Formative Instructional and Assessment Tasks
Birthday Cake
5.NF.5 – Task 4
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication and division to multiply
and divide fractions.
5.NF.5 Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a
product greater than the given number (recognizing multiplication by whole numbers
greater than 1 as a familiar case); explaining why multiplying a given number by
a fraction less than 1 results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
Additional Standard:
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction
or whole number by a fraction.
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of
the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
Task handout, graph paper
Birthday Cake
Birthday Cakes are for sale at the bake shop. The price depends on the size of the cake.
Part 1:
The vanilla cake is 12 inches wide, 9 inches long and 5 and 1/2 inches high.
Calculate the volume of the vanilla cake.
Part 2:
The store’s strawberry cake is 7/6 the width of the vanilla cake.
Without calculating, how does the size of the strawberry cake compare to the size of the
vanilla cake? How do you know?
Calculate the volume of the strawberry cake.
Part 3:
The store’s chocolate cake is 1/3 the width of the vanilla cake, but its length is triple the
height.
Without calculating, how does the size of the chocolate cake compare to the size of the
vanilla cake? How do you know?
Calculate the volume of the chocolate cake.
Part 4 (Extension):
If the price of the cake is $1.25 per cubic inch what are the prices are the various cakes?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE
Formative Instructional and Assessment Tasks

Level I
Student uses inappropriate
solution strategy and does not
get the correct answer.
Rubric
Level II
Not Yet Proficient
 Finds the correct answer, but
there may be inaccuracies or
incomplete justification of
solution
OR
 Uses partially correct strategy,
but gets the wrong answer.
Level III
Proficient in Performance
 Accurately solves problem
 Part 1: 594 cubic inches.
 Part 2: The strawberry cake
will be larger since 7/6 is
larger than 1. The volume is
693 cubic inches.
 Part 3: The chocolate cake is
the same size as the vanilla
cake. The width is 1/3 and the
length is tripled so the volume
will be the same. The volume
is 594 inches.
 Part 4: The cost of the vanilla
cake is $742.50. The cost of
the strawberry cake is
$866.25. The cost of the
chocolate cake is $742.50.
 Use appropriate equations to
justify the solution
*Level IV: student uses multiple models to support their reasoning (i.e., equations, arrays, etc.). Student also notices additional patterns.
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE
Formative Instructional and Assessment Tasks
Birthday Cake
Birthday Cakes are for sale at the bake shop. The price depends on the size of the
cake.
Part 1:
The vanilla cake is 12 inches wide, 9 inches long and 5 and 1/2 inches high.
Calculate the volume of the vanilla cake.
Part 2:
The store’s strawberry cake is 7/6 the width of the vanilla cake.
Without calculating, how does the size of the strawberry cake compare to the size of
the vanilla cake? How do you know?
Calculate the volume of the strawberry cake.
Part 3:
The store’s chocolate cake is 1/3 the width of the vanilla cake, but its length is triple
the height.
Without calculating, how does the size of the chocolate cake compare to the size of
the vanilla cake? How do you know?
Calculate the volume of the chocolate cake.
Part 4 (Extension):
If the price of the cake is $1.25 per cubic inch what are the prices are the various
cakes?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE