Mathematics

1
Mathematics
Problem of the Day
Answer Key
Answer Key
Fifth Grade
Third Quarter
2
Performance Task
Mathematics
Answer Key
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
Draw other sets of complementary angles.
Check drawings to be sure all angle pairs
measure 90 degrees
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
3
Short Answer
Mathematics
Answer Key
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
4
Performance Task
Mathematics
Answer Key
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!
Check for accuracy. Drawings of supplementary
angles equal 180 degrees
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
5
Performance Task and Short Answer
Answer Key
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.
Student drawings will vary. Check for accuracy.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
6
Performance Task and Short Answer
Mathematics
Answer Key
Problem of the Day
List the capital letters of the alphabet that are
consonants. Which letters have acute angles?
Which have obtuse angles? Do any letters have
both? Do some letters contain no angles? Design
a tree map to sort the letters using these
categories. Write sentences explaining your
thinking.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
7
Performance Task and Short Answer
Mathematics
Answer Key
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.
Acute Angles
Check drawings for accuracy and understanding of
acute and obtuse angles.
Fifth Grade Third Quarter Weeks 1-2 Objective 2.02
8
Performance Task and Short Answer
Answer Key
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.
Supplementary Angles Pairs of angles that when
put together measure 180 degrees. Complementary
Angles Pairs of angles that when put together
measure 90 degrees.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
9
Performance Task and Short Answer
Mathematics
Answer Key
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
10
Performance Task and Short Answer
Mathematics
Answer Key
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
Formula for finding diagonals n (n 3)

2
11
Performance Task and Short Answer
Answer Key
F
Mathematics
Problem of the Day
Look at these polygons. Some are regular and
some are not regular. 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.
Regular polygons have all equal sides and angles.
Irregular polygons have different size sides
and angles.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
12
Performance Task and Short Answer
Mathematics
Answer Key
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?
Scalene Triangles No equal sides, no equal
angles Examples
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
13
Performance Task and Short Answer
Mathematics
Answer Key
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.
Check drawings to be sure students can name the
different polygons used in the design. Check
that students can discuss the attributes of each
shape.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
14
Performance Task and Short Answer
Answer Key
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.
Check students lists of polygons in the room for
accuracy.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.01
15
Short Answer
Mathematics
Answer Key
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 3.02
Tommy chose the rectangle.
16
Short Answer
Answer Key
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.
P 376 in. or 31 ft. 4 in.
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
Change P 432 in or 36 ft.
17
Short Answer
Answer Key
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?
2
A 10, 880 cm
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
18
Performance Task and Short Answer
Answer Key
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.
Irregular polygons have different length sides
and angles. Regular polygons have the same
length sides and angles.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
19
Short Answer
Mathematics
Answer Key
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.
There are several ways a student may write a
number sentence to explain how to find the
answer. The sum of all the angles in a
quadrilateral ( 4 sided figure) has to equal
360 degrees. Example Number Sentence a 360
(b c d) a 360 (120 60 60) a 120
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
20
Performance Task and Short Answer
Mathematics
Answer Key
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?
There are 43 hexagons. 2 of the hexagons will
have 5 sides in the perimeter (one on each
end). 41 of the interior hexagons will have only
4 sides in the perimeter. 43 total hexagons 2
end hexagons 41 hexagons 41 interior hexagons x
4 sides 164 sides 164 sides x 7 cm (side
length) 1148 cm. 2 end hexagons x 5 sides 10
sides 10 sides x 7 cm (side length) 70 cm. 70
cm (length of ext. hexagons) 1148 cm (length of
int. hexagons) 1218 cm P 1218 cm.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
21
Short Answer
Answer Key
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?
Fifth Grade Third Quarter Weeks 3-5 Objective 3.02
2/8 or 1/4 of the shape is shaded.
22
Performance Task and Short Answer
Mathematics
Answer Key
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 3.04
To find the total number of degrees in a polygon
use this formula (n 2) 180
23
Performance Task and Short Answer
Mathematics
Answer Key
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?
The sum of the measures of the angles in a
triangle is 180 degrees. Therefore, the measure
of angle DAE is 50 degrees. Because of the
special properties of the rhombus, angle BAE is
equal in measure to angle DAE. (In a rhombus, all
four right triangles created by the diagonals are
congruent.) The measure of angle DAB is 50 50
100 degrees.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
24
Performance Task and Short Answer
Mathematics
Answer Key
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.
An isosceles triangle with a perimeter of 46
inches and one side is 22 inches would have
another side with 22 inches and a remaining side
of 2 inches. Another combination would be one
side with 22 inches and the remaining two sides
with 12 inches each.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
25
Short Answer
Mathematics
Answer Key
Problem of the Day
Which lines are parallel? Which lines are
perpendicular?
Parallel Lines a and b. Perpendicular Lines a
and d Lines b and d
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
26
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
How many perpendicular diagonals does a regular
pentagon have? How many parallel diagonals does
a regular pentagon have?
The answer to both questions is none.
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
27
Performance Task and Short Answer
Mathematics
Answer Key
Problem of the Day
What shape is created when all of the diagonals
are drawn in the figure below?
A Star
Fifth Grade Third Quarter Weeks 3-5 Objective 3.04
28
Performance Task and Short Answer
Mathematics
Answer Key
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.
12
11
10
9
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
Two acute angles would be formed.
29
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Draw 3 regular polygons that have rotational
symmetry? How many lines of symmetry does each
figure have?
All regular polygons have rotational symmetry.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
30
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Can a figure have rotational symmetry without
having a line of symmetry? Prove your answer.
No, a figure can not have rotational symmetry
without having a line of symmetry. Check over
student drawings for accuracy.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
31
Performance Task and Short Answer
Mathematics
Answer Key
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
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
32
Performance Task and Short Answer
Answer Key
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.
Letters that have at least 1 line of symmetry A
B C D E H I K M O T U V W X Y Letters that have
rotational symmetry H, I, O, X
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
33
Performance Task and Short Answer
Mathematics
Answer Key
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.
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
34
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Which figures have a diagonal that is also a
line of symmetry.
Square, Hexagon
Fifth Grade Third Quarter Weeks 6-9 Objective 3.03
35
Performance Task and Short Answer
Mathematics
Answer Key
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.
It has line symmetry. It does not have
rotational symmetry. Drawings may vary.
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
36
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Andrew and Hilda designed parking lots from
straws like the following
How many straws would be used to build a parking
lot ten spans long? Write an expression to find
the answer.
21 straws n x 2 1 Example 4 x 2 1 9
straws 5 x 2 1 11 straws 10 x 2 1 21
straws
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
37
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Using the figures below, how many S will be in
the 5th figure?
Figure 3 S SS SSS
Figure 1 S
Figure 2 S SS
Answer 15 S SS SSS SSSS SSSSS
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
38
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
(8.5, 5) Add 2 to coordinate X each time Add 1 to
coordinate Y each time

C

3
B

A
1

Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
x
5
39
Performance Task and Short Answer
Answer Key
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
Output 27 n x 2 1 output 14 x 2 1 27
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
40
Performance Task and Short Answer
Answer Key
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?
52, 61 Yes, this is a growing pattern.
Fifth Grade Third Quarter Weeks 6-9 Objective 5.01
41
Performance Task and Short Answer
Answer Key
Mathematics
Problem of the Day
Build triangles to extend the pattern.
Answer 57 triangles 1 x 2 7 9 9 x 2 7
25 25 x 2 7 57