Grade 4 › G4U10 Sequences

Grade 4 › G4U10 Sequences › L3
GRADE 4 · ALBERTAOUTCOME AB-G4-4P1

L3 · Special Sequences: Fibonacci, Triangular Numbers, Square Numbers

Learning goal

“I can continue and explain three famous sequences - Fibonacci (each term is the sum of the two before it), triangular numbers, and square numbers - by describing in words how each term is built from the ones before.”

Fibonacci sequence — the sequence 1, 1, 2, 3, 5, 8, 13, ... where each term is the sum of the two terms right before it. It shows up in nature, for example in petal counts and pinecone spirals.
Triangular numbers — the numbers 1, 3, 6, 10, 15, ...: the total dots in triangle-shaped dot patterns that grow by one row at a time.
Square numbers — the numbers 1, 4, 9, 16, 25, ...: the total dots in square arrays.
Pattern rule (in words) — a sentence that says how to build the next term, such as "add the two terms before it." In this grade, rules are always sentences, never formulas.
Worked example

Build the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ... Step 1: It starts with two terms: 1, 1. Step 2: Every term after that is the SUM of the two terms right before it: 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8. Step 3: Next term: 5 + 8 = 13. Say it plainly: Fibonacci is neither arithmetic (gaps: 0, 1, 1, 2, 3 - not constant) nor geometric (multipliers not constant). It has its own rule, in words: "add the two terms before it." Nature uses it - petal counts and pinecone spirals often follow these numbers.

Check yourself — explain it

To find the next Fibonacci term, you...

Paired problem — example still visible

Continue: 2, 3, 5, 8, ___ -> 13 (5 + 8)

Faded completion — last step is yours

"Fibonacci: 1, 1, 2, 3, 5, 8, 13, ___. The missing term is 8 + ___ = ___" -> 13; 21

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz