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
Each SEAG paper has 28 maths questions. Questions 29 to 50 are multiple choice with five possible answers, and questions 51 to 56 need a short written answer. With 56 questions in 60 minutes across English and maths, that is about a minute per question.
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
Try three free questions from our triangular numbers course. They start easy and get harder, so you can see where your child's confidence runs out. If they manage the last one without a hint, this topic is probably secure. If not, the steps above show where to start.
Daniel's first five triangular orange arrangements contain 1, 3, 6, 10 and 15 oranges. How many oranges will the next arrangement contain?
Poppy knows the 12th triangular number is 78 (which is 1+2+3+...+12). What is the 13th triangular number?
Sarah notices that 36 is both a triangular number AND a square number. Which triangular number comes immediately before 36 in the sequence?
This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.
Amara 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, ?
Look at the gap between each pair
Step 1 of 4
Amara 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...
Common mix-up: 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.
Sitting the SEAG test this November? Read our last-month revision plan, Paper 1 vs Paper 2 and test day guide.
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.
Free to start · no card needed