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Free Fall 2026 NC Math 1 Weekly Support

Week 4

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Thursday

Thursday - Predictions: Interpolation & Extrapolation

I can make and evaluate predictions using a linear model.

Short Lesson

Not Every Prediction Is Equally Reliable

Interpolation

Predicting within the range of observed data.

Extrapolation

Predicting outside the range of observed data.

Prediction Language

A model can estimate a value, but it does not guarantee the exact result.

Guided Examples

Check the Data Range First

Example 1

A data set includes observations from 0 to 10 hours. Predict at x=5.

Decide whether this is interpolation or extrapolation.

Step-by-step interpretation:

  1. Observed range: 0 to 10 hours Identify the data range.
Example 2

A data set only extends from 0 to 10 hours. Predict at x=20.

Decide how much caution the prediction needs.

Step-by-step interpretation:

  1. Observed range: 0 to 10 hours Identify the data range.

Thursday Practice

Make and Evaluate Predictions

Ask whether the input is inside the data range and whether the result makes sense.

Problem 1

A data set contains values from 0 to 10 hours. Predicting a value at 5 hours is what type of prediction?

Choose one

Problem 2

A data set contains values from 0 to 10 hours. Predicting a value at 100 hours is what type of prediction?

Choose one

Problem 3

Use y=3x+10 to predict y when x=4.

Problem 4

Compare y=2x+10 and y=3x+5 when x=5.

Choose one

Problem 5

Why should we be cautious when extrapolating?

Choose one

Thursday Reflection

What should you check before trusting a prediction?

Mistake Analysis

Diagnose the Mistake First

Choose the best diagnosis. Then reveal the full analysis.

Student says: "The slope is 4."

What is the mistake?

Student says: "The model predicts 82, so the actual value will definitely be 82."

What is the mistake?

Student says: "Because the association is positive, all the data values must be positive."

What is the mistake?

End of Thursday

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