1.9 Number Line Addition

Unit 1: Arithmetic to Algebra

Any Order Any Grouping (AOAG)Easy way to remember Commutative

Property and Associative propertyBasically what it says is that when adding

or multiplying we can multiply by grouping or ordering the terms in any manner we please5 + 4 = 4 + 54 + (3 + 5) = (4 + 3) + 55 4 = 4 55 (3 4) = (5 3) 4

Number Line AdditionHow do we represent 4.5 + 3.5 on a number line?

Is there another way we can represent this addition?

What if we started the arrow for 3.5 at 0?

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

+4.5 +3.5

Example 2 7 + (-2)

What is different about the arrow for positive and negative numbers?

Are there any numbers we cannot represent in this way? Why does addition with negative numbers use arrows going

left? How does addition with arrows represent the AOAG

properties? Select different numbers; do the AOAG with those numbers

as well? What about -3 and -5.5?

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

+7-2

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

7 -2

How can you represent 0 as an arrow?

How do we arrange the arrows when doing addition on the number line? Compare and contrast what happens when we do this with positive and negative numbers.

How can we use the number line to demonstrate that:

7 + -2 = -2 + 7, BUT 7 - 2 ≠ 2 – 7?

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

0 1 2 3 4 5 6 7-4 -3 -2 -1-6 -5 8

HomeworkHow can we use the number line to model

AOAG properties?How is adding using the number line similar to

and different from adding using the addition table?

Page 49 - 50Core: 7, 8, 9, 10, 11Optional: 12,13