1. MATH SECOND GRADE
GEOMETRY
CATS
DOGS

2. GEO – METRY When we learn about GEO-METRY we are learning about measuring all the things on the Earth.

3. When you were in Kindergarten and First Grade you learned about shapes in our world. There were: circles squares triangles and rectangles.

4. There were: trapezoids pentagons hexagons octagons rhombus and ovals.

5. Now we are going to look more closely at each shape
Now we are going to look more closely at each shape. Each shape has SIDES and ANGLES. TRI stands for 3. So a TRIangle has 3 angles and it also has 3 sides. Each angle point has a special name. It is called the VERTEX.
VERTEX
A tricycle has 3 wheels! TRI = 3

6. Circle all the TRIangles!

7. This is a square. A square has 4 equal sides and 4 equal angles and 4 equal vertices. What makes a square special is that all the sides must be exactly the same. If they are not the same then we call it a RECTANGLE!

8. Circle all the Squares.

9. Rectangles also have 4 sides and 4 angles and 4 vertices, but the sides are NOT all the same size. Opposite sides are parallel. __________

10. Circle all the Rectangles.

11. Rhombus also have 4 sides, 4 angles and 4 vertices but two of the sides are tipped over. A rhombus looks like a square or a rectangle that someone sat on. SQUISH!
rhombus
Rhombus

12. Trapezoids also have 4 sides, 4 angles and 4 vertices
Trapezoids also have 4 sides, 4 angles and 4 vertices. Two of the sides are parallel to each other. When lines are parallel it means they stay the same distance apart forever! Train tracks are parallel.

13. Do you see the TRAP in Trapezoid?

14. Did you know that they have a special name for all the shapes that have 4 sides, 4 angles and 4 vertices? They are called QUADRILATERALS! QUAD means 4. A quad runner has 4 wheels. All quadrilaterals have 4 sides and 4 angles and 4 vertices.

15. All shapes that have 4 sides, 4 angles, and 4 vertices are called QUADRILATERALS.
REMEMBER: Any SHAPE with 4 SIDES
and 4 ANGLES or 4 VERTICES
is called a QUADRILATERAL.

16. 5. A pentagon has 5 sides, 5 angles and 5 vertices.
The prefix PENT means 5.
Any word with the prefix
PENT has something
to do with 5.
The Pentagon is located in Washington, D.C.
It has 5 sides and 5 angles and 5 vertices.

17. THE PENTAGON

18. Anything with the prefix hex has
The hexagon has 6 sides,
6 angles and 6 vertices.
The prefix HEX means 6.
Anything with the prefix hex has
something to do with 6.

19. Look at each shape. Circle all vertices. Put a line through each side
Look at each shape. Circle all vertices. Put a line through each side. I did the first one for you.
TRI = QUAD = PENT = HEX = 6

20. But there are many other shapes
But there are many other shapes. Shapes with more than 3, or 4, or 5, or even 6 sides. What about an OCTAGON? The prefix OCT means 8. So an octagon has 8 sides, 8 angles and 8 vertices. Can you circle the vertices and put a line through each side?

21. Do all octagons have to be so perfect. NO
Do all octagons have to be so perfect? NO! Any shape with 8 sides, 8 angles and 8 vertices is an Octagon! Can you find each Octagon?

22. The shapes we have looked at are called 2-D or 2 dimensional
The shapes we have looked at are called 2-D or 2 dimensional. That means that they are flat. If the shape is not flat than it is 3-D or 3 dimensional. This is a CUBE. A cube is not flat but it has 6 flat sides or faces. Each side has a flat square shape. A cube is not a square but you need 6 squares to make a cube!

23. This pattern is called a net
This pattern is called a net. If you fold the 6 squares you can make the cube. When we look at a cube We can only see 3 faces, but if you look behind and under you will count 6 faces on a cube.

24. Just like the 2-D shapes each 3-D geometric solid has the same parts
Just like the 2-D shapes each 3-D geometric solid has the same parts. They each have a flat surface called the face, they each have vertices where the points come together and they each have edges where the faces come together.

25. These are cubes. They are geometric solids. They have 6 equal faces
These are cubes. They are geometric solids. They have 6 equal faces. They have 8 equal vertices. Count them. One is hiding… They have 12 equal edges. Count them. Three are hiding…

26. There are many different 3-D geometric solids
There are many different 3-D geometric solids. These all have faces, edges, and vertices. Can you name some of these?

27. This is a very fancy house. Do you see the front porch?
The roof to the porch is
held up with columns.
Columns go up and down. They are VERTICAL.

