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Transcript
```Unit 1: Arithmetic to Algebra
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
5+4=4+5
 4 + (3 + 5) = (4 + 3) + 5
54=45
 5  (3  4) = (5  3)  4
 How do we represent 4.5 + 3.5 on a number line?
-6
-5
-4
-3
-2
-1
0
1
2
3
4
+4.5
 Is there another way we can represent this addition?
 What if we started the arrow for 3.5 at 0?
5
6
+3.5
7
8
Example 2
-6
-5
-4
-3
7 + (-2)
-2
-1
0
1
2
3
4
5
6
7
8
4
5
6
7
8
+7
-2
-6
-5
-4
-3
-2
-1
0
1
2
3
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?
 How can you represent 0 as an arrow?
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
 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.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
6
7
8
 How can we use the number line to demonstrate that:
7 + -2 = -2 + 7, BUT 7 - 2 ≠ 2 – 7?
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
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