Fifth Grade

1
Unit 3

• Fifth Grade

2
Unit Goals

• Determine angle measures based on relationships
  between angles.
• Estimate the measure of an angle.
• Measure an angle to within 2.
• Identify types of angles.
• Identify types of triangles.
• Identify place value in numbers to billions.
• Know properties of polygons.
• Define and create tessellations.

3
Determine angle measures based on relationships
between angles.

• You can use your knowledge of angles to estimate
  angle measures.
• Remember- a circle is 360, a straight line is
  180

4
For example
What is the measure of this angle?

• I know that this is a right triangle next to a
  square.
• The squares corner measures 90, and the angle
  of the triangle is about half that.
• Together, the angle should measure about 90 45,
  or 135

5
What is the measure of this angle?
180
225
240
150
6
Correct!

• This angle measures 240. You can know this
  because
• - the angles in the equilateral triangles are
  each 60 (60 60 120)
• the corner of the parallelogram could be made up
  using two equilateral triangles (60 60 120)
• for a combined total of 240.

Far Out! Click me to go back to the goals page.
60
60
7
Keep Trying!

• This angle measures 240. You can know this
  because
• - the angles in the equilateral triangles are
  each 60 (60 60 120)
• the corner of the parallelogram could be made up
  using two equilateral triangles (60 60 120)
• for a combined total of 240.

Read through the description carefully- click to
go back to the explanation page.
60
60
8
Estimate the measure of an angle.

• Think about the angle in relationship to 90

• A complete circle is 360
• A half circle (or straight line) is 180
• A quarter circle is 90
• If an angle is acute, it will be less than 90
• If an angle is obtuse, it will be between 91
  -179
• If the angle is a straight line, it will be equal
  to 180

90
90
90
90
9
Estimate the measure of an angle.
Which of these angles is equal to about 175?
A
C
D
B
10
Correct!
A
This angle is closest to 175. - It is slightly
less than 180 (which is a straight line)
Groovy! Click me to GO for the GOALS.
11
Keep Trying!
A
This angle is closest to 175. - It is slightly
less than 180 (which is a straight line)
You might want to read the description more
carefully. Ask for help if you still need it.
12
Measure an angle to within 2

• For a demonstration, visit
• http//www.mathopenref.com/constmeasureangle.html
• For practice with this skill, visit
• http//www.kidport.com/Grade5/Math/MeasureGeo/Meas
  uringAngles.htm
• http//www.amblesideprimary.com/ambleweb/mentalmat
  hs/protractor.html
• If you need a protractor, you can print one up
  at
• http//www.ossmann.com/protractor/conventional-pro
  tractor.pdf
• Make sure you line your protractor up carefully!

Click me to go back to the goals page.
13
Identify types of angles
A right angle is 90. It looks like the corner
of your paper or the letter L.
An acute angle is LESS THAN 90. It is a cute
little angle ?.
An obtuse angle is MORE THAN 90
A reflex angle is MORE THAN 180
14
Try One!
C
D
B
A
E
F
Which of these is an obtuse angle?
ltABE
ltFCD
ltABC
ltABF
15
CORRECT!
C
D
B
A
E
F
Awesome Work! Click me to go back to the goals.
ltABF is obtuse because it measures more than 90
but less than 180.
16
Try Again!
C
Stick with it- Click me to go back to the
explanation.
D
B
A
E
F
ltABF is obtuse because it measures more than 90
but less than 180. ltABE is a straight angle
because it measures exactly 180.
17
Identify types of triangles

• Meet the triangle family

Im Ivan Isosceles and while Im not as equal as
an equilateral triangle, I do still have two
equal sides and two equal angles.
Were Roger and Randy Right- The Right Brothers!
We like to think that were always right, but
really were called right triangles because we
both have a right angle that measures 90.
Thats right, but one thing my brother Randy
forgot to mention is that Im a special right
triangle. I take after the Isosceles side of the
family because not only do I have a right angle,
I also have two other equal angles and sides.
That makes me a Right Isosceles triangle.
Im Evelyn Equilateral, and Im always worried
that everything should be equal. I have three
equal sides and three equal angles.
Im Salvador Scalene. Im the oddball of the
family- I dont have any equal sides or angles.
18
Equilateral
Isosceles
Can you name us?
Right
Right Isosceles
Scalene
19
Try One!

