1. Patterns, Functions and Magic Pots
Two of Everything
Patterns, Functions and Magic Pots

2. Chinese Folktale about Mr. and Mrs. Haktak who buy a magic pot
The magic pot doubles everything that is put in it
They multiply their belongings and everything is fine until………

3. Mrs. Haktak is hugging the pot one day and falls in it – then there are two Mrs. Haktaks
The two women fight over Mr. Haktak and he trips, falls into the pot and….
There are now two Mr. Haktaks
Everything they own is duplicated and they have ready made friends!
They live happily ever after.

4. So how can we use this book to help us develop algebraic thinking?
The magic pot turns into a function machine
One object goes in – the value of it changes in the pot
The “rule” of the pot can change – it doesn’t have to double each time.

5. Mr. and Mrs. Haktaks Magic Pot+2
x 2

6. From this we can now make a T-chart from the Haktak’s Magic PotIn
Out 1 2 4 3 6 12 24
The Out number is equal to the In number added to itself. OR
The Out number is equal to the In number times “2”.

7. Another variation----?
What is the rule?

8. What is the rule?
x 3

9. T-chart In
Out 2 3 12 6 9 36

10. Now let’s introduce the concept of variables here – Let’s make “In” =
From the Haktak’s Pot
Now let’s introduce the concept of variables here –
Let’s make “In” =
And “Out” = In
Out 1 2 4 3 6

11. What does this look like in equation form?= + OR x 2 =

12. What about our 2nd Magic Pot?x 3 =

13. Let’s make a new rule for the pot1 3 2 5 7 4 9 5 11 6 13 7 15 41

14. Do I need to add anything?
What is the rule?
+ 1 = + OR ( )
x 2
+ 1 =
Do I need to add anything?

15. Tricky Rule 1
1 ½ 2 3
2 ½ 4 3 5
3 ½ 6 4 7
4 ½
What is the rule here?

16. Hmmmmm ………… =
÷ 2 + 1 ( )

17. Representations of algebraic thinking and their relationships
Table
Algebraic Formula
Graph
Concrete
or Pictorial
Verbal Description

18. Choose one of the examples from our presentation and make sure that each the following is represented from the data. Create what is missing.
Table
Algebraic Formula
Verbal Description
Concrete/Pictorial
Graph

19. Let’s Improve a Math Lesson
Lesson from Wetpaint