Middle school math at home: fractions to algebra
Middle school math is where many parents feel they should hand teaching off to someone else.
You do not have to. The three years follow one clear line. Once you see it, you can teach each step in order.
The line through grades 6, 7 and 8
Think of it as three moves.
6th grade: numbers get bigger in every direction. Fractions divide. Numbers go below zero. Ratios compare two amounts at once. A student starts writing expressions with letters.
7th grade: the rules for signs. Adding, subtracting, multiplying and dividing positive and negative numbers. Proportional relationships. Equations with more than one step.
8th grade: lines and functions. Slope. Systems of two equations. Functions as rules that turn one number into another. The Pythagorean theorem.
At the end of the line, a student is ready for Algebra 1.
The topics that matter most
If you only have energy to get three things right, get these right.
1. Ratios and rates (6th grade)
Ratios teach a student to hold two quantities in mind at once. "3 cups of flour for every 2 eggs." Unit rates follow: "$4.50 for 3 pounds is $1.50 a pound."
This idea comes back in percents, in scale drawings, in slope, and in every science lab. Spend time here.
2. Positive and negative numbers (7th grade)
This is the one that decides how algebra goes. A student who is unsure whether −3 − (−5) is 2 or −8 will lose points on every algebra problem for years.
Teach it with a number line first, then rules. And practice it until it is boring. Our flashcards include a negative numbers deck for 7th grade, read aloud, for exactly this.
3. Slope and linear equations (8th grade)
Slope is a rate, the same idea as 6th grade unit rates, now drawn as a line. If your student sees that link, slope stops being a formula to memorize.
How to teach a topic you do not remember
Every topic in our math books follows the same five steps.
- Quick Check. A few questions before you teach. If your student gets most right, move on faster.
- Learn It. Key words, step-by-step teaching with lines you can read aloud, worked examples, and the common mistakes.
- We Do It Together. Work side by side. The answer and the reason are right under each question.
- You Try. Your student works alone.
- Show What You Know. New questions at the end. Compare with the Quick Check.
You do not need to know the answer before the lesson. You need to read the lesson ten minutes ahead.
Practice: short and most days
For fluency, a short set most days beats a long set once a week. One page is one session.
Our free practice pages work on screen, with the answers: 6th grade math, 7th grade math and 8th grade math.
For facts that need to become automatic, the flashcards have a deck for each grade: fractions, decimals and percents for 6th, negative numbers for 7th, and squares, roots and powers for 8th.
Watch the errors, not the score. The same wrong answer every time means a rule is wrong, and the topic needs re-teaching. Careless slips with the right method mean more practice. We wrote more on this in how much math practice.
Bridging the summers
The summer between grades is a good time to close gaps. Each Prepare book is a short math book with a check at the start and another at the end:
- Prepare for Middle School: Math, after 5th grade
- Prepare for 7th Grade: Math, after 6th grade
- Prepare for 8th Grade: Math, after 7th grade
- Prepare for High School: Math, after 8th grade
Each is $9.99 as a printable PDF.
Where to start
- See every topic: 6th, 7th and 8th grade math.
- Try one full topic free: 6th, 7th or 8th grade.
- Each math workbook is $19.99 in the store.
We publish kindergarten through 8th grade now. High school is coming soon.
Questions: support@uponlylearning.com.
Common questions
What math should a student know before 6th grade?
Multiplication and division facts, adding and subtracting fractions, and place value with decimals. If any of these are shaky, spend time there first. Prepare for Middle School: Math is a short summer book built for exactly this gap.
Which middle school topic matters most for algebra?
Operations with positive and negative numbers, taught in 7th grade. Almost every algebra mistake later traces back to a sign error. Ratios and proportional reasoning are a close second.
I am not good at math. Can I still teach it?
Yes. Our lessons give you the words to say, worked examples and the common mistakes to watch for, and every question has an answer and a short explanation. You do not need to know the answer before the lesson.
Is 8th grade math the same as Algebra 1?
No. Our 8th grade math follows the Common Core grade 8 standards: linear equations, systems, functions, and the Pythagorean theorem. It is the grade that gets a student ready for Algebra 1.