MidSchoolMath 1

Two-way tables are useful for organizing bivariate data and determining if there is association between the two variables (although it should be stressed that association does not imply causation). In Bubonic Plague, the dottore, Dorotea Bucca, is troubled over the horrific atrocities brought on by the Plague. She desperately wants to help keep the local townspeople healthy, and she has a theory: cats! She believes that having a cat in the home may help prevent the Plague! She requested that Angelo, her assistant, go gather some data. The data provided are the information gathered by Angelo, as well as the two-way table the dottore has set up for her analysis.

LESSON: BUBONIC PLAGUEIs there evidence to support the dottore's theory?

Bubonic Plague

Understand that patterns of association can also be seen in bi-variate 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 Math SimulatorTM

ImmersionPlay Bubonic Plague Immersion video, whole-class. Restate the question: Is there evidence to support to the dottore's theory?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Bubonic Plague Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

8.SP.A.4Statistics & Probability

MidSchoolMath 2Bubonic Plague

Clicker QuizLaunch the Clicker Quiz, whole-class.

8.SP.A.4Statistics & Probability

Gladys: Two-way tables show categorical data classified in two different ways, and they are used to identify possible associations between the variables.

Kevin: Help students understand that column relative frequencies calculate percentages out of the column totals, while row relative frequencies calculate percentages out of the row totals.

Megan: When row relative or column relative frequencies are similar, we can say it's not likely an association exists between the two variables. If the row-relative or column-relative frequencies are different, we can say it's likely there is an association between the two variables.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #6Standard Math Procedures

Instruction at a Glance

1 Check each statement against the data for accuracy.

I. True. 30 + 28 + 33 + 49 = 140

III. False. = 45%, not greater than 50%

IV: False. 28 + 49 = 77

V. True. = 35%

II. True. ≈ 60%

C: I, II, and V2 Select appropriate option.

4982

63140

49140

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BUBONIC PLAGUEIs there evidence to support the dottore’s theory?Dottore Dorotea Bucca and her assistant Angelo are working very hard to determine whether having a cat in the home actually helps ward off the Plague. They have just collected a new set of data and have organized the data in a two-way table.

Compute the column relative frequencies, and determine if there is evidence to support the dottore’s theory that having a cat helps ward off the Plague.

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?

About this standard

Date PeriodName

MidSchoolMath Bubonic Plague 1 of 2

Is there evidence to support the dottore’s theory? Explain your reasoning.

APPLYING THE STANDARD

Shown is a two-way table displaying the results of a survey asking students which superpower they would most like to have.

1)

How many students prefer Invisibility? __________a)

How many female students prefer Time Travel or Other? __________ b)

What percent of males prefer Invisibility? __________ Time Travel? __________d)

What percent of all students prefer Flight? __________ Other? __________c)

Of those students who prefer Invisibility, what percent are female students? __________e)

MidSchoolMath Bubonic Plague 2 of 2

Date PeriodName

How might this standard appear on a test?

Shown are the row relative frequencies for a survey about curfew and chores. What does the value “0.56” mean?

2)

A random sample of 120 8th grade students is asked two questions: whether they carry a backpack at school and if they like math. The results are summarized below.

4)

Use the survey results to complete the two-way table.

a)

Is there evidence of an association between the variables? Explain your reasoning.c)

Calculate the row relative frequencies. Record the values in the table.

b)

Shown are the column relative frequencies for a survey about curfew and chores. What does the value “0.6” mean?

3)

• 40 students carry a backpack at school.• 58 students do not carry a backpack and like math.• 10 students carry a backpack and do not like math.• 32 students do not like math.

Check out my worked example #1c

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