Lesson: Missing Mean

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Lesson Objective

SWBAT find the missing data point of a data set to attain a desired mean.

Lesson Plan

- see attached file for formatted lesson plan-
STANDARD
6DASP.1 – Describe and compare data sets using the concepts of median, mean, mode , maximum, and range.
AIM/OBJECTIVE:
SWBAT calculate the value of an unknown to attain a desired mean using the teeter-totter method.

KEY POINTS


• The mean is an average of a data set.
• Understanding the mean is putting all the data together and spreading it equally can help us to find missing data points to attain a desired mean.
ASSESSMENT
Jamal is growing plants for his science project. The height of 4 of his plants are shown in the table below.

Plant Height (cm)
1 41
2 50
3 53
4 48
5 ?

Jamal predicted that the mean height of all five plants was 50cm. What would the height of plant 5 need to be for Jamal’s prediction to be true?


Warm Up: (3 mins)
Look at the problems below. How are they different? How are they the same?
• 48 + 53 = _____
• 48 + ____ = 64


Opening: (10 mins)
• Look at the two questions below – how are they different? How are they the same?
Victoria practiced piano four times this week. The number of minutes are listed below for the week:
35, 40, 30, 25

Victoria will practice on more time this week. If Victoria wants to have an average of practicing for 35 minutes this week, how many minutes must she practice?
__________________________________________________________________________________
Kaiyonna practiced violin four times this week. The number of minutes are listed below for the week:
35, 40, 30, 25

Kaiyonna will practice on more time this week. If Kaiyonna practices for 35 minutes, what will be the average (mean) number of minutes she practiced this week?

• Discuss students’ responses
• Tell students that the first problem is like knowing the end but not having all the parts and having to figure out that missing piece but the second problem is much more straight forward.
• Tell personal story of how useful of a skill this was for me in high school when I wanted to figure out how much I would have to get on a test to keep my average up.
Intro/Direct Instruction: (15 mins)
Review:
• Over the past couple of lessons we have been analyzing data sets using statistics. We are given a data set and we use the appropriate procedures to find the desired statistic.
• Like we discussed in our warm up – sometimes we don’t have all the points but we do know where we are headed.
• Today we are going to look at problems where we know what we want the final mean to be but we will have to figure out the missing data point in order to attain that desired mean.
• Look back at the example (#1) from the warm up with the students – re-read it.
• Underlined what is known about the problem. Highlight what we are trying to figure out.
• Describe that there are many different ways to solve this problem but today we are going to use the teeter totter method.
• Model for students drawing on the left side what we already have (the four amounts of time practiced for the piano.
35, 40, 30, 25___ |____________
• Then ask students what we want the average to be.
• Since we want the average for five different practice sessions to be 35, we can put 5 35s on the other side of the teeter totter
35, 40, 30, 25___|35, 35, 35, 35, 35
• Explain that we can put the 35s there because we know that the object of finding the mean is to divide all the data equally – so if each set has 35 then our mean will also be 35.
• Now, the goal is to have both sides have a mean of 35, so to see what we need to put in the box in order for that to happen, we should add up what we know on both sides.

35, 40, 30, 25___|35, 35, 35, 35, 35

• On the left side we have 130. On the right side we have 175.
• Since we know we want the left side to be equal to the right side, all we need to do is find the difference between our two sides and that will tell us what we need our missing data point to be.
• In this example we see that 175– 130 is equal to 45 minutes. So if Victoria wants to have an average of practicing for 35 minutes this week, she will need to practice for 45 minutes the last day.
• Check by making sure that your left side does equal the mean you want. Show that the data adds up to 175 and when we divide by 5 we get 35.
Guided Practice: (15mins)
• Tell students that we are going to walk through a couple examples together. The first one we are going to do just one step at a time with the teacher guiding them through.
• Guide students through the first example of notes. Check after each step whether students have it correct.
o First I want you to put the given data points on the left side of your teeter totter.
o Next you want to put a box on the left side of the teeter-totter to represent that missing point we are trying to figure out.
o Next on the right side of your teeter totter, you are going put your desired mean for each data point you have on the left side.
o Okay, now you want to add up the two sides to see what they equal.
o Next we are going to find the difference between those sums.
o Now we have our answer – we can check to make sure our answer is correct by finding the mean of the left side.
• Walk through another example with students. This time ask students for the steps and do multiple steps at time.
o What are the first two things I need to do? (write the given data points and a box for the missing point on the left side_
o Okay, now that I have my left side with the given data points and a box for my missing point, what should I do next? (write the mean on the right side for each data point on the left)
o Okay, now I have all of the information I need to find the value of the box. How am I going to figure it out? (add each side and then find the difference between the two)
• Check for understanding – and which groups of students to pull for independent practice with final guided practice problem.
Independent Practice: (15 mins)
• Students complete worksheet – teacher circulates to monitor understanding/practice – or pull a small group of students who struggled during the guided practice

Closing: (5 mins)
• Review the steps.
• Ask students why we put information on the right side.
• Ask students how you can tell the difference between a regular mean question like we practiced earlier this week and a problem like we are doing today.

Lesson Resources

CW Find the missing data point for a desired mean   Classwork
2,492
CW Find the missing data point for a desired mean MODIFIED  
1,331
Hw Missing Mean  
1,634
Lesson Plan - Missing Mean   Lesson Plan
1,106
Notes Missing Mean   Notes
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