Build number sense.
Move between representations and explain relationships with numbers.
- Ratios and unit rates
- Dividing fractions
- Decimals and negative numbers
- Expressions and coordinate-plane ideas
GENIUS PRACTICE · MIDDLE SCHOOL
Mathematics for Grades 6–8.
Build understanding one idea at a time. Explore important middle school math topics, see why a method works, and try an original practice question with a clear explanation.
Find your mathematics path
Start with the skills that matter.
These are representative learning topics, not an exhaustive syllabus. Classroom order and assignments vary.
Reason proportionally.
Connect quantities, write equations, and make sense of positive and negative values.
- Proportional relationships
- Operations with rational numbers
- Two-step equations
- Geometry and probability foundations
Think algebraically.
Model patterns and use equations to explain how quantities change.
- Linear equations and slope
- Functions and input-output relationships
- Systems of linear equations
- Transformations and the Pythagorean theorem
Learn the reasoning
Worked examples, step by step.
Notice how each answer follows from a mathematical relationship rather than a memorized shortcut.
How much does one notebook cost?
Three notebooks cost $12. Each notebook has the same price. What is the cost of one?
Step 1: Identify the total cost ($12) and quantity (3 notebooks).
Step 2: Divide 12 by 3 to find the cost per notebook.
Answer: $4 per notebook. Check: 3 × $4 = $12.
A unit rate describes a quantity for one unit.
Solve a two-step equation.
A number is multiplied by 3, then increased by 5, giving 20. Find the number.
Step 1: Write 3x + 5 = 20.
Step 2: Subtract 5 on each side: 3x = 15.
Step 3: Divide both sides by 3: x = 5.
Check: 3(5) + 5 = 20.
Genius Practice
Try a problem. Understand the answer.
Select Grade 6, 7, or 8, then choose an answer. Your response stays in this page; no account, tracking, or student information is required.
GRADE 6 · RATIOS
A recipe uses 2 cups of rice for 5 servings. How many cups are needed for 10 servings?
Choose an answer to see the reasoning.
For NYC families
Support starts with a good question.
Ask your student to explain what a number represents, how they chose a strategy, and how they can check whether the answer makes sense.