# Understanding Data!

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## Objective

SWBAT use data to discover that stem/leaf plots can be used to represent data.

#### Big Idea

Students will gear up to explore how to find the means, median, and modes to represent data.

## Warm Up

20 minutes

Because means, median, and mode are a new concept for my students to learn I begin a
math investigation by doing something concrete. For finding median, we use 5 students lined up at the front of the classroom. I take a student away from each end of the line until we are left with the middle person. I explain to students that they have to apply that same concept when working with numbers, except they must be arranged from least to greatest beforehand. In order to find the median we line up in order from least to greatest (left to right) and find the exact middle person. We talk about how the middle person gives us information about what is typical for whichever numerical data we are
investigating. I ask students to  demonstrate examples using an even number of pieces
of data and an odd number of pieces of data so students can see how that works.

The Mode

To explore mode I write a bunch of random numbers on the board. I ask student write the numbers down on their note paper.  I give them about a minute or so to exaime the numbers to see if they can establish a pattern.  I want to see if they will detect the numbers that occur most frequetntly. If they can not see the number that occurs the most, then I ask them to put them in order from least to greatest.

Examples:

Find the mode of:
9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,
Put the numbers is order for ease:
3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,
The Mode is 15 (15 occurs the most at 3 times)

I repeat this a couple times more to make sure students understand exactly how to find the mode.

Ok guys! You all have done an excellent job at finding median and mode.  Let's try finding the range.  How many of you wonder how your grades are averaged up. Several students say, " I do."  Who would like to volunteer to average out some scores?  To encourage students, I tell them that they would get to pretend to be the teacher.  Of course, almost everyone volunteered.

I call out a set of grades.  67, 78, 80, and 96.  I tell them to write them on the board. In this case guys it does not matter what order you place the numbers in.  Can anyone tell me what to do next? You need to add all the numbers together.  Great! I remind the volunteer to  line the numbers up according to their place value.

T   O

6   7

7   8

8   0

9   6

+ ___

So, the answer is 321. Some students wonder how 321 could possibly be a grade.  I tell them that we are not done yet.  We have to do one more step to figure out the average. Can anyone tell me what to do now? Since, we have a total of 5 grades to average, we need to divide 321 by 4 to determine the actual average.

So then, the average is 80.  I call on a couple of more volunteers just to make sure students understand how to find the means.

## Get into gear!

20 minutes

Materials: Online resource, Checking For Understanding.docx

In this portion of the lesson, I want my students to have some extra practice.

Statistics for kids can be fun! So having my students to find the median, means, and mode of a variety of numbers help them to gather the given data and solve for each concept.  I want my struggling students to have a fun creative way to approach this concept that can motivate them to master this concept. To do this, I ask students to quickly move into their assigned seat so that they can participate in a fun and exciting online resource that will help them reinforce their skills.  Each group will work together solving problems.  Their points will be recorded on the board, to help me check for understanding.  As students are working in their groups, I carefully ask guided questions to reinforce finding the median, means, and mode. I use group scores and student responses to question to determine if additional support should be administered for these skills.

## Power Off!

20 minutes

My students enjoyed working in groups to find the means, median, and mode. I think they are ready to explore a bit with a partner!.

I ask students to move with their assigned partner. I tell them that they are going to work a bit on explain how to solve means, median, and mode to see if they can gain a deeper understanding.  It is my goal to have them work in pairs to reveal their current understanding and difficulties.  I will review their responses after students have openly discussed how to solve.  Because I want students to fully understand what they will be doing in this activity. I ask a couple of questions for students to consider when working together. How do you find the means, median, and mode? A couple of students respond. It is important that, students are allowed to answer the questions without assistance.  I tell them not to worry much if they cannot understand or do everything, because in the next portion of the lesson they will have time to work on a similar task, which should help them gain a better understanding.  I give students about twenty minutes or so to work on the given task. As students are working I circle the room to check for understanding and to reinforce key concepts in solving means, median, and mode.  I remind students they are exploring and it is okay to ask questions if they need to. I invite a couple of students to share what they learn with the class.

## Final Destination!

20 minutes

Materials: Student's Journal Questions!

In this portion of the lesson I want my students to have time focusing on their areas of concerns. I want to help them progress by summarizing their difficulties as a series of questions.

I base the list off of common difficulties observed in trails of this unit. I write one or two questions on the board for students to write and explain in their math journals. I give them about ten minutes or so to finish up this assignment. As students are working I circle the room to check for understanding, and to provide help when needed.

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