Understanding triangular numbers as sums of consecutive integers (1, 3, 6, 10, 15...) and recognising the pattern.
Where your child meets this in real life: Recognising and continuing number patterns, understanding sequential sums
SEAGReady breaks triangular numbers into 2 steps, taught in order so each skill builds on the last.
Identify and continue the triangular number sequence by recognising the increasing differences
Calculate triangular numbers using cumulative sums of consecutive integers starting from 1
Three free sample questions from our triangular numbers course. Every question comes with a full explanation, and hints that guide without giving the answer away.
Oisin is stacking oranges in a pyramid display. The rows have 1, 3, 6, 10, 15 oranges so far. How many oranges will the next row have?
Answer: B. 21
Find the differences between each pair: 3-1=2, 6-3=3, 10-6=4, 15-10=5 The differences increase by 1 each time: +2, +3, +4, +5... Next difference is +6 15 + 6 = 21
Stuck? Start here: Look at the gaps between each number: 3-1=2, 6-3=3, 10-6=4, 15-10=5
Declan is stacking cups in rows. Row 1 has 1 cup, row 2 has 2 cups, and so on. How many cups are in 6 rows altogether? (Find 1 + 2 + 3 + 4 + 5 + 6)
Answer: A. 21
The 6th triangular number = 1 + 2 + 3 + 4 + 5 + 6 Add step by step: 1 + 2 = 3 3 + 3 = 6 6 + 4 = 10 10 + 5 = 15 15 + 6 = 21 Answer: 21 cups
Stuck? Start here: The 6th triangular number is the sum of 1 + 2 + 3 + 4 + 5 + 6.
These are triangular numbers: 1, 3, 6, 10, 15, 21. What is the next triangular number after 21?
Answer: C. 28
The differences between triangular numbers increase by 1: +2, +3, +4, +5, +6... The difference between 15 and 21 is 6. So the next difference is 7. 21 + 7 = 28
Stuck? Start here: Find the difference between 15 and 21. It's +6.
This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.
Niamh is arranging cans in a pyramid display. Each row has one more can than the row above. The rows have 1, 3, 6, 10, 15 cans so far.
How many cans will the next row have?
1, 3, 6, 10, 15, ?
Step 1 of 4
Niamh is arranging cans in a pyramid display. Each row has one more can than the row above. The rows have 1, 3, 6, 10, 15 cans so far.
How many cans will the next row have?
The next row will have 21 cans.
The key insight: The jumps grow by 1 each time: +2, +3, +4, +5, +6...
Watch out: Adding 5 again to get 20. The difference increases each time - it's not constant like in times tables.
These are the misconceptions we see most often in triangular numbers, including the ones our practice questions are specifically designed to catch.
Struggling with triangular numbers? The real gap is often in one of these earlier topics.
SEAGReady finds the exact step where your child gets stuck, teaches it with worked examples like the one above, and brings it back for review so it sticks.