1. Investigation 2.1 Drawing Wumps Stretching & Shrinking
What is a WUMP?
Let's find out!

2. Zach and Marta’s computer game involves a family called the Wumps
Zach and Marta’s computer game involves a family called the Wumps. The members of the Wump family are various sizes, but they all have the same shape. That is, they are similar. Mug Wump is the game’s main character. By enlarging or reducing Mug, a player can transform him into other Wump family members.
Zack and Marta experiment with enlarging and reducing figures on a coordinate grid. First, Zack draws Mug Wump on graph paper.

3. Mug Wump This is Mug Wump! Yeah! Yeah! Yeah! Rule (Point) (x, y) A
(0, 1) B
(2, 1) C
(2, 0) D
(3, 0) E
(3, 1) F
(5, 1) G
(5, 0) H
(6, 0) I
(6, 1) J
(8, 1) K
(6, 7) L
(2, 7) M
START OVER
Rule
(Point)
(x, y) N
(2, 2) O
(6, 2) P
(6, 3) Q
(2, 3) R
START OVER S
(3, 4) T
(4, 5) U
(5, 4) V W
(2, 5) (make a dot) X
(6, 5) (make a dot)
This is Mug Wump!
Yeah!
Yeah!
Yeah!

4. Let’s make the other Wump family members! Who do you want to draw first? Zug Lug Bug Glug
Click here
when the
Wump
family is
complete!

5. Zug This is Zug! The rule for Zug is (2x, 2y)
(Point)
(x, y)
(2x, 2y) A
(0, 1)
(0, 2) B
(2, 1)
(4, 2) C
(2, 0)
(4, 0) D
(3, 0)
(6, 0) E
(3, 1)
(6, 2) F
(5, 1)
(10, 2) G
(5, 0)
(10, 0) H
(12, 0) I
(6, 1)
(12, 2) J
(8, 1)
(16, 2) K
(6, 7)
(12, 14) L
(2, 7)
(4, 14) M
START OVER
The rule for Zug is (2x, 2y)
Which means that you must multiply each x value and y value in the coordinate pair by 2. This will give you the coordinate pairs for Zug.
GOODLUCK!
This is Zug!
Rule
(Point)
(x, y)
(2x, 2y) N
(2, 2)
(4, 4) O
(6, 2)
(12, 4) P
(6, 3)
(12, 6) Q
(2, 3)
(4, 6) R
START OVER S
(3, 4)
(6, 8) T
(4, 5)
(8, 10) U
(5, 4)
(10, 8) V W
(2, 5) (make a dot)
(4, 10) (make a dot) X
(6, 5) (make a dot)
(12, 10) (make a dot)
Yeah!
Yeah!
Yeah!

6. Is Zug a member of the Wump family or is he an imposter
Is Zug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER!
YES NO
Zug
Mug Wump

7. Zug IS a member of the Wump family!
GREAT JOB!
but WHY?

8. but WHY?
Zug Wump
Mug Wump
Let’s try
another
family
member!

9. Lug This is Lug! The rule for Lug is (3x, y)
(Point)
(x, y)
(3x, y) A
(0, 1) B
(2, 1)
(6, 1) C
(2, 0)
(6, 0) D
(3, 0)
(9, 0) E
(3, 1)
(9, 1) F
(5, 1)
(15, 1) G
(5, 0)
(15, 0) H
(18, 0) I
(18, 1) J
(8, 1)
(24, 1) K
(6, 7)
(18, 7) L
(2, 7) M
START OVER
The rule for Lug is (3x, y)
Which means that you must multiply each x value in the coordinate pair by 3 and each y value in the coordinate pair by 1. This will give you the coordinate pairs for Lug.
GOODLUCK!
Rule
(Point)
(x, y)
(3x, y) N
(2, 2)
(6, 2) O
(18, 2) P
(6, 3)
(18, 3) Q
(2, 3) R
START OVER S
(3, 4)
(9, 4) T
(4, 5)
(12, 5) U
(5, 4)
(15, 4) V W
(2, 5) (make a dot)
(6, 5) (make a dot) X
(18, 5) (make a dot)
This is Lug!
Yeah!
Yeah!
Yeah!

