enVision Mathematics Topic 4
8th Grade;Â December (3 weeks);Â 2nd Quarter
Embedded Files
Topic Title(s):
Investigate Bivariate Data
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP7. Look for and make use of structure.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
8.SP.A. Statistics & Probability: Investigate patterns of association in bivariate data.
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. (CCSS: 8.SP.A.1)
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. (CCSS: 8.SP.A.2)
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. (CCSS: 8.SP.A.3)
Explain 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? (CCSS: 8.SP.A.4)
Recognize and describe patterns in bivariate data. (Entrepreneurial Skills: Inquiry/Analysis)
Interpret the contextual meaning of slope and y-intercept, where applicable in a linear model fit to bivariate data. (MP2)
Build statistical models to explore, describe, and generalize the relationship between two variables. (MP4)
Use scatter plots and two-way tables to describe possible associations in bivariate data. (MP7)
Inquiry Questions
In what ways is a scatter plot useful in describing and interpreting the relationship between two quantities?
Why would we create a linear model for a set of bivariate data?
How do you know when a credible prediction can be made from a linear model of bivariate data?
What does a pattern of association look like for categorical data?
Coherence Connections
This expectation supports the major work of the grade.
In previous grades, students apply and extend previous understandings of numbers to the system of rational numbers.
In Grade 8, this expectation supports using functions to model relationships between quantities.
In high school, students summarize, represent, and interpret data on two categorical and quantitative variables, interpret linear models, and understand independence and conditional probability.
Academic Vocabulary & Language Expectations:
Cluster, gap, negative association, outlier, positive association, scatter plot, trend line, categorical data, relative frequency table
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 4
Let's Investigate! Tasks
Let's Investigate! Snack Attack (TE) (relates to Lesson 4-2)
Let's Investigate! Get a Grip (TE) (relates to Lesson 4-2)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: None since this Unit Plan supports the major work of the grade
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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