What name would you give each table? How would you fill in the missing numbers? What patterns do...

What name would you give each table? How would you fill in the missing numbers? What patterns do you see in the tables?

Warm-Up: September 8, 2014

The Tables of Arithmetic

Investigation 1ASections 1.01-1.05

How many numbers are there between zero and ten?

Question

How would you show the number 3? How would you show the number -2? How can a number line help you do math?

We will discuss number lines in more detail in Investigation 1B.

Number Lines

What is the opposite of 5?

What is the opposite of -5?

“Negative” means the same as “opposite of.”

Opposite Numbers

Extended Addition Table

Extended Multiplication Table

Represented by a capital ℤ

Integers

...,5,4,3,2,1,0,1,2,3,4,5...,

Commutative Property:◦ Order of addition does not matter

Associative Property:◦ When you add more than two numbers, the way

you group them does not matter.

Additive Identity:◦ When you add zero to any number, the result is

the number itself.◦ The number 0 is the additive identity.

Properties of Addition

Commutative Property:◦ Order of multiplication does not matter

Associative Property:◦ When you multiply more than two numbers, the

way you group them does not matter.

Multiplicative Identity:◦ When you multiply 1 by any number, the result is

the number itself.◦ The number 1 is the multiplicative identity.

Properties of Multiplication

Read Investigation 1A (pages 8-31) Page 33 #1-8 Read Investigation 1B (pages 34-52)

Assignment