10. Is Lug a member of the Wump family or is he an imposter
Is Lug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER!
YES NO
Mug Wump
Lug

11. Lug IS NOT a member of the Wump family!
IMPOSTER!!!
but WHY?

12. but WHY?
Mug Wump
Lug
Let’s try
another
family
member!

13. Bug This is Bug! The rule for Bug is (3x, 3y)
(Point)
(x, y)
(3x, 3y) A
(0, 1)
(0, 3) B
(2, 1)
(6, 3) C
(2, 0)
(6, 0) D
(3, 0)
(9, 0) E
(3, 1)
(9, 3) F
(5, 1)
(15, 3) G
(5, 0)
(15, 0) H
(18, 0) I
(6, 1)
(18, 3) J
(8, 1)
(24, 3) K
(6, 7)
(18, 21) L
(2, 7)
(6, 21) M
START OVER
This is Bug!
The rule for Bug is (3x, 3y)
Which means that you must multiply each x value and y value in the coordinate pair by 3. This will give you the coordinate pairs for Bug.
GOODLUCK!
Rule
(Point)
(x, y)
(3x, 3y) N
(2, 2)
(6, 6) O
(6, 2)
(18, 6) P
(6, 3)
(18, 9) Q
(2, 3)
(6, 9) R
START OVER S
(3, 4)
(9, 12) T
(4, 5)
(12, 15) U
(5, 4)
(15, 12) V W
(2, 5) (make a dot)
(6, 15) (make a dot) X
(6, 5) (make a dot)
(18, 15) (make a dot)
Yeah!
Yeah!
Yeah!

14. Is Bug a member of the Wump family or is he an imposter
Is Bug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER!
YES NO
Bug
Mug Wump

15. Bug IS a member of the Wump family!
GREAT JOB!
but WHY?

16. but WHY?
Bug Wump
Mug Wump
Let’s try
another
family
member!

17. Is Glug a member of the Wump family or is he an imposter
Is Glug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER!
YES NO
Mug Wump
Glug

18. The rule for Glug is (x, 3y)
(Point)
(x, y)
(x, 3y) A
(0, 1)
(0, 3) B
(2, 1)
(2, 3) C
(2, 0) D
(3, 0) E
(3, 1)
(3, 3) F
(5, 1)
(5, 3) G
(5, 0) H
(6, 0) I
(6, 1)
(6, 3) J
(8, 1)
(8, 3) K
(6, 7)
(6, 21) L
(2, 7)
(2, 21) M
START OVER
This is Glug!
The rule for Glug is (x, 3y)
Which means that you must multiply each x value in the coordinate pair by 1 and each y value in the coordinate pair by 3. This will give you the coordinate pairs for Glug.
GOODLUCK!
Rule
(Point)
(x, y)
(x, 3y) N
(2, 2)
(2, 6) O
(6, 2)
(6, 6) P
(6, 3)
(6, 9) Q
(2, 3)
(2, 9) R
START OVER S
(3, 4)
(3, 12) T
(4, 5)
(4, 15) U
(5, 4)
(5, 12) V W
(2, 5) (make a dot)
(2, 15) (make a dot) X
(6, 5) (make a dot)
(6, 15) (make a dot)
Yeah!
Yeah!
Yeah!

19. Glug IS NOT a member of the Wump family!
IMPOSTER!!!
but WHY?

20. but WHY?
Mug Wump
Glug
Let’s try
another
family
member!

21. Look at those again!
Remember they must have the same shape. The only difference can be their size!
Click to
try again

22. The Wump Family thanks you!
Mug Wump
Bug Wump
Zug Wump

23. (4x,3y) Would this rule create a Wump or an imposter? How would the
rule change Mug?

25. (2x,2y) Would this rule create a Wump or an imposter? How would the
rule change Mug?

27. (1.5x,1.5y) Would this rule create a Wump or an imposter?
How would the
rule change Mug?

29. (3x,y) Would this rule create a Wump or an imposter? How would the
rule change Mug?