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Investigation 2.1 Investigation 2.1 Drawing Wumps Drawing Wumps Stretching & Stretching & Shrinking Shrinking

Investigation 2.1 Drawing Wumps Stretching & Shrinking

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Investigation 2.1 Drawing Wumps Stretching & Shrinking. What is a WUMP?. Let's find out!. - PowerPoint PPT Presentation

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Page 1: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Investigation 2.1 Investigation 2.1 Drawing WumpsDrawing Wumps

Stretching & ShrinkingStretching & Shrinking

Page 2: Investigation 2.1  Drawing Wumps Stretching & Shrinking

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.

Page 3: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Mug WumpMug WumpRuleRule(Point)(Point)

(x, y)(x, y)

AA (0, 1)(0, 1)

BB (2, 1)(2, 1)

CC (2, 0)(2, 0)

DD (3, 0)(3, 0)

EE (3, 1)(3, 1)

FF (5, 1)(5, 1)

GG (5, 0)(5, 0)

HH (6, 0)(6, 0)

II (6, 1)(6, 1)

JJ (8, 1)(8, 1)

KK (6, 7)(6, 7)

LL (2, 7)(2, 7)

MM (0, 1)(0, 1)

START OVERSTART OVER

RuleRule(Point)(Point)

(x, y)(x, y)

NN (2, 2)(2, 2)

OO (6, 2)(6, 2)

PP (6, 3) (6, 3)

QQ (2, 3)(2, 3)

RR (2, 2)(2, 2)

START OVERSTART OVER

SS (3, 4)(3, 4)

TT (4, 5)(4, 5)

UU (5, 4)(5, 4)

VV (3, 4)(3, 4)

START OVERSTART OVER

WW (2, 5) (2, 5) (make (make a dot)a dot)

XX (6, 5) (6, 5) (make (make a dot)a dot)

Yeah!

Yeah!

Yeah!

Page 4: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Let’s make the other Wump Let’s make the other Wump family members!family members!

Who do you want to draw first?Who do you want to draw first?ZugLugBugGlug Click here

when the Wump

family is complete!

Page 5: Investigation 2.1  Drawing Wumps Stretching & Shrinking

ZugZugRuleRule(Point)(Point)

(x, y)(x, y) (2x, 2y)(2x, 2y)

AA (0, 1)(0, 1) (0, 2)(0, 2)

BB (2, 1)(2, 1) (4, 2)(4, 2)

CC (2, 0)(2, 0) (4, 0)(4, 0)

DD (3, 0)(3, 0) (6, 0)(6, 0)

EE (3, 1)(3, 1) (6, 2)(6, 2)

FF (5, 1)(5, 1) (10, 2)(10, 2)

GG (5, 0)(5, 0) (10, 0)(10, 0)

HH (6, 0)(6, 0) (12, 0)(12, 0)

II (6, 1)(6, 1) (12, 2)(12, 2)

JJ (8, 1)(8, 1) (16, 2)(16, 2)

KK (6, 7)(6, 7) (12, 14)(12, 14)

LL (2, 7)(2, 7) (4, 14)(4, 14)

MM (0, 1)(0, 1) (0, 2)(0, 2)

START OVERSTART OVER

RuleRule(Point)(Point)

(x, y)(x, y) (2x, 2y)(2x, 2y)

NN (2, 2)(2, 2) (4, 4)(4, 4)

OO (6, 2)(6, 2) (12, 4)(12, 4)

PP (6, 3) (6, 3) (12, 6)(12, 6)

QQ (2, 3)(2, 3) (4, 6)(4, 6)

RR (2, 2)(2, 2) (4, 4)(4, 4)

START OVERSTART OVER

SS (3, 4)(3, 4) (6, 8)(6, 8)

TT (4, 5)(4, 5) (8, 10)(8, 10)

UU (5, 4)(5, 4) (10, 8)(10, 8)

VV (3, 4)(3, 4) (6, 8)(6, 8)

START OVERSTART OVER

WW (2, 5) (2, 5) (make a (make a

dot)dot)

(4, 10) (4, 10) (make a (make a

dot)dot)

XX (6, 5) (6, 5) (make a (make a

dot)dot)

(12, 10) (12, 10) (make a (make a

dot)dot)

Yeah!

Yeah!

