Curriculum / Math / 8th Grade / Unit 8: Bivariate Data / Lesson 7
Math
Unit 8
8th Grade
Lesson 7 of 9
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Lesson Notes
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Create and analyze two-way tables representing bivariate categorical data.
The core standards covered in this lesson
8.SP.A.4 — 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?
The foundational standards covered in this lesson
7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.A.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Prior to this lesson, it may be valuable to review univariate data and representative samples from seventh gade. A good resource for this is Exercises 1–8 from EngageNY, Grade 8, Module 6, Lesson 13.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A double bar graph and a segmented bar graph are shown below, representing the same data set.
Name two things you notice and two things you wonder about.
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Grade 8 Unit 6 Lesson 9 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed April 20, 2018, 4:12 p.m..
A reporter in a small town polled some residents and asked them if they were in favor of increasing the minimum wage or against it. The two-way table summarizes the data.
a. Name two things you notice and two things you wonder about.
b. How many people did the reporter survey?
c. How many people in the age group of 16–30 years old were against the increase in minimum wage?
d. Were more people in favor of the increase or against the increase?
Marlo takes the bus to school. He notices that the bus tends to arrive late to school when it is raining. Marlo decides to investigate the timeliness of the buses based on the morning weather. He records answers to the following questions each school morning for the entire 180-day school year:
Some highlights of Marlo's results:
a. Draw a two-way frequency table to summarize the data.
b. Of all the school days, what proportion did the bus arrive on time?
c. Of all the school days, what proportion did the bus arrive on time when there was no precipitation?
d. Of the days it rained or snowed, what proportion did the bus arrive late?
e. Of the days the bus arrived late, what proportion did it rain or snow?
f. On a day of school without precipitation, would you predict the bus to be on time or late? Explain your reasoning.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A random group of 6th and 8th grade students at a school are asked the question: Do you prefer to complete your homework on a computer or on paper?
a. Create a two-way table to represent the data. Label your rows as 6th graders and 8th graders.
b. What is the proportion, of all of the students, who are in 8th grade and prefer to complete their homework on a computer?
c. Of the students who prefer to complete their homework on paper, what proportion are in 6th grade?
d. A student is selected at random from either the 6th or 8th grade at this school. What do you predict is this student's preferred method of completing their homework? Explain your reasoning.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Calculate relative frequencies in two-way tables to investigate associations in data.
Topic A: Associations in Bivariate Numerical Data
Define bivariate data. Analyze data in scatter plots.
Standards
8.SP.A.1
Create scatter plots for data sets and make observations about the data.
Identify and describe associations in scatter plots including linear/nonlinear associations, positive/negative associations, clusters, and outliers.
Informally fit a line to data. Judge the fit of the line and make predictions about the data based on the line.
8.SP.A.2
Write equations to represent lines fit to data and make predictions based on the line.
8.SP.A.3
Interpret the slope and $$y$$-intercept of a fitted line in context.
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Topic B: Associations in Bivariate Categorical Data
8.SP.A.4
Complete two-way tables and identify associations in the data.
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