Transcript MATH SECOND GRADE - TEACHEZ

MATH SECOND GRADE
GEOMETRY
CATS
DOGS
GEO – METRY
When we learn about GEO-METRY we are learning
about measuring all the things on the Earth.
When you were in Kindergarten and First Grade
you learned about shapes in our world.
There were:
circles
squares
triangles
and
rectangles.
There were:
trapezoids
pentagons
hexagons
octagons
rhombus
and
ovals.
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.
A tricycle has 3 wheels! TRI = 3
VERTEX
Circle all the TRIangles!
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!
Circle all the Squares.
Rectangles also have
4 sides and 4 angles
and 4 vertices,
but the sides are
NOT
all the same size.
Opposite sides are parallel.
__________
__________
Circle all the Rectangles.
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
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.
Do you see the TRAP in Trapezoid?
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.
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.
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.
THE PENTAGON
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.
Look at each shape.
Circle all vertices. Put a line through each side.
I did the first one for you.
TRI = 3
QUAD = 4
PENT = 5