Fall special: 20% off all fall engagements.

Blog

The middle school math gaps that show up in Algebra 1

, 2 min read

Most students who struggle in Algebra 1 aren't struggling with algebra. They're struggling with something from sixth or seventh grade that never fully settled, and algebra is the first class that uses it on every single problem.

These are the five gaps Gabe sees most often, in roughly the order they cause trouble.

1. Fractions

Adding, multiplying and dividing fractions has to be automatic by Algebra 1, because equations are full of them. A student who has to stop and remember whether to find a common denominator loses the thread of the actual problem.

2. Negative numbers

Sign errors are the single most common reason a correct method produces a wrong answer. The biggest trap is distributing a negative: −3(x − 4) is −3x + 12, not −3x − 12.

3. Order of operations

Students often know the acronym but not the idea. Solving an equation is doing the order of operations in reverse, so a shaky order of operations means shaky equation solving.

4. What the equals sign means

Many students read = as "now write the answer." In algebra it means both sides balance, and every step has to keep them balanced. Once that clicks, rules like "do the same thing to both sides" stop being rules to memorize.

5. Ratios and proportional reasoning

Slope, rates, percent change and unit conversion are all the same idea. Students who are comfortable with ratios find linear functions far easier.

A two-minute check

Ask your student to try these without a calculator. Hesitation matters as much as wrong answers.

  1. 2/3 ÷ 4/5 (answer: 5/6)
  2. −7 − (−3) (answer: −4)
  3. Expand −3(x − 4) (answer: −3x + 12)
  4. 8 − 2 × 3 + 1 (answer: 3)
  5. If 3 notebooks cost $4.50, what do 7 cost? (answer: $10.50)

If two or more of these take real effort, it's worth fixing now, before the gaps compound. The first session with Gabe starts with exactly this kind of check, and the report afterward tells you which skills are solid and which need work.