NC 6
th
Grade Math Unpacking - Revised June 2022
Represent and analyze quantitative relationships between dependent and independent variables.
NC.6.EE.9 Represent and analyze quantitative relationships by:
● Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.
● Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).
Checking for Understanding
Students describe and analyze how one variable changes in relation to the other.
Using variables to represent two quantities in a real-world or mathematical
context that change in relationship to one another.
Students analyze the relationship between variables in a given situation and
represent that situation as a two-variable equation. Students may be given a partially
completed table or graph along with the context of the situation.
In 6
th
grade, students write an expression from a context and set that expression
equal to a variable that represents the value of the created expression (output). This
variable will be in a dependent relationship to the variable in the created algebraic
expression. From this, students can describe the mathematical relationship between
the variables.
For example: The cost to get into a high school basketball game is $5 for each
ticket. Write an equation to represent this situation and describe the relationship
between the variables.
Solution: Sample answer: = 5 ∙
Possible description: As the number of tickets increases by 1, the cost increases 5 dollars.
is in a dependent relationship to .
Analyze the relationship between quantities in different representations
(context, equations, tables, and graphs).
Students create tabular and graphical representations of equations. In 6
th
grade,
students are expected to create the graphical representation from the corresponding
tabular representation. Student can use a tabular or graphical representation to
analyze the relationship between variables. Students can then relate their finding
back to the equation and the context.
Students understand that:
● A table is an organized list of solutions to its corresponding equation.
● A graph is a visual representation of the solutions to its corresponding
equation.
From the context, equation, or graph, students determine which variable is in a
dependent relationship. Students recognize that on a coordinate plane, the variable
that is in a dependent relationship is graphed on the y-axis. From the example above,
since cost, , is in a dependent relationship with tickets, , cost would be graphed on
the y-axis and tickets would be graphed on the x-axis.
In 6
th
grade, the relationships analyzed should focus on proportional and linear
relationships. Students are not required to use the terms proportional or linear at this
level. The restrictions placed on ratios tables apply to this standard. The initial values
given should be whole numbers.
Chris and his friends are going to the ice cream shop that is having a
sale on milkshakes. Each milkshake cost $2.
a) Write an equation that represents the total cost of buying any
number of milkshakes for Chris and his friends.
b) Create a table and a graph to represent this situation.
c) Describe how the variables relate to each other and explain how
you see these relationships in the equation, table and graph.
The student government is hosting a breakfast for charity and they
need to know how many people will attend so they can make plans.
The four members of the student government will attend the breakfast
along with the number of people who bought a ticket.
a) Write an equation that represents the total attending the
breakfast.
b) Create a table and a graph to represent this situation.
c) Describe how the variables relate to each other and explain how
you see these relationships in the equation, table and graph.
Looking at the two tables created in the
previous examples. One table contains
equivalent ratios, the other does not. How
could you have determined this from the
equations written?
A traveling basketball team is selling candy
bars to raise money for new uniforms. There
are 36 candy bars in each box and each
candy bar costs $1.75 each. The team sold
20 boxes.
a) Complete the table that shows how
much money was collected for each
box.
b) Create an equation to represent the
amount of money collected based on
the number of boxes sold.
c) Graph the equation from the ordered
pairs in the table.
Return to: Standards