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MATH UNIT 16
4TH GRADE
line
rhombus quadrilateral
line segment triangle
1. A polygon with three sides is known as a ____
2. A part of a line that has one endpoint is a ___
3. A four-sided polygon in which opposite sides
are parallel and all sides are the same length
is a ____
4. A _______ is a straight path of points that goes
on without end in two directions.
Find the area of each
polygon.
13’
8’
2’
5’
5’
9’
16’
3’
Find the perimeter of each
4”
polygon.
4”
6”
9”
7”
5”
6”
3”
2”
2”
3”
2”
2”
2”
How do you classify angles
using benchmark angles?
An angle is a figure formed
by two rays that have the
same endpoint. That
endpoint is also known as
the vertex of the angle.
Angles are usually
measured in units called
degrees.
The symbol
indicates degrees.
You can use benchmark
angles to classify angles.
Benchmark angles are
STANDARDS.
You use benchmark angles
to figure out the degrees
of other angles.
90
180
45
A 90 angle makes a
square corner.
A 45 angle is and angle
that is open half as much as
a 90 angle.
A 180 angle is an angle
that forms a straight line.
You can use benchmark
angles to estimate angle
measures.
a.
b.
Less than 45
45
c. less than 90
d. 90
Classify each angle.
A roller coaster has a
brace support that forms
a square corner.
What is the angle measure
of the angle formed by
the brace support?
Classify each angle.
Classify each angle.
Classify each angle.
Sonny drew a
rectangle that has a
length of 6 inches and
a width of 4 inches.
Describe a different
rectangle with the same
perimeter as Sonny’s.
Now tell which rectangle
has the greater area.
The hands on a
clock show that the time
is 6:00 How can you
classify the angle formed
by the hands on the
clock?
Write an equation to
represent:
“three times a number is
15. Then solve for n.
Ron drew an angle
that is less than 45
degrees. Which of the
following could NOT be
its measure?
a. 12 degrees
b. 35 degrees
c. 41 degrees
d. 86 degrees
A protractor is a tool
that is used to measure
and draw angles.
Draw an angle with a
measure of 360 degrees.
Draw a ray and label the
endpoint B and another point on
the ray A.
Place the protractor so the middle
of the bottom edge is over the
endpoint of the ray. Find the 0
mark on the protractor and place
a point. Label it C. Draw ray BC.
Draw an angle with
a measure of 360
degrees.
Draw a ray and label
the endpoint B and
another point on
the ray A.
Place the protractor
so the middle
of the bottom edge
is over the
endpoint of the ray.
Find the 0
mark on the
protractor and place
a point. Label it C.
Draw ray BC.
Do the MATH
45 degrees
90 degrees
180 degrees
60 degrees
25 degrees
80 degrees
10 degrees
30 degrees
120 degrees
150 degrees
5 degrees
50 degrees
170 degrees
360
degrees
Tina draws an
angle that is a
straight line.
What is the measure
of her angle?
Draw it.
Frederica made a 5
point star on her paper.
Identify each angle she
used.
Brianna made 5
three-point shots in her
first game and 3 three-point
shots in her second game.
She also made 4 two-point
shots in each game and
no one-point free throws
in either game. How many
total points did she score?
Lottie is reading a
book containing 3 chapters.
The first chapter is 120
pages long. The second
chapter is 136 pages long.
There are 583 pages in the
book. How many pages are in
the third chapter?
Look at the angles
shown on the home
plate used in baseball.
Label each angle.
The point where two
streets cross each other
forms four square corners.
Draw a picture of the streets
crossing each other and label
each angle with the number
of degrees.
TRANSLATIONS
What is one way to move a
figure?
A translation moves a figure
up, down, left, or right.
In this honeycomb, the hexagon
is translated to the right.
slide
Which have been
TRANSLATED?
Which have
translated?
KITES
kites
sticks
1
2
2
4
3
6
How many sticks would you need
to make 12 kites?
If Alex made 2 kites and Kolby
made 5 kites, how many sticks
did they use in all?
Which of the following
best represents a
translation?
a.
b.
c.
d.
An ice cube melting
A plant growing
A windmill spinning
A hockey puck sliding
In this picture which
shows a translation
of the horse labeled X?
V
W
Y
X
Z
Translations are often
called SLIDES……
Is this an example
of a slide?
REFLECTION
What is another way to
move a figure?
