Concept 5 of 6
Growing Figure Patterns: How Many in the Next?
Today's big idea
Count each figure, write the counts in a row, and a number series appears.
Hunting the per-step increase beats staring at any single drawing.
How it works
👀 What's going on?
Someone building a wall of matchsticks adds the same few sticks for every new square. By the fourth square nobody counts the whole wall any more. They count what one extra square costs and add it on.
💡 Here's the trick
Look at the five boxes above. Each box holds two more dots than the box on its left, so the counts read 2, 4, 6, 8, 10. Once you write the counts in a row, the drawing is gone and a plain number series is left. Solve that instead.
🪄 How to do it
- 1.Count the dots in the strip above, one figure at a time.
- 2.Write those counts out in a row as a number series.
- 3.Find the jump between counts, then push it one figure further.
✍️ Try it
- 1.Figures hold 2, 5, 8, 11 sticks. How many sticks are in Figure 5?
- 2.Figures hold 5, 9, 13, 17 tiles. How many tiles are in Figure 7?
Pattern 1 adds 3 to every figure, so Figure 5 holds 11 + 3 = 14 sticks. Pattern 2 adds 4 each time, and you need two more figures. Figure 6 holds 17 + 4 = 21 tiles, so Figure 7 holds 21 + 4 = 25 tiles.
⚠️ Watch out
You might be thinking the drawing is the thing to study. Stare at Figure 4 all day and it does not tell you a thing about Figure 5. What you actually need is the jump between two figures, and that is a number you get by counting twice. Counting a whole figure dot by dot is easy to get wrong. Count Figure 3, count Figure 4, take the difference.
🌟 Why this matters
Growing patterns show up whenever something is built in equal steps. A brick wall gains the same row of bricks each course. A stack of chairs gains the same height per chair. Turn the drawing into counts and you can say what the tenth one holds without building it.
Exam tip: These questions hide a simple series behind a drawing, so count first and reason afterwards.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Figures have 5, 8, 11, 14 dots. How many dots in Figure 5?”
- 1
Turn the picture into a list
Counts: 5, 8, 11, 14, ?
- 2
Find the jump
5 → 8 is +3. 8 → 11 is +3. 11 → 14 is +3. Same jump every time.
- 3
Apply +3 to Fig 4
14 + 3 = 17
- 4
Answer ✓
Fig 5 = 17 dots
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Each figure adds 2 dots. Grow the pattern until Figure 5.
GROWING PATTERN · ROUND 1 OF 3
Quick check
✅ VERIFICATION
A dot pattern has 3 dots in Figure 1, 7 dots in Figure 2 and 11 dots in Figure 3. Which figure has 19 dots?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Machine Rules
Two pairs, not one. Then send your number through.