CCSS.Math.Content.6.EE.B.5
The Standard
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Common Core State Standards for Mathematics · Expressions and Equations
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students substitute each candidate value for the variable and compute both sides. They decide whether the result is true and identify all candidates that work.
What Mastery Looks Like
- Given a set such as {2, 4, 6}, a student tests each value accurately. The student shows substitution, compares the results, and reports every solution or states that none work.
Common Misconceptions
- Students may test only one candidate and stop, even when several values could work. They may replace only one occurrence of the variable, reverse an inequality sign, or make arithmetic errors.
How to Assess It
- Exit ticket: From {0, 2, 4, 6}, which values make 3x + 1 > 10 true? Show each substitution and circle all solutions.
Lesson moves
Ways to Teach It
Give pairs candidate-value cards and equation mats; students place each card into the variable slot, calculate both sides, and sort true or false.
Ask students to write: How does substituting 5 prove whether 2x + 3 = 13 is true?
Play Solution Set Relay: teams test one value at a time from a posted set and earn points only with shown work.
Present a $20 budget with a $5 fee and $3 items; students test listed quantities that keep the total within budget.
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Printable 6.EE.B.5 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.6.EE.B.5, 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
See the whole path on the Expressions & Equations progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.EE.A.2c
Checking whether a value makes an equation or inequality true requires substituting it and accurately evaluating the resulting expressions.
- CCSS.Math.Content.6.EE.A.2
Substituting a value into an equation or inequality requires reading variable expressions and evaluating them accurately.
- CCSS.Math.Content.6.NS.C.7a
Understanding inequality symbols as number order helps students judge whether substituted values make an inequality statement true.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.EE.C.7a
Substitution and the meaning of a solution carry into recognizing when transformed equations are true, false, or give one value.
- CCSS.Math.Content.8.EE.C.8a
Students must understand solutions as values that make equations true before seeing intersection points as values satisfying both equations.
- CCSS.Math.Content.8.EE.A.2
Substituting values to check equations supports seeing square and cube roots as the numbers that make x²=p or x³=p true.
- CCSS.Math.Content.6.EE.B.7
Knowing a solution makes an equation true supports setting up and checking one-step equations with rational numbers.
- CCSS.Math.Content.6.EE.B.8
Testing values in inequalities supports understanding which numbers satisfy x > c or x < c and why solutions form a ray.
- CCSS.Math.Content.7.EE.B.4b
Students must understand that inequality solutions are all values making the statement true before solving, graphing, and interpreting solution sets.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-REI.B
Solve equations and inequalities in one variable
- CCSS.Math.Content.HSA-REI.A
Understand solving equations as a process of reasoning and explain the reasoning
- CCSS.Math.Content.HSA-REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the or...
- CCSS.Math.Content.6.EE.B
Reason about and solve one-variable equations and inequalities.
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