Student Actions

Teacher Actions

• Develop a Deep and Flexible Conceptual Understanding when using technology to create a scatter plot with real world context from a data set.  Explore the  line of best fit and its role in trying to describe the relationship between the points. Extend the line out to make predictions. 

• Develop Accurate and Procedural Fluency by collecting data and representing it on a scatterplot using appropriate titles, labels, and units.

• Develop Ability to Make Conjectures, Model and Generalize when given a scatterplot, analyze the data presented and create a line of best fit to make predictions and discuss the situation for data that has not been collected.

• Develop Mathematical Reasoning by looking at a scatterplot, identify the relationship between the points as being positively correlated, negatively correlated, or an unpredictable relationship.

• Develop a Productive Mathematical Disposition by creating a variety of scatterplots, grapple with the idea that the line of best fit will not always go through (0,0) and that it might not go through any points on the graph.

• Promote procedural fluency by continually referring to slope and posing all question of slope as the rate of change when looking at examples, the students will begin making that same connection that slope is rate of change.  

• Implement tasks that promote reasoning and problem solving by askingstudents to examine relationships between various scatter plots and determine a line of best fit when the data represents a linear functions.   

• Promote procedural fluency by allowing students to collect data and represent it on a scatter plot. Discuss with students the appropriate titles, labels and units that should be included.

• Facilitate mathematical discourse by giving pairs of students multiple sets of data representable as scatterplots. Allow the students to discuss with their partner how they should classify each graph.  Ask the students to look for patterns. After the students have classified the graphs, ask for ideas of the vocabulary that could be used.  Provide the conventional vocabulary after the activity ( positive correlation/relationship, negative correlation/relationship, no correlation/unpredictable relationship). 

Key Understandings

Misconceptions

• Collect data and display the data on a scatterplot using appropriate titles, labels, and units.

• Interpret data on a scatterplot.

• Based on the information given, draw an approximate line of best fit (graph model) and write the equation for their approximate line of best fit.

• Use the line (graph model) and/or the equation to make predictions about the situation for data that has not been collected.  Also use the graph model to give  more information about the original context, describe the approximate rate of change and interpret the reasonableness of their solutions.

• Classify scatterplots as having a positive relationship, negative relationship, or an unpredictable relationship (no relationship). 

• Students will often times only chose data points that are plotted on the graph in order to find the line of best fit.  Sometimes this will work because their line will go through two of the original data points.  However, often times the line may NOT go through any of the data points and students still pick only the plotted points.

• Students think the line of best fit must go through (0,0).  This is sometimes true, but students need to be able to understand what the y-intercept means in the situation and determine if it makes sense given the situation.

• Students often lose the meaning of the rate of change and don’t connect it back to the context and variables in the problem.

• When trying to decide correlation of a data set students will sometimes have confusion about whether there is positive, negative, or no correlation.  They will also have confusion when different terms are used (relationship versus correlation)