Integer Basics

The lesson below is still images taken from the fully animated PowerPoint I created that is available in my Teachers Pay Teachers store page. If the PowerPoint is not one of my freebies, you may also head over to my YouTube channel to see the slideshow fully animated and can pause as needed to be sure you grasp each concept before moving forward (each lesson will always be free there!).

This lesson will introduce the idea of integers (our group of Positive and Negative whole numbers). Each slide will go through how to recognize integers as well as their locations on the number line. We then transition into what it means for a number to be negative and how to find the absolute value of any number.

So without further ado, read through the slides below to get a feel for what integers are, how they work, and how to go about familiarizing yourself with their locations in respect to one another!

Integers Basics

Integers Basics 2

Integers Basics 3Integers Basics 4Integers Basics 5Integers Basics 6Integers Basics 7Integers Basics 8Integers Basics 9Integers Basics 10Integers Basics 11Integers Basics 12Integers Basics 13Integers Basics 14

Phew, that’s a lot to take in. Once you’ve gone over this and found some practice problems to cement the idea in your head what integers are, you may move on to the next lesson below!

Adding and Subtracting Integers

Just in case the slides aren’t your thing, here is a text outline of the main points of the lessons above!

  • Integers
  • An introduction
  • Objectives
  • By the end of this lesson you should feel comfortable:
  • Identifying positive and negative numbers
  • Finding the absolute value of a number
  • Utilizing integers to represent values in real-world scenarios
  • What are Integers?
  • You are hopefully familiar with numbers at this point and how to use them to count.
  • Even the concept of zero isn’t a crazy idea anymore!
  • Numbers get larger and larger as they proceed on a number line:
  • But lines go forever in both directions!
  • What does that mean for numbers?
  • What can be less than 0?
  • Negative numbers!
  • What are integers?
  • So we know positive numbers, the ones you have already seen, grow larger and larger forever as we follow the number line to the right.
  • Notice the negative numbers are getting bigger and bigger as we follow left along the line.
  • But don’t let this fool you!
  • Larger negative numbers are still less than positive numbers.
  • The value of numbers decreases the farther left we go on the number line.
  • What are Integers
  • But doesn’t that leave one specific number out?
  • Anything?
  • Something between the positive and negative numbers perhaps?
  • Ah yes, ZERO!
  • Zero is neither positive nor negative, which we will see as we begin to use these numbers.
  • Together the set of positive and negative numbers along with zero are called integers.
  • Integers in Real Life
  • Alright, so now we’ve got all these positive and negative numbers, what are they used for?
  • Let’s talk about elevation:
  • As you can see in this AMAZING drawing by yours truly, we have the sea and some land next to it.
  • The land dips down and then shoots up.
  • Elevation is given in terms of sea level, or even with the water.
  • So if we want a point of land at its lowest:
  • How far down is that?
  • Or perhaps the highest point:
  • How far above sea level is this?
  • Integers in Real life
  • This is where integers are useful for designating direction in relation to a point.
  • Both positive and negative numbers are a distance from a center point, which we call ZERO.
  • In our sea level situation, we assume the sea is at 0.
  • Thus our low point would be:
  • Or 10 meters below sea level.
  • And our highest point would be:
  • Or 15 meters above sea level
  • Another example
  • Perhaps sea level just isn’t your thing, so how about another way of looking at things?
  • Ever heard of money? Yeah? Well what a coincidence.
  • Integers are great at helping figure out pretty much any situation where money is involved, regardless of the currency in your country of residence.
  • For instance:
  • Let’s say you are selling lemonade.
  • You’re going to earn money for every glass you sell.
  • But you’re also going to lose money when you buy stuff to make the lemonade.
  • Another example
  • As you can see from another artistic masterpiece to the right, your supplies cost $10.
  • This would be a negative value because it is money you are losing.
  • But all is not lost! You now get to sell your lemonade.
  • As the sign says, you sell lemonade for $1 per cup.
  • Assuming you sell 25 cups, you earned $25.
  • This will be a positive number because it is money you acquired or gained.
  • Absolute value
  • Later we will return to our lemonade stand to figure out if we earned a profit, but for now we have one more topic to discuss.
  • The absolute value of a number is its distance from the center, or zero.
  • Hmmm, math speak. Let’s look at a number line.
  • Say we want to look at -3.
  • The absolute value of -3 looks like this: |-3| where the bars mean “absolute value of.”
  • On the number line we can observe what this actually denotes as a distance.
  • Starting at 0, we move 3 to the left to get to -3.
  • Absolute value
  • Alight, then let’s try another point.
  • How about |3|?
  • Our point is 3, so:
  • And how far do we travel from 0?
  • So our distance is 3 again.
  • |-3| = 3 and |3| = 3
  • This is because the distance to either is 3 away from 0.
  • Thus another way to think about absolute value is it always spits out a positive of what goes in.
  • Opposites
  • It is interesting that |-3| = |3| = 3. So what does this mean?
  • Let’s return to our number line yet again.
  • -3 is here.
  • And 3 is here.
  • And both are the same distance away from zero.
  • Thus we can say -3 and 3 are opposites.
  • Any number and the negative of that number are opposites of one another.
  • This idea will be important later, so keep in mind that negative can mean opposite!
  • Comparisons
  • Alright, so then let’s put it all together and try comparing some integers!
  • Which is larger, -3 or 3?
  • Negative numbers are always less than positive numbers so:
  • *Remember that < denotes less than and > is greater than.
  • Alright, how about different numbers?
  • 10 is larger than 2, but:
  • Negative numbers are smaller than positive ones because they are farther to the left on the number line.
  • Comparisons
  • Excellent! Now for some absolute values thrown in!
  • How would |-10| compare to 3?
  • While it is true that negative numbers are smaller than positive numbers:
  • The absolute value of -10 is 10, so we can actually imagine this problem like this to help visualize what it is asking:
  • One more. How would |-3| compare to |3|?
  • Remember that |-3| = 3 and |3| = 3, so:
  • Conclusion
  • Integersthe set of positive and negative whole numbers and zero.
  • Numbers decrease as you travel left along a number line and grow as you travel right.
  • The larger a negative number becomes, the smaller its value is.
  • Zero is neither positive nor negative.
  • Absolute Valuethe distance a number is from zero.
  • The absolute value of any number, positive or negative, is ALWAYS positive.
  • A positive number and negative number with the same absolute value are opposites of one another.
Advertisements