📐 Pre-Algebra Visual Learning

Move the sliders — watch math come alive interactively

Grades 5-7 Middle School Math Foundations
1
Integers & Negatives — Understanding the Number Line
Key Concept
The Number Line has positive numbers (+) to the right of 0 and negative numbers (−) to the left.
Negatives represent values less than zero — like debt, below ground, or sub-zero temperatures.
🎮 Drag the sliders to explore the number line
Number A 3
Number B -2
A = 3, B = −2, A + B = 1
Absolute Value | |
Absolute value is the distance from 0 on the number line — it's always positive or zero.
|−7| = 7    |+7| = 7    |0| = 0
|−5| = ?
5
(−5 is 5 steps from 0)
−3 + 7
= 4
(move 7 steps right)
5 − (−2)
= 7
(minus negative = plus)
−4 × −3
= +12
(neg × neg = positive)
2
Factors, Multiples & Prime Numbers
Key Concept
Factor — a number that divides evenly into another
Multiple — the result of multiplying a number by an integer
Prime — a number with exactly two factors: 1 and itself (2, 3, 5, 7, 11...)
🎮 Choose a number to visualize its factors
Number 12
1
Fractions — Dividing the Whole
Key Concept
A fraction a/b means dividing a whole into b equal parts and taking a of them.
Numerator (a) / Denominator (b)
🎮 Move the sliders to visualize the fraction
Denominator (b) 4
Numerator (a) 3
Adding Fractions Rule
Same denominator? Just add the numerators.
Different denominators? Find a common denominator (LCD) first.
1/4 + 2/4 = 3/4   |   1/3 + 1/4 = 4/12 + 3/12 = 7/12
2
Decimals & Percent Conversions
🎮 Slide to see fraction, decimal & percent at once
Value (0→100) 75
1
Ratio — Comparing Two Quantities
Key Concept
A ratio compares two quantities a and b, written as a : b or a/b.
Example: 3 red : 2 blue → ratio is 3 : 2
🎮 Adjust both groups to explore ratios
🔴 Group A 3
🔵 Group B 2
Proportion
A proportion states two ratios are equal.
a : b = c : d means a × d = b × c (cross-multiplication)
2 : 3 = 4 : 6 → 2×6 = 3×4 → 12 = 12 ✓
1
Variables — Using Letters for Unknown Numbers
Key Concept
A variable represents an unknown or changing value — usually x, y, or n.
A constant is a fixed number that never changes.
2x + 3    (x is the variable; 2 and 3 are constants)
🎮 Change x — watch the expression evaluate in real time
x = 3
Combining Like Terms
Only add or subtract terms with the same variable.
3x + 5 + 2x − 1 = 5x + 4
1
Equations — Think of a Balance Scale
Key Concept
An equation is a mathematical statement with an equals sign (=).
Like a balance scale — both sides must weigh the same.
Whatever you do to one side, do the same to the other side.
🎮 Find x — balance the scale: x + __ = __
x = 4
Add value 3
Step-by-step: Solve x + 3 = 7
1
Subtract 3 from both sides: x + 3 − 3 = 7 − 3
2
Simplify: x = 4
3
Check: 4 + 3 = 7 ✓
🧩 Solve: What is x if 2x − 4 = 10?
1
The Coordinate Plane & Linear Functions
Key Concept
A coordinate is an (x, y) pair that locates a point on the plane.
In the linear function y = mx + b, m is the slope and b is the y-intercept.
y = mx + b
🎮 Adjust slope (m) and y-intercept (b) to draw the line
Slope m 1
y-intercept b 0
1
Exponents — Repeated Multiplication
Key Concept
aⁿ = multiply a by itself n times (a: base, n: exponent)
Example: 2³ = 2 × 2 × 2 = 8
2⁴ = 2 × 2 × 2 × 2 = 16
🎮 Change base and exponent — see the grid grow!
Base (a) 2
Exponent (n) 4
Laws of Exponents
×
Multiply same base: aᵐ × aⁿ = aᵐ⁺ⁿ   e.g. 2³ × 2² = 2⁵ = 32
÷
Divide same base: aᵐ ÷ aⁿ = aᵐ⁻ⁿ   e.g. 2⁵ ÷ 2² = 2³ = 8
( )
Power of a power: (aᵐ)ⁿ = aᵐⁿ   e.g. (2³)² = 2⁶ = 64
0
Zero exponent: a⁰ = 1   Any nonzero number to the power of 0 equals 1