Geometry

1
Geometry
What polygons do you see?

• Everyday Mathematics
  Unit 6 Mr. Brumfield

2
Investigating Line Segments, Rays, and Lines
6.1

• Our objective is to review line segments and to
  introduce rays and lines.

What are line segments, rays, and lines?
3
Mental Math

• Write the following numbers on your slates.
• Pay close attention to the place values.

• four and three tenths
• eleven and thirty-two hundreths
• sixty-three and one thousandth
• four thousand three hundred twenty-eight and
  sixty-two hundredths
• one hundred and sixteen thousandths

4
Math Message

• Take 5 straws
• Use them to make 2 triangles

5
Math Message Follow Up

• How could you make two triangles?

If your triangles share a side, you would be able
to make two triangles.
What would you call the type of line shared by
the triangles?
6
Line Segments

• A line that has a beginning and ending endpoint
• Endpoints
• The beginning and ending points on the line
  segment
• Rules
• A line segment can be any length but must have
  two endpoints
• A line segment is always straight, it marks the
  shortest path
• A line segment can go in any direction in space
• All shapes are made up of line segments

Can you find examples of line segments around the
room?
7
Rays

• A line that has one endpoint and goes in one
  direction forever
• Arrowhead
• We cannot draw a line that goes forever, so the
  arrowhead symbolizes that the ray continues
  forever
• Rules
• A ray must have one endpoint and one arrowhead
• A ray is always straight
• A ray can go in any direction in space

Can you think of any examples of rays?
8
Lines

• A line that has two arrowheads and extends
  forever
• Arrowhead
• We cannot draw a line that goes forever, so the
  arrowhead symbolizes that the ray continues
  forever
• Rules
• A line must have two arrowheads
• A line can go in any direction in space
• A line is always straight
• A line is infinite, it never begins or ends

What word means forever and ever?
9
Naming Line Segments, Rays, and Lines

• There is a different way to name each type of
  line.

A
B
A
B
A
B
Line Segment
Ray
Lines
B
A
B
A
A
B
Line Segments and Lines can be reversed because
of the turnaround rule. With a ray though, you
have to be very careful to match the endpoint
with the correct letter name and the arrowhead
with the correct name.
10
Practice Identifying Types of Lines

• Write S next to the line segments
• Write R next to the rays
• Write L next to the lines

11
Practice Drawing Types of Lines

• Draw line segment RT
• Draw ray TA
• Draw line ZW
• Draw line segment SB
• Draw ray CO
• Draw line MN

12
Independent Practice

• Complete math journal page 129.
• When you are finished you will work with a
  partner to check each others work.
• Complete the math boxes on page 130.

13
Parallel and Intersecting
6.2

• Our objective is to find, form, and draw
  parallel and intersecting lines.

What are parallel and intersecting lines?
14
Mental Math

• Write the following numbers on your slates.
• Identify the place values as I instruct.

• four hundred eleven
• one thousand three hundred twelve
• six million three hundred forty-one thousand six
  hundred
• thirty-two thousand six hundred eighty-five
• nine hundred six and forty-two hundredths

Find the difference between the greatest and
least numbers.
15
Math Message

• Take 3 straws and 3 twist ties
• Use them to represent 3 rays

Review the differences between lines, line
segments, and rays.
16
What do you know about parallel lines?

• Parallel lines, rays, and line segments are lines
  that run the same direction and remain the same
  distance apart. They never meet or cross.

List some examples of where we might find
parallel lines.
17
What do you know about intersecting lines?

• Intersecting lines, line segments, and rays are
  lines that cross. They meet at some point,
  forming angles.

List some examples of where we might find
intersecting lines.
18
Who wants to help me make parallel and
intersecting lines?

• We will be using rope and Chinese jump ropes to
  make parallel and intersecting lines.
• If you are working with partners, work
  cooperatively. Take turns, follow directions, and
  share responsibilities.

19
Prepare yourself for a Line Safari

• We will be scouring Lawnton in search of parallel
  and intersecting lines.
• When you find an example, record your discoveries
  on math journal page 131.

Parallel
Intersecting
20
Independent Practice

• Complete the math boxes on page 132 of your math
  journal.

21
Angles and Turns
6.3

• Our objective is to use angles and record turns
  (rotations).

Super Genius Question What does this symbol
actually represent?
What is a right angle?
22
Mental Math

• A. 4,896,007 B. 3,014,998 C. 9,100,832

• Which number is
• a little less than five million
• about one million less than four million
• about one million more than eight million
• a little more than three million
• about one half as much as eighteen million
• about twice as much as one million five hundred
  thousand?

23
Math Message

• Take 2 straws and a twist tie. Connect the straws
  with the twist tie to form an angle.

What is an angle?
24
Get up off of your chair!

• We are going to practice turns.
• You need to know
• Half-turn
• Quarter-turn
• Whole-turn

25
Vocabulary

• Angle
• A figure that is formed by two lines meeting
• Vertex
• The point where two lines meet (corner)
• Right Angle
• The angle formed when two straight lines
  intersect or meet

26
Class Work

• As a group we will complete math journal page
  133.
• You will need your straws to help you diagram the
  turns in each problem.

27
Independent Practice

• Complete the math boxes on page 134 of your math
  journal.

28
Triangles
6.4

• Our objective is to explore various types of
  triangles.

What are the different types of triangles?
29
Mental Math
Extend your arm straight out in front of
you. Bend your elbow and slowly move your hand
toward your face. Think of the parts of your arm
above and below your elbow as two sides of an
angle. The angle becomes smaller as your hand
moves closer to your face. Now do the following
Make a large angle. Make a small angle. Make a
right angle (square corner)
30
Math Message

• Take out a ruler and complete part one of math
  journal page 135. Use line segments to connect
  three points on the circle.

What figure have you drawn?
31
Parts of a Triangle

• There are three parts to a triangle.

Sides
Angle
Vertex
Sides are the line segments that form the
perimeter. There are 3 sides in a triangle.
The vertex is where the lines meet. There are 3
vertices in a triangle.
An angle is a figure that is formed by two rays
or line segments share an endpoint.
32
Naming Triangles

• There are six ways to name a triangle, you just
  need to make sure you include all points.

A
Example One way to name this triangle
is Triangle ABC
C
B
See if you can name the triangle the other five
ways on your slate.
33
Angles in Triangles

• The angle is formed where two line segments meet.
• There are three types of angles.
• Right Acute Obtuse

Can you tell the differences between these three
angles?
34
Rules of Angles

• Right Acute Obtuse

35
Group Activity

• You will complete math journal page 135 with a
  partner.
• I will be checking on your group, to make sure
  you are on track.
• You will need several straws for part C.
• You will need a ruler for part D.

36
Independent Practice

• Complete the math boxes on page 136 of your math
  journal.

37
Quadrangles
6.5

• Our objective is to explore various types of
  quadrangles.

What in the world is a quadrangle?
38
Mental Math
We will use our bodies to practice ¼, ½, and ¾
turns. Make a half-turn clockwise Make a quarter
turn clockwise Make a ¾ turn clockwise Make a ¾
turn counterclockwise Make a ½ turn
counterclockwise Make a ¼ turn counterclockwise Gi
rls make a ¾ turn clockwise while boys make a ¼
turn counterclockwise. What do you notice?
39
Math Message

• Use a ruler to complete part one of math journal
  page 137.

What is a quadrangle?
40
Quadrangle

• The shape you created is a quadrangle.
• What can you tell about this shape?

What is a Quadrangle?
A shape with 4 Sides 4 Angles 4 Vertices
41
Types of Quadrangles

• Now that you know a quadrangle has four sides
  and four angles, what shapes would be quadrangles?

Rectangle
Square
Rhombus
Parallelogram
Kite
Trapezoid
42
Types of Quadrangles
Use your SRB to look up the definitions of each
type of quadrangle.
Square Rectangle Rhombus Trapezoid Kite Parallelog
ram
A rectangle whose sides are the same and angles
are the same
A four-sided shape, with parallel sides being the
same side, and 4 right angles.
A parallelogram with 4 equal sides. If the angles
are right angles, a rhombus is a square.
A 4 sided shape with 1 pair or parallel sides.
The sides do not have to be the same length.
A 4 sided shape with two pairs of adjacent sides
the same length. A rhombus is not a kite.
A 4 sided shape with opposites sides that are
parallel, like a square or rectangle.
43
Matching Quadrangles
Write an R on the rectangle Write an S on the
square Write a T on the trapezoid Write an Rh on
the rhombus Write a K on the kite
Circle the parallelograms
44
Compare the Square Rhombus
45
Independent Practice

• Finish math journal page 137.
• Complete the math boxes on page 138 of your math
  journal.

46
Polygons
6.6

• Our objective is to review the characteristics of
  regular polygons.

What are the different polygons you know?
47
Mental Math
Find the median of the following
numbers. 1,400 737 1,945 2,543
1,464 Find the range of these numbers (subtract
the greatest and the least)
Draw as many different shapes as possible on your
slates.
What are the names of the shapes you drew?
48
Polygons Many Sides

• Use the straws I have given you to construct the
  following shapes.

A 3-sided shape A 4-sided shape A 5-sided shape A
6-sided shape A 7-sided shape An 8-sided shape A
9-sided shape A 10-sided shape
49
Regular Polygons

• Triangle
• Quadrangle
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon

50
Identifying Polygons
Label the following polygons using the word bank.
trapezoid rectangle square octagon
hexagon triangle rhombus
51
Independent Practice

• Complete math journal page 139, using the pattern
  blocks I provide. You will also need your ruler.
• Complete the math boxes on page 141 of your math
  journal.