Autumn Tree Coloring Worksheet
Whimsical Tree Equations
Algebra Review: Consecutive Integers & Geometric Perimeter
Name:
Date:
Period:
Directions: Solve each problem below. You must define your own variables, write an algebraic equation, and show all work. Your answers reveal the color for each number on the Whimsical Tree scene on Page 2!
Problem 1 Consecutive Odd
The sum of five consecutive odd integers is nine times the smallest. Find the integers.
Define Variable(s):
Show Algebraic Equation & Solving Steps:
Integers: ____, ____, ____, ____, ____
1st Integer: Purple
2nd Integer: Blue
3rd Integer: Green
4th Integer: Orange
5th Integer: Red
Problem 2 Hexagon Perimeter
A hexagon has three sides each 6 less than twice the smallest side. The other two sides are each 12 more than twice the smallest side. Perimeter is 215 units. Find each side.
Define Variable(s):
Show Algebraic Equation & Solving Steps:
Sides: Small: ____ | Mid(x3): ____ | Long(x2): ____
Smallest side: Yellow
Middle sides (x3): Teal
Longest sides (x2): Dark Blue
Problem 3 Quadrilateral Surveyor
In a quadrilateral, one side is 14 more than the smallest. Another is 6 less than twice the smallest. The last is 2 times the smallest. Perimeter is 80 units. Find all 4 sides.
Define Variable(s):
Show Algebraic Equation & Solving Steps:
Sides: ____, ____, ____, ____
Smallest side: Gray
Second side: Light Green
Third side: Black
Fourth side: Light Blue
Problem 4 Consecutive Even
Find three consecutive even integers that have a sum that is 8 less than twice the middle integer.
Define Variable(s):
Show Algebraic Equation & Solving Steps:
Integers: ____, ____, ____
Smallest value: Pink (Trunk & Branches)
Middle value: Orange (Ground Hills)
Largest value: Purple (Sky)
Check your calculations carefully before coloring Page 2! Page 1 of 2 • Math Equations
Whimsical Tree & Falling Leaves
Use your calculated values from Page 1 to color each numbered region!
Color by Solution
Locate each number inside the scene below and color it according to the assignment you found for that number on Page 1!
Self-Checking Math
-6 -6 -6 -8 -8 -8 -10 -10 -10 -10 -10 -10 50 50 32 32 19 19 5 5 7 7 7 9 9 11 11 13 13 13 26 26 24 24 24 18 12 18 12 18 12
Checklist: All 4 Equations Solved Variables Defined Every Leaf Colored
Page 2 of 2 • Whimsical Masterpiece
Autumn Tree Answer Key
Whimsical Tree Equations
Teacher Answer Key
Complete Variable Definitions, Equation Models & Step-by-Step Proofs
Algebra 1 / Pre-Algebra Review
Check student independent variable definitions (any variable letter is acceptable if properly stated). Total: 25 Points
Problem 1 Solution 6 Points
Sum of 5 consecutive odd integers is 9 times the smallest.
1. Variable Definition:
Let \( n = \) smallest (1st) odd integer
Integers: \( n, \, n+2, \, n+4, \, n+6, \, n+8 \)
2. Equation & Solving:
\( n + (n+2) + (n+4) + (n+6) + (n+8) = 9n \)
\( 5n + 20 = 9n \)
\( 20 = 4n \implies n = 5 \)
Check: \( 5+7+9+11+13 = 45 = 9(5) \) ✓
Answers: 5, 7, 9, 11, 13
5 → Purple 7 → Blue 9 → Green 11 → Orange 13 → Red
Problem 2 Solution 7 Points
Hexagon: 3 sides are \( 2s-6 \), 2 sides are \( 2s+12 \), perimeter \( = 215 \).
1. Variable Definition:
Let \( s = \) length of smallest side
Sides: \( s \), three of \( (2s-6) \), two of \( (2s+12) \)
2. Equation & Solving:
\( s + 3(2s - 6) + 2(2s + 12) = 215 \)
\( s + 6s - 18 + 4s + 24 = 215 \)
\( 11s + 6 = 215 \implies 11s = 209 \implies s = 19 \)
Check: \( 19 + 3(32) + 2(50) = 215 \) ✓
Sides: 19, 32, 32, 32, 50, 50
19 → Yellow 32 → Teal 50 → Dark Blue
Problem 3 Solution 6 Points
Quadrilateral: \( x+14, \, 2x-6, \, 2x \), and smallest \( x \); perimeter \( = 80 \).
1. Variable Definition:
Let \( x = \) smallest side
Sides: \( x, \, x+14, \, 2x-6, \, 2x \)
2. Equation & Solving:
\( x + (x + 14) + (2x - 6) + 2x = 80 \)
\( 6x + 8 = 80 \implies 6x = 72 \implies x = 12 \)
Sides: \( 12, \, 12+14=26, \, 2(12)-6=18, \, 24 \)
Check: \( 12+26+18+24 = 80 \) ✓
Sides: 12, 18, 24, 26
12 → Gray 26 → Light Green 18 → Black 24 → Light Blue
Problem 4 Solution 6 Points
3 consecutive even integers: sum is 8 less than twice the middle integer.
1. Variable Definition:
Let \( n = \) 1st even integer
Integers: \( n, \, n+2 \, (\text{middle}), \, n+4 \)
2. Equation & Solving:
\( n + (n+2) + (n+4) = 2(n+2) - 8 \)
\( 3n + 6 = 2n + 4 - 8 \implies 3n + 6 = 2n - 4 \)
\( n = -10 \)
Check: \( -24 = 2(-8)-8 = -24 \) ✓
