Finding an Average
Grades: 4th - 7th

Objectives:

• The student will be able to find the range and mode of a given set of data.
• The student will be able to describe what it means to find the "Average" or "Mean" of some given data.
  

Strands:

• Mathematics as Problem Solving
• Mathematics as Communication
• Mathematical Connections
• Computation and Estimation
• Number
• Patterns & Functions
  

Materials Needed:

• Unifix Cubes of different Colors for each student to use.
• Pencil and Paper for recording
  

Procedure:

• I initially have the students working in groups of four.
• Give the groups of students a baggy containing the unifix cubes.
• It is important for the students (especially at the lower grades) to have time to "play" with the manipulatives. I would suggest giving them 5 to 10 minutes just to play. Then talk about the difference between "Play" time and "Math" time and how it is now time for "Math".
• Not wanting to miss an opportunity for the students to work with patterns I ask the students to select 10 of the cubes at their table and "snap" together a pattern. I then ask for volunteers who would be willing to share their pattern with the rest of the class.
• Next I ask the student to count how many total pets they have at their home at this time. Another good question would be to ask how many total people are living in their home right now. You could also ask how many children are a part of their family (siblings). Any of these questions would work. Using the "pet" question you are going to have some students with ZERO as an answer. That is all right.
• Now ask the students to take one cube per number and place them in a tower, snapped together.
• Students are now asked to hold their towers in front of them and get in order from the lowest tower to the highest tower.
• Once they are in order have the students get in rows. All students with Zero stand in a single line, behind one another. All students with one cube form a single line, behind one another and so on. Some lines will have only one person and others will not have any.

Depending on your room try to get the students to line up in an orderly fashion. You could even take this activity outside at this point if you prefer. Your class should somewhat resemble the diagram below.

• Now have the students look at the arrangement that has been formed. Ask them to identify the number that has the most students lined up behind it. This was the "MODE" or "Most" as I explain to students.
• The students are then asked to tell me the difference between the smallest number and the largest number represented (in are example the difference between 9 and 0 = 0). We talk about this being the "Range".
• Now the fun begins. Ask the students to go around the room and compare their tower with another students tower. They are to try and make their towers as close to the same size as possible. For example if one student had 9 and the other student had 5 then the student with 9 would give the other student two of their cubes so that both towers are now 7 cubes tall. Each would then now find another student to compare towers with.
• After this has gone on for about 10 minutes you will notice some of the students getting frustrated. When asked they will probably respond like, "I can't find anyone else to share towers with." At this point ask all students to return to their desks.
• As for a show of hands as to how many have....lets say 3, then 4, then 5. If there are students with 3 cube in their tower and other students with 5 cubes ask them what they should do. Continue this until everyone has either one number or another number in our example it would be either 4 cubes or 5 cubes.
• Introduce the word "Mean" to the students and tell them that this is the average. I then ask the students, "If someone came into this classroom and asked, "About how many pets does each student have at their home?", the answer would be, "about four". This would be the estimate of the average for this class.
• Students can then be asked to record what they have learned today. Ask them to draw the following: One tower with 4 squares, one tower with 6 squares, one tower with 3 squares and another tower with 4 squares. On their paper ask them to write what the "Range" would be and then using a complete sentence record how they arrived at this number. Then ask them to record the "Mode" or "Most" for this set of number and again using a complete sentence record how they arrived at this number. Now ask the students to use arrows or any other method they prefer to show how they would "share" squares so they could make each tower as close to the same size as possible. They are to then record their answer for the "Mean" or "Average" of our example and again using complete sentences record how they arrived at this average.