Unit 1: Arithmetic to Algebra 1.9 Number Line Addition

Any Order Any Grouping (AOAG) Easy way to remember Commutative Property and Associative property Basically what it says is that when adding or multiplying we can multiply by grouping or ordering the terms in any manner we please 5 + 4 = 4 + 5 4 + (3 + 5) = (4 + 3) + 5 5  4 = 4  5 5  (3  4) = (5  3)  4

Number Line Addition How 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? 1 2 3 4 5 6 7 -4 -3 -2 -1 -6 -5 8 +4.5 +3.5

Example 2 7 + (-2) 1 2 3 4 5 6 7 -4 -3 -2 -1 -6 -5 8 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? +7 -2 1 2 3 4 5 6 7 -4 -3 -2 -1 -6 -5 8 -2 7

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

Homework How 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 - 50 Core: 7, 8, 9, 10, 11 Optional: 12,13