CCSS.Math.Content.HSA-CED.A.4
The Standard
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite a formula so one chosen variable stands alone. They apply inverse operations to both sides and may need to factor or clear fractions.
What Mastery Looks Like
- Students isolate any named variable and keep the formula equivalent. They use inverse operations, factor when needed, and check by substituting numbers into both forms.
Common Misconceptions
- Students may divide only one term instead of the entire side of a formula. They may reverse operations incorrectly or think a formula cannot be solved because it has several variables.
How to Assess It
- Give students A = 2lw + 2lh and ask them to isolate h. Require one line explaining each operation.
Lesson moves
Ways to Teach It
Give pairs algebra tiles to model x + xy = z, factor the variable terms, and isolate x.
Ask students to explain why dividing every term by the same expression preserves equality.
Play Formula Relay, where teams draw a formula card and race to isolate the variable named on a second card.
Use d = rt to calculate the required travel time after rearranging the formula to isolate t.
Free download
Printable HSA-CED.A.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-CED.A.4, 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.A.1
Justifying equation steps with equality properties supports rearranging formulas by applying the same operations to isolate a chosen variable.
- CCSS.Math.Content.8.EE.C.7
Solving one-variable linear equations provides the inverse-operation reasoning needed to isolate a chosen variable in a formula.
- CCSS.Math.Content.HSA-REI.B.3
Rearranging a formula is solving an equation for a chosen variable, using inverse operations and handling letter coefficients.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSG-SRT.C.8
Solving right triangles often requires isolating a missing side or angle from trig ratios or the Pythagorean formula.
- CCSS.Math.Content.HSF-BF.B.4a
Finding an inverse formula requires isolating the input variable in an equation, exactly the rearranging skill from formula work.
- CCSS.Math.Content.HSF-LE.A.4
Solving the exponential equation requires isolating the exponential term and the variable before applying a logarithm.
- CCSS.Math.Content.HSF-BF.B.4
Solving for a chosen variable carries over directly when finding an inverse by switching input and output and isolating the new output.
- CCSS.Math.Content.HSG-SRT.D.11
Isolating sides or angles in sine and cosine formulas uses the same equation-rearranging skills from formula work.
Keep exploring
Related Standards
- CCSS.Math.Content.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning ab...
- CCSS.Math.Content.HSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- CCSS.Math.Content.7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
- CCSS.Math.Content.HSA-SSE.B
Write expressions in equivalent forms to solve problems
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.