SWBAT:
â¢ Calculate the mode, mean, and median of a data set.
â¢ Make a prediction of how a new value will affect the mean, median, and mode.
â¢ Explain how a new value in a data set will affect the mean, median, and mode.

What will happen to the mode, median, and mean of data set when you add a new value? Students work to make predictions and understand how new data will affect measures of central tendency.

8 minutes

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to analyze a line graph in order to answer questions. Scholastic News has a 5^{th}-6^{th} grade edition that typically includes a graph on its back page.

I ask for students to share their thinking. I am interested to hear about the strategies students used to determine the answer to question 3. I ask students what we should get when we add up all parts of a circle graph. I want students to understand that the entire circle graph represents 100%. I also want students to realize that this circle graph is not accurate because the sum of all of the pieces is 99%. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others**.

8 minutes

I have students work in partners to complete this review from the previous lesson. The most common mistakes I see are that students confuse the median, mean, and mode. I want to make sure students understand what each term means and how to find it. Another common mistake is that students divide the new sum by 5 rather than 6.

Problem two gets to the big idea of this lesson. It is important that before calculating the changes, students make predictions. I ask students to share out their findings for problem 1 and 2. I ask students:

- Why did the mode and the median stay the same?
- Why did the mean change?

I want students to understand that the mode stayed the same, since $3 is still the value that occurs most often. The median stayed the same, since $3 is still in the middle. The mean increased because we added a game that was more money. Our new sum was $30, and we divide it by 6 since there are now 6 games. Some students may not see this pattern yet, and that is okay. I want students to start to recognize and anticipate how changes will affect the mode, median, and mean of a data set during their group work.

22 minutes

**Notes:**

- Before this lesson, I use the exit tickets from the previous lesson to
**Create Homogeneous**groups of 3-4 students. - I copy sheets A-E and place them in the back of the room.
- Each group also gets a
**Group Work Rubric.** - I create and
**Post a Key.**

Students move into groups and I pass out materials. We work together to calculate the mean, median, and mode of the six games. I have a volunteer read the directions for the groups. I make sure that students understand that with each new problem, they are starting with the original set of six games and making a change.

Students work in their groups while I walk around to monitor student progress and behavior. Students are engaging in **MP2: Reason abstractly and quantitatively, MP6: Attend to precision, **and** MP8: Look for and express regularity in repeated reasoning.**

If students are struggling, I may ask them one or more of the following questions:

- How do you calculate the mode/median/mean?
- What do you think will happen with this new piece of information? Why?
- How did your prediction compare with the new mode, median, mean? Why is this?

If students are on track and need some extension I may ask them one or more of the following questions?

- What will happen if you add another game that is more than the original mean? Prove it.
- What will happen if you add another game that is less than the original mean? Prove it.
- What will happen if you add another game that is the same price as the original mean? Prove it.

When students finish a page, I quickly check in with them. If they are on track, I let them use the key to check their work and move on. If groups complete all of this work, they can work on the challenge problems.

12 minutes

I ask students to share what patterns they noticed when they added a new game to the original six games. Students participate in a **Think Pair Share**. I want students to be able to anticipate how a new piece of information will affect the mode, median, and mean of a data set. Students are participating in **MP3: Construct viable arguments and critique the reasoning of others **and** MP8: Look for and express regularity in repeated reasoning**.

If I have time I ask students, “What if we add one game to the original set and the new game causes the mean to change from $7 to $8. How much did the new game cost?” Students participate in a **Think Pair Share**. I am interested to see the strategies students use. Students should be able to understand that the new game must be more than the original mean of $7. Some students may guess and check. Other students may work backwards and realize that the sum of the 7 games must equal $56, since 56 divided by 7 equals $8.

I pass out the **Ticket to Go **and the **Homework.**