Hilarious Histograms. Analzying and Creating
Lesson 10 of 23
Objective: The students will be able to create and analzye Histograms.
The DO NOW portion of the lesson sets the stage for the learning for the day. The students will be answering the surveying question “how many 12-ounce cans of soda do your classmates consume in a day” . They begin by stating how much they drink, then they decide whether or not they feel their number will be a typical answer. Once this is done, they can survey the rest of the class to determine how many cans of soda are consumed by their classmates. After the data collection is complete, I want the students to see a histogram. We will discuss the components of a histogram (title, bars not separated, frequency and equal intervals, and labels.) While looking at the histogram, ask students if it is necessary that the numbers be equal along the x axis. We’ve already established that numbers need to be equal on the y axis. Next, I will have them compare and contrast the histogram with a bar graph using a venn diagram. Once we have established that a histogram can show numerical data using intervals, I will have the students use their survey question and create their first histogram. (SMP 1,2,6)
Histograms and the Mean
Refer back to the survey question about the amount of cans of soda consumed by their classmates. Ask the students to calculate the mean (if needed, review how to find the mean and have them use a calculator) Randomly choose students to explain how they made their calculations. It is fine if students explain it all the same way. Students in the class that are struggling will benefit from the repetition. I’m expecting some students to say that they grouped same numbers together and multiplied by their frequency, while others may have added all numbers together and divided by how many numbers were in the data set. Next, ask the students if they think the mean is a good way to describe the amount of soda their classmates consume? (accept reasonable answers… some may say yes if all data is about the same and some may say no if there is an outlier)
Pass out the grid paper and have the students make a histogram displaying the data collected. (Before creating, I may once again discuss what a histogram needs to have.)As I walk around the room, I’m looking to see if the data along the x axis shows the number of cans, the data on the y axis is the frequency, the bars are connected, intervals are equal and there are titles and labels. Once all histograms are complete, have the students compare their results with a partner. Before cutting out their histogram, have the students estimate the mean and then calculate it.
Next, have all the students cut out their histogram and tell them to balance it on their pencil (the fold should represent the mean). Ask students to tell you what number the fold is on (depending on the survey, the histogram should be balanced on the mean)
Using slide 5, the students will make a histogram of the new data collected for 7th grade. (New graph paper). Ask the students to first estimate the mean (write it down), then ask them to calculate the mean and ask how well did you estimate.
Ask the students how the data compares to their 6th grade data (the histogram for 7th grade is symmetrical, the mean is 2.5 cans per day and the mean does not seem to represent most of the students, who either drank much more or much less than the mean)
Finally, ask them if it would be helpful to compare the data for the two classes using the mean? (this will depend on the data collected for 6hh grade. If there are outliers, then the mean would not be the best way to compare the data)
Again, have the students create a histogram for the 8th grade class. Using all 3 classes, have them compare the data (center, spread, shape, mean and range). We haven’t talked about range in the other data displays, but it may be a good idea to have them look at the spread of the data to determine how to describe the data set. For example, the comparison between 7th and 8th grade would show that there is a small spread of data, while the range for 8th grade is a larger spread which means there may be really large data points pulling up the mean.
Each graph can be cut out and the pencil test can be used to show the mean. (Good visual for those that struggle to determine the mean)
Tools: Graph paper, calculator, scissors,
Closure + Homework
The students were creating and analyzing histograms in today’s lesson. In order to effectively assess their learning, I’m going to have them write a few sentences comparing the 6th and 8th grade soda consumption using the mean and ranges. Once they have written their thoughts down on paper, I’m going to have them share their responses with a partner. To insure proper communication, have students decide on who will be an A or a B. Have one of them go first. Students that are listening will be instructed that they will need to paraphrase what their partner was telling them after they are done speaking. So, A goes first and reads what they wrote down. The B says, “I like what you said about”. Then they switch turns. A is now listening and B is speaking. A will respond with “I like what you said about” After the partner share and if time permits, allow the students to share whole class.
This information can be used as whole class discussion or it can be turned in for evidence of student learning.
Homework: Histogram homework. (students will be combining their learning of stem and leaf, histograms and line plots to tell how they could estimate the mean). Then they will be describing a situation when the mean could give the wrong impression of the data.