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8th grade · Math · Unit 2 of 17

Patterns & Two-Step Equations

Expressions, patterns and solving for x

What your child practices

Writing and evaluating expressions like 3n + 2, solving two-step equations, and finding the rule for a growing pattern or a cost made of whole items such as tickets.

Arizona Academic Standards learning standard: 8.EE.C.7 · solving linear equations in one variable

How we explain it

Children can open this short lesson before they practice.

  1. Do the same thing to both sides to keep the equation balanced.
  2. Undo adding and subtracting first.
  3. Then undo multiplying and dividing.

Example: 3x − 5 = 16 Add 5 to both sides: 3x = 21. Divide both sides by 3: x = 7. Answer: x = 7

Patterns & Two-Step Equations in Arizona

In the Arizona Academic Standards, this is unit 2 of 17 in 8th grade Math, after Squares, Cubes & Roots and before Pythagorean Theorem.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Arizona Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Solve for x: 2x + 5 = 3

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  2. Question 2

    Solve for x: x ÷ 6 + 9 = 15

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  3. Question 3

    Solve for n: 60 = 4n + 20

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  4. Question 4

    Evaluate 6n + 8 when n = 6.

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  5. Question 5

    Which expression means “5 more than 4 times a number n”?

    • 5n + 4
    • 9n
    • 4(n + 5)
    • 4n − 5
    • 4n + 5

  6. Question 6

    I think of a number, multiply it by 4 and add 9. The result is 29. Which equation matches?

    • 4n − 9 = 29
    • 4n + 9 = 29
    • 4 + 9n = 29
    • n + 36 = 29
    • 4(n + 9) = 29

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