Number Detectives: The Big End-of-Year Investigation

Here is a challenge to wake up your brain! Look at these numbers: 2, 4, 6, 8, 10. What do you notice? Can you guess what comes next? Now look at these: 1, 3, 6, 10, 15. Something different is happening here. These are called triangle numbers — you will find out why in a moment. Think about which maths skills you have used this year. Addition? Multiplication? Spotting patterns? You will need all of them today!

A pattern is a set of numbers or shapes that follow a rule. Today you are going to investigate triangle numbers. A triangle number is made by adding dots together in a triangle shape. Start with 1 dot. Add 2 dots below. Add 3 dots below that. Keep going! Here is how it works: • Row 1 → 1 dot → triangle number = 1 • Rows 1–2 → 1 + 2 = 3 dots → triangle number = 3 • Rows 1–3 → 1 + 2 + 3 = 6 dots → triangle number = 6 • Rows 1–4 → 1 + 2 + 3 + 4 = 10 dots → triangle number = 10 The rule is: add the next whole number each time. We call each addition a step. So the steps go +2, +3, +4, +5… A good investigator always asks: 'Will this rule always work?' That is your job today — to test the rule and look for more patterns inside the triangle numbers.