Find Missing Values in a Two-Way Table Lesson Plan

Warm-Up

Start the class by reviewing how to read two-way tables. The student resource sheet has a copy of each two-way table students will see today.

Allow students a few minutes to use the table to answer the questions. Students should be able to recognize how to read the two-way table; however, make sure students can explain their reasoning and how they found the answer.

Student Problem Solving

For this first example, give students a couple of minutes to process the information they are given. Encourage students to try and fill in the blanks if they can. To help with the discussion later, have students indicate the operation they used to find the value.

Student-guided discussion

When reviewing with students, allow them to lead the discussion on the order that the blanks are filled. Be sure to have students explain how they decided what values and operation were needed to be used to find each missing value. 

• If students can fill in all of the blanks: Ask students to explain the pattern for when values were added or subtracted.
• If students cannot fill in all of the blanks: Start by asking students how they can figure out the total number of people surveyed. They should recognize that they can add to find the total. Ask students if there are any other blanks that would require addition. Repeat this process with subtraction. To help students realize they have to subtract, phrase questions like, “if `10` people under `13` prefer apples, and `27` people under `13` were surveyed, how can we find how many preferred bananas?”  

Eventually, you want students to recognize that they need to start with rows or columns that only have one value missing. 

Two-Way Tables with multiple rows

This next example may be trickier for students because there are two columns and three rows of data. This can also complicate students’ calculations; however, give students an opportunity to try and fill in the table. To help with discussion later, encourage students to write how they found each missing value, such as “`26 – 11 = 15`”.

Class discussion

Similar to the previous example, ask students to explain how they determined each missing value. Consider asking students if they are able to start anywhere to help students recognize that they can’t always fill in a blank, such as the total number of boys. Make sure you also ask students if they all found the missing value the same way or not. For example, the total number of people who chose yellow can be solved two different ways. Make sure students are able to explain when they add or subtract the values. 

Additional example

The slideshow contains one more example for the class. Have students try it on their own first, or with a partner. Then ask for volunteers to come to the board and fill in missing values while explaining how they found them.