Concept 5 of 6
Growing Figure Patterns: How Many in the Next?
Today's big idea
Count the parts in each figure and the picture becomes a number series.
Dot counts 2, 4, 6, 8 give a gap of +2, so figure 5 holds 10 dots.
How it works
👀 What's going on?
A growing pattern is a row of pictures, each one holding more than the last. Counting turns those pictures into a number series, and number series you already know how to handle.
💡 Here's the trick
Look at the figures above. Counting their dots gives 2, 4, 6, 8, which is an ordinary number series with a gap of +2. So figure 5 must hold 8 + 2 = 10 dots. The pictures are only a disguise, and writing the counts in a row removes it.
🪄 How to do it
- 1.Count the parts in each figure and write the numbers in a row, as under the picture above.
- 2.Find the gap between those numbers.
- 3.Apply that gap to the last count to reach the next figure.
✍️ Try it
One pattern has 4, 8, 12, 16 dots. Another has 1, 3, 6, 10 dots. How many dots does figure 5 hold in each?
The first has a steady gap of +4, so figure 5 holds 16 + 4 = 20. The second has gaps of +2, +3, +4, growing by one each time, so the next gap is +5 and figure 5 holds 15.
⚠️ Watch out
You might be thinking you have to draw figure 5 to count it. You do not, and drawing it is exactly where mistakes creep in. Trust the number series once three or four counts are written down.
🌟 Why this matters
Tins stacked in a shop display, seats in a fan-shaped theatre and rows in a stadium all grow like this. Counting one row and finding the rule beats counting the lot.
Exam tip: Count the parts of each figure twice before starting, because one miscount early wrecks every figure after it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Figures have 7, 10, 13, 16 dots. How many dots in Figure 5?”
- 1
Turn the picture into a list
Counts: 7, 10, 13, 16, ?
- 2
Find the jump
7 → 10 is +3. Same jump each time.
- 3
Apply +4 to Figure 4
16 + 3 = 19
- 4
Answer ✓
Fig 5 = 19 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
Figures hold 6, 12, 18, 24 sticks. How many sticks does figure 6 hold?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Machine Rules
Do the first step, write the middle number, then the second.