Two way tables can be quite confusing for some of my students. I've designed these Launch Tasks to help them visually interpret the tables correctly. Most students probably have not worked with two way tables before, so this particular exercise is a good start in this learning process.
When I hand out the Tasks I ask my students to complete each two way table using its corresponding word bank. This can be done by simply writing in the words in the appropriate box. I make students use a pencil when writing in the words because we will use the tables in our following activity.
As I walk through, I hint that the easiest boxes should be completed first. I pay special attention to my ELL students. They may need some guidance with the phrases. I especially check whether these students completely understand the phrases in the word banks so they can be able to carry out the tasks correctly. Previously cutting out the words for ELL students instead of having them write them in, is helpful and saves time.
Students should try completing the tables independently and once they are done, discuss the tables with shoulder partner (MP3). Finally, I project the Launch Task Answers on the board so students can self check and discuss any further corrections if any.
After the Launch is complete, I let my students know that two way tables are often used to analyze survey results. I say, "When a lot of information is obtained, it is often helpful to condense this information into a table by grouping the data into categories. A two-way table is one way to do this." Then I will demonstrate how the rows indicate one category and the columns, the other category.
Next, I announce to the class that we will be collecting data using a survey method today. Our sample for the survey will be the class. I project Tables A and B on the board. I tell the class that each student should go up to the board in an orderly manner and mark a tally in an appropriate box in each of the two tables.
Once all students make one mark in each table, they should tally the marks and complete the tables at their desks with a partner. Here is an example: Board and Student Table Example.
As my students work on the task I watch out for a common mistake: adding the bottom row and far right column of "totals" and placing this value in the lower right hand box. Actually this number should be the sum of either the bottom row, or right column. In my case this number is 19. Students may write 38.
When the students have completed their tables, I introduce the term frequency as the statistic that describes the number of tallies in each box. We will discuss the relevance of the frequency to the categories in each table, making connections to our class (since this data describes us).
In the second part of today's activity, I get a chance to see how well students are able to interpret their two way frequency tables. I hand each student a set of questions (Student Questions for Tables A and B) and I ask that they discuss and answer each question with their partner.
Students normally take about 10 minutes to answer these questions. Before calling on volunteers to share their responses out loud, I make sure both completed tables are projected on the board to serve as a reference.
To help students reflect back on their work today, I ask my students to circle the appropriate thumb symbol for each question (see Student Questions for Tables A and B), according to how well they understood what they were asked to do. If time allows, I ask that students discuss sideways or thumbs-down questions with any classmate nearby that has a thumbs up for the same question. This sometimes works well enough that my students change their response before I collect the papers. Either way, I make sure I check these out carefully before Part 2 of the lesson.
For homework I ask my students to explore this internet resource on Two Way Tables. I encourage my students to spend 10-15 minutes exploring the information on this WWW worksheet.