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Building Strength in Numbers by Watching Basketball: Adding & Subtracting Integers

1/23/2024

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​Did you see the NBA game last night where Joel Embiid of the Philadelphia 76ers scored 70 points? That’s a lot of points if you don’t follow basketball. Anyway, the game wasn’t really close in the end – obviously. 

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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Building Strength in Numbers... But Those Darn Letters

5/29/2023

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For many of you things were going great in math – well maybe you'd say "OK" – but things got crazy around 7th grade when one particular thing changed in math class.

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: x + 0 = x
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 x + 0 = x.
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 x?
Because that one little letter, x, which we will call a “variable”, represents ALL numbers, or ANY number. In that equation , we could say that the  could be any number: Any number plus zero equals that same number.
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 x + 7 = 23 actually requires this concept. You would ask What number, when you add 7 to it, becomes 23? Would it be more than 23 or less than 23? If you said LESS, you’re right. Well then, how much less? 7 less! So you would subtract 7 from 23.
But here’s the thing. If you only subtract 7 from 23 your equation would be x + 7 = 16 and that’s different from what we started with.
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 x + 0 which as we know equals ... x.
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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The Question: When am I Ever going to use this?

10/20/2021

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You've asked the question. You've heard someone ask it. You know The Question. 

When am I ever going to use this?

It's a rite of passage that all teenagers ask The Question in their high school math classes. We've all asked it. Maybe it was in Algebra, or maybe it was in Trigonometry, but I know you asked it. I did. 

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Goal Setting #3: Offend Yourself (you read that right)

1/11/2021

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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.

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Goal Setting #2: You should climb Mt. Everest (I did... sort of)

1/3/2021

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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.
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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
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    Mark B. Anderson
    Tutor & Founder
    Strength in Numbers Tutoring  

    I started Strength in Numbers to help people develop their own strength in numbers.   

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