28. In math lines that go up and down are called VERTICAL LINES
In math lines that go up and down are called VERTICAL LINES. I like to think of the V in Vertical as the point of the arrow. We are going to use vertical lines to cut a rectangle into equal sections. V

29. In math any lines that go side to side are called HORIZONTAL ROWS
In math any lines that go side to side are called HORIZONTAL ROWS. Horizontal is a really big word so we just say: ROWS! Rows go from one side of a shape to the other. Remember the word parallel? Rows need to be spaced equally. Rows should be parallel to each other.

30. The rectangle was partitioned
We are going to use columns l and rows to partition or section off a rectangle. Let’s do one together. Split this rectangle into 2 rows and 3 columns.
The rectangle was partitioned
into 6 equal sections.

31. Now you try some. 4 rows & 2 columns
3 rows & 2 columns rows & 4 columns
____ equal sections ____ equal sections ____ equal sections

32. Let’s do some more. 3 rows & 5 columns
4 rows & 3 columns rows & 6 columns
____ equal sections ____ equal sections ____ equal sections

33. Partitioning a rectangle into rows and columns is not the only way to make equal sections in a rectangle. What about cutting the rectangle into equal sections using triangles?
We have made 4 equal
sections by slicing the rectangle from corner to corner.

34. Another way to partition a rectangle into 4 equal parts is to think of it as a rectangular clock. Make your line from 12 o’clock down to 6 o’clock and make another line from 9 o’clock to 3 o’clock.

35. Now you try some. Make your line from 12 to 6 and another line from 9 to 3.

36. Of course you can always use rows and columns to partition a rectangle into 4 equal parts. Because we made 4 equal parts we can call each part one of four or 1/4th. In this picture 1/4th of the rectangle is red. The number under the line tells us how many parts the rectangle was cut into. The top number tells us how many of those parts are red.

37. Can you partition each rectangle using rows and columns?
Can you shade in 1 of the 4 equal parts and
write 1/4 by your rectangle?
Remember that the number under the line shows how many pieces you cut it into and the number on top shows how many of those parts are shaded.

38. There is one more way to partition a rectangle into
4 equal parts. It is a little tricky!
First you are going to cut your rectangle in 2 parts.
Anything that is cut into 2 equal parts is cut in HALF.
After making your line from
12 o’clock to 6 o’clock you
will draw a line from the
top corner to 6 o’clock.
Now draw a line from 12 o’clock to the lower right corner.

39. Now it is your turn to practice. If you need help look at the examples.

40. These are all different ways you can cut or partition a rectangle into 4 equal parts.

41. You have probably helped cut a pizza into equal sections
You have probably helped cut a pizza into equal sections. Try to cut this pizza into 4 equal slices or sections. 12
Think of the pizza as a clock.
Draw your line from the 12
down to the 6. Now draw a
line from the 9 to the 3.
You just divided your pizza
into 4 equal pieces! 9 3 6

42. Your pizza should have looked like this
Your pizza should have looked like this. Now partition this clock into 4 equal sections.

43. Now partition or divide each circle into 4 equal sections.
If you shade 1 of the 4 sections you have shaded 1/4 or
one fourth of the parts. Shade 1/4 of each.
What would you write if you shaded 2 of the 4 parts? or ½. 4

44. Maybe you don’t want to cut your pizza into 4 sections
Maybe you don’t want to cut your pizza into 4 sections. Maybe you only need 3 sections. How could you use the clock to make 3 equal sections?

45. Now partition or divide each circle into 3 equal sections.
If you shade 1 of the 3 sections you have shaded 1/3 or
one third of the parts.
Shade 1/3 of each. What would you write if you shaded 2 of the 3 parts? 3

46. When you cut something into 2 equal parts we say you cut it into halves. If you shade 1 section then you shaded one half or ½ of the shape.
The number under the line shows
how many parts you cut it into.
The number above the line shows
how many of the parts are shaded.

47. When the number on the top of the line is the same as the number under the line then you shaded the whole thing.
3/3 = 1 whole
2/2 = 1 whole
4/4 = 1 whole

48. If I cut a pizza into 3 equal pieces and I eat all 3 pieces then I ate the WHOLE thing!

49. If I cut a pizza into 4 equal pieces and I eat all 4 pieces then I ate the WHOLE thing!

50. You can cut or partition any rectangle by using rows and columns.
We have only looked at halves, thirds, and fourths,
but you can partition a rectangle into as many parts as you want.
Instead of writing down the words rows and columns
we just write down the number of rows first with an
X and then the number of columns we want to have.
So 2 rows with 5 columns would be written 2 x 5
and look like this. 2 x 5

