When a student fails Algebra 1 in 9th grade, the failure almost never starts in 9th grade. It starts two or three years earlier, in the pre-algebra years, when a specific foundational skill didn't quite set — and then every course afterward quietly assumed it had. The student isn't "bad at algebra." They're doing algebra while carrying a gap that makes every problem twice as hard as it should be.
The encouraging part is that the load-bearing skills are few and nameable. Algebra readiness mostly comes down to four things: integer operations (especially negatives), fraction fluency, order of operations, and early comfort with expressions and variables. A 6th or 7th grader who is solid on those four walks into Algebra 1 with the hard part already done. A student missing even one of them will feel like algebra itself is impossible, when really one specific pipe is leaking.
This guide takes the four skills one at a time: why each one breaks algebra later, and how to practice it with games and activities — digital and offline. Then, because "practice everything" is bad advice, an honest section on figuring out which gap your student actually has. One note up front: we make Infinilearn, one of the games mentioned below, and we'll be plain about where it fits and where it doesn't.
Skill 1: Integer Operations (Especially Negatives)
Under Common Core, students meet negative numbers in 6th grade — ordering them, placing them on a number line — and learn to actually compute with them in 7th grade. Then Algebra 1 assumes the skill so completely that it stops being taught at all.
Here's why it's load-bearing: almost every equation a student solves in algebra passes through negative territory. Solving 3x + 7 = 1 requires being comfortable that x is -2. Distributing -(x - 4) requires knowing that two negatives flip. Moving a term across the equals sign is really adding its opposite. A student who is shaky on integers doesn't fail one unit of Algebra 1 — they leak points on every assignment forever, and sign errors are among the most common mechanical errors algebra teachers see.
How to practice it:
- Digital: We've rounded up the best options in our guide to integer games for middle school. Infinilearn covers the 6th and 7th grade integer standards inside its battles, which matters for a reason we'll get to below.
- Integer war: A deck of cards where red cards are negative and black are positive. Each player flips two cards and adds them; higher sum wins the hand. Ten minutes of this, a few times a week, builds the number sense worksheets don't.
- Number-line walking: Tape a number line on the floor. Adding means facing positive; subtracting means turning around; a negative number means walking backward. "Subtracting a negative" stops being a slogan when your body has done it.
- Zero pairs: Two-color chips (or coins, heads and tails) where one positive and one negative cancel. Great for making -5 + 3 something you can see.
Skill 2: Fraction Fluency
Fraction operations are supposed to be finished business by the end of 6th grade — dividing a fraction by a fraction is a 6th grade standard — and 7th grade expects fluent work with all rational numbers. Algebra 1 then leans on fractions in ways students don't see coming: equations with fractional coefficients like (2/3)x = 8, proportional relationships, and above all slope, which is a fraction. Rise over run is a ratio; a student who can't compare, simplify, or divide fractions cannot reason about slope, full stop.
The tell for a fraction gap is avoidance: the student converts every fraction to a decimal instantly, then gets stranded when the decimal doesn't terminate or the answer is supposed to stay in fraction form. That habit works just well enough in middle school to hide the gap until algebra exposes it.
How to practice it:
- Digital: Our roundup of fraction games for middle school covers options that go beyond pizza slices.
- Fraction war: Flip two cards each to make a fraction (smaller card on top); the larger fraction wins. Comparing 3/7 to 4/9 with something at stake is real fraction reasoning.
- Recipe scaling: Take a recipe that serves four and cook it for ten. The kitchen forces multiplying and dividing fractions with a purpose, and dinner depends on getting it right.
- Tape-measure projects: Build anything — a birdhouse, a shelf — from a plan marked in eighths and sixteenths of an inch. Adding 3/8 and 5/16 with a saw in your hand is unforgettable in a way a worksheet isn't.
Skill 3: Order of Operations
Order of operations arrives in 5th grade with grouping symbols and gets its full form in 6th, when exponents and variables join in. It looks like a small convention — and that's exactly why it's underestimated. In algebra, order of operations stops being an occasional worksheet topic and becomes the grammar of everything: evaluating 3x² - 2x at x = -1, deciding what to distribute before what to combine, simplifying any multi-step expression. Every algebraic simplification is order of operations applied over and over.
The classic symptom is left-to-right computation: the student who "simplifies" 3 + 4 × 2 to 14, or later merges 3 + 4x into 7x. Notice that second error is the same error wearing algebra clothes — which is exactly how pre-algebra gaps resurface.
How to practice it:
- Digital: See our guide to order of operations games for options that make PEMDAS a puzzle instead of a chant.
- Target number: Roll four dice; use all four values with any operations and parentheses to hit a target number (say 24). This is the rare game where inserting parentheses is the winning move, which is precisely the skill.
- Error hunting: Show a worked solution containing one deliberate order-of-operations mistake and offer points for finding it. Students love grading; catching someone else's left-to-right error inoculates against their own.
