Mean

5 min

Teacher Prep
Setup
Students in groups of 2. A minute of quiet work time, followed by partner and whole-class discussions.

Narrative

The purpose of this Warm-up is to prepare students to find the mean of a data set. While the goal of the activity is for students to create an expression with a value close to 4, the discussions should focus on the reasoning and strategies that students used to create their expression. Students should notice that they would get the same result if they divided the value of the entire expression in the numerator by 4 as they would if they divided each number in the numerator by 4 because there are 4 numbers in the numerator. 

During the partner discussions, identify students with different strategies for creating an expression with a value of 4. Ask them to share during the whole-class discussion.

Launch

Arrange students in groups of 2. Give students 1 minute of quiet work time, and then 2 minutes to share their response with a partner. Follow with a whole-class discussion. If students finish early finding a solution close to 4, challenge them to find numbers that result in exactly 4.

Student Task

Use the digits 0–9 to write an expression with a value as close as possible to 4. Each digit can be used only one time in the expression.

(TEST+TEST+TEST+TEST)÷4\displaystyle \left(\boxed{\phantom{TEST}}+ \boxed{\phantom{TEST}}+ \boxed{\phantom{TEST}}+ \boxed{\phantom{TEST}} \right) \div 4

Sample Response

Sample response: (2+8+5+1)÷4(\boxed{ 2 }+\boxed{ 8 }+\boxed{ 5 }+\boxed{ 1 }) \div 4. Because the expression should be close to 4, the total inside the parentheses should be close to 16.

Activity Synthesis (Teacher Notes)

Poll the class on whether the value of their expression is exactly 4 or is close to 4. Ask selected students to share their strategy for creating an expression with a value of 4. Record and display their responses for all to see.

As students share their reasoning, consider asking some of these questions:

  • “How did you decide on the value inside the parentheses?” (To get a final result of 4, we want the parentheses to have a total of 16.)
  • “How might your strategy change if the divisor was a different number, say, 6 or 10?” (The total for the parentheses would need to be 4 times the divisor. For example, if it was 6, then the sum of the values inside the parentheses should be 24.)
  • “How might your strategy change if the parentheses had more numbers or fewer numbers inside them?” (The total would still need to be 16, so if there were more numbers, they would have to be smaller. If there were fewer numbers, they would have to be greater.)
Anticipated Misconceptions

Some students may think that they need to use all of the digits from 0 to 9. Tell them that only 4 digits need to be used, although they are welcome to try to find a good solution using 2-digit numbers if they want to.

Standards
Building On
  • 4.OA.A·Use the four operations with whole numbers to solve problems.
  • 4.OA.A·Use the four operations with whole numbers to solve problems.
Building Toward
  • 6.SP.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  • 6.SP.A.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

15 min

15 min