Mathematics

1
Mathematics
Problem of the Day
Fifth Grade
Third Quarter
2
Directions and Information
Each Problem of the Day is correlated to our
Cumberland County Task Analysis for the purpose
of practicing each objective through problem
solving. Each problem will be either a
performance task, short answer, or multiple
choice which allows students to work with
problems through many avenues. When using
Problem of the Day provide students with
manipulatives (which may include a calculator)
and a mathematics journal. Expect that each
student solves the problems and records his/her
answer in a math journal. Students should
include his/her answer along with a number
sentence, a unit, a drawing (proof picture), and
a written explanation of how the problem was
solved. After students have time to solve the
problem, students should discuss solution
strategies with their team. Following team
discussions review the correct answer, the reason
it is correct and in the case of multiple choice
answers review why answers are incorrect.
Special thanks to the fifth grade members of the
Mathematics Leadership Team Brandi Newell, Wanda
Ussery, Sherrie McDonald and Joy Davis who worked
so hard to make these problems possible. Also,
many thanks to Renee Collins who helped with the
editing process.
3
Performance Task
Mathematics
Problem of the Day
Two angles are called complementary angles if the
sum of their degree measurements equals 90
degrees. One of the complementary angles is said
to be the complement of the other. Here is an
example of complementary angles
Example B
Example A
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
Draw other sets of complementary angles.
4
Short Answer
Mathematics
Problem of the Day
List all of the names for the angle in the
diagram. One example is .
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
5
Performance Task
Mathematics
Problem of the Day
Two angles are called supplementary angles if the
sum of their degree measurements equals 180
degrees. One of the supplementary angles is said
to be the supplement of the other. Example
These two angles are supplementary. Note
that these two angles can be "pasted" together to
form a straight line!
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
Draw three other examples of supplementary angles.
6
Performance Task and Short Answer
Mathematics
Problem of the Day
Design a creature using different types of
angles. Color your creature. Label the angles
and use arrows to point to them. Below your
creature, write a simple definition of each angle
that you used.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
7
Performance Task and Short Answer
Mathematics
Problem of the Day
List the capital letters of the alphabet that are
consonants. Which capital letters have acute
angles? Which have obtuse angles? Do any
capital letters have both? Do some capital
letters contain no angles? Design a tree map to
sort the capital letters using these
categories. Write sentences explaining your
thinking.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
8
Performance Task and Short Answer
Mathematics
Problem of the Day
Draw four polygons that have all acute
angles. Draw four polygons that have at least
one obtuse angle. Draw two polygons that at
least one right angle. Write sentences
explaining how you designed your shapes.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
Acute Angles
9
Performance Task and Short Answer
Mathematics
Problem of the Day
Draw two angles. One angle measures 45º and one
measures 60. Draw the complementary and
supplementary angles for each. List the steps
that you used to complete this problem.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
10

Performance Task and Short Answer
Mathematics
Problem of the Day
Draw a Tree Map with the following categories
Shapes with 1 pair of congruent sides Shapes
with 2 pairs of congruent sides Think about
these shapes Trapezoid, Hexagon, Square,
Regular Octagon, Rhombus, Kites Sort the shapes
into one or more of the categories. Do all of
the shapes fit into these categories? Were some
shapes in additional categories? Why?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
11
Performance Task and Short Answer
Mathematics
Problem of the Day
Draw a trapezoid, a square, a triangle, and a
hexagon. How many diagonals are there in each
shape? How did you find your answers?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
12
Performance Task and Short Answer
Mathematics
Problem of the Day
Look at these polygons. Some are regular and
some are not regular (irregular). Sort the
polygons into these two categories. Can you add
other shapes to the categories? Write sentences
explaining how you selected a category for each
shape.
A
G
F
B
E
D
C
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
13
Performance Task and Short Answer
Mathematics
Problem of the Day
Think about the characteristics of a scalene
triangle. Do all scalene triangles look the
same? Can you draw three scalene triangles that
look different?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
14
Performance Task and Short Answer
Mathematics
Problem of the Day
Grandma Frances needs new flooring in her
bathroom. She wants the floor to have a new
modern design. Using pattern blocks and graph
paper, create a design for a new type of floor
tile. Color your design. Write sentences
explaining your pattern and which polygons you
used.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
15
Performance Task and Short Answer
Mathematics
Problem of the Day
Look around the classroom. Find objects that are
shaped like a variety of polygons. Create a tree
map with categories of different polygons. List
the objects in the room under each category. Be
sure to look for a variety of polygons including
triangles, quadrilaterals, pentagons, hexagons,
etc Write sentences to explain why you listed
objects in certain categories.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
16
Short Answer
Mathematics
Problem of the Day

• Tommy chose one of the figures above.
• The figure he chose was shaded.
• The figure he chose was not a triangle.
• The figure he chose was a quadrilateral.
• Which figure did he choose?
• Write about the steps you used to
• find the answer.

Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
17
Short Answer
Mathematics
Problem of the Day
A dog pen in the shape of a rectangle is to be
built so that the width is 68 inches and the
length is 120 inches. What is the perimeter of
the rectangle? Show your answer in feet.
What if an additional 2 feet were added to length
and 4 inches to the width? How would that
change the perimeter? Show the answer in feet.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
18
Short Answer
Mathematics
Problem of the Day
Uncle David wanted to put a fence around his
prize winning vegetable garden. His vegetable
garden is in the shape of a rectangle. The
garden will need 432 centimeters of fencing. The
width of the garden is 80 centimeters. What is
the area of the vegetable garden in square
centimeters?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
19
Performance Task and Short Answer
Mathematics
Problem of the Day
Make a double bubble map to compare and contrast
the attributes of regular and irregular polygons.
Write a statement summarizing the information.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
20
Short Answer
Mathematics
Problem of the Day
Compose a number sentence to find the unknown
quantity on the interior angle of the following
polygon. Explain how you found the answer.
60
60
120
?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
21
Performance Task and Short Answer
Mathematics
Problem of the Day
Glenda was admiring the tile on the wall of a
museum. Some hexagons were put together in a
row. Each side of the hexagon is 7 cm long. If
the row has 43 hexagons, what is the perimeter of
the row? Prove your answer.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
22
Short Answer
Mathematics
Problem of the Day
A, B, C, and D are midpoints on the sides of
the rectangle. What fraction of the rectangle is
shaded?
B
A
C
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
D
23
Performance Task and Short Answer
Mathematics
Problem of the Day
Write the sum of the interior angles of the
following polygons. Is there a pattern?
Explain how you determined the answer.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
24
Performance Task and Short Answer
Mathematics
Problem of the Day
The figure below is a rhombus. If the measure of
angle AEB is 90 degrees and the measure of angle
ADE is 40 degrees, what would the measure of
angle DAB be?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
25
Performance Task and Short Answer
Mathematics
Problem of the Day
An isosceles triangle has a perimeter of 46
inches and one side is 22 inches. How many
different triangles could you build with these
dimensions? Draw and label the triangles.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
26
Short Answer
Mathematics
Problem of the Day
Which lines are parallel? Which lines are
perpendicular?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
27
Performance Task and Short Answer
Mathematics
Problem of the Day
How many perpendicular diagonals does a regular
pentagon have? How many parallel diagonals does
a regular pentagon have?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
28
Performance Task and Short Answer
Mathematics
Problem of the Day
What shape is created when all of the diagonals
are drawn in the figure below?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
29
Performance Task and Short Answer
Mathematics
Problem of the Day
A clock shows 900. The second hand was
pointing at the 1000 spot. What two angles
would be made on the inside of the right
angle? Draw your solution. Write about what
you found out.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
30
Performance Task and Short Answer
Mathematics
Problem of the Day
Draw 3 regular polygons that have rotational
symmetry? How many lines of symmetry does each
figure have?
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
31
Performance Task and Short Answer
Mathematics
Problem of the Day
Can a figure have rotational symmetry without
having a line of symmetry? Prove your answer.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
32
Performance Task and Short Answer
Mathematics
Problem of the Day
Sort the numerical digits in the correct place
on the Venn Diagram. 0, 1, 2, 3, 4, 5, 6, 7, 8,
9
Numbers that Have Rotational Symmetry
Numbers that Have Line Symmetry
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
33
Performance Task and Short Answer
Mathematics
Problem of the Day
List the capital letters in our alphabet that
have at least 1 line of symmetry. Circle the
letters on your list with rotational symmetry.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
34
Performance Task and Short Answer
Mathematics
Problem of the Day
Draw a Venn diagram. Label one side rotational
symmetry. Label the other side line
symmetry. Sort these figures using a Venn
diagram.
C
D
A
B
G
E
F
H
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
35
Performance Task and Short Answer
Mathematics
Problem of the Day
Which figures have a diagonal that is also a
line of symmetry.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
36
Performance Task and Short Answer
Mathematics
Problem of the Day
Does the following figure have a line of
symmetry? Rotational symmetry? Add to the
drawing a figure so that it has both line and
rotational symmetry.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
37
Performance Task and Short Answer
Mathematics
Problem of the Day
Andrew and Hilda designed parking lots from
straws like the following
_______________
4 spans
5 spans
How many straws would be used to build a parking
lot ten spans long? Write an expression to
find the answer.
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
38
Performance Task and Short Answer
Mathematics
Problem of the Day
Using the figures below, how many S will be in
the 5th figure?
Figure 1 S
Figure 2 S SS
Figure 3 S SS SSS
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
39
Performance Task and Short Answer
Mathematics
Problem of the Day
y
If this pattern continues, what will be the
ordered pair for the point E? What rule can be
used to find any ordered pair for this pattern?

5
D

C

3
B

A
1

Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
x
0
5
40
Performance Task and Short Answer
Mathematics
Problem of the Day
Based on this pattern, if you input 14, what is
the output?
Write a number sentence to show the pattern that
you found. Try these additional numbers using
the pattern 5, 23, 16
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
41
Performance Task and Short Answer
Mathematics
Problem of the Day
Use a hundreds board to extend the pattern
below 7, 16, 25, 34, 43, _____, ______ Is this
a growing pattern or repeating pattern?
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
42
Performance Task and Short Answer
Mathematics
Problem of the Day
Build triangles to extend the pattern. Describe
it.
___________ ?
1
9
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
25