- Two ways to write it: Give an answer like 22 and ask for two different expressions that produce it — one that needs parentheses and one that doesn't. Writing expressions cements the rules better than evaluating them.
Skill 4: Early Expressions and Variables
The Common Core progression here is precise: 6th grade introduces variables, expressions, and one-step equations; 7th grade brings two-step equations; 8th grade builds to linear equations and functions. But the concept underneath is easy to miss: what the equals sign means. Many students spend elementary school reading "=" as "the answer comes next." Algebra needs it to mean "these two sides are the same thing" — and a student holding the old meaning will find equations genuinely incomprehensible, no matter how many procedures they memorize.
The related hurdle is accepting an expression as an object. A student needs to read 3(x + 2) as one quantity you can work with, and to tolerate "2x + 5" as a final answer even though it isn't a number. Students who ask "but what is x?" on every problem are telling you this model hasn't formed yet.
How to practice it:
- Digital: DragonBox Algebra (about $8, one-time) is the best pure intuition-builder we know — students manipulate visual puzzles that gradually turn into real equations, absorbing "do the same thing to both sides" before they ever see notation. Its scope is narrow and finite, so treat it as an on-ramp. For fuller coverage, our roundup of algebra games for middle school goes tool by tool.
- Balance puzzles: Draw a hanger or scale on a whiteboard with shapes on both sides and ask what each shape must weigh to keep it level. This is equation-solving with the equals sign made physical.
- Function machines: One person invents a rule ("multiply by 2, then add 3"); the other feeds in numbers and must deduce the rule from the outputs. It's guess-my-rule, and it's also the entire concept of a function.
How to Tell Which Gap Your Student Actually Has
Practicing all four skills at once dilutes the effort; the whole advantage of naming the gaps is that you can target one. Here's what each gap looks like from the outside:
- Integer gap: Answers that are right except for the sign. Always subtracting the smaller number from the larger, regardless of order. Freezing on "subtract negative 4." If the mistakes cluster around minus signs, this is your gap.
- Fraction gap: Instant conversion of every fraction to a decimal. Adding denominators. Refusing to leave an answer as a fraction. Managing fractions fine on a page titled "Fractions" but missing them when they appear inside other problems.
- Order of operations gap: Strict left-to-right computation. Answers that change when the same problem is written with different spacing. Combining unlike terms, like turning 3 + 4x into 7x.
- Variable gap: Asking "what is x?" as though it must be a fixed secret number. Solving x + 5 = 12 correctly by inspection but having no method when the numbers get uglier. Discomfort with any answer that still contains a letter.
The cheapest diagnostic is watching your student work five mixed problems out loud — not checking the answers, watching where the reasoning bends. If you'd rather have data, Infinilearn's free teacher accounts include a built-in diagnostic that locates each student's level topic by topic, and the free parent dashboard shows accuracy by topic for one child, so the weak foundation shows up as a number instead of a hunch.
Where Infinilearn Fits (and Where It Doesn't)
Disclosure again: Infinilearn is ours. It's a free browser-based fantasy RPG for grades 5-9 — students battle monsters, run quests across 15 zones, and fight bosses, with every attack powered by a real multiple-choice problem matched to Common Core standards.
The reason it belongs in a pre-algebra article specifically is the adaptive engine. The game tracks each student's accuracy topic by topic, and weapon attacks pull problems from the student's weakest subjects. In practice that means the four readiness skills take care of themselves: if integers are the weak wall, battles quietly serve more integer problems until the wall holds; if it's fractions, the mix shifts there instead. The student experiences it as playing the game. The engine experiences it as closing their most algebra-relevant gap first. For a typical 6th or 7th grader, that beats any schedule of targeted worksheets a busy parent will actually sustain — our guide to math games for 7th graders shows where it sits among the alternatives.
The whole game is free — every zone, quest, and all grades 5-9 math, no ads. The optional premium ($9.99/month or $59.99/year as of this writing) adds deeper parent-dashboard insights like progress trends and standards tracking, plus student cosmetics; it never gates math content or progression. And to be honest about limits: it's practice, not instruction. If your student needs a concept taught from scratch, a lesson (a teacher, a tutor, Khan Academy) comes first; the game is where the reps happen. Problems are multiple choice, and it runs in a browser — great on a Chromebook, not built for phones.
The Bottom Line
Algebra readiness isn't a mystery and it isn't a talent. It's four skills: integers, fractions, order of operations, and early variables. Nearly every Algebra 1 struggle traces back to one of them, and 6th and 7th grade is exactly the right time to find and fix the weak one — before the gap starts compounding under new material.
So diagnose first: watch your student work, or run a proper diagnostic, and name the gap. Then target it from two directions — an offline activity that makes the concept physical, and a game that delivers repetitions without the fight. A student who patches their one leaking pipe in 7th grade walks into Algebra 1 ready for it to be merely new, instead of new and impossible at the same time.