How to Improve Math Skills Before High School: A Parent’s Guide

To improve math skills before high school, find out which of five foundations your child is shaky on — fractions, negative numbers, ratios and percents, expressions and equations, or linear relationships — and fix those first, with short, mixed practice sessions a few times a week. Start in 7th grade if you can. Algebra I, one of the courses New Jersey requires for a high school diploma, is built almost entirely on those five skills, and most “I’m bad at algebra” problems turn out to be a fraction or negative-number problem from two years earlier.

This guide gives you a 10-question readiness check you can do at the kitchen table tonight, explains what each wrong answer tells you, and lays out a grade-by-grade plan for 6th, 7th and 8th grade and the summer before 9th.

Why high school math feels like a jump

Through elementary school, math is mostly about numbers. In Algebra I it becomes about relationships between quantities, written in symbols. A student who could reason their way to the right answer with concrete numbers now has to manipulate x and y, and every shaky rule from earlier grades shows up at the same time.

That is why the trouble often seems sudden. Take a 9th grader who “was always fine at math” and gets 3(x − 4) − 2(x − 5) wrong. Algebra isn’t the issue. They never got fully comfortable with how negative numbers multiply and subtract. That gap was already there in 7th grade, and algebra just exposed it.

It is also more common than parents tend to assume. On the 2024 National Assessment of Educational Progress, 37% of New Jersey 8th graders scored Proficient or above in math and 35% scored below Basic. That is in a state that outscores the national average (282 vs 272).

And the course can’t be skipped. New Jersey requires 15 credits of high school math for a diploma, including Algebra I, Geometry and a third year that builds on both.

A 10-question math readiness check, grade by grade

Have your child try these without a calculator. Allow about 20 minutes and ask them to show their work, because the working tells you more than the score does. This is not a placement test. It is a quick way to see where to look.

The questions are grouped in the order schools teach the skills, from 6th grade to 8th. Have your child do the groups for every grade they have finished: a rising 8th grader does questions 1–7, and a rising 9th grader does all ten. Later in the school year, add the group for the grade they are in. A miss on a grade they haven’t finished doesn’t count against them. For grades K–5, use our grade-by-grade math checklist instead.

Answer key, and what a wrong answer tells you

Question	Answer	Common wrong answer, and what it means
Grades 5–6
1. 3/4 + 2/3Fractions	17/12 (or 1 5/12)	5/7: added the tops and the bottoms. The student sees a fraction as two separate whole numbers rather than one quantity.
2. 2/3 ÷ 4/9Fraction division	3/2 (or 1 1/2)	8/27: multiplied without flipping the second fraction. They half-remember a rule but don’t know why it works.
3. Flour for 20 muffinsRatios and proportions	7.5 cups	15 cups: reasoned “12 more muffins, so 12 more cups.” That is additive thinking where the situation calls for multiplication, and it is one of the most important errors on this list to catch before Algebra I.
Grade 7
4. −7 − (−3)Negative numbers	−4	−10: treated “minus a negative” as more subtraction.
5. −32 + (−3)2Negatives and order of operations	0	18: squared the negative sign in −32. The exponent applies only to the 3, so −32 = −9. An answer of −18 is the same mix-up the other way round, treating (−3)2 as −9.
6. $40 to $50Percents	25%	20%: divided the $10 change by the new price instead of the original one.
7. 3(x − 4) − 2(x − 5)Expressions	x − 2	x − 22: worked out −2 × −5 as −10 instead of +10. A negative times a negative is positive, and distributing a negative is where that rule gets tested.
Grade 8
8. 5x − 7 = 2x + 11Equations	x = 6	x = 4/7: moved terms across the equals sign without changing their signs.
9. Phone planLinear relationships (word problems)	20 + 0.10t; $35	20t + 0.10: swapped the fixed cost and the rate. The student can calculate but can’t yet model a situation.
10. Slope through (1, 2) and (4, 11)Linear relationships (graphs)	3	1/3: divided run by rise instead of rise by run.

One rule for scoring: if your child got an answer right but can’t explain how, count it as half. A method that works but isn’t understood is exactly the kind that falls apart in Algebra I, when the numbers get messier.

• Everything correct for the grades they’ve finished: the foundations are solid. Enrichment is a better use of time than more review: harder multi-step problems, or competition-style math.
• Misses clustered in one area (say, questions 1 and 2, both fractions): work on that one skill for a few weeks, then try a fresh set of similar questions.
• Misses spread across three or more areas: start with fractions and negative numbers, even if those weren’t the questions missed. The other three skills sit on top of those two.

The five skills Algebra I is built on

In 2008 the U.S. National Mathematics Advisory Panel named whole numbers, fractions and parts of geometry and measurement as the “critical foundations” of algebra. It said proficiency with fractions, which includes decimals, percents and negative fractions, “seems to be severely underdeveloped.” A 2012 study by Robert Siegler and colleagues showed why it matters. Students’ knowledge of fractions and division in 5th grade predicted their algebra and overall math achievement in high school, five or six years later. That is why fractions come first below.

1. Fractions and division

What ready looks like: adds, subtracts, multiplies and divides fractions without a calculator; can place 5/8 and 2/3 on a number line and say which is bigger; can explain that 2/3 ÷ 4/9 asks “how many 4/9s fit into 2/3?”

Why it matters: solving 2/3x = 8 is fraction division, every slope is a fraction, and rational expressions in Algebra II are fractions with variables in them.

How to practice: ask for an estimate before every calculation (“will the answer be more or less than 1?”). A child who can estimate understands the size of the numbers and isn’t just following steps.

2. Negative numbers

What ready looks like: all four operations with integers, done reliably, plus knowing why −3² and (−3)² are different.

Why it matters: sign errors are among the most common mistakes in first-year algebra. Distributing a negative and subtracting a whole expression both rely on this skill.

How to practice: use a vertical number line like a thermometer. “It’s −7° and the temperature drops 3 more degrees” and “it’s −7° and a drop of 3 is cancelled” are different questions, and a child who can say why is ready for −7 − (−3).

3. Ratios, rates and percents

What ready looks like: sets up a proportion, finds a unit rate, calculates percent change from the original amount, and can tell when a situation is multiplicative and not additive (question 3).

Why it matters: proportional reasoning connects arithmetic to algebra. y = kx is a proportional relationship, and slope is a rate.

How to practice: scaling recipes, comparing unit prices, and working out discounts and sales tax.

4. Expressions and equations

What ready looks like: simplifies expressions using the distributive property and like terms; solves multi-step equations with the variable on both sides; checks the answer by substituting it back in.

Why it matters: this is the first unit of Algebra I.

How to practice: make checking by substitution non-negotiable. It takes 30 seconds and catches most errors before a teacher does.

5. Linear relationships and graphs

What ready looks like: turns a description in words into an expression or equation; finds slope from two points or a table; reads what a graph’s starting value and steepness mean in context.

Why it matters: linear functions are the backbone of Algebra I, and 8th grade is where they are introduced.

How to practice: look for “a starting amount plus a rate times something” in real life: phone plans, taxi fares, savings that grow by the same amount each week.

A grade-by-grade plan, 6th grade to the summer before 9th

New Jersey’s math standards, like most states’, teach these topics in a fairly predictable order, so the plan follows the school year instead of fighting it.

Grade	What school is usually covering	What to make solid at home
6th	Ratios and rates, dividing fractions, writing and evaluating expressions	Fraction fluency, especially division, and unit rates. If fractions are shaky, fix them this year, before negative numbers get added on top. Check with questions 1–3.
7th	Operations with negative numbers, proportional relationships, percent problems, multi-step equations	Integer fluency and percents. This is the key year: in many districts, placement for 8th-grade Algebra I is decided during 7th grade, so ask your school what the criteria are and when they are applied. Check with questions 4–7.
8th	Linear equations, functions and slope, systems of equations, the Pythagorean theorem (or Algebra I itself on an accelerated track)	Multi-step equations and turning word problems into equations. For Bergen County Academies applicants: timed, calculator-free practice by the fall. Check with questions 8–10.
Summer before 9th	—	Review, not preview. Two or three short sessions a week of mixed problems from 6th–8th grade topics. Move into Algebra I material only once the 10-question check comes back clean.

A note for BCA applicants

Bergen County Academies only accepts applications in 8th grade, and its entrance math test is 40 multiple-choice questions in 60 minutes with no calculator. That is 90 seconds a question on basic skills and word problems. A student who still reaches for a calculator on fraction arithmetic loses time on every question. So for these families the foundations need to be solid by the fall of 8th grade, not the summer after. Our BCA entrance exam preparation guide covers the rest of the test.

How to practice so it sticks

How a child practices matters as much as how much. Three techniques have strong research behind them, and all three run against the way most homework is set up.

Spread it out

A 2013 review by John Dunlosky and colleagues compared ten common study techniques. Only two earned the top rating: spacing practice out over time, and testing yourself. Rereading and highlighting, which students rely on most, rated low. In practice, four 20-minute sessions across the week beat one 80-minute session on Sunday.

Mix the problem types

A typical homework set has 20 problems of the same kind, so the student knows the method before reading the question. On a test, and in high school, they have to pick the method themselves. In a 2020 randomized trial across 54 seventh-grade math classes, Doug Rohrer and colleagues gave some classes mixed (“interleaved”) practice. On a surprise test a month later, those classes scored 61%, against 38% for classes that practiced one skill at a time. To do this at home, take two problems from this week, two from last month and two from last year, and shuffle them.

Test instead of rereading

Looking back over a worked example feels productive, but it mostly builds familiarity. Instead, cover the solution and have your child redo the problem from a blank page. If they get stuck, they’ve found exactly what to study.

Keep a mistake log

A notebook page with three columns: the problem, what went wrong, and the corrected solution. For “what went wrong,” pick from a short list: didn’t understand the concept, chose the wrong operation, misread the question, arithmetic slip, skipped a step. Redo the logged problems a week later. After a few weeks a pattern usually shows up, and it tells you what to do next. Eight “arithmetic slips” call for a checking habit, not more teaching. Eight “didn’t understand” entries on one topic call for re-teaching it.

A realistic week for a 7th or 8th grader: four sessions of 20–25 minutes, each with 5 minutes on a problem from the mistake log, 10 minutes of mixed review and 5–10 minutes on this week’s class topic. That is under two hours a week on top of homework.

Word problems: where strong calculators get stuck

Word problems add a reading task on top of the math. A student who calculates perfectly can still stall because they can’t tell what the question wants. A four-step routine (understand, plan, solve, check) gives them somewhere to start. Here it is on question 9 from the check:

1. Understand. Restate it in one sentence starting with “I need to find…”: I need to find the monthly bill for any number of texts. What changes? The number of texts. What stays fixed? The $20.
2. Plan. Cost = the fixed amount + the price per text × the number of texts.
3. Solve. 20 + 0.10t. For 150 texts: 20 + 0.10(150) = 20 + 15 = 35, so $35.
4. Check. Is $35 reasonable? 150 texts at ten cents is $15, plus the $20 base. Yes.

That shape, a starting value plus a rate times a quantity, is the y = mx + b that students spend much of Algebra I on. A child who can build it from words in 8th grade has already done the hard part.

How parents can help without re-learning the math

You don’t need to remember how to factor a trinomial to help. Asking good questions does more than explaining, because the child has to do the thinking:

• “What is the question actually asking?”
• “Why did you choose that method?”
• “How could you check that answer?”
• “Is there another way to get there?”

Watch the language, too. “You’re just not a math person” (or “I was never good at math either”) turns a fixable skill gap into a fixed identity. “Let’s find which step is giving you trouble” keeps the problem small and specific.

Talk to the teacher early, before report cards. Ask which units your child is weakest in, and ask how and when the district decides math placement for the following year.

