1. OPERATIONS AND ALGBRAIC THINKING
MATH
4TH GRADE
UNIT 4
MEASUREMENT AND DATA
GEOMETRY
OPERATIONS AND ALGBRAIC THINKING

2. Students will identify and draw the following two-dimensional
attributes: point, line, line segment, ray, right angle, acute angle,
obtuse angle, straight angle, perpendicular lines, and parallel lines.
Students will represent geometric objects with geometric notation.
Students will classify angles of 2 – dimensional figures as
right, acute, obtuse, or straight.
Students will identify the two-dimensional attributes in
two-dimensional shapes.
MAFS.4.G.1.1

3. POINT
point: A point is an exact location. It has no size, only position. The exact location of a point can be shown using Coordinates. ( x, y )
POINT

4. LINE
line: In geometry a line: • is straight and has no curves, • has no thickness, • and it extends in both directions without end - infinitely.

5. LINE SEGMENT
line segment: The part of a line that connects two points. It has definite end points. Adding the word "segment" is important, because a line normally extends in both directions without end.

6. RAY
ray: One way to think of a ray is a line with one end. A ray starts at a given point and goes off in a certain direction forever, to infinity.
endpoint
ray
Sun is endpoint

7. RIGHT ANGLE
right angle: A right angle is exactly 90°. See the special symbol that looks like a box in the angle? If you see the box in the corner you know it is a right angle. The 90° is rarely written in.

8. RIGHT ANGLE TRIANGLE
right angle triangle: a right triangle or right-angled triangle is a triangle in which one angle is a right angle - A right angle is exactly 90°.

9. ACUTE ANGLE
acute angle: The acute angle is a small angle which is less than 90°. It is small and “cute” = a cute angle.

10. OBTUSE ANGLE
obtuse angle: The obtuse angle is more than 90° and less than 180°.

11. STRAIGHT ANGLE
straight angle: is an angle of 180°.

12. PERPENDICULAR LINES
perpendicular lines: at an angle of 90° to a given line, plane, or surface.

13. PARALLEL LINES
parallel lines: two lines on a plane that never meet - they are always the same distance apart
TRAIN TRACKS ARE PARALLEL

14. CONGRUENT
congruent: Identical in form - exactly the same when superimposed

15. PLANE
plane: a plane in mathematics is a flat, two-dimensional surface that extends infinitely far - forever

16. PROTRACTOR
protractor: an instrument for measuring angles, usually in the form of a flat semicircle marked with degrees along the curved edge

17. VERTEX - VERTICES
Vertex single / Vertices plural: a vertex is the point where two or more curves, lines, or edges meet the point where two lines meet to form an angle and the corners of polygons are vertices

18. GEOMETRIC NOTATION

19. GEOMETRIC NOTATION

20. GEOMETRIC NOTATION

22. SHOW WHAT YOU KNOW
LABEL

23. SHOW WHAT YOU KNOW
LABEL

24. SHOW WHAT YOU KNOW
LABEL

25. SHOW WHAT YOU KNOW
LABEL

26. SHOW WHAT YOU KNOW
LABEL QUIZ

27. RIGHT - OBTUSE - ACUTE - STRAIGHT
LABEL

28. RIGHT - OBTUSE - ACUTE - STRAIGHT
LABEL
REFLEX ANGLE

29. RIGHT - OBTUSE - ACUTE - STRAIGHT
LABEL

30. RIGHT - OBTUSE - ACUTE - STRAIGHT
LABEL

31. RIGHT - OBTUSE - ACUTE - STRAIGHT
LABEL QUIZ Q E T F G S R J K L U V

32. PERPENDICULAR LINES

33. PERPENDICULAR LINES

34. PERPENDICULAR LINES

35. 2D – 2 DIMENSIONAL ATTRIBUTES

36. 2D – 2 DIMENSIONAL ATTRIBUTES

37. 2D – 2 DIMENSIONAL ATTRIBUTES

38. <B or <ABC or <CBA
GEOMETRIC NOTATION
Identify and label: point, line, line segment, ray, right angle, acute angle, obtuse angle, straight angle,
perpendicular lines, parallel lines, congruent sides, angle P
<B or <ABC or <CBA

39. ARE WE RIGHT, ACUTE, OBTUSE, OR STRAIGHT?

40. Students will define an angle.
Students will explain an angle as a series of
“one-degree turns”.
Students will explain that it takes one-unit degrees to
make a circle.
1/360 of a circle is a “one degree angle”
Students will explain the relationship between a circle and
the number of degrees in an angle.
Students will use the geometric notation for degrees to label
the measure of an angle.
MAFS.4.MD.3.5

41. CIRCLE = DEGREES

44. PROPERTIES OF CIRCLES
RADIUS D

45. turns has the sprinkler
A sprinkler system
rotates one-degree
at each interval. If
the sprinkler rotates
a total of degrees,
how many one-degree
turns has the sprinkler
made?

46. Students will use appropriate terminology to describe angles and rays.
( right - acute - obtuse - straight )
Students will compare a given angle to the
BENCHMARK right angle of 90 degrees
to determine which set of numbers to use on a protractor.
Students will use a protractor to create an angle given
a specific measurement.
Students will determine if the measure of an angle is reasonable
based on the relationship of the angle to a right angle.
MAFS.4.MD.3.6

47. USING A PROTRACTOR

48. USING A PROTRACTOR A B C

49. USING A PROTRACTOR

50. USING A PROTRACTOR D E F

51. USING A PROTRACTOR

52. USING A PROTRACTOR

53. USE A PROTRACTOR
LABEL
QUIZ

54. Students will explain that the angle measurement of a
larger angle is the sum of the angle measures of its
decomposed parts.
Students will write an equation using a symbol to represent
an unknown angle measurement.
Students will use addition and subtraction to solve for
the missing angle measurement.
Students will solve word problems involving unknown angles.
MAFS.4.MD.3.7

55. What We Know
There are 90 degrees in a right angle. If we cut the right angle into smaller parts then those smaller parts add together to make 90 degrees. 50 degrees + ? degrees = 90 degrees
50 degrees
? degrees

56. What We Know < > or = Look at the pizza. How many degrees
is the whole pizza?
Look at the blue slice.
Is the slice
< > or =
to 90 degrees?

57. BENCHMARK < > or =
We use the RIGHT ANGLE of 90 degrees as our BENCHMARK.
The BENCHMARK is the angle we compare other angles to.
Is the new angle
< > or =
to the BENCHMARK?

58. < > or = a. Compare each angle to the
BENCHMARK angle of 90 degrees.
< > or = a. b. c. d. e. f. g.

59. A lawn sprinkler rotates a total of 90 degrees but pauses during its cycle according to the diagram that came in the box. How many degrees does it rotate between the 25 and 20 degree pause? Write an equation to represent the situation. 30 A U
20 degrees
U = 90 degrees

60. U Let’s look at this problem again. In this equation they are using
as the unknown angle.
U is a VARIABLE.
Any letter or symbol that
is used for an unknown is
called a variable – because the
number can vary – or change. 30 A U
20 degrees
U = 90 degrees

61. Use what you know. This tire has some wear
Use what you know. This tire has some wear. Use your BENCHMARK angle to find the missing angle d = 90 degrees d 60

62. Our Earth looks like a huge circle
Our Earth looks like a huge circle. Our Earth has 360 degrees just like every circle. Use your BENCHMARK angle to decide if the angle is < > or = to the BENCHMARK.

63. Now Let’s Add
Write the equation and solve for each unknown angle or VARIABLE. f = ____ degrees c = ____ degrees a = ____ degrees
110 degrees

64. Write the equation and solve for each unknown angle. x = ____ degrees

65. Write the equation and solve for the variable.

66. Write the equation and solve for the variable.

67. Students will classify two-dimensional shapes into
the following categories:
parallel lines, perpendicular lines,
both parallel and perpendicular lines,
or those with no parallel or perpendicular lines.
Students will classify two-dimensional shapes into categories
based on presence or absence or acute, obtuse, or right angles.
MAFS.4.G.1.2

68. Sort into the Venn Diagram.
PARELLEL BOTH PERPENDICULAR

69. Sort angles into the Venn.
ACUTE RIGHT OBTUSE

70. Sort shapes based on presence of acute, obtuse, or right angles.
ACUTE OBTUSE RIGHT

71. Students will identify different types of quadrilaterals
based on defining attributes.
Students will identify different types of right triangles:
scalene or isosceles.
Students will classify right triangles.
MAFS.4.G.1.2

72. QUADRILATERALS
quadrilaterals: all four-sided figures having four straight sides quad means 4 lateral means side

73. RIGHT TRIANGLES
right triangles: a triangle with a right angle

74. SCALENE
scalene triangle: scalene triangle has three unequal sides

75. ISOSCELES
isosceles triangle: having two sides of equal length

76. IDENTIFY
A B C

77. s
Sort
right scalene isosceles

78. Students will identify and describe figures that have line symmetry.
Students will draw lines of symmetry in both regular
and non-regular polygons.
MAFS.4.G.1.3

79. SYMMETRY
Exactly the same parts facing each other. If you fold each of these figures on the fold line they match up perfectly. Symmetry!

80. Which are Symmetrical?

81. Draw all lines of symmetry.