SME
Grade 9 Science · Problem type
Counting chromosomes
Use this for “A body cell has 46 chromosomes. How many are in a gamete, and in a zygote?”
Diagram
Body cell: 2n = 8 chromosomes in 4 pairs, each pair one from each parent.
At metaphase each is two chromatids: 2 × 8 = 16.
Meiosis
leaves
one
of
each
pair:
n
=
8
2
=
4.
Fertilization: 4 + 4 = 8.
Each pair goes either way: 2⁴ = 16 kinds of gamete.
This is an example. Type your own values to start a new problem.
n
=
2n
÷
2
X
Chromatids after S phase
worked out (not typed)
Z
Chromosomes in a zygote
worked out (not typed)
C
Kinds of gamete
worked out (not typed)
Formulas
n
=
2
n
2
4
=
8
2
X
=
2
×
(
2
n
)
16 = 2 × 8
Z
=
n
+
n
8 = 4 + 4
C
=
2
n
16
=
2
4
Assumptions
•
A body cell holds 2n chromosomes: n pairs, one of each pair from each parent.
•
Meiosis leaves one chromosome of each pair in a gamete; fertilization joins two gametes.
•
A human has 2n = 46 and a fruit fly 2n = 8; crossing over is left out of the count of gametes.
Step-by-step
WE KNOW
2n = 8
FIND
chromosomes in a gamete (n), chromatids after S phase (X), chromosomes in a zygote (Z), kinds of gamete (C)
Step 1 · Find chromosomes in a gamete (n)
Use n = (2n) ÷ 2
A gamete keeps one chromosome of each pair.
n
=
8
2
n
=
4
Step 2 · Find chromatids after S phase (X)
Use X = 2 × (2n)
S
phase
copies
each
chromosome:
two
sister
chromatids.
At
anaphase
of
mitosis
they
part
into
2
×
2
n
chromosomes.
X
=
2
×
8
X
=
16
Step 3 · Find chromosomes in a zygote (Z)
Use Z = n + n
An
egg
and
a
sperm
join,
each
with
n
chromosomes.
Z
=
4
+
4
Z
=
8
Step 4 · Find kinds of gamete (C)
Use C = 2ⁿ
Each pair lines up either way round, so every pair doubles the kinds of gamete.
C
=
2
4
C
=
16
Check
Put the numbers back in. Both sides should match.
4
=
8
2
✓
16 = 2 × 8 ✓
8 = 4 + 4 ✓
16
=
2
4
✓
Topic check
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