Autumn Leaves Coordinate Mystery
🍁
Autumn Leaves Mystery Plot
Part 1: Ordered Pairs Checklist & Foliage Guide • Scale: –10 to 10
Name:
Date:
Period:
Score: / 100
🍂 How to Graph Your Mystery Picture
- Locate each ordered pair (x, y) on Page 2. Check off as you plot.
- Connect consecutive points with a straight line using a ruler.
- When you see STOP, lift your pencil! Do not connect to the next shape.
- When finished plotting, shade each leaf according to the color guide.
🧭 Quadrant Sign Guide (x, y)
Quad II: (–, +)
Quad I: (+, +)
Quad III: (–, –)
Quad IV: (+, –)
🍁 Leaf 1: Sugar Maple Color: Crimson / Red
Stem: ( 1, -2 ) → ( 2, 0 ) STOP
Leaf Outline (Connect in Order):
( 2, 0 ) ( 0, 1 ) ( -1, 2 ) ( 0, 3 ) ( -1, 4 ) ( -3, 5 ) ( -1, 6 ) ( 0, 5 ) ( 1, 7 ) ( 2, 9 ) ( 3, 7 ) ( 4, 5 ) ( 6, 6 ) ( 8, 5 ) ( 6, 4 ) ( 5, 3 ) ( 6, 2 ) ( 4, 1 )
Connect to ( 2, 0 ) STOP
Veins: (2, 0) → (2, 8) [STOP] (1, 2) → (-2, 4) [STOP] (3, 2) → (7, 4) [STOP]
🍃 Leaf 4: Fluttering Elm & Breeze Color: Olive Green
Stem: ( -7, 8 ) → ( -6, 7 ) STOP
Outline:
( -6, 7 ) ( -5, 6 ) ( -3, 6 ) ( -1, 7 ) ( -2, 8 ) ( -4, 9 ) ( -6, 8 ) ( -6, 7 )
Vein: (-6, 7) → (-2, 8) STOP
💨 Wind Trails (Light Blue):
(-9, 9) → (-7, 10) → (-4, 10) [STOP] (0, -4) → (2, -3) → (3, -1) [STOP]
🌿 Leaf 2: Northern Red Oak Color: Amber / Brown
Stem: ( -4, -9 ) → ( -4, -7 ) STOP
Outline (Connect in Order):
( -4, -7 ) ( -6, -6 ) ( -7, -5 ) ( -5, -4 ) ( -8, -3 ) ( -6, -2 ) ( -9, 0 ) ( -7, 1 ) ( -8, 3 ) ( -6, 3 ) ( -6, 4 ) ( -4, 5 ) ( -3, 4 ) ( -2, 3 ) ( -3, 2 ) ( -1, 0 ) ( -2, -1 ) ( -1, -3 ) ( -3, -4 ) ( -2, -5 )
Connect to ( -4, -7 ) STOP
Veins: (-4,-7) → (-4,4) [STOP] (-4,-4) → (-7,-4) [STOP] (-4,-1) → (-8,0) [STOP] (-4,2) → (-7,2) [STOP]
🍂 Leaf 3: Golden Aspen Color: Gold / Yellow
Stem: ( 2, -9 ) → ( 4, -8 ) STOP
Outline (Connect in Order):
( 4, -8 ) ( 5, -9 ) ( 7, -8 ) ( 9, -6 ) ( 10, -4 ) ( 9, -2 ) ( 7, -1 ) ( 5, -2 ) ( 4, -4 ) ( 3, -6 )
Connect to ( 4, -8 ) STOP
Veins: (4,-8) → (7,-1) [STOP] (5,-6) → (8,-6) [STOP] (6,-4) → (9,-4) [STOP]
🔍 Mystery Foliage Analysis & Mathematical Thinking Answer after graphing on Page 2
1. In which quadrant is the Golden Aspen Leaf primarily located?
Answer:
2. Name two points on the Oak Leaf outline that lie on the x-axis:
Points: ( ____, ____ ) and ( ____, ____ )
3. What ordered pair represents the highest tip of the Sugar Maple Leaf?
Coordinates: ( ____, ____ )
4. In which quadrant do both coordinates have negative values? Name one point:
Quad: Pt: ( ____, ____ )
Autumn Leaves Mystery Plot • Coordinate Plane
Plot accurately with a sharp pencil • Use a straightedge for all connected segments
Name:
Period:
Quadrant I (+, +) Quadrant II (–, +) Quadrant III (–, –) Quadrant IV (+, –) x y -10 -8 -6 -4 -2 2 4 6 8 10 10 8 6 4 2 -2 -4 -6 -8 -10 0
🎨 Coloring Guide:
Maple (Red) Oak (Amber) Aspen (Gold) Elm (Green) Wind (Blue)
Teacher Check: Points (40) Lines (30) Analysis (30)
Autumn Foliage Answer Key
🍁
Autumn Leaves Mystery Plot
Teacher Answer Key
Solutions, Pedagogical Insights, & Mathematical Analysis Guide
Grade Level: 5th – 8th CCSS: 6.NS.C.6c • 6.NS.C.8
📋 Mystery Plotting Breakdown
Total Plotted Vertices: 72 Ordered Pairs 58 outline + 14 vein/wind points
Foliage Revealed: 4 Native Tree Leaves Maple, Oak, Aspen, Elm
🧭 Quadrant Coverage All 4 Quadrants
Quad II (–, +): Elm & Upper Oak
Quad I (+, +): Sugar Maple Body
Quad III (–, –): Lower Oak & Stem
Quad IV (+, –): Golden Aspen & Stem
✓ Page 1 Mathematical Analysis — Official Answer Key
Total: 30 Points (7.5 pts each)
1. In which quadrant is the Golden Aspen Leaf primarily located?
Correct Answer: Quadrant IV (or Quad 4 / + , –) Explanation: All points have positive x values and negative y values.
2. Name two points on the Oak Leaf outline that lie directly on the x-axis:
Correct Answer: ( -9, 0 ) and ( -1, 0 ) Points with y = 0 lie directly on the horizontal x-axis.
3. What ordered pair represents the highest tip of the Sugar Maple Leaf?
Correct Answer: ( 2, 9 ) Apex tip in Quadrant I with the maximum y-value (y = 9).
4. In which quadrant do both coordinates have negative values? Name one point in it:
Correct Answer: Quadrant III (or Quad 3 / – , –) Accept any of: (-4,-7), (-6,-6), (-7,-5), (-5,-4), (-8,-3), (-6,-2), (-1,-3), (-3,-4), (-2,-5), (-4,-9)
💡 Common Student Graphing Misconceptions & Fixes
1. X/Y Transposition: Plotting (1, -2) as (-2, 1). Remind students: "Walk down the hall (x) before taking the elevator (y)."
2. Negative Direction Confusion: Moving right instead of left for negative x. Guide students to check the Quadrant Sign Box on Page 1 before every section.
3. Ignoring STOP Dividers: Connecting the stem to the leaf outline or connecting leaf to leaf. Emphasize lifting the pencil whenever STOP appears.
🌟 Enrichment & Extension Prompt: Ask advanced students to calculate the perimeter of the Aspen Leaf stem, or find the reflection of the Maple Leaf apex (2, 9) across the y-axis: .
