SME
Grade 9 Science · Problem type
Pyramid of numbers
Use this for “2 oak trees each carry 3,000 caterpillars, and a warbler eats 250 a season. How many warblers can they feed?”
Diagram
Pyramid of numbers, bottom up: oak trees 2, caterpillars 6,000, warblers 24.
This is an example. Type your own values to start a new problem.
N₁
Oak trees
example
a
Caterpillars on each tree
example
N₂
Caterpillars
worked out (not typed)
b
Caterpillars one warbler eats a season
example
N₃
Warblers fed
worked out (not typed)
Formulas
N₂
=
N₁
×
a
6,000 = 2 × 3,000
N₃
=
⌊
N₂
b
⌋
24
=
⌊
6,000
250
⌋
Assumptions
•
A pyramid of numbers counts the organisms at each feeding level, whatever their size.
•
One large producer can feed thousands of small consumers, so the bottom tier can be the narrowest.
•
Each predator eats many prey over a season, so the top level holds far fewer animals.
Step-by-step
WE KNOW
N₁ = 2, a = 3,000, b = 250
FIND
caterpillars (N₂), warblers fed (N₃)
Step 1 · Find caterpillars (N₂)
Use N₂ = N₁ × a
Every tree carries a caterpillars.
N₂
=
2
×
3,000
N₂
=
6,000
Step 2 · Find warblers fed (N₃)
Use N₃ = ⌊N₂ ÷ b⌋
Each
warbler
needs
b
caterpillars:
share
them
out
b
to
a
bird,
whole
birds
only;
the
leftover
caterpillars
feed
no
one.
N₃
=
⌊
6,000
250
⌋
N₃
=
24
Check
Put the numbers back in. Both sides should match.
6,000 = 2 × 3,000 ✓
24
=
⌊
6,000
250
⌋
✓
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