Lesson Title: ______Two-Way Tables_________________ Course: Common Core 8
Date: _____________ Teacher(s): ____________________ Start/end times:
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the 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 two variables.
MP1: Make sense of problems and persevere in solving them.
MP3: Construct viable arguments and critique the reasoning of others.
MP4: Model with mathematics.
MP6: Attend to precision.
Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson?
Do you have a dog at home?
Do you exercise for at least 1 hour a day?
Be prepared to share your answers to these questions
Lesson Closure Notes: tables.
Exactly what summary activity, questions, and discussion will close the lesson and connect big ideas? List the questions. Provide a foreshadowing of tomorrow.
Describe how you were able to complete each two- way table to summarize the survey results for each poster.
Generate a list of questions that can be answered from the
(Tomorrow students will be interpreting and describing possible associations between the two variables.)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices.
1.
Ask students if they have a dog at home. Have the students that have a dog go to one corner and the rest go to a different corner. Record he number of students who have a dog and do not have a dog. Have students return to their seats. Ask students if they exercise for at least 1 hour daily. Have students who exercise for at least 1 hour daily go to a corner and the others go to a separate corner. Record the data.
2.
Using the questions from the lesson launch, ask how many students in the class have a dog and exercise at least an hour daily. Allow students to answer and justify their reasoning. (Look for evidence of MP3.)
3.
Lead students to the four options: have a dog and exercise, have a dog and do not exercise, no dog and exercise, no dog and no exercise. Place the four options in the 4 corners of the room. Have students go to the corner that best describes them. Record the data for each category.
4.
Assign students to pairs or small groups. Have groups make a visual representation for the data. (Students may create a bar graph, dot plot, tally count, frequency table, table, etc.) Have each group share their visual representation of all four categories. Discuss the pros and cons of each representation. Lead students to constructing a two-way table. (Look for evidence of MP1, MP3, and MP4.)
Example:
Has a dog No dog Total
10 6 16 Exercises at least an hour a day
Does not exercise for an hour a day
Total
8
18
5
11
13
29
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: ______Two-Way Tables_________________ Course: Common Core 8
Date: _____________ Teacher(s): ____________________ Start/end times:
Ask what can you tell by looking at this table? (Students should be able to describe what each number in the table represents.)
5.
Display 4 pieces of chart paper with different yes/no survey questions around the room. Have students record their answer to each question next to their name (see sample). Once all students have answered the questions have them return to their seats and create a two-way table for the data on each piece of chart paper. (Look for evidence of MP4 and MP6.)
Sample possible data collecting questions:

Do you have a curfew? Do you have assigned chores?

Do you have a TV in your bedroom? Do you spend more than an hour on your homework?

Do you participate in sports? Do you musical instrument?

Do you like to try new foods? Do you eat in a restaurant more than once a week?
Example of how to set up chart paper/poster:
Student name
Mary
Brett
Susie
Do you have a curfew?
Y
Y
N
Do you have assigned
Chores
N
Y
N
6.
After collecting data from the class ask: (Look for evidence of MP6.)

Is there any evidence that students who have a curfew also tend to have chores?

Is there any evidence that students who participate in sports tend not to play a musical instrument?

What percent of students who eat in a restaurant more than once a week like to try new foods?

What percent of students have a TV in their room and spend more than an hour on their homework?
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding.
Students will be able to construct a two-way table summarizing data on two categorical variables. Use the tables created from the posters as evidence for success.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary: Two-way tables, frequency, categorical variables
Connections: selecting appropriate data displays
Misconception: Make sure students place the numbers in the correct location in the table. Students may also have difficulty understanding what each entry means within the table (especially the total columns and rows).
Resources: What materials or resources are essential for students to successfully complete the lesson tasks or activities?
Chart paper/ poster paper
Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson?
Write two true and one false statement for each table.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: ______Two-Way Tables_________________ Course: Common Core 8
Date: _____________ Teacher(s): ____________________ Start/end times:
Corner cards for lesson launch
Copy of blank tables Create two of your own categorical variable questions to be shared in class tomorrow.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to create a two-way table from categorical data?
Can students identify the meaning of each individual entry?
Can students make predictions based on the information in the tables?
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .