Lesson 14 of 23
Objective: The students will be able to identify when a data display is misleading.
The DO NOW problem is designed to sum up student learning about graphs. A table of data is given to the students and they are to use that information to display in a chart. The students can use any data display to represent this information(MP1 and4). Once the data is displayed, the students will be writing about the center, shape and spread of the data(MP2). It may be a good idea to partner students up that have displayed the data differently to allow for discussion about why they chose the graph they did and if the distribution of data is same even though they chose different data displays. (MP3)
How are graphs misleading?
My thoughts for this lesson are that the students will be able to come up with their own discoveries as to why graphs are misleading. They have seen many different data displays and are aware of what is needed to create them. However, I may go over the usefulness of each display and what elements need to be present before they begin looking at the graphs. I will also explain to them that in the real world, graphs misrepresent information on a regular basis. For example, when Trident says that 4 out of 5 dentists prefer Trident gum, this could be misleading because we do not know how many dentists were surveyed. The goal of today’s discovery is to look at each graph and decide why it is misleading. Each slide on the power point shows different misleading graphs. The students should look at the graphs and decide whether the or not the graph is misleading. Once they have decided that the graph is misleading, I want them to look at the graph and explain why (MP3). They can first write down their thoughts and then share with their tablemates. My vision for this is that the teacher will manage the discussion while the students are formulating their own thoughts. The teacher can walk around the classroom asking questions like:
Why do you think this graph is misleading?
What are the elements of a line/bar graph that might help you to identify why the graph is misleading?
What do the numbers on the vertical axis represent? (MP2) How should the numbers be placed on the vertical axis?
I would let the students look at one graph at a time and then have whole group discussion about their findings. Do this for each slide.
Slide 2: I chose this slide because it was a double bar graph. I wanted the students to look beyond what the graph was intended to display. I will be asking about the elements of a bar graph. I would like students to tell me that the intervals on the y axis need to be equal and start at zero. When they see that the graph doesn’t start at zero, the graph becomes misleading because the bar heights are not representative of the data.
Slide 3: I chose this slide because the interval markings are not equal which then makes the data skewed. All too often students will not have equal intervals and they don’t see anything wrong with this. These graphs show how the interval markings can make you believe that Graph A sold more than B or C when in fact they all sold the same. Again, I would have the students really compare the data that is being represented to see the misleading part.
Slide 4: I choose this graph because of the break in data. I want the students to know that a break in data is ok as long as it represents the amount of missing data. In this case, the break in data is misrepresented which makes it appear that soccer is much more popular than lacrosse. Looking specifically at the data, shows that there is a nominal difference in attendance. I would ask the students to look to compare the actual numbers of attendees to prove it and then have them make the statement of what people might believe by looking at this graph.
Slide 5: I chose this graph because it was comparing graphs. The students will need to look at the data collected and what it represents. They will see a break in data and look to see if it affects the representation of the data collected. Then they will need to make a statement of what people might believe. I’m looking to hear, people will believe that Albany has higher temperatures than New York City when they really are about the same. The break in data misrepresents the data collected.
Next, the student will be demonstrating their knowledge in an activity called mixed freeze group (see video)
This activity will allow students to engage in MP3. They will be sharing their thoughts and justifying their answers.
Once mix-freeze-group activity is over, have the students return to their desks for the final wrap up.
In order for me to effectively assess the students, I’m going to ask them about the essential question for the day….How are data displays misleading? I want them to sum up their learning in the following ways.
- Look at the scale to determine if the intervals are equal
- Look at the scale to see if it starts at zero
- If there is a break in data, is it representative of the amount
- When comparing two graphs, are the comparing the same criteria
- In pictographs, are the pictures equally drawn