51. This is a 2 X 5. But if you flip it over it becomes a 5 X 2
This is a 2 X 5. But if you flip it over it becomes a 5 X 2. These can be written as addition sentences = 10 or = 10 2 X 5 5 X 2

52. It is your turn to write the addition sentences to go with each rectangle below. When you line up objects in rows and columns it is called a rectangular ARRAY. __+__+__+__+__+__=___ __+__+__+__=___ 4 X 6 6 X 4

53. Use an addition sentence to tell how many objects are in each rectangular ARRAY.

54. ARRAYS can be fun to make. They can also help you solve math problems
ARRAYS can be fun to make. They can also help you solve math problems. Let’s try one together. Quintin has 8 chairs. He wants to arrange them in equal rows. What are some ways that he can arrange the chairs? There are 4 possible arrays to solve this problem.
1 X 8 = 8 or
8 X 1 = 8
4 X 2 = or X 4 = 8

55. These are all the ways you can arrange 16 chairs
These are all the ways you can arrange 16 chairs. It is easy to make little squares in your array but if you wanted to you could draw the little chairs.
This is a 2 X 8 = 16 array.

56. Label and solve each picture array. Rows X Columns =
Label and solve each picture array. Rows X Columns = ? ___ X ___ = ___ ____ X ____ = ____ ____ X ____ = ____

57. Label and solve each picture array
Label and solve each picture array. Write the addition sentences that go with each array. 2
+ 2 8
= 8

58. Paul makes an array with 12 tennis balls as shown below
Paul makes an array with 12 tennis balls as shown below. Write two different equations to represent his arrangement.
Equation is a fancy math word that means a math sentence with equal = signs.

59. Joannie arranges 15 penguins into a rectangular array as shown below
Joannie arranges 15 penguins into a rectangular array as shown below. Write two different equations to represent her arrangement.

60. Mark arranges 12 ice cream cones into a rectangular array as shown below. Write two different equations to represent his arrangement.

61. Keith arranges triangles into a rectangular array as shown below
Keith arranges triangles into a rectangular array as shown below. Write two different equations to represent his arrangement.

62. Look at each building array
Look at each building array. Write two equations to represent each array.

63. Barbara draws a rectangle on grid paper
Barbara draws a rectangle on grid paper. She needs to count the number of small squares within the rectangle. How many small squares are found in the shaded rectangle? a. 22 b. 30 c. 28 d. 24

64. Adam designed a sign for his bedroom door to keep his sister out of his room. The shape of the sign has 4 equal sides and 4 equal angles. What shape is his sign? a. square b. triangle c. sphere d. trapezoid

65. Ellsa wants to build a go kart
Ellsa wants to build a go kart. As she builds the go kart she notices many different shapes in her design. She grabs the last piece of the go kart and begins to attach it to the hood. What is the name of this shape? a. square b. trapezoid c. rhombus d. rectangle

66. Carter is having a birthday party. His mother is baking cupcakes
Carter is having a birthday party. His mother is baking cupcakes. He notices that the cupcake pan is divided into smaller parts. How many small sections are within the cupcake pan? a. 10 c. 15 b. 12 d. 16

67. Leah likes to practice math at home
Leah likes to practice math at home. She has a chalkboard so she can draw different shapes. Today she drew a rectangle and split it into 5 rows and 2 columns. How many small squares did Leah make? a. 8 b. 14 c. 10 d. 6

68. Easton is helping his dad make a checker board
Easton is helping his dad make a checker board. Eaton paints the black squares in the rectangle and his dad paints the red squares. How many small squares make up the checker board? a. 18 b. 26 c. 30 d. 36

69. Naomi and her mom want to make a blanket to give to her baby brother
Naomi and her mom want to make a blanket to give to her baby brother. Naomi decides on this pattern. How many small airplanes are within the rectangle of her pattern? a. 4 b. 12 c. 16 d. 20

70. Melanie arranges 8 ice cream cones into a rectangular array as shown below. Which equation represents her arrangement? a b = 8 c. 8 – 4 = 4 d = 4

71. Ronan is baking brownies with his
friend. They partition the pan into
equal shares or sections like the
picture.
What do we call these equal parts?
halves b. thirds
c. fourths d. whole

72. Willow loves working with the geoboards
Willow loves working with the geoboards. She uses rubber bands to make different shapes. She even uses rubber bands to partition the geoboard into equal sections. How did she partition her geoboard? a. halves b. thirds c. fourths d. fifths

73. Micah likes to eat a sandwich
for snack after school every day.
He cuts his sandwich into equal
pieces as pictured.
How can he describe how he cut his whole sandwich?
one half b. two halves
c. three thirds d. four fourths

