POP ‘Rules’Before we investigate some rules about pop-ifying, we need to know what it means to pop-ify!

Get into groups of 4. Explore the table below.

⊙ 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

3 4 5 6 7 8 9 10 11

5 6 7 8 9 10 11 12 13

7 8 9 10 11 12 13 14 15

9 10 11 12 13 14 15 16 17

11 12 13 14 15 16 17 18 19

13 14 15 16 17 18 19 20 21

15 16 17 18 19 20 21 22 23

17 18 19 20 21 22 23 24 25

19 20 21 22 23 24 25 26 27

Write an expression for a⊙b. Explain how you reasoned to this expression.

a⊙b =

Evaluate: ! 10⊙5! 21⊙23! a⊙a

✦ Number yourselves off 1 to 4. Get into your expert groups.✦ In your expert group, investigate the given expressions and come up with a general rule for each.✦ When instructed to do so, return to your initial group and explain the rules you discovered.

✦ Using the concept of pop-ifying, investigate each expression and develop a general rule expressed in terms of ⊙.

✦ Explain your reasoning.

a × k( ) b × k( )

akbk

✦ Using the concept of pop-ifying, investigate each expression and develop a general rule expressed in terms of ⊙.

✦ Explain your reasoning.

a + c( ) b + d( )

a + k( ) b + k( )

a − c( ) b − d( )

a − k( ) b − k( )

✦ Using the concept of pop-ifying, investigate each expression and develop a general rule expressed in terms of ⊙.

✦ Explain your reasoning.

a 0

0 a

a1

1 a

✦ Using the concept of pop-ifying, investigate each expression and develop a general rule expressed in terms of ⊙.

✦ Explain your reasoning.

even even

even odd

odd even

odd odd