Yeah!

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!

Page 6: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Is Zug a member of the Wump Is Zug a member of the Wump family or is he an imposter?family or is he an imposter?

He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!

Mug Wump

Zug

NO

YES

Page 7: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Zug Zug ISIS a member of the a member of the Wump family!Wump family!

Page 8: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Mug Wump

Zug Wump

Let’s tryanotherfamily

member!

Page 9: Investigation 2.1  Drawing Wumps Stretching & Shrinking

LugLugRuleRule(Point)(Point)

(x, y)(x, y) (3x, y)(3x, y)

AA (0, 1)(0, 1) (0, 1)(0, 1)

BB (2, 1)(2, 1) (6, 1)(6, 1)

CC (2, 0)(2, 0) (6, 0)(6, 0)

DD (3, 0)(3, 0) (9, 0)(9, 0)

EE (3, 1)(3, 1) (9, 1)(9, 1)

FF (5, 1)(5, 1) (15, 1)(15, 1)

GG (5, 0)(5, 0) (15, 0)(15, 0)

HH (6, 0)(6, 0) (18, 0)(18, 0)

II (6, 1)(6, 1) (18, 1)(18, 1)

JJ (8, 1)(8, 1) (24, 1)(24, 1)

KK (6, 7)(6, 7) (18, 7)(18, 7)

LL (2, 7)(2, 7) (6, 7)(6, 7)

MM (0, 1)(0, 1) (0, 1)(0, 1)

START OVERSTART OVER

RuleRule(Point)(Point)

(x, y)(x, y) (3x, y)(3x, y)

NN (2, 2)(2, 2) (6, 2)(6, 2)

OO (6, 2)(6, 2) (18, 2)(18, 2)

PP (6, 3) (6, 3) (18, 3) (18, 3)

QQ (2, 3)(2, 3) (6, 3)(6, 3)

RR (2, 2)(2, 2) (6, 2)(6, 2)

START OVERSTART OVER

SS (3, 4)(3, 4) (9, 4)(9, 4)

TT (4, 5)(4, 5) (12, 5)(12, 5)

UU (5, 4)(5, 4) (15, 4)(15, 4)

VV (3, 4)(3, 4) (9, 4)(9, 4)

START OVERSTART OVER

WW (2, 5) (2, 5) (make a (make a

dot)dot)

(6, 5) (6, 5) (make a (make a

dot)dot)

XX (6, 5) (6, 5) (make a (make a

dot)dot)

(18, 5) (18, 5) (make a (make a

dot)dot)

Yeah!

Yeah!

Yeah!

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!

Page 10: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Is Lug a member of the Wump Is Lug a member of the Wump family or is he an imposter?family or is he an imposter?

He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!

Mug Wump

NO

YES

Lug

Page 11: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Lug Lug IS NOTIS NOT a member of the a member of the Wump family!Wump family!

Page 12: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Mug WumpLet’s tryanotherfamily

member!

Lug

Page 13: Investigation 2.1  Drawing Wumps Stretching & Shrinking

BugBugRuleRule(Point)(Point)

(x, y)(x, y) (3x, 3y)(3x, 3y)

AA (0, 1)(0, 1) (0, 3)(0, 3)

BB (2, 1)(2, 1) (6, 3)(6, 3)

CC (2, 0)(2, 0) (6, 0)(6, 0)

DD (3, 0)(3, 0) (9, 0)(9, 0)

EE (3, 1)(3, 1) (9, 3)(9, 3)

FF (5, 1)(5, 1) (15, 3)(15, 3)

GG (5, 0)(5, 0) (15, 0)(15, 0)

HH (6, 0)(6, 0) (18, 0)(18, 0)

II (6, 1)(6, 1) (18, 3)(18, 3)

JJ (8, 1)(8, 1) (24, 3)(24, 3)

KK (6, 7)(6, 7) (18, 21)(18, 21)

LL (2, 7)(2, 7) (6, 21)(6, 21)

MM (0, 1)(0, 1) (0, 3)(0, 3)

START OVERSTART OVER

RuleRule(Point)(Point)

(x, y)(x, y) (3x, 3y)(3x, 3y)

NN (2, 2)(2, 2) (6, 6)(6, 6)

OO (6, 2)(6, 2) (18, 6)(18, 6)

PP (6, 3) (6, 3) (18, 9) (18, 9)

QQ (2, 3)(2, 3) (6, 9)(6, 9)

RR (2, 2)(2, 2) (6, 6)(6, 6)

START OVERSTART OVER

SS (3, 4)(3, 4) (9, 12)(9, 12)

TT (4, 5)(4, 5) (12, 15)(12, 15)

UU (5, 4)(5, 4) (15, 12)(15, 12)

VV (3, 4)(3, 4) (9, 12)(9, 12)

START OVERSTART OVER

WW (2, 5) (2, 5) (make a (make a

dot)dot)

(6, 15) (6, 15) (make a (make a

dot)dot)

XX (6, 5) (6, 5) (make a (make a

dot)dot)

(18, 15) (18, 15) (make a (make a

dot)dot)

Yeah!

Yeah!

Yeah!

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!

Page 14: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Is Bug a member of the Wump Is Bug a member of the Wump family or is he an imposter?family or is he an imposter?

He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!

Mug Wump

NO

YES

Bug

Page 15: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Bug Bug ISIS a member of the a member of the Wump family!Wump family!

Page 16: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Mug WumpLet’s tryanotherfamily

member! Bug Wump

Page 17: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Is Glug a member of the Wump Is Glug a member of the Wump family or is he an imposter?family or is he an imposter?

He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!

Mug Wump

NO

YES

Glug

Page 18: Investigation 2.1  Drawing Wumps Stretching & Shrinking

GlugGlugRuleRule(Point)(Point)

(x, y)(x, y) (x, 3y)(x, 3y)

AA (0, 1)(0, 1) (0, 3)(0, 3)

BB (2, 1)(2, 1) (2, 3)(2, 3)

CC (2, 0)(2, 0) (2, 0)(2, 0)

DD (3, 0)(3, 0) (3, 0)(3, 0)

EE (3, 1)(3, 1) (3, 3)(3, 3)

FF (5, 1)(5, 1) (5, 3)(5, 3)

GG (5, 0)(5, 0) (5, 0)(5, 0)

HH (6, 0)(6, 0) (6, 0)(6, 0)

II (6, 1)(6, 1) (6, 3)(6, 3)

JJ (8, 1)(8, 1) (8, 3)(8, 3)

KK (6, 7)(6, 7) (6, 21)(6, 21)

LL (2, 7)(2, 7) (2, 21)(2, 21)

MM (0, 1)(0, 1) (0, 3)(0, 3)

START OVERSTART OVER

RuleRule(Point)(Point)

(x, y)(x, y) (x, 3y)(x, 3y)

NN (2, 2)(2, 2) (2, 6)(2, 6)

OO (6, 2)(6, 2) (6, 6)(6, 6)

PP (6, 3) (6, 3) (6, 9) (6, 9)

QQ (2, 3)(2, 3) (2, 9)(2, 9)

RR (2, 2)(2, 2) (2, 6)(2, 6)

START OVERSTART OVER

SS (3, 4)(3, 4) (3, 12)(3, 12)

TT (4, 5)(4, 5) (4, 15)(4, 15)

UU (5, 4)(5, 4) (5, 12)(5, 12)

VV (3, 4)(3, 4) (3, 12)(3, 12)

START OVERSTART OVER

WW (2, 5) (2, 5) (make a (make a

dot)dot)

(2, 15) (2, 15) (make a (make a

dot)dot)

XX (6, 5) (6, 5) (make a (make a

dot)dot)

(6, 15) (6, 15) (make a (make a

dot)dot)

Yeah!

Yeah!

Yeah!

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!

Page 19: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Glug Glug IS NOTIS NOT a member of the a member of the Wump family!Wump family!

Page 20: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Mug WumpLet’s tryanotherfamily

member!

Glug

Page 21: Investigation 2.1  Drawing Wumps Stretching & Shrinking

Remember they must have the Remember they must have the same shape. The only same shape. The only

difference can be their size!difference can be their size!Click to try again

Page 22: Investigation 2.1  Drawing Wumps Stretching & Shrinking

The Wump Family thanks you!The Wump Family thanks you!

Mug Wump

Zug Wump

Bug Wump

Page 23: Investigation 2.1  Drawing Wumps Stretching & Shrinking
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