6EE-Represent+and+analyze+quantitative+relationships+between+dependent+and+independent+variables

6.EE.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 equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard**===
 * Make sense of problems and persevere in solving them.
 * Reason abstractly and quantitatively.
 * Construct viable arguments and critique the reasoning of others.
 * Model with mathematics.
 * Look for and make use of structure.
 * Look for and express regularity in repeated reasoning. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking: Analyzing, Evaluating**=== ||

The purpose of this standard is for students to understand the relationship between two variables, which begins with the distinction between dependent and independent variables. The independent variable is the variable that can be changed; the dependent variable is the variable that is affected by the change in the independent variable. Students recognize that the independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

Students recognize that not all data should be graphed with a line. Data that is discrete would be graphed with coordinates only. Discrete data is data that would not be represented with fractional parts such as people, tents, records, etc. For example, a graph illustrating the cost per person would be graphed with points since part of a person would not be considered. A line is drawn when both variables could be represented with fractional parts. Students are expected to recognize and explain the impact on the dependent variable when the independent variable changes (As the x variable increases, how does the y variable change?) Relationships should be proportional with the line passing through the origin. Additionally, students should be able to write an equation from a word problem and understand how the coefficient of the dependent variable is related to the graph and /or a table of values.

Students can use many forms to represent relationships between quantities. Multiple representations include describing the relationship using language, a table, an equation, or a graph. Translating between multiple representations helps students understand that each form represents the same relationship and provides a different perspective.

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...represent and analyze relationships between dependent and independent variables.**===


 * I can define independent and dependent variables.
 * I can use independent and dependent variables to write equations.
 * I can explain the relationship between independent and dependent variables using tables and graphs.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary:**
dependent variables, independent variables, discrete data, continuous data

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**
Thinkgate
 * Daily Spiral Review**
 * Signaling**
 * Questioning**
 * Teacher Observation**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Teaching the Common Core Math Standards with Hands-On Activities: Examining Relationships (page 51) Teaching the Common Core Math Standards with Hands-On Activities: Comparing Heart Rates (page 52)

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Activities will be used from Instructional Resources List

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Activities will be used from Instructional Resources List ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (page 51) Carnegie Learning: Lesson 9.7 Quantiles 1 Notes/Examples

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===