Algebra · Lesson 1

Patterns & the Mystery Number

Every algebra problem hides a number somewhere. Learn to spot the hidden number, keep an equation balanced, and crack the rule behind a pattern.

Part 01

A Number in Hiding

Sometimes a math sentence is missing a piece. We know almost everything — except one number. We can draw a box where that missing number goes:

3 + ? = 7

What number goes in the box so the sentence is true? You probably said 4 — because 3 + 4 = 7. That hidden number is the whole idea behind algebra.

The big idea 💡

A box — or a letter like x or n — is just a stand-in for a number we haven't figured out yet. We call it a variable. Your job is to discover what it really is.

So these three all mean exactly the same thing:

3 + ? = 7 · 3 + = 7 · 3 + x = 7
Part 02

Keep It Balanced

The = sign means "the same as." A good way to picture it is a balance scale: whatever sits on the left weighs exactly the same as whatever sits on the right. The cup 🥤 hides the mystery number.

Try it below. How many blocks are hidden inside the cup so the scale balances? Type your guess and watch what happens.

Interactive · Balance the Scale
? + 2 6
Cup holds:

Why this works

When both pans weigh the same, the scale sits level. The cup's hidden number is whatever makes the two sides match — so balancing the scale is the same as solving for the mystery number.

Part 03

The Function Machine

A function machine takes a number in, follows a secret rule, and sends a new number out. Feed it some numbers, watch what comes out, and see if you can figure out the rule.

Interactive · Crack the Rule
?

Feed in a number:

Drop a number in to see what comes out.

What's the secret rule?

Part 04

Finding the Rule in a Pattern

Patterns are function machines in disguise. Look at the jump from one number to the next — that jump is the rule.

2 +2 → 4 +2 → 6 +2 → 8 +2 → ?

Each step adds 2, so the mystery number is 8 + 2 = 10. Once you know the rule, you can keep the pattern going forever.

1

Compare two numbers next to each other

How do you get from the first to the second? Did it grow or shrink, and by how much?

2

Check that the rule keeps working

Try the same jump on the next pair. If it fits every time, you've found the rule.

3

Use the rule on the last number

Apply your rule one more time to find the mystery number at the end.

Your Turn!

Practice & Earn Your Score

Solve each problem to find the mystery number. Type your answer and press Check. You earn a point for every one you get on the first try — finish all eight to see your score.

Answered 0/8
Score 0

Nice work!

0/8