A rule such as "start at 3 and add 4" builds 3, 7, 11, 15, 19.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The pattern does more than the rule said
That rule never mentioned odd numbers, yet every term is odd.
Say why
Adding 4 to an odd number keeps it odd, because 4 is even.
Shapes work the same way
A growing square pattern has side lengths 1, 2, 3 and totals 1, 4, 9.
Follow the rule exactly
Given "start at 3 and add 5 each time", the pattern is 3, 8, 13, 18, 23. Apply the rule mechanically first, before looking for anything clever. Generating the terms correctly is the foundation for everything you might notice afterwards.
Notice what the rule did not say
That pattern alternates odd and even, and every term ends in 3 or 8. The rule never mentioned either property — they emerged. Spotting emergent features is the real work of this lesson, and it is genuine mathematics.
Explain why the feature appears
The terms alternate odd and even because adding 5, an odd number, always flips a number from odd to even or back. That is an explanation, not an observation. A pattern you can explain is one you can trust to continue.
Test before you trust
A rule that fits four terms can fail on the fifth. Generate one more term than you used to form the conjecture and check it. Mathematicians do exactly this, and the discipline of testing is worth more than the pattern itself.
Step 2: Try It Yourself
Tap and try it out.
The ringed squares are the multiples of 4. They land in a pattern.
Step 3: Watch an Example
One step at a time.
Watch Leo Spot the Hidden Feature
Leo follows "start at 2 and add 6".
- Step 1
He writes 2, 8, 14, 20, 26.
Step 4: Your Turn
Practice makes it stick.
The Chairs
Problem 1 of 2
Each table seats 4, plus 2 at the ends. With 5 tables, how many seats?
seats
The Savings
Problem 2 of 2
Ana starts with 5 pounds and adds 3 each week. How much after 6 weeks?
pounds
Follow the Rule
1 of 4
Start at 3, add 5. What is the 4th term?
2 of 4
Start at 100, subtract 7. What is the 3rd term?
3 of 4
Start at 1, double each time. What is the 5th term?
4 of 4
Start at 4 and add 10. Are the terms all even?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Start at 7, add 4. What is the 5th term?
Question 2 of 2
Why does "start at 3, add 4" keep every term odd?
What You Learned
- A rule builds a pattern one step at a time.
- The pattern often has features the rule never mentioned.
- Say why the feature happens, not just that it does.