Math 1 Strand
Build confidence with scatterplots, linear models, residuals, correlation, and real-world data decisions.
Data questions ask students to make sense of real patterns, not just calculate. The goal is to connect graphs, tables, models, and context so predictions feel reasonable and conclusions stay honest.
A linear model uses y = mx + b. The slope explains the rate of change, the y-intercept explains the starting prediction, and residual = actual - predicted tells how far the model missed for one data point.
Standards-Aligned Overview
Based on the Math 1 standards for bivariate data, residuals, linear models, correlation, and causation.
Represent data on two quantitative variables with scatterplots and describe how the variables are related.
Fit a least squares regression line to linear data using technology and use the fitted function to solve problems.
Assess the fit of a linear function by analyzing residuals.
Interpret the rate of change and intercept of a linear model in context, including interpolation and extrapolation.
Use scatterplots, correlation coefficients, and residual plots to judge the strength, direction, and appropriateness of a linear model.
Distinguish between association and causation.
Key Vocabulary
These terms support scatterplot, model interpretation, residual, and association questions.
A graph of paired data values that helps show whether two quantitative variables are related.
A relationship where the points generally rise from left to right.
A relationship where the points generally fall from left to right.
A relationship where the points do not show a clear upward or downward pattern.
A line that models the overall trend in a scatterplot.
The rate of change in a linear model. In y = mx + b, the slope is m.
The predicted value of y when x = 0. In y = mx + b, the y-intercept is b.
A prediction made inside the range of the observed data.
A prediction made outside the range of the observed data. These predictions need extra caution.
The difference between an actual value and a predicted value: residual = actual - predicted.
A table that organizes counts for two categorical variables at the same time.
A pattern showing that two variables are related. Association does not automatically prove causation.
Student-Friendly Review
Start with the story the data tells, then use calculations to support that story.
Positive association rises left to right. Negative association falls left to right. No association has no clear pattern.
In y = mx + b, m is the slope and b is the y-intercept. Substitute x-values to make predictions.
Residual = actual - predicted. A positive residual means the actual value was above the prediction.
In two-way tables, compare percentages within the right row or column before making a statement about association.
Practice Questions
Start with DOK 1 fluency, then build toward applications, analysis, and EOC-style mixed practice.
Practice Set 1
Scatterplot trends, model parts, residuals, and table basics
Practice Set 2
Predictions, correlation, residuals, and conditional percentages
Practice Set 3
Model fit, residual patterns, outliers, and causation claims
Practice Set 4
Models, residuals, tables, and association
Practice Set 5
Units, model limits, categorical data, and fit
Practice Set 6
A compact EOC-style readiness check