Research Lesson
Research Theme: Students’ ability to persevere through problems and communicate effectively with peers.
Lesson Topic: Reading Data from Graphs
Lesson Objectives: Students will identify patterns and relationships between variables using information in a graph.
Students will create a table from data in a coordinate graph.
Students will compare patterns of change in a table and graph.
(This lesson is adapted from materials provided in CMP2 – Variables and Patterns)
Lesson Outline- Main sequence
- Key problems
- Approx. times
Students have gone through previous lessons on constructing a table and determining patterns in tables. Also students have been introduced to coordinates and graphing data. Students have seen how patterns can be analyzed in graphs as well.
LAUNCH (5 minutes):
Review with students:
Draw a graph on the board and ask students what each term is (label as discussion progresses)…
-Dependent variable: y-axis
-Independent variable: x-axis
-How does the independent variable relate to the dependent variable?
-x and y axis
-coordinate pairs
EXPLORE (20-25 minutes):
Use popsicle sticks to separate students into groups of 3 or 4.
Pass out the worksheetwith questions 1-3 to each student. Give one copy of question #4 to the group to work on as a whole. Each student does not need their own of #4.
Explain that they should work as a group on the worksheet however each student needs to answer each question on their own worksheet.
Remind students that they will be working collaboratively on the story so being on the same page and discussing each question as a group will be helpful later.
Explain and discuss the graph and the axes with the focus of it being a cumulative graph vs. an interval graph. Also look at the unit labels for the graph to eliminate various misconceptions with what the graph represents.
Question 4 is having students develop a story based on the graph they see. This can be a bullet pointed list to keep time down. In addition, only one student in the group needs to write the story down.
Question 5 is on a separate sheet of paper. Give this to groups to work on if they are done with questions 1-4 before it is time to summarize as a class.
SUMMARIZE (5 minutes):
Bring students back together as a class. Discuss worksheet.
-Have students put their pencils away to ensure that they don’t change their answers.
What sort of table did you create? What were the columns you created?
What answers did you come up with for the total distance traveled? If there are differing answers ask students to explain their reasoning.
In this graph does it make sense to connect the points in the graph?
So, if we agree to connect the points, how might you connect them?
What would it mean if the points were connected with straight line segments?
STORY TIME (10-15 minutes):
Ask a student from each group to “read” their story they came up with to describe the graph. They can read this at the front of the class or standing at their seat.
Read stories for the remainder of the class. Use Elmo to display a large graph so students can follow along with stories.
Ask students to turn in their worksheets before they leave the classroom at the end of the lesson. / Expected Student Responses/Actions
- Methods & strategies
- Misconceptions
-“on x-axis” not y-axis
-“vertical axis or line”
-What is the dependent variable? Example answer: distance from home or the starting point.
-Independent variable: could be mixed up with dependent
-“on y-axis” not x-axis
-“horizontal axis or line”
-X/Y axis should be cleared up when talking about independent/dependent variables
-Coordinate Pairs: may not know what this is or may not remember where the x or y point goes. It is an x and y value of a specific point. “It’s a point on a graph.”
Make sure students are aware of question #3 on the back of the worksheet.
One student may want to “take charge” but all should give input.
Question #2) Students may struggle making data points from the graph into a table.
Question #3) Students need to decide which presentation of the data is the one they prefer. Ask for strengths and weaknesses of each.
Question #5) (if they get to it) this is a computation problem, various answers will be given. Answer: 81+8+8=97miles
Question #5) Students may think this is a graph of total distance traveled for each point on graph, not just distance from a starting point
If they say no, ask if that means the riders make progress between points. You want them to realize that time passes and distance may be covered between points, so it makes sense to connect them.
They may have various ideas.
They were going at a constant speed during each half-hour interval.
STORY TIME:
Students reading the stories may catch some of their own errors or classmates errors.
Example #1 “at hour 1.5-2 that they are going at a constant speed” (really they are stopped for 1/2hr.)
Example #2 Student says “at hour 2.5-3 that they ‘slowed down.’” (they backtrack 10 miles)
Example #3 Student describes graph as an interval graph or histogram. / Notes for the Teacher
- Suggestions to guide instruction
- Questions
Ask students quick questions about each of these terms. Address misconceptions briefly, students should be familiar with these terms from previous lessons.
Restrain yourself for the first 10 minutes, let students work through and flounder on the first problems on theirown. But do ask questions of the students and what they are writing for answers. See where misunderstandings are happening
Do not bother groups that are working well on the worksheet, although after 10 minutes if there is a group(s) having difficulties then use the following questions sparingly to guide a discussion and progress on the worksheet:
What does the decrease mean between 2.5 and 3 hours? (something/someone backtracked)
What two variables are represented in the graph?
What role do variables play when making a table?
What does this point on the graph tell you? What does the x-coordinate of the point represent? What does the y-coordinate represent?
Show how you would enter the information about the point we looked at into the table.
What might have happened between hours 2 and 4? What do you think may have happened between 1.5 and 2?
During which interval is the most progress made? Least progress made?
Is the line steeper anywhere, what does that mean?
Please remind students they do not need to write down details for their story, create a list of main points to discuss the important aspects of the graph.
STORY TIME: (put enlarged graph on Elmo so students can reference it.)
Smooth over issues when students catch their own mistakes. Address these next class time after looking at the worksheets.
-for Example #1: Make compare the graph the example of a constant speed and therefore gaining distance versus at 1.5-2hrs there is no distance gained or lost.
-for Example #2: Once again make comparisons hour 3-3.5hrs where they are gaining distance versus 2.5-3hr they are backtracking.
-for Example #3: Have students focus the labels of the axis’ and discuss what a cumulative graph means.
If students are continually doing the same mistake (interval vs. cumulative graphs), read the stories out loud and correct them as a class.
Have students at the end of class staple their worksheets together as groups and turn them in as they leave class. Look at worksheets and correct and discuss misunderstandings on the graph the next class period. / Key Observation Points
- What to watch for in student thinking & understanding
See student’s perseverance.
See what they can do with a set of data.
Can you put it into a table?
Launch:
Does the launch activate the right prior knowledge to persevere through the worksheet?
Group Cooperation/Dynamics
Each person observes two groups (approximately 6 kids)
If students get stuck what is their reaction? (Turn to self? Turn to group? Turn to teacher?)
What percentage of the students are engaged?
Are there leaders in the groups?
Record deep conversations/debates/differences of opinion…
Notice how students communicate with each other…
Are students following directions on sheet: are they drawing a table, etc.
One person will collect student work and see if answers are accurate.
Are groups realizing mistakes during storytelling? Are others changing their story in case of mistakes, etc?
Are students understanding the mistakes and knowing how to correct them as a class?