• Click on the scalene triangle.

20
Correct!
Thats right, another odd-ball. This triangle is
scalene because it has no equal sides or angles.
Click for the next problem.
21
Try Again!
This triangle is scalene because it has no equal
sides or angles.
Click for the next problem.
22
Try One!

• Click on the right isosceles triangle.

23
Correct!
Thats right, this is a right isosceles triangle.
This triangle is isosceles because it has two
equal sides and angles. It is right because it
has a 90 angle.
Click for the next problem.
24
Try Again!
This is a right isosceles triangle. This
triangle is isosceles because it has two equal
sides and angles. It is right because it has a
90 angle.
Click for the next problem.
25
Try One!

• Click on the isosceles triangle.

26
Correct!
Thats right, this is an isosceles triangle.
This triangle is isosceles because it has two
equal sides and angles.
Click for the next problem.
27
Try Again!
This is an isosceles triangle. This triangle is
isosceles because it has two equal sides and
angles.
Click for the next problem.
28
Try One!

• Click on the equilateral triangle.

29
Correct!
Thats right, this is an equilateral triangle.
This triangle is equilateral because it has all
equal sides and angles.
Click for the next problem.
30
Try Again!
This is an equilateral triangle. This triangle
is equilateral because it has all equal sides and
angles.
Click for the next problem.
31
Try One!

• Click on the right triangle.

32
Correct!
Thats right, this is a right triangle. This
triangle is right because it has a 90 angle.
Click me to go to the goals.
33
Try Again!
Thats right, this is a right triangle. This
triangle is right because it has a 90 angle.
Click me to go back to the explanation.
34
Identify place value in numbers to billions
For each set of three, there is a pattern of
units, tens, and hundreds. Remember that when
naming numbers, you name each group of three.
For example, the number above is one billion,
three hundred fifty four million, two hundred six
thousand, five hundred ninety nine. Notice that
when you name numbers, the only time you use the
word and is when you are referring to a decimal
point. For example, 5.2 is five and two tenths.
NOT five point two.
35
Try One!
Which digit is in the hundred thousands place?
3
2
7
0
36
Correct!
Click for the next problem
Which digit is in the hundred thousands place?
3
2
7
0
37
Try Again!
Click for the next problem
Which digit is in the hundred thousands place?
3
2
7
0
38
Try One!
Which digit is in the ten millions place?
5
8
4
0
39
Correct!
Click for the next problem
Which digit is in the ten millions place?
5
8
4
0
40
Try Again!
Click for the next problem
Which digit is in the ten millions place?
5
8
4
0
41
Try One!
Which digit is in the billions place?
3
5
4
1
42
Correct!
Click me to go to the goals.
Which digit is in the billions place?
3
5
4
1
43
Try Again!
Click me to go back to the explanation.
Which digit is in the billions place?
3
5
4
1
44
Know properties of polygons

• A polygon is a plane shape having 3 or more
  sides.
• The number of degrees in a polygon depends upon
  the number of sides it has.
• The name of a polygon depends upon the number of
  sides it has and the relationship of those sides
  to one another.

45
Some examples of polygons
pentagon
trapezoid
hexagon
Right triangle
square
rectangle
Equilateral triangle
octagon
rhombus
How many can you name?
46
Some polygon terms

• A regular polygon has equal sides and angles.
• A quadrilateral describes any four-sided polygon.
• A parallelogram describes any quadrilateral with
  two sets of parallel sides of equal length with
  equal angles.

47
Naming Polygons

• The prefix in the name of a polygon indicates the
  number of sides it has.

pent
tri
quad
hex
oct
48
Explore Polygons

• Check out the polygon playground!
• Learn more about figures and polygons.

Click me to go back to the goals.
49
Define and create tessellations

• A tessellation is a pattern of shapes that has no
  gaps or overlaps
• A regular tessellation is made up of regular
  polygons (polygons with equal sides and angles)
• Tessellations are described by listing the number
  of sides of the polygons around each vertex.

50
Examples of Tessellations

• Learn more about tessellations
• Try a think quest on tessellations
• Try making some tessellations!
• Tessellations can be a form of art. Check out
  some galleries!