Trend Line Teacher Guide Drawing the Line
Trend Lines & Predictions | Teacher Guide
9th Grade Algebra
65 Minute Lesson
Learning Objective
Students will construct a trend line on a scatter plot and use that linear model to make predictions for unknown data points through interpolation and extrapolation.
Vocabulary
Trend Line: General path of data.Interpolation: Inside data range.Extrapolation: Outside data range.
Standards Alignment
HSS-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Informally fit a straight line and assess model fit.
Materials Needed
Spaghetti Activity Worksheet
Making Predictions Worksheet
Exit Ticket & Answer Key
Uncooked Spaghetti (1 piece/student)
Instructional Arc (65 Minutes)
0-10m
The Hook: Ice Cream Sales vs Temp
Introduce the concept of using current trends to predict tomorrow's needs.
10-25m
Direct Instruction: The Best Fit Rules
Discuss balance and linearity. Define Interpolation vs. Extrapolation.
25-45m
Activity: Spaghetti Modeling
Students use noodles to physically find the "pivot point" of the data cloud.
45-55m
Practice: Making Future Predictions
Independent work using trend lines to estimate unknown Y-values.
55-65m
Wrap-up & Assessment
Review common errors (connecting dots) and collect Exit Tickets.
Instructional Strategy & Differentiation
Pro-Tip: The "Pivot" Method
Pick one point at the far left and one at the far right. Place the spaghetti there, then "pivot" the center until there is an equal "cloud" of data above and below the line.
Addressing Misconceptions
The Connector Trap: Many students will try to "connect the dots". Emphasize that a trend line is a single straight line.
Origin Bias: Remind students that the line doesn't always start at (0,0).
Scaffolding
Provide scatter plots with the "mean point" (x-bar, y-bar) already plotted.
Use highlighters to shade the "upper half" and "lower half" of the data cloud.
Extension
Calculate residuals to mathematically prove fit quality.
Analyze Outliers and their pull on the line.
© 2026 Lenny Educational Resources Math Modeling: Linear Unit
Trend Line Slides Algebra I: Data Modeling
Drawing the Line
Using Trend Lines to Predict the Future
The Ice Cream Dilemma
The owner of "Cold Cones" noticed that the hotter the weather, the more ice cream they sell.
BIG QUESTION:
If the forecast for tomorrow is 92°F, how much ice cream should they prep?
Temperature (°F)
Sales ($)
What is a Trend Line?
Also known as the "Line of Best Fit"
1. Modeling
A straight line that represents the general direction of a scatter plot.
2. Balance
Should have approximately half the points above and half below the line.
3. Prediction
We use the equation of this line to estimate values we haven't seen yet.
Two Types of Predictions
Interpolation
Making a prediction inside the range of known data points.
Predicting ice cream sales for 75°F if we have data for 70°F and 80°F.
Extrapolation
Making a prediction outside (beyond) the range of known data points.
Predicting sales for 110°F when our highest recorded temp was 95°F.
The "Best Fit" Test
FAIL
"The Connector"
Trend lines MUST be straight.
SUCCESS
"The Middle Ground"
Captures the average trend.
Spaghetti Time!
Grab your trend line tools (Spaghetti or Rulers).
Activity: Spaghetti Trend Lines
Spaghetti Activity Worksheet Spaghetti Trend Lines
Data Modeling & Visual Fit
Name:
Date:
Physical Modeling: Lay your spaghetti noodle across the data cloud. Pivot until points are balanced above and below the line. Trace with pencil.
1
The "Morning Coffee" Plot
Happiness Level (1-10)
Cups of Coffee (0-8)
0
10
0
8
Analysis & Findings:
2
The "Study Time" Plot
Test Score (%)
Hours Studied
0
100
0h
10h
Analysis & Findings:
v1.2 Polished Edition Lenny Educational Resources • Trend Line Activity • 2026
Prediction Practice Worksheet Trimmed Making Predictions
Interpolation & Extrapolation Practice
Name: __________________________
1
Case Study: Charging Your Phone
The scatter plot shows the battery percentage as it charges. Draw a trend line and use it to estimate the values below.
A) Predict the battery % at 40 minutes.
Type: Interpolation or Extrapolation?
B) Predict the battery % at 120 minutes.
Type: Interpolation or Extrapolation?
Battery Charge (%)
Charging Time (Minutes)
0
50
100
0
50
100
120+
The grid extends past 100 for your 120-minute prediction.
2
The Reliability Challenge
Scientist A draws a steep trend line. Scientist B draws a shallow one. Whose prediction for 50 years will be higher? Explain.
Which prediction is technically more "risky" (likely to be significantly wrong): 5 years or 100 years? Why?
Drawing the Line • Modeling Practice © 2026 Lenny Ed
Trend Line Exit Ticket Check for Understanding
Exit Ticket
Name
Period
1. Use a straight edge to draw a trend line for this dataset:
Y-Axis Units
X-Axis Units
2. Predicting a value outside the known data range is:
Interpolation
Extrapolation
Student Reflection
Circle the icon that matches your comfort level with trend lines:
Trend Line Answer Key Answer Key & Teacher Reference
Lesson: Drawing the Line
Spaghetti Activity
Plot 1 (Coffee):
Positive correlation. The line should bisect the data cloud from the bottom-left toward the top-right. Slope ≈ 1.
Plot 2 (Study Time):
Positive correlation but scattered. Line should pass through the "center of gravity" of the points without connecting them.
Exit Ticket Key
Graph: Straight line rise. Points balanced.Vocab: Extrapolation.
Predictions Practice
Problem 1: Battery
A) 40m: ~40-45%. [Interpolation]B) 120m: ~125%. [Extrapolation]Limit of model: Battery cannot exceed 100%.
Problem 2: Scientists
Higher: Scientist A (Steeper slope).Risky: 100 years. Small initial slope errors compound over time.
Grading Rubric
Needs Work (1)
Jagged lines or missed data cloud. Vocabulary missed.
Approaching (2)
Straight but biased line. Vocabulary swapped.
Mastery (3)
Balanced trend line. Accurate predictions. Clear understanding.
