SME
Grade 7 Science · Problem type
How many offspring to expect
Use this for “Two Tt plants produce 40 seeds. About how many seedlings will be tall?”
Diagram
T
t
T
TT
Tt
t
Tt
tt
Tt × Tt: 3 of 4 boxes have a T, so 3 in 4 show the trait.
1 in 4 do not.
N = 40 (offspring)
This is an example. Type your own values to start a new problem.
t
4
×
N
=
n
a
First parent
example
b
Second parent
example
r
Boxes with tt (short)
worked out (not typed)
Formulas
r
=
small
t
’s
in
a
×
small
t
’s
in
b
(boxes
with
tt
(short)
=
small
t’s
in
first
parent
×
small
t’s
in
second
parent)
1
=
small
t
’s
in
Tt
×
small
t
’s
in
Tt
t
=
4
−
r
(boxes
with
a
T
(tall)
=
4
−
boxes
with
tt
(short))
3 = 4 − 1
n
=
t
4
×
N
(offspring
expected
to
be
tall
=
boxes
with
a
T
(tall)
over
4
×
offspring)
30
=
3
4
×
40
Assumptions
•
Expected means on average over many offspring. Real counts come out a little off, as coin flips do.
•
T is tall and t is short: TT and Tt are tall, tt is short.
•
Offspring come in fours here so the boxes share evenly.
Step-by-step
WE KNOW
a: Tt, b: Tt, N = 40 (offspring)
FIND
boxes with tt (short) (r), boxes with a T (tall) (t), offspring expected to be tall (n)
Step 1 · Find boxes with tt (short): r
Use r = small t’s in a × small t’s in b (boxes with tt (short) = small t’s in first parent × small t’s in second parent)
tt
needs
a
small
t
from
each
parent:
count
each
parent’s
small
t
’s
(Tt
has
1,
tt
has
2)
and
multiply.
r
=
1
Step 2 · Find boxes with a T (tall): t
Use t = 4 − r (boxes with a T (tall) = 4 − boxes with tt (short))
The other boxes have at least one capital letter, so they show the dominant trait.
t
=
4
−
1
t
=
3
(3
tall
to
1
short)
Step 3 · Find offspring expected to be tall (n)
Use n = t/4 × N (offspring expected to be tall = boxes with a T (tall) over 4 × offspring)
t
of
the
4
boxes
are
tall,
so
t
4
of
the
offspring
are.
n
=
3
4
×
40
n
=
30
Check
Put the numbers back in. Both sides should match.
1 = 1 × 1 ✓
3 = 4 − 1 ✓
30
=
3
4
×
40
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.