Use everyday math, with a question attached

Everyday math only helps if there is an actual problem to solve. Some that practice the skills above:

• Grocery store (ratios): which is the better deal, 24 oz for $4.29 or 32 oz for $5.49? (The 32 oz, at about 17.2¢ an ounce against 17.9¢.)
• Sales tax (percents): what does a $60 video game cost with New Jersey’s 6.625% sales tax? ($63.98)
• Driving (rates): at an average of 50 mph, how long is an 85-mile drive down the Parkway? (1.7 hours, or 1 hour 42 minutes)
• Saving (linear equations): you have $15 and save $10 a week. When do you reach $95? (15 + 10w = 95, so 8 weeks)

When to get extra math help

Some signs that practice at home isn’t closing the gap:

• The same mistake on the same skill keeps showing up for weeks.
• Homework grades are fine but test grades keep slipping, which usually means the understanding is shallow.
• Math homework regularly ends in tears or avoidance.
• The readiness check shows gaps in three or more areas.
• The opposite: your child finishes everything easily, is bored in class, and is ready for more challenge than school offers.

Start with the school. The teacher can tell you which units are weak and whether there are extra-help periods or intervention programs. If that isn’t enough, a tutor works best when there is a specific target, not a general “get better at math.” Our guide to the signs your child may need a tutor covers the decision in more detail.

At MindzQ Education in Fair Lawn, math tutoring runs on two tracks. The remedial track follows the student’s school curriculum, with homework support and preparation for class quizzes and tests, and it focuses on understanding rather than just finishing assignments. The accelerated track is for students who are ahead, with grade advancement and preparation for competitions like Math Kangaroo and AMC. Tutoring starts with a free math assessment, so the work begins from what your child actually needs.

Frequently asked questions

What math should my child know before 9th grade?

Your child should know five things: all four operations with fractions; operations with negative numbers; ratios, rates and percents; simplifying expressions and solving multi-step linear equations; and basic linear relationships, such as slope and writing an equation from a word problem. Algebra I builds directly on these, and the 10-question check in this article tests each one.

How do I know if my child is ready for Algebra I?

A student ready for Algebra I can solve an equation like 5x − 7 = 2x + 11, simplify 3(x − 4) − 2(x − 5) without a sign error, turn a word problem into an equation, and explain each step. If fractions or negative numbers still cause regular errors, fix those first.

Should my child take Algebra I in 8th grade?

Only if the foundations are solid. Taking Algebra I in 8th grade leaves room for calculus by senior year. But a student who moves ahead with gaps often struggles later in Geometry and Algebra II, or ends up repeating material. Ask your district what placement criteria it uses. They are usually applied during 7th grade.

How much math practice does a middle schooler need outside of homework?

For most students, 20–25 minutes on three or four days a week is enough, as long as the practice is spread out and mixes problem types. Four short sessions do more than one long session on the weekend.

Is it too late to catch up in 8th grade or the summer before 9th?

No, but it changes the approach. Focus on the one or two weakest areas the readiness check flags, especially fractions and negative numbers, instead of reviewing everything. Trying to fix five gaps in the three weeks before 9th grade starts is the plan that doesn’t work. Use the summer for review, not for previewing Algebra I.

Does middle school math matter for the SAT?

Yes, a great deal. According to the College Board’s specifications, about 35% of Digital SAT math questions are Algebra (linear equations, functions and inequalities, the same material as 8th grade and Algebra I) and another 15% are Problem-Solving and Data Analysis (ratios, rates and percents). Read more about the Digital SAT.

When should I consider a math tutor?

Consider a tutor when the same errors persist for several weeks despite help at home, when math homework regularly ends in frustration, or when the readiness check shows gaps in three or more areas. A tutor can also help a student who is ahead and needs more challenge than their class offers.

The bottom line

Improving math skills before high school is less about racing ahead and more about making sure nothing is missing underneath. Run the 10-question check, find the one or two weakest areas, and work on them in short, mixed sessions a few times a week. Start in 7th grade if you can. If you start in 8th grade or the summer before 9th, there is still time, as long as you stay focused on those few areas.

Sources

• National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel. U.S. Department of Education.
• Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., et al. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697.
• Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58.
• Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112(1), 40–52.
• National Center for Education Statistics. 2024 NAEP Mathematics State Snapshot Report: New Jersey, Grade 8.
• New Jersey Administrative Code N.J.A.C. 6A:8-5.1, Graduation requirements.
• College Board. The Digital SAT Suite of Assessments: Specifications Overview.