Mean, Median and Mode Madness!
After finishing the lesson, students will be able to define and determine the mean, median, and mode for a set of data.
Introduction (5 minutes)
- Explain to students that we will be learning about three math terms: mean, median, and mode.
- Give students the following definitions that relate to a set of numbers: the middle number, the average number, and the number that appears the most. Have students guess which definition belongs to which term by writing it in a notebook or scrap piece of paper.
- Explain that students will understand the meaning of each term by the end of the lesson. Do not give students the meanings yet!
Explicit Instruction/Teacher Modeling (10 minutes)
- Hand out an index card to each student. Have students count the number of buttons they have on their outfits. Remind them to check their pants and their shoes, too!
- Ask students to write the number of buttons they have on the index card large enough so it can be seen across the room.
- Create the outline of a bar graph on the whiteboard. Have each student share how many buttons are on his/her outfit and record these numbers on the graph. You may have a student volunteer to help you record or have each student record his/her numbers on the graph, time-permitting.
Guided Practice/Interactive Modeling (15 minutes)
- Have students talk to a neighbor about the number of buttons they see the most on the graph. Ask for a student to provide the answer. Circle the correct number on the board. Explain that this number is called the mode and that the mode represents the number that appears the greatest number of times. They can remember it because mode and most sound similar.
- Tell students to stand up with their index cards. Have the student(s) with the least number of buttons stand on one side of the classroom. Have the student(s) with the most number of buttons stand on the opposite side.
- Then, have the rest of the students line up in between so that their number cards are in order. Students should hold their number cards facing out so they can be seen easily. Point out the mode once again.
- In a domino-like effect, have students on opposite sides of the line kneel down two at a time until there is one student left in the middle (or two, if there are an even number of students). Explain that this middle number, found when all of the numbers are put in order, is the median. They can remember it because a median is found in the middle of the road.
- Have students return to their seats. Explain that to find the mean, students will add up all the buttons and divide by the number of students in the class. Allow students to use calculators for this as well as work with a partner to ensure that no mistakes are made. Tell students they can round in the case of a decimal. Check this answer as a class and discuss why there may be differences in answers (calculator errors or skipping a number are both possibilities).
Independent Working Time (20 minutes)
- Review the definition of each term and have students correct their definitions from the start of class if necessary.
- Pass out copies of the worksheet titled "Finding the Average: Mean, Median, and Mode". Give students several minutes to complete the worksheet.
- Once students have completed the worksheet, check answers as a class.
Enrichment: Students can complete "Find the Batting Average" worksheet. Challenge these students to think of other real-life examples when mean, median, and mode would be used.
- Support: Have students highlight key words found in the definitions on the worksheet (for mean, "add" and "divide;" for median, "middle;" for mode, "most."). If additional support is needed, pull a small group of students and continue guided practice.
Assessment (5 minutes)
- Pick one or two of the problems from the "Find the Average: Mean, Median, and Mode" worksheet to determine students' understanding. Look for instances where students may have mixed up two or more of the terms, or may have forgotten to put the numbers in numerical order, as these are common mistakes.
Review and Closing (5 minutes)
- Pose the following scenario to your students: Your younger sibling or cousin asks you what mean, median, and mode are. How would you describe these terms in a way that is simple enough for them to understand?
- Have students turn and talk to a partner as if their partner were a younger sibling or cousin to complete the scenario.
- Have some students share their responses with the whole class.