Middle school math help for grades 6 to 8

What students learn in grades 6, 7 and 8

Under the California Common Core State Standards for Mathematics, middle school follows a clear storyline: ratios lead to proportional relationships, which lead to linear equations and functions. Work with expressions and equations grows alongside, so by grade 8 students are solving equations and systems that would have looked like a foreign language in grade 5.

Grade 6 introduces ratios and unit rates (if 3 pounds cost $6, one pound costs $2), dividing fractions by fractions, and negative numbers on the number line and coordinate plane. Students write and evaluate expressions with variables, solve one-step equations such as x + 7 = 15, and begin statistics with mean, median, and how spread out data is.

Grade 7 centers on proportional relationships and percent: tax, tips, discounts, markups, and percent change. Students add, subtract, multiply, and divide positive and negative numbers, solve two-step equations and inequalities, and use the formulas for the area and circumference of a circle. Probability appears for the first time.

Grade 8 is close to a first course in algebra. Students work with integer exponents, scientific notation, square roots, and the idea of irrational numbers.

They graph lines, interpret slope as a rate of change, solve linear equations with variables on both sides, and solve systems of two linear equations. Functions are defined formally, and geometry includes transformations, the Pythagorean theorem, and the volume of cylinders, cones, and spheres.

Some California students take Algebra I or an accelerated course in grade 8 instead. What is offered varies by district, so it is worth asking your school how its pathway works.

Where middle schoolers usually struggle

• Negative numbers. Rules like two negatives make a positive get misapplied to addition: −3 + (−5) is −8, not 8. A number line keeps the meaning in view.
• Fraction gaps from elementary school. Dividing fractions, unit rates with fractions, and many equations depend on the fraction skills from grades 4 and 5.
• Percent problems that stop halfway. For a jacket that costs $60 at 25 percent off, students often find the $15 discount and stop there instead of answering $45.
• Translating words into equations. Five less than a number is n − 5, not 5 − n.
• Doing the same thing to both sides. Students who learned equation solving as move the number and flip the sign make sign errors as soon as equations get longer.
• Slope. Mixing up rise and run, or misreading a graph's scale, is common when lines first appear in grade 8.

Worked example: a two-step equation from a word problem

Two-step equations are a grade 7 standard and the foundation for almost everything in grade 8 and Algebra I. The goal is to write an equation that matches the story, then undo the operations in reverse order.

Maya has $50. She buys 3 notebooks that each cost the same amount and has $32 left. If x is the cost of one notebook, the cost of the notebooks plus the money left over equals what she started with, so 3x + 32 = 50.

Why the check step matters

Notice that the last step goes back to the original equation, not the line just above it. Substituting the answer back in catches most sign and arithmetic slips before homework is turned in, and it is a habit students will rely on through Algebra II.

A second kind of check is asking whether the answer is reasonable. A notebook that costs $6 makes sense; one that costs $600 or negative $6 would be a signal to look again.

Signs your middle schooler needs help

• Grades drop at the start of grade 7 or grade 8, when the course moves from computation toward algebra.
• Homework scores are fine but test scores are much lower, which can mean they follow worked examples without being able to start a problem alone.
• They skip writing steps, do everything in their head, and cannot find their own mistakes.
• They say they get it but cannot explain why a step works.
• Comments like I was good at math until this year, or a new reluctance to talk about math class.

How to help a middle schooler with math

Middle schoolers often want independence, so the most useful help is usually a question rather than an explanation.

• Ask them to explain the problem to you out loud before they start. Many students find their own mistake while explaining.
• Encourage one step per line. Neatly written steps make errors visible.
• Make checking routine: substitute the answer back in, or ask whether it makes sense.
• Look for gaps, not just the current topic. Trouble with equations is often really trouble with fractions or negative numbers.
• Use real percents: sale prices, restaurant tips, and sports statistics.
• Stay in touch with the teacher, especially in grade 7, when decisions about grade 8 courses may be made.