M.6.R.EE.9

The first look at two quantities changing together, which grows into functions in Grade 8.

Not yet reviewed by a teacher

Builds on

Where to go for intervention

Grade 6

M.6.R.EE.6PriorityOne variable becomes two that change together.Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or depending on the purpose at hand, any number in a specified set.

Grade 5

M.5.DA.OA.3Two patterns that change together, paired up and graphed. The idea of a relationship starts here, before there are variables.Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.M.5.SR.G.2PriorityGraphing points and saying what their coordinates mean in a situation.Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

M.6.R.EE.9

Priority

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.

Common Core: 6.EE.C.9

Resources2 IM tasksWIDAOSPI

Illustrative Mathematics tasks2

From the Illustrative Mathematics task library, CC BY-NC-SA 4.0

WIDA language connections1

Explain · Expressivespeaking, writing and representing

ELD-MA.6-8.Explain.Expressive · Language for Mathematics, Grades 6-8

Construct mathematical explanations that…

Introduce concept or entity
Share solution with others
Describe data and/or problem-solving
State reasoning used to generate solution

OSPI's example connections to the WIDA ELD Standards Framework. How to read these

From OSPI

Washington OER Hub · Free, openly licensed materials for M.6.R.EE.9

Smarter Balanced interim assessment

Grade 6: Dependent and Independent Variables · Focused interim block, items 1, 2, 3, 4, 5, 6, 7, 8, 9, 10*, 11*

A star marks an item aligned to Smarter Balanced claims 2, 3 or 4: problem solving, reasoning or modeling on this content.

On the SBA

PRISM's read

Its own focused block: move between a situation, an equation, a table and a graph, and say which quantity depends on which.

Smarter Balanced target

Claim 1 (Concepts and Procedures), Target G: Represent and analyze quantitative relationships between dependent and independent variables.

Major work of the grade, DOK 2.

OSPI's interim connections

Grade 6: Dependent and Independent Variables · items 1, 2, 3, 4, 5, 6, 7, 8, 9, 10*, 11*

A star marks an item aligned to Smarter Balanced claims 2, 3 or 4: problem solving, reasoning or modeling on this content.

Smarter Balanced publishes its claims and targets in its content specifications, written to the Common Core. A 2026 standard reaches them through OSPI's crosswalk. Check them before anything official.

Builds to

Where it goes next

Grade 7

M.7.R.RP.2PriorityTable, graph and equation together again, now asking whether the relationship is proportional.Recognize and represent proportional relationships between quantities.

Grade 8

M.8.R.F.1A rule that gives one output for each input is what a dependent variable already was.Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.M.8.R.F.4PriorityBuilding a model of a linear relationship from a description, a table or a graph.Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Connects to

Taught alongside it, including its supporting standards.

M.6.SR.NS.8PriorityGraphing a relationship from its table, in a situation, puts these points to use.Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.M.6.R.RP.3PriorityA ratio table and a table of two related variables are the same picture, and an equation can describe both.Efficiently, flexibly, and accurately demonstrate understanding of ratio and rate reasoning by solving real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations to find different ways to express the same ratio.