Lesson: Calculate Mean
6DASP.1 – Describe and compare data sets using the concepts of median, mean, mode , maximum, and range.
SWBAT calculate the mean of a data set.
(whole numbers only – this standard will be spiraled throughout the year as students gain proficiency with computation of other types of numbers)
· The mean is the “average” of a data set
· To find the mean, add the numbers of the data set together and divide by the number of data points
· The mean of a data set will always be within the range of the set – the mean will ALWAYS be greater than the minimum data point and less than the maximum data point
1. The list below shows the number of yards Clinton Portis ran for his 5 carries during the first half.
9 11 16 4 10
What is the average (mean) number of yards Clinton Portis ran for in the first half?
2. The table below shows the temperature recorded for five days in River Valley.
Based on the information in the table, what was the mean temperature in the River Valley during the five days?
Warm Up: (5 mins)
Review categorical and numerical data with students with an “Ink, Pair, Share”
1. Write one question that will provide you with categorical data about your classmates
2. Write one question that will provide you with numerical data about your classmates
Have students share with partner. Choose 6 students to share their own or their partners’ response to the questions above.
· Unifix Cubes
Opening: (10 mins)
· Today we are going to look only at numerical data.
· When we look at numerical data sometimes it is hard to make sense of it because you might have a lot of different numbers to reason with.
· Because of this, sometimes you want to be able to make sense of the data or summarize into just one simple number. One way to do this is to find and use the mean of a data set.
· Pass out Unifix cubes to each group of students. Each group should get one stack of Unifix cubes (or each group can get all of the unifix cubes below if there are enough materials) and cards that say how many cubes they started with:
o 8 white cubes
o 12 red cubes
o 3 blue cubes
o 5 yellow cubes
o 7 green cubes
o 1 black cube
· Ask class – let’s say we wanted each group to have the exact same amount of cubes – what can we do to make each group have the same amount of cubes?
· Student will suggest we can take some from the people that have more and give them to the people that have less until everyone has the same amount.
· Facilitate the class leveling out the Unifix cubes
· Ask students how many cubes are now in each group
· Explain to students that they have used materials to find the mean of the data set.
· Display for students on the board “mean” and show the process of what students had and now what they have – this is what it means to “average” the numbers or find the mean
· Tell students that one way to understand mean is to think about sharing equally – how can you take everything that is represented and share it among all the people so that each group/thing has the same amount.
Intro/Direct Instruction: (10 mins)
· Students take notes with teacher – define mean
· Tell students that unfortunately we won’t always be able to use cubes or sometimes we won’t have enough cubes to represent the numbers, so we can use a pencil and paper way to find the mean of any numbers given to us.
· Give students the steps:
o First we are going to add all of the numbers together – this is like when we combined all of our cubes together to see how many there were
o Second, we are going to divide our sum by the number of data points we started with – this is like when we divided our pieces equally among all of our tables
· Share Chant with students – explain that this is one way to help us remember the steps for finding the mean
o The mean is the average
You add and divide
· Model for students finding the mean – Pull Ups – example
o Add the numbers together
o Count the numbers of sets accomplished
o Divide by 6 – make it really clear why you are dividing by 6
· Relate back to the idea of making the groups even and then splitting the numbers between the groups
Guided Practice: (10mins)
· Students should find the mean for the following data sets: Guide students through each one – determine which students have clear understanding and which may need extra small group help
o 40, 40, 40, 40, 40
o 22, 23, 24, 23, 26, 23
o 95, 87, 89, 97
· Discuss with students – what they notice about the answer choices
· Emphasize key point number three – the answer for mean will ALWAYS fall within the data set – it will always be larger than the smallest number and smaller than the greatest number.
· Ask students to “think ink” (write about) why they think that is - Discuss with group
Independent Practice: (15 mins)
· Students complete worksheet – teacher circulates to monitor understanding/practice
Closing: (8 mins)
· Complete frayer model as a class for "mean" - write a definition, procedure for finding it, the part of the data chant refering to mean and a picture or example.
· Ask students to look at the following data set and ask them to answer without solving/calculating:
Which of the following is the mean of the data set below?
100, 90, 90, 80, 60
· Give students exit ticket
|CW CalculatingMean Classwork||
|HW CalculatingMean Homework||
|Exit Ticket Calculating Mean Assessment||
|Notes Calculate Mean Notes||