Unit 5: Linear Relationships

Students study proportional and non-proportional linear relationships, solve systems of linear equations graphically and algebraically, and use scatter plots and lines of fit to analyze numerical and categorical data.

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Unit

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Concept

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Practice

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Set 1

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Set 2

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Advanced

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Set 2

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What this unit covers

A Proportional Relationships · 3 lessons

Goals

• Create an equation and a graph to represent proportional relationships, including an appropriate scale and axes.
• Interpret multiple representations of a proportional relationship in context.

Lessons

1. Understanding Proportional Relationships
2. Representing Proportional Relationships
3. Comparing Proportional Relationships

B Representing Linear Relationships · 4 lessons

Goals

• Create an equation that represents a linear relationship.
• Create and compare graphs that represent linear relationships with the same rate of change but different initial values.
• Interpret the slope and y-intercept of the graph of a line in context.

Lessons

1. Introduction to Linear Relationships
2. More Linear Relationships
3. Representations of Linear Relationships
4. Translating to y=mx+b

C Finding Slopes and Linear Equations · 5 lessons

Goals

• Create multiple representations of a linear relationship, including a graph, equation, and table.
• Determine pairs of values that satisfy or do not satisfy a linear relationship using an equation or graph.
• Interpret the slope of a non-increasing line in context.

Lessons

1. Slopes Don't Have to Be Positive
2. Calculating Slope
3. Equations of All Kinds of Lines
4. Solutions to Linear Equations
5. More Solutions to Linear Equations

D Systems of Linear Equations · 5 lessons

Goals

• Categorize systems of equations, including systems with infinitely many or no solutions, and calculate the solution for a system using a variety of strategies.
• Comprehend that solving a system of equations means finding values of the variables that make both equations true at the same time.
• Create a system of equations that represents a situation and interpret the solution in context.

Lessons

1. On Both of the Lines
2. Systems of Equations
3. Solving Systems of Equations
4. Solving More Systems
5. Writing Systems of Equations

E Associations in Numerical Data · 6 lessons

Goals

• Create a scatter plot from a table of data, and describe the trend of the data.
• Describe the relationship between two variables using a line fit to data on a scatter plot.
• Interpret features of data on a scatter plot, including linear and non-linear association, outliers, slope of a linear model, and clustering.

Lessons

1. Organizing Data
2. What a Point in a Scatter Plot Means
3. Fitting a Line to Data
4. Describing Trends in Scatter Plots
5. The Slope of a Fitted Line
6. Observing More Patterns in Scatter Plots

F Associations in Categorical Data · 2 lessons

Goals

• Calculate relative frequencies, and describe associations between variables using a relative frequency table.
• Create a two-way table and a segmented bar graph that represent relative frequencies, and interpret the frequencies in context.

Lessons

1. Looking for Associations
2. Using Data Displays to Find Associations

G Let's Put It to Work · 3 lessons

Lessons

1. Using Linear Relations to Solve Problems (Optional)
2. Solving Problems with Systems of Equations (Optional)
3. Gone in 30 Seconds (Optional)