A REFLECTION of a figure
gives its mirror image.
MIRROR IMAGE
= REFLECTION
Are these
REFLECTIONS?
When a figure is reflected,
the size and shape of the
figure DO NOT change!
They are
FLIPPED
over.
Which are examples
of REFLECTIONS?
Another name
for a REFLECTION
is a FLIP.
Which are examples of Flips or Reflections?
Flip - Flip - Flip
Yes or No?
Draw a REFLECTION.
Draw a flip / reflection
of each figure.
G
Z
3
6
P
E
7
5
Q
S
9
C
J
K
2
M
B
Y
4
L
Sharon can run
five miles in fifty minutes.
If she keeps this pace,
how many miles can she
run in sixty minutes?
The Hall of Mirrors
in the Palace of
Versailles in France is
73 meters long.
A guide posted at one end of
the room walks in a straight
line to the mirror at the
other end, and then back to
his post. How far in all did
he walk?
SYMMETRY
What is a line of symmetry?
A figure is SYMMETRIC if it
can be folded on a line to
form two congruent halves
that fit on top of each other.
The fold line is called a
LINE OF SYMMETRY.
A figure can have
many lines of
symmetry.
Which have lines
of symmetry?
How many lines
of symmetry?
How many lines
of symmetry?
Anya drew a figure
and said that it had
an infinite
number of lines of
symmetry.
What figure did she draw?
Florida’s Capitol
in Tallahassee has one line
of symmetry.
Draw the line of symmetry.
Draw the lines of
symmetry for each
isosceles triangle.
Generalize to all isosceles
triangles.
Write capitol letters
that have only 1 line
of symmetry.
Draw examples of
quadrilaterals that
do not have lines
of symmetry.
Generalize about
lines of symmetry
for scalene triangles.
How many lines of symmetry
does each have?
ROTATIONS
What is another way to
move a figure?
A rotation moves a figure
around at a point.
Rotations
The figure does not change
size or shape.
90
180
360
Miguel says that a
180 degree turn of any
figure is the same as a
reflection of a figure.
Draw a picture to prove
this it either true or false.
What figure is formed
when a triangle has
rotated 90 degrees?
ROTATIONAL
SYMMETRY
When a figure can rotate
onto itself in less than
360 degrees, the figure has
ROTATIONAL SYMMETRY.
This figure has rotational
symmetry because it can be
rotated back to land on itself.
Many figures
rotational
Which do
rotational
B
M
do not have
symmetry.
not have
symmetry?
ROTATIONAL SYMMETRY
True or False - Explain
Do they have
Rotational Symmetry?
Write YES or NO and give the least
angle measure that will rotate the
figure onto itself.
L
H
X
Y
T
N
Ronnie has 16 yards of
fencing material to build a
fence around his garden.
He wants to fence a rectangular
area. List all possible ways he
can fence his garden.
SIDE A
1 YD
2 YD
3 YD
4 YD
SIDE B
AREA
7 SQ YD
There are 48 boxes
in a warehouse. If there
are 24 packages of paper
in each box, how many
packages of paper are
in the warehouse?
Each pack holds 50 sheets.
How many sheets of paper
are in the warehouse?
The Megaray Kite
has an area of almost
1,500 square meters. Suppose
the wind suddenly changed
and the kite moved 25 meters
east. Has the shape or size of
the kite changed? What type
of movement occurred?
25 Meters East
TESSELLATIONS
A tessellation is a
repeating pattern of
shapes without any
gaps or overlays.
How to make a Tessellation.
Start with a square and an
equilateral triangle.
Use reflection to get
adjacent figures.
Rotate 180 degrees.
Finally, use a translation
to continue the pattern.
v
THINK
Which of these shapes
will TESSELLATE?
Not all shapes can make a
tessellation.
Notice the gaps – there can
be no gaps or overlays in
a tessellation.
3-D
3 - Dimensional Shapes
A solid figure has three
dimensions:
Length, width, and height.
Solids can have curved surfaces.
Some solids have
all flat surfaces.
They are named by
referring to their faces.
Vertex – point
where 3 or more
edges meet
Face – flat
surface of a
solid
Edge – line segment
where 2 faces meet
Identify faces, vertices, and
edges of each.
TRIANGULAR PRISM
SQUARE
Rectangular pyramid
Flat surfaces of solids that
have some curved
surfaces are called bases.
BASE
BASE
BASE
Guess
I have four triangular
faces and one square
face. What am I?
I have six square faces.
What am I?
I have one rectangular
face and four triangular
faces. What am I?
I have two triangular
faces and three
rectangular faces. What
am I?
Fill in the table.
SOLID
FACES
EDGES
RECTANGULAR
PYRAMID
SHAPES
OF FACES
6
RECTANGULAR
PRISM
CUBE
VERTICES
RECTANGLES
6
8
Geometric Solids in the
real world.
Mitchell’s mom offered
to drive members of the
soccer team to their game.
Her car can hold 4 players at
a time. She drives 10 players
from her home to the game.
How many one-way trips must
she make if she stays to
watch the game?
In one soccer season, the
Cougars scored six times as
many goals as Walter
made all season. If
Walter scored 12 goals,
how many goals did the
Cougars score throughout the
season?
NETS
How can you use a two-dimensional
shape to represent a three-dimensional
solid?
A NET is a pattern that can be used to
make a solid. You can open up a threedimensional objects to show the net.
If you peel the skin off
of a can you have the
NET or pattern to make
the can.
Name the solid
that can be made
from each NET.
Name the solid
that can be made
from each NET.
Name the solid
that can be made
from each NET.
NETS
A pattern
that can
be used
to make
a solid.
Ralph made the net
below by tracing around
each face of a solid.
What solid did he trace?
Reggie traced
the net below. What
solid is he making?
Seziel has baseball
pennants hanging on
all 4 walls of his
bedroom. There are
9 pennants on each
wall. How many
pennants are there?
Florida’s state insect
is the zebra longwing
butterfly. How many
lines of symmetry does
the butterfly have?
Does it have rotational symmetry?
ZEBRA LONGWING
BUTTERFLY
List possible ways to find the total
area of this figure?
Draw two different rectangles that
have an area of 24 square units.
What is the perimeter of each?
Leslee says that the net
for any prism will always
include at least one
rectangle. Is she correct?
Explain why or why not.
Think Instruments.
I am a percussion
instrument. I have a
cylinder shape.
What am I?
I am a three sided figure
named for my shape. You
hit me with a metal wand.
What am I?
I am made of a long,
narrow rectangular prism
and a short cylinder.
What am I?
I am a long cylinder with
holes in my side.
What am I?
Hope plays three instruments. The drum
weighs 5 pounds more than the guitar.
The trumpet weighs 5 pounds less that
the guitar. The trumpet weighs 3
pounds. How many pounds does the
drum weigh?
PERSPECTIVES
How can you get information about
a solid from different
perspectives?
Think about the solid. What would the solid look
like from the front? Side? Top?
Front
Right side
Top view
Draw all six views
of this shape.
Draw all six views.
Draw all six views.
Keith says that 1/2 is
always the same amount
as 2/4.
Torrence says that 1/2
and 2/4 are equivalent
fractions,
but that they could be
different amounts.
Explain your thinking.
Gwendolyn wants to cut
a triangle into thirds.
Her sister told
her to cut it like
this.
What is your
thinking?
Karen and Arlene knit the
same size scarves.
Karen’s scarf is 3/5 yellow
while Arlene’s scarf is 3/4
yellow. Draw a picture to
show whose scarf has
more yellow yarn.
The school newspaper has
a total of 18 articles and
some ads. There are 6
more articles than ads.
How many articles and
ads are there?
Kenneth gets $25 a week
to buy lunch at school.
He spends $3.50 each day
and saves the rest. Write
an expression that can be
used to find how much
money Kenneth will save
at the end of 4 weeks.
During recess, Kirstin
played on the bars and
slides. She spent 10
minutes on the bars and
twice as long on the
slides. Write an expression
to find how much time
she spent on the slides.
Three streets intersect
With one another. East Street runs
horizontally, North street runs
vertically, and Fourth Street runs
diagonally and intersects both
East and North Street. What
geometric figure is formed by
the intersection of these three
streets?
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 18
+
= 20
+
= 14
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 27
+
= 23
+
= 24
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 30
+
= 22
+
= 20
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 115
+
=
+
= 200
95
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 4
+
= 1
+
= 5.5
Look at the number sentences
below. What numbers replace
Explain your answer.
+
= 1
+
=
+
= 1 1/2
1/2
Turn
Rotation
Slide
Translation
size
Flip
Reflection