In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Plots
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3 - Construct (Scatter plots)
2 - Interpret (Scatter plots)
4 - Investigate (Patterns of association)
2 - Describe (Patterns of association)
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3 - I can construct a scatter plot for bivariate data.
2 - I can interpret scatter plots with bivariate data.
4 - I can investigate patterns of association between two quantities in a scatter plot.
2 - I can describe patterns in a scatter plot.
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A. Scatter plots for bivariate data can be constructed to investigate patterns of association between the two quantities.
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A.1 What is a scatter plot?
A.2 What does the term clustering mean?
A.3 What does the term outlier mean?
A.4 What is positive association?
A.5 What is negative association?
A.6 What is linear association?
A.7 What is non linear association?
A.8 How does one construct a scatter plot for bivariate measurement data?
A.9 How does one describe the patterns for the scatter plot?
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Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Variables
Plots
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1 - Know (Straight lines are used to model relationships between two variables)
3 - Fit (Straight line into scatter plot)
5 - Assess (Closeness of the data points to the line)
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1 - I know that straight lines are widely used to model relationships between two quantitative variables.
3 - I can informally fit a straight line into a scatter plot that models linear association.
5 - I can assess the scatter plot for linear association and the closeness of the data points to a straight line.
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A.1 When a scatter plot suggests a linear association, a straight line can be informally fit to model the data.
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A.1 What are quantitative variables?
A.2 How does one determine if a scatter plot suggests linear association?
A.3 How does one informally fit a straight line into their scatter plot?
A.4 How does one assess the model fit by judging the closeness of the data points to the line?
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Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Equation
Context
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3 - Use (Equation of a linear model)
3 - Solve (Problems with bivariate data)
2 - Interpret (Slope)
2 - Interpret (Intercept)
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3 - I can use the equation of a linear model.
3 - I can solve problems in the context of bivariate measurement data.
2 - I can interpret slope of a linear equation or model.
2 - I can interpret the intercept of a linear equation or model.
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A. The slope and the intercept from the equation of a linear model can be used to solve problems in the context of bivariate measurement data.
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A.1 How does one use the equation of a linear model to solve problems in the context of bivariate measurement data?
A.2 How does one interpret slope?
A.3 How does one interpret the intercept?
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Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Patterns
Data
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1 - Understand (Patterns of association in a table)
3 - Construct (Two way table)
2 - Interpret (Two way table)
2 - Summarize (Data on two categorical variables)
2 - Calculate (Relative frequencies)
3 - Use (Relative frequencies)
2 - Describe (Association between two variables)
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1 - I understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two way table.
3 - I can construct a two way table for two categorical variables.
2 - I can interpret a two way table summarizing data on two categorical variables.
2 - I can summarize data on two categorical variables.
2 - I can calculate relative frequencies for rows or columns.
3 - I can use relative frequencies calculated for rows or columns to describe association.
2 - I can describe possible association between two variables by using the relative frequency.
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A. The construction of a two way table that displays frequencies and relative frequencies can be helpful for finding patterns of association between bivariate data.
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A.1 What are patterns of association?
A.2 What does the term frequency mean?
A.3 What does the term relative frequency mean?
A.4 How does one construct a two way table?
A.5 How does one interpret a two way table?
A.6 How does one summarize the data in a two way table?
A.7 How does one calculate relative frequencies for columns or rows?
A.8 How does one use relative frequencies to describe possible association between two variables?
A.9 How does one summarize data on two categorical variables in a two way table?
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