CCSS.Math.Content.HSA-CED.A.2
The Standard
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose variables for quantities in a situation and write an equation that links them. They graph valid pairs, label both axes with quantities and units, and choose a scale that shows the relationship clearly.
What Mastery Looks Like
- Given a situation such as a rental cost, a student writes an equation and explains what each term represents. The student plots valid points, uses clear labels and units, and limits the graph to values that fit the situation.
Common Misconceptions
- Students may use a rate but leave out the starting value. They may plot coordinate pairs in the wrong order or include values that do not satisfy the equation. They may omit units, use uneven scales, or graph values that do not make sense in the situation.
How to Assess It
- Exit ticket: A bike rental costs $8 plus $3 per hour. Define variables, write an equation, and graph 0 to 5 hours with labeled axes and a sensible scale.
Lesson moves
Ways to Teach It
Have pairs weigh an empty cup, then add marbles one at a time, record total mass, write an equation, and graph the data.
Ask, “How do the rate and starting value appear in an equation and its graph?” Students answer using a taxi fare example.
Give teams matched sets of scenario, equation, table, and graph cards; they race to assemble sets and explain every match.
Use a local phone plan or gym fee to model monthly cost, then graph and compare two pricing options.
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Printable HSA-CED.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-CED.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSA-REI.D.10
Students use the idea that graph points are equation solutions when graphing their own equations with meaningful axes and scales.
- CCSS.Math.Content.8.F.B.4
Constructing linear functions from rates, intercepts, tables, and graphs supports writing and graphing two-variable equations from relationships.
- CCSS.Math.Content.HSN-Q.A.2
Choosing meaningful variables and units supports writing and graphing equations that represent relationships between real quantities.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-CED.A.3
Writing and graphing equations for relationships supports forming constraint systems and judging which solutions make sense in context.
- CCSS.Math.Content.HSF-BF.A.1a
Writing equations for quantity relationships supports turning contexts into function rules, including explicit formulas and calculation steps.
- CCSS.Math.Content.HSG-GPE.A.2
Deriving a parabola uses the same skill of turning a two-variable relationship into an equation and interpreting its coordinate graph.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rati...
- CCSS.Math.Content.HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...
- CCSS.Math.Content.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...
- CCSS.Math.Content.HSA-CED.A
Create equations that describe numbers or relationships
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