Math Tutorials
Learn step by step with our interactive guides!
Choose Your Topic
Select what you want to learn today!
Algebra
Learn about equations and variables
Calculus
Understand rates of change
Geometry
Master shapes and spaces
Statistics
Learn about data and patterns
Solving Simple Equations
Understanding Variables
A variable (like x) is like a mystery box that holds a number we need to find!
Think of x as a mystery box:
"The mystery number plus 5 equals 12"
Balancing Equations
Think of an equation like a balance scale - whatever you do to one side, you must do to the other to keep it balanced!
Let's solve x + 5 = 12:
2. Subtract 5 from both sides:
x + 5 - 5 = 12 - 5
3. Simplify: x = 7
👉 Try This!
Solve: x + 3 = 10
Checking Your Answer
Always check if your answer makes sense by plugging it back into the original equation!
Original equation: x + 5 = 12
Plug in 7: 7 + 5 = 12
Simplify: 12 = 12 ✓
It works! Our answer is correct!
🌟 Pro Tip!
When checking your answer, write out each step clearly. This helps you catch any mistakes and makes it easier to explain your work!
Real-World Examples
Algebra is everywhere in real life! Here are some fun examples:
- 🎮 Game scores: Your total points = Base points + Bonus points
- 🍕 Pizza slices: Total slices - Eaten slices = Remaining slices
- 💰 Saving money: Money saved + Weekly allowance = Target amount
🌟 Challenge Problem!
Sarah has saved $15 and gets $5 allowance each week. She wants to buy a game that costs $35. How many weeks will it take?
Write it as: 15 + 5x = 35
📚 Want to Learn More?
Understanding Rate of Change
What is Rate of Change?
Rate of change is how fast something is changing over time - like your height growing or a car speeding up!
Common Examples:
- 🏃♂️ Speed: How fast you're moving
- 📏 Growth: How tall you're getting
- 🌡️ Temperature: How hot it's becoming
Positive vs Negative Slope
A slope tells us if something is increasing (going up) or decreasing (going down).
🟢 Going Up = Positive Slope (like climbing a hill)
🔴 Going Down = Negative Slope (like sliding down a slide)
👉 Try This!
If a car's speed goes from 0 to 60 mph in 6 seconds, what's the rate of change?
Graphs in Motion
Let's see how different rates of change look on a graph!
🌟 Pro Tip!
The steeper the line, the faster the change! A flat line means no change at all.
Real-World Examples
Rate of Change in Action:
- 🎢 Roller coaster speed changes
- 📱 Phone battery draining
- 🌱 Plant growth over time
- 🏊♂️ Swimming speed in a race
🌟 Challenge Problem!
A plant grows 2 inches every week. After 4 weeks, how tall will it be if it started at 3 inches?
📚 Want to Learn More?
Exploring Shapes and Their Properties
Understanding Area
Area is how much space a shape takes up - like how much paint you'd need to cover it!
Common Shape Areas:
Rectangle Area = length × width
Triangle Area = (base × height) ÷ 2
👉 Try This!
What's the area of a square with sides of 5 inches?
Understanding Perimeter
Perimeter is the distance around a shape - like walking around the edge of a swimming pool!
Common Shape Perimeters:
Rectangle Perimeter = 2 × (length + width)
Triangle Perimeter = side1 + side2 + side3
👉 Try This!
What's the perimeter of a rectangle that's 4 inches long and 3 inches wide?
Shapes in 3D
When shapes pop out into 3D, they become even more interesting!
Common 3D Shapes:
- 📦 Cube: Like a dice or box
- 🎾 Sphere: Like a ball
- 🔺 Pyramid: Like ancient Egyptian buildings
- 🎪 Cylinder: Like a can or paper towel roll
🌟 Pro Tip!
3D shapes have faces (flat surfaces), edges (where faces meet), and vertices (corners)!
Geometry in Real Life
Where to Find Geometry:
- 🏠 Houses and buildings
- 🎨 Art and design
- 🌺 Nature (flowers, snowflakes)
- 🎮 Video games and animations
🌟 Challenge Problem!
A square pizza has sides of 12 inches. How many inches of crust (perimeter) does it have, and what's its area in square inches?
📚 Want to Learn More?
Understanding Numbers in Groups
Finding the Mean (Average)
The mean is like finding the "fair share" if you divided everything equally!
To find the mean:
- Add all the numbers
- Divide by how many numbers there are
1. Add: 2 + 4 + 6 + 8 = 20
2. Count numbers: 4 numbers
3. Divide: 20 ÷ 4 = 5
Mean = 5
👉 Try This!
Find the mean of: 5, 8, 11, 14, 17
Finding the Median
The median is the middle number when all numbers are in order - like the middle person in a line!
To find the median:
- Put numbers in order (smallest to largest)
- Find the middle number
- If two middle numbers, take their mean
1. Order: 1, 3, 5, 7, 9
2. Middle: 5
Median = 5
🌟 Pro Tip!
When you have an even number of values, take the mean of the two middle numbers!
👉 Try This!
Find the median of: 12, 5, 8, 15, 3, 10
Finding the Mode
The mode is the number that appears most often - like your favorite ice cream flavor!
To find the mode:
- Count how many times each number appears
- The number that appears most is the mode
2 appears once
4 appears three times ⭐
6 appears once
8 appears once
Mode = 4
Data in Real Life
Where to Find Statistics:
- 📊 Class test scores
- ⚾ Sports statistics
- 🌡️ Daily temperatures
- 📱 App ratings
🌟 Challenge Problem!
A student's test scores are: 85, 92, 78, 95, 88
Find the mean, median, and highest score!