Grade 3 – Statistics and Probability
Pizza Toppings
How many different double-topping pizzas can you make with four different toppings?
1 – Statistics and Probability
Pizza toppings
How many different double-topping pizzas can you make with four different
toppings?
3–1–1
CU
4
The work shows a translation of the key concepts (four toppings
selected two at a time; the number of distinct combinations) is
completed.
PS
4
Beginning with four corners and using the “shaking hands” model of
finding all pairings is an effective strategy that is completed.
V
4
Starting with 4 toppings and creating a list while finding the
combinations that select two toppings at a time is a completed
review of the concepts and may have involved a different
perspective for the strategy. The work verifies the original answer.
C
4
Telling us the four toppings are a, b, c, & d and then numbering
each of the pairings is a clear translation and process. This
connects to the verification which identifies specific toppings and
creates a listing of pairings. The connecting path is complete.
Acc.
5
6 different double-topping pizzas is a mathematically justifiable
solution to this task.
1 – Statistics and Probability
Pizza toppings
How many different double-topping pizzas can you make with four different
toppings?
3–1–2
CU
4
The work shows a translation of the key concepts (four toppings
selected two at a time; the number of distinct combinations) is
completed.
PS
3
Starting with four particular toppings (although two were the same)
and creating a list of their pairings was only partially effective. This
strategy fell short when s/he omitted the diagonal pairings.
V
4
The review including the key concepts (4 toppings selected two at a
time); the strategy (numbering the pairings) and the answer (both
parts yielded 4 pizzas) is complete.
C
4
This connecting path contains no significant gaps. The reader can
tell s/he has numbered the four toppings, made pairings (the
rectangle and the list) and counted the pairings. The verification
helps the reader see the purpose of the rectangle.
Acc.
1
4 pizzas is not mathematically justifiable. There is no evidence to
suggest s/he would not always end up with the number of toppings
matching the number of combinations, so there is instruction
needed in the key concept of finding all combinations available.
1 – Statistics and Probability
Pizza toppings
How many different double-topping pizzas can you make with four different
toppings?
3–1–3
CU
2
The work shows a translation of the concepts of four toppings and
different pizzas, but not the toppings selected two at a time (doubletoppings), or the number of distinct combinations --- making this
underdeveloped.
PS
1
Putting the four toppings into groups of 1, 2, 3 or 4 toppings on a
pizza is an ineffective strategy for this task.
V
3
The review included four toppings and using different toppings from
the original approach found the same answer of 4 ways. This is
only partially effective as the pattern of toppings is different and not
addressed.
C
2
The connecting path has more than significant gaps between the
translation ignoring “double-topping” pizzas, and the strategy used
having different “third” pizzas without explanation. Were three of
the four in the verification different pizzas than the first three in the
original solution, or did the verification only have three different
pizzas?
Acc.
1
4 pizzas is not correct and further instruction is needed.