Pre-algebra practice focused on solving for x

Free, no-login pre-algebra drills for grades 6–7. Six progressive levels of one-step and two-step equations with integer solutions.

Pre-algebra is the first place most kids meet a variable, and it reveals exactly how solid (or shaky) their arithmetic actually is. Solving 3x + 7 = 22 isn’t hard conceptually — subtract 7 from both sides, divide by 3 — but it requires a child to do mental arithmetic on the spot, twice, in a specific order, without losing track of which side they’re working on. Num Drill’s pre-algebra track drills that loop directly so the moves become automatic and your child has cognitive bandwidth left for the conceptual side of algebra.

What kids practice in Num Drill’s pre-algebra track

Levels 1–2: one-step equations

• Level 1. Single-operation equations like x + 7 = 12, 4x = 28, x − 5 = 9. Solutions are positive integers from 1–20. Right for advanced 5th graders or 6th graders just starting.
• Level 2. Same shapes, larger numbers and a wider solution range. The classic 6th-grade fluency target.

Levels 3–4: two-step equations

• Level 3. Two-step equations like 3x + 5 = 17, 2x − 4 = 10. Positive integer solutions only. The bridge to real algebra.
• Level 4. Two-step equations including negative coefficients and negative constants, e.g. −2x + 9 = 15. Solutions still positive integers; the negative arithmetic is the new challenge.

Levels 5–6: full pre-algebra fluency

• Level 5. Larger ranges, including negative solutions for x. e.g. 5x − 12 = −47. End-of-6th-grade or 7th-grade material.
• Level 6. Full integer range on both coefficients and solutions, including coefficients up to ±25 and constants up to ±200. Useful for 7th graders preparing for first-year algebra.

Who this page is for

The fit is best for typical 6th and 7th graders, plus advanced 5th graders working ahead. The product assumes your child has fluency in:

• multiplication and division facts — pre-algebra constantly asks for “what times 7 is 84?” in disguise;
• integer arithmetic with negatives — if your child has to stop and think about “what is −3 + 8?”, levels 4–6 will feel hard for the wrong reason;
• order-of-operations basics (PEMDAS) — pre-algebra equations are read “multiply first, then add” in reverse.

If those foundations are wobbly, pre-algebra practice will surface it quickly. The most common reason a 6th grader stalls on this page is not the algebraic move; it’s the underlying arithmetic. Drill that first, then come back.

Why solving for x gets easier with arithmetic fluency

Working memory is the bottleneck. When your child looks at 3x + 5 = 17 and has to:

1. recognize this is a two-step equation,
2. plan the inverse moves (subtract 5, divide by 3),
3. execute 17 − 5 = 12,
4. execute 12 ÷ 3 = 4,
5. verify mentally that 3(4) + 5 = 17,

— every step that requires effort steals capacity from the next. Kids with fluent arithmetic do step 3 and step 4 essentially for free, leaving full capacity for the planning and verification steps. Kids who don’t have fluent arithmetic get stuck mid-equation and lose track of which side they were working on. The research literature on working-memory capacity in math is consistent on this point.

How to start at the right level

Have your child take a 10-question quiz at level 2. Note the accuracy and the average time per question.

• Accuracy below 70%, time above 15 seconds: drop to level 1. The procedure isn’t consolidated yet.
• Accuracy 70–90%, time 8–15 seconds: stay at level 2 for a week. This is the sweet spot for building fluency.
• Accuracy 90%+, time under 8 seconds: advance to level 3 (two-step equations). The one-step procedure is solid.

Once your child is solid through level 4, level 5 introduces negative solutions for x, which is the next conceptual jump. Don’t skip levels 3–4; the procedure stability they build matters.

Pre-algebra worked examples

Pre-algebra practice questions

Work each one out, then tap it to check.

Prefer paper? The free order of operations worksheet practises the arithmetic rules that solving equations depends on; the order of operations guide explains them.

Related reading: multiplication practice · percentage practice · fractions practice · why this works · for parents and homeschoolers