Shape Shifter Equation Worksheet
1
Shape Shifter Equations
Part 1: The Shape Inventory (Combining Same Shapes)
Name:
Date:
Core Rule Only shapes of the exact same kind can be combined together into one total!
3▲ + 2▲ = 5▲
#1 Combine triangles & circles
3▲ + 4● + 2▲ + 1● =
_____ ▲ + _____ ●
#2 Combine stars & squares
5★ + 2■ + 3★ + 6■ =
_____ ★ + _____ ■
#3 Combine diamonds & circles
7◆ + 1● + 4◆ + 8● =
_____ ◆ + _____ ●
#4 Watch the single shape
▲ + 9■ + 6▲ + ■ =
_____ ▲ + _____ ■
#5 Three shape clusters
2● + 4★ + 3▲ + 5● + 1★ =
_____ ● + _____ ★ + _____ ▲
#6 Reordered shapes
6■ + 8◆ + 2■ + 5◆ =
_____ ■ + _____ ◆
#7 Group scattered shapes
10★ + 3▲ + 4★ + 7▲ =
_____ ★ + _____ ▲
#8 Three shape varieties
4◆ + 5■ + 2● + 3◆ + 7● =
_____ ◆ + _____ ■ + _____ ●
#9 Larger counts
12▲ + 8● + 15▲ + 9● =
_____ ▲ + _____ ●
#10 Quad cluster consolidation
★ + 4■ + 6★ + 3★ + 11■ =
_____ ★ + _____ ■
Unit: Expressions & Equations Prep Page 1 of 4 • Inventory Stage
2
Shape Shifter Equations
Part 2: Positive & Negative Shape Clusters
Name:
Date:
Core Rule The sign belongs to the shape that follows it! Group positives and negatives for each shape.
7● - 3● = 4●
#11 Basic subtraction
8▲ + 6● - 3▲ + 2● =
_____ ▲ + _____ ●
#12 Subtracting both shapes
9★ + 7■ - 4★ - 5■ =
_____ ★ + _____ ■
#13 Reaching zero shapes
5◆ + 4● - 5◆ + 6● =
_____ ◆ + _____ ●
#14 Negative results allowed
4■ + 3▲ - 9■ + 5▲ =
_____ ■ + _____ ▲
#15 Triple shape signs
10● - 3★ + 4▲ - 6● + 8★ =
_____ ● + _____ ★ + _____ ▲
#16 Leading negative term
-2◆ + 8■ + 9◆ - 3■ =
_____ ◆ + _____ ■
#17 Multiple subtractions
15★ - 4▲ - 8★ - 3▲ =
_____ ★ + ( _____ ▲)
#18 All negative mix
-6● - 4◆ + 11● - 7◆ =
_____ ● + ( _____ ◆)
#19 Single shapes with signs
7▲ - ▲ + 5■ - 8■ =
_____ ▲ + ( _____ ■)
#20 Complex coefficient challenge
-3★ + 14● - 9★ - 10● + 2★ =
_____ ★ + _____ ●
Unit: Expressions & Equations Prep Page 2 of 4 • Signs & Coefficients Stage
3
Shape Shifter Equations
Part 3: The Equation Bridge (Both Sides Balanced)
Name:
Date:
Core Rule Combine like shapes on the LEFT, then combine like shapes on the RIGHT!
2▲ + 3▲ = 4▲ + ▲ ➔ 5▲ = 5▲
#21 Simplify each side
3▲ + 2● + 4▲ = 1● + 5▲ + 3●
____ ▲ + ____ ● = ____ ▲ + ____ ●
#22 Simplify each side
6★ + 1■ + 2★ = 3■ + 4★ + 5■
____ ★ + ____ ■ = ____ ★ + ____ ■
#23 Diamonds and circles
5◆ + 8● + 2◆ = 4● + 6◆ + 4●
____ ◆ + ____ ● = ____ ◆ + ____ ●
#24 Find the missing shape count
7■ + 3▲ + 2■ = [ ? ]■ + 3▲
Missing [ ? ] = _____
#25 Find the missing shape count
4★ + 9● + ★ = 5★ + [ ? ]●
Missing [ ? ] = _____
#26 Subtraction on both sides
8▲ - 2▲ + 5■ = 3▲ + 9■ - 4■
____ ▲ + ____ ■ = ____ ▲ + ____ ■
#27 Combine then compare sides
10◆ + 3★ - 4◆ = 2◆ + 7★ - 4★
____ ◆ + ____ ★ = ____ ◆ + ____ ★
#28 Are these sides balanced? (True/False)
4● + 6■ + 3● vs 9■ - 3■ + 7●
L: ____ ● + ____ ■ Balanced? [YES / NO]
#29 Are these sides balanced? (True/False)
12▲ - 5▲ + 2★ vs 3▲ + 4▲ + 5★ - 2★
L: ____ ▲ + ____ ★ Balanced? [YES / NO]
#30 Three shape equation sides
2■ + 4● + 5◆ + ■ = 3● + 3■ + ● + 5◆
____ ■ + ____ ● + ____ ◆ = ____ ■ + ____ ● + ____ ◆
Unit: Expressions & Equations Prep Page 3 of 4 • Equation Bridge Stage
4
Shape Shifter Equations
Part 4: The Algebra Master Bridge (Combining Across Sides)
Name:
Date:
Core Rule Subtract or add matching shapes from both sides to simplify! Just like algebraic variables: ▲ = \(x\), ● = \(y\).
5▲ = 2▲ + 6 ➔ 3▲ = 6
#31 Subtract shapes from both sides
7▲ = 3▲ + 12
Subtract 3▲ from both sides: ____ ▲ = 12
#32 Subtract shapes from both sides
9● = 4● + 20
Subtract 4● from both sides: ____ ● = 20
#33 Combine first, then move shapes
5★ + 3★ = 2★ + 18
Combine L, then - 2★: ____ ★ = 18
#34 Shapes on both sides with constants
8■ + 4 = 3■ + 19
Move shapes left: ____ ■ + 4 = 19
#35 Two different shapes balanced
6▲ + 5● = 2▲ + 9●
Subtract 2▲ and 5●: ____ ▲ = ____ ●
#36 Two shapes relationship
10◆ + 2■ = 4◆ + 14■
Simplify to lowest terms: ____ ◆ = ____ ■
#37 Negative terms across sides
4★ - 3 = ★ + 12
Move ★ left: ____ ★ - 3 = 12
#38 Translate shapes to algebra variables
If ▲ = \(x\), rewrite: 5▲ + 3 + 2▲ = ▲ + 15
Equation: _____ \(x\) + 3 = \(x\) + 15
#39 Solve for the single shape
6● + 2● - 3● = ● + 16
Simplify and solve: 1 ● = _____
#40 Master Challenge: The Ultimate Bridge
7▲ + 4■ - 2▲ + 6 = 2▲ + 9■ - 5■ + 21
Simplified: ____ ▲ + ____ ■ + 6 = ____ ▲ + ____ ■ + 21
Unit: Expressions & Equations Prep Page 4 of 4 • Master Bridge Stage