6.EE.B.5+B.6 6th Grade Expressions & Equations

Solutions to Equations & Writing Variables

Understand that solving an equation or inequality means finding the values that make it true, and use variables to represent numbers in real-world and mathematical problems.

How to explain it

At this standard, students use variables to represent unknowns and write expressions and equations from word phrases (6.EE.B.6), then use substitution to check whether a given value is a solution (6.EE.B.5). Ramp: P1-4 write expressions, P5-8 write equations, P9-12 check solutions YES/NO, P13-16 write + check integrated. B.5 inequality domain deferred to #26.

The anchor students hold onto: Substitute the value -> evaluate both sides -> equal = SOLUTION

Solution-checking extends directly to inequalities: test a value in x > c or x < c. Leads to 6.EE.B.8 (#26 InequalitiesAndGraphs) and 7.EE.B equation-solving in 7th grade.

Worked examples

Example 1 Writing an Expression

Six more than a number

Step 1'Six more than' -> add 6 to the number

Step 2'A number' -> variable n

Step 3Expression: n + 6

Answern + 6

Example 2 Writing an Equation and Checking

A number minus 3 equals 8

Step 1Write the equation: n - 3 = 8

Step 2Check n = 11: 11 - 3 = 8 -- TRUE

Step 3n = 11 is a SOLUTION

Answern - 3 = 8; n = 11 is the solution

Common mistakes

What students write Writing 3 - n for "3 less than n" -- reversing the order of subtraction.

The fix "3 less than n" subtracts 3 FROM n: write n - 3, not 3 - n.

Try this Student work: "3 times a number equals 12" 3 + n = 12 (WRONG) A student wrote 3 + n = 12 for "3 times a number equals 12." Find and fix the error. Then test n = 4 to confirm your correction.

What students write Substituting correctly but comparing only one side -- not checking that BOTH sides are equal.

The fix After substituting, simplify both sides separately, then compare: if they match, it IS a solution.

Teacher tip

Head off the two predictable errors before they happen. First: "3 less than n" subtracts 3 FROM n: write n - 3, not 3 - n. Second: After substituting, simplify both sides separately, then compare: if they match, it IS a solution.