Unit 2
Expressions of Integers
Expressions of Integers
On Sunday, I bought three (3) oranges.
I ate one for lunch.
On Monday, I had two (2) oranges left. I ate one after school for a snack.
On Tuesday, I owned only one (1) orange.
In mathematics, we call these the natural numbers. The set of natural numbers is {1, 2, 3, 4...}
The last orange seemed special. I decided to cook it, with a turkey, for dinner.
On Wednesday, (to my horror) I woke up and realized I had zero oranges left.
No oranges! At all! (where can I get some more oranges??)
If we put zero into the set of natural numbers, we call this the set of whole numbers. The set of whole numbers is {0, 1, 2, 3, 4...}
By definition, a line goes on forever in both directions. Numbers can get infinitely bigger and infinitely smaller. There is no highest number and there is no lowest number.
On Thursday...
Theoretically, if Jerry would keep letting Mr. Barnes borrow oranges, Mr. Barnes could have (-2) oranges on Friday, (-3) oranges on Saturday, (-4) oranges on Sunday and so on, until Jerry just puts his paw down and tells Mr. Barnes "PLEASE BUY YOUR OWN ORANGES I AM NOT AN ORANGE TREE."
If we look at the other side of zero on the number line, we are looking at the opposites of the natural numbers. We call the set of all the whole numbers and their opposites the set of integers. The set of integers is {...-3, -2, -1, 0, 1, 2, 3...}
Integers can be positive, negative, or zero.
You can most easily visualize negative numbers as a debt. If you get a birthday check for fifty dollars and put it in the bank, the bank will tell you that you have 50 dollars. If you spend 65 dollars, you are adding a (-65) onto your bank account. You will end up with a debt of 15 dollars, or you have exactly (-15) dollars. The bank will then probably penalize you 35 dollars. In other words, they will add a (-35) dollar charge to your account and you will have (-50) dollars. What a bummer of birthday! Better luck next year.
By the way: 50 dollars is the opposite of (-50) dollars. More on that in the next lesson.
But what about all the numbers
in between each integer?
We can put these numbers into two groups:
rational numbers and irrational numbers.
We will go more into depth into
rational numbers during Unit 6
and you will explore the wonders
of irrational numbers in 7th and 8th grade
(numbers that never stop or repeat??
That's madness).
in between each integer?
We can put these numbers into two groups:
rational numbers and irrational numbers.
We will go more into depth into
rational numbers during Unit 6
and you will explore the wonders
of irrational numbers in 7th and 8th grade
(numbers that never stop or repeat??
That's madness).
Notebook:
Classwork & Homework:
-- EngageNY
California Standards
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
CCSS.Math.Content.6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
CCSS.Math.Content.6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.