74. Lillian made a pie with her mother.
She cut the pie into equal pieces as pictured.
How can the whole pie be described?
one half c. two halves
four fourths d. three thirds

75. Zoe likes to pretend she is a teacher
Zoe likes to pretend she is a teacher. She has a whiteboard so she can draw different shapes. Today she drew a rectangle and split it into 3 rows and 6 columns. How many small squares did Zoe make? a. 18 b. 16 c. 14 d. 12

76. Zander is baking a round cake to
take to school for the bake sale.
He partitions the cake into equal
shares or sections like the picture.
What do we call these equal parts?
whole b. halves
c. thirds d. fourths

77. Hunter uses partitioned baby plates
when he serves dinner to his little brother.
What do we call the way
this plate is partitioned?
one whole b. one half
c. halves d. thirds

78. Evan is having a birthday party. His mom is serving pizza
Evan is having a birthday party. His mom is serving pizza. He notices that the pizza is divided into smaller parts. How many small sections are within the round pizza? a. 4 c. 6 b. 8 d. 10

79. Ian has been assigned an art project
Ian has been assigned an art project. He must create a work of art using only shapes with 5 sides and 5 angles. What is the name of the shape he will be using? a. pentagon b. rhombus c. trapezoid d. triangle
Can
you draw
his shape
here?

80. Dylan designed a sign for his lemonade stand.
The shape of the sign has
6 sides and 6 angles. What shape is his sign?
rectangle b. pentagon
c. hexagon d. trapezoid

81. Eva is helping the teacher clean up after math centers.
She puts all of the squares, rectangles, and trapezoids
into one of the math tubs.
What is Eva sorting by?
size of the faces c. color of the edges
number of sides, vertices and angles d. number of sharp corners

82. Parker draws a rectangle on grid paper
Parker draws a rectangle on grid paper. He needs to count the number of small squares within the rectangle. How many small squares are found in the shaded rectangle? a. 20 b. 34 c. 40 d. 42

83. Bennett wants to build a boat out of Legos
Bennett wants to build a boat out of Legos. As he builds the boat he notices many different shapes in his design. He grabs the last Lego piece of the boat and begins to attach it. What is the name of this shape? a. triangle b. trapezoid c. hexagon d. rectangle

84. Iris buys a box of candy to give to her Mom. The top of the box has
5 sides, 5 vertices, and 5 angles. Which box contains the candy? c.
b d.

85. Tanaya is cleaning up the math manipulatives after centers
Tanaya is cleaning up the math manipulatives after centers. She threw some wrong shapes into the quadrilateral tub. Circle the shapes she should remove? Why? _______________________

86. Sienna is sorting shapes during math centers
Sienna is sorting shapes during math centers. She pulls out all of the yellow shapes to create a bee hive. What shape is she using? a. pentagon b. octagon c. hexagon d. rhombus

87. Elias and his brother make a cake for Father’s Day.
They decide to cut the cake into four equal pieces.
What is the name of the equal shares or equal parts?
fourths
halves
thirds
fifths

88. Ryder designs a sign for his clubhouse
Ryder designs a sign for his clubhouse. He wants the sign to have 4 sides, 4 angles, and 4 vertices, but he wants the sign to look like someone sat on it. Which shape should he use? Can you draw his shape? a. trapezoid b. rhombus c. square d. rectangle

89. Sienna draws a rectangle on grid paper. She needs to count
the number of small squares outside of her rectangle.
How many of the small squares are NOT shaded? 42 50 52
100

90. Martin is making soup for dinner with toasted cheese sandwiches
Martin is making soup for dinner with toasted cheese sandwiches. He cuts the sandwiches into equal shares or equal parts. How can the whole sandwich be described? a. one half b. one third c. two halves d. four fourths

91. Katrina always has a snack after dance practice. Today she
decided to have a banana and a glass of milk. She slices the
banana into equal shares or equal pieces as shown.
How can the whole banana be described?
one half
two halves
two thirds
three thirds

92. Isaiah loves making shapes on the geoboards. Today he decides
to partition the geoboard with rubber bands and makes the
geoboard pattern shown.
How did he partition his geoboard?
whole
halves
thirds
fourths

93. Autumn wants to make a big game board to play hop scotch on
the playground. She creates the board and divides it into
5 rows and 3 columns.
How many small squares make up her board? 8 10 12 15

94. Which equation describes this rectangular array. a
Which equation describes this rectangular array? a = 16 b = 16 c. 16 d

95. Which cake is partitioned into equal fourths?b.
c d.

96. MATH SECOND GRADE
GEOMETRY
CATS
DOGS