District Formative Assessment

Variables and Patterns

Investigation #2

Components

Standard: 6.EE.C.9 – Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equations. For example: in a problem involving motion at constant speed, list and graph ordered pairs of distance and times, and write the equation d-65t to represent the relationship between distance and time.

Item–Tablets Sold at School Problem

Misconception (s)-

-Dependent vs Independent.

-Change in dependent variable. Understanding that the change is the “total” and not by each individual week.

-Graphing. Some students will start the origin with the first set of data, not zero (0).

-Using a constant interval.

-Inaccurate labeling of the axis.

-Intervals not constant.

-Points are plotted incorrectly.

-Draw a bar graph.

Categorizing Responses –

Indicators
-Labels present
-Axes Labeled with correct variable.
-Appropriate and consistent intervals.
-Plotting points
-Variables are identified.
-Identify the greatest rate of change.
-Identify the lowest rate of change.
-Accurate description of the story told by the data. / Right On (7-8 Indicators)
Developing (4-6 Indicators)
Not Yet (Less than 4 Indicators)

Next Steps – Refer to Attachment

Variables & PatternsName: ______

Formative AssessmentDate: ______

Post Investigation #2Class: ______

Jenkins Middle School is selling tablets for students to use in school. At the end of each month, they tracked their total sales for the year and put the information in a table.

Month / Month 1 / Month 2 / Month 3 / Month 4 / Month 5 / Month 6
Total Sales / 50 / 120 / 150 / 200 / 210 / 215
  1. Make a coordinate graph of the data.

Total Tablet Sales

b.Identify the independent variable ______

Identify the dependent variable ______

  1. During which time period did the store sell the most tablets? ______
  1. During which time period did the store sell the least tablets? ______
  1. Describe the story the graph tells about the sales of tablets.

Variables & PatternsName: ______

Formative AssessmentDate: ______

Post Investigation #2 Answer KEYClass: ______

Indicator 1 – Labels Present

Indicator Met / Indicator Not Met
The words “Sales” or “Total Sales” and the word “Month” are present on the graph. / Labels are not existent or irrelevant.

Indicator 2 – Axes Labeled Correctly

Indicator Met / Indicator Not Met
The word “Month” is written as a label on the x-axis and the word “Sales” is written on the y-axis. / The word “Month” is written as a label on the y-axis and the word “Sales” is written on the x-axis.

Indicator 3 - Intervals

Indicator Met / Indicator Not Met
  • The intervals on the x-axis are labeled 1, 2, 3, 4, 5, and 6. The intervals on the y-axis count at a consistent interval. Students may have counted by 15, 20, 25, or another reasonable value.
  • The spacing between the intervals is consistent.
/
  • The intervals are labeled according to the values shown in the table.
  • The intervals are labeled at an inconsistent interval – ex: starting counting by 10’s and then switch to 20’s.

Indicator 4 – Points

Indicator Met / Indicator Not Met
Five or more points are accurately placed, regardless of interval selected. / More than five points are not accurately placed.

Indicator – Variables Identification

Indicator Met / Indicator Not Met
Both the independent variable, months, and the dependent variable, total sales, are correctly identified in question b. / Either or both of the variables have been incorrectly identified.

Indicator 6 – Most Sales

Indicator Met / Indicator Not Met
“Month 2” or “Between month 1 and month 2” are given as an answer for question c. / Answer does not identify the correct month or answer is irrelevant.

Indicator7 – Least Sales

Indicator Met / Indicator Not Met
“Month 6” or “Between month 5 and month 6” are given as an answer for question d. / Answer does not identify the correct month or answer is irrelevant.

Indicator 8 – Story

Indicator Met / Indicator Not Met
Student response describes the rapid increase of sales in the beginning months, followed by a slower increase of sales in the later months. / Student describes an increase if sales but does not discuss how sales generally change over time.
Student response is wrong.

District Formative Assessment

Variables and Patterns

Investigation #2

Student Response(s)
Right On / Developing / Developing / Not yet
Possible Indicators / Possible Indicators / Possible Indicators / Possible Indicators
a.) Student correctly labeled and plotted the coordinates.
b.) Student correctly identified the variables.
c.) Student correctly identified which time period sold the most tablets.
d.) Student correctly identified which time period sold the least tablets.
e.) Student correctly explained the rate of change throughout the graph. / a.) Student incorrectly label axes, but did scale the axes correctly
b.) Student incorrectly identified the variables.
c.) Student correctly identified which time period sold the most tablets.
d.) Student correctly identified which time period sold the least tablets.
e.) Student incorrectly explained the rate of change throughout the graph. / a.) Student did not label the axes, but did plot the coordinates correctly.
b.) Student correctly identified the variables.
c.) Student incorrectly identified which time period sold themost tablets.
d.) Student incorrectly identified which time period sold the least tablets.
e.) Student correctly explained the rate of change throughout the graph. / a.) Student correctly labeled the graph, but did not scale the y-axis correctly.
b.) Student incorrectly identified the variables.
c.) Student incorrectly identified which time period sold the most tablets.
d.) Student incorrectly identified which time period sold the least tablets.
e.) Student incorrectly explained the rate of change throughout the graph.
Next Steps
Student / Closing the Loop
(Interventions/Extensions) / In the Moment Questions/Prompts
Student incorrectly created the graph; including errors labeling the axis, scaling the intervals, and plotting the coordinates. / Variables & Patterns
Inv. 1: ACE 1,4,6
Additional Practice Inv. 1: #3 & #5 / Q: What are the two variables being compared?
Q: Which variable should go on the x-axis & y-axis?
Q: How can you scale each axis?
Q: How do you plot a point on this graph?
Student incorrectly identified the variables. / Variables & Patterns
Additional Practice Inv. 1: #4
/ Q: How can you identify which variable depends on the other?
Q: Which variable is dependent?
Q: Which variable is independent?
Student incorrectly identified which time period sold the most tablets and the least. / Variables & Patterns
Inv. 1: ACE 3a, 4, 6, 7, 9c / Q: Where on the graph would you find the most and least amount of tablets sold?
Student incorrectly explained the rate of change throughout the graph / Variables & Patterns
Inv. 1: ACE 4d, 9e, 12
Inv. 2: ACE 1, 10, 12
Additional Practice Inv. 1: #3 / Q: What patterns do you see in graph?
Q: What would explain the patterns that you see?