Pascal’s Triangle Basics
A triangle where each entry is the sum of the two above it.
Key idea
A triangle where each entry is the sum of the two above it.
In depth
Each entry is the sum of the two above it. Row n lists the binomial coefficients C(n, k), the number of ways to choose k items from n. Rows also give the coefficients of (a+b)ⁿ.
Worked example
Row 4: 1, 4, 6, 4, 1, so (a+b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴.
Real-world uses
- Counting combinations for lottery and team choices
- Expanding brackets such as (a + b)³
Common mistake
Starting row numbering at 1 instead of 0.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Pascal’s Triangle Basics?
A triangle where each entry is the sum of the two above it. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Pascal’s Triangle Basics used in real life?
Real-world examples: Counting combinations for lottery and team choices; Expanding brackets such as (a + b)³.
What should I learn before Pascal’s Triangle Basics?
Make sure you are comfortable with Fibonacci Numbers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Pascal’s Triangle Basics?
Starting row numbering at 1 instead of 0.
How can I practise Pascal’s Triangle Basics?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Pascal’s Triangle Basics?
Move on to Casting Out Nines next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.