764 stairs to say I climbed Mount Everest.

OK, the equivalent of Mount Everest... without the snow... and without deadly freezing temperatures. The point is this: I found something that motivated me, and who cares if it's silly.

On Dec 31, 2014 I reached the summit - the locked door of the 13th-floor roof access inside an endless stairwell, echoing my gasps for air. But I did it.

Like many goals, it wasn't so much the last step that was so glorious, although it was a good feeling. It was looking back on my spreadsheet seeing all those days when I climbed 400 steps or more.

I had achieved my goal to improve my overall fitness.

What's your Mount Everest?

Share your wild goal for 2021. Or share whatever your raw goal is ("I want to lose weight") and I'll be happy to help you craft your own "Mount Everest" ... "I will lose the equivalent of 25 Big Macs" perhaps?

Next post: Setting*Reasonable* Goals, which kind of sounds like the opposite of this post. You'll have to read and see for yourself.

Mark B. Anderson

Tutor & Founder, Strength in Numbers Tutoring

]]>I had achieved my goal to improve my overall fitness.

What's your Mount Everest?

Share your wild goal for 2021. Or share whatever your raw goal is ("I want to lose weight") and I'll be happy to help you craft your own "Mount Everest" ... "I will lose the equivalent of 25 Big Macs" perhaps?

Next post: Setting

Mark B. Anderson

Tutor & Founder, Strength in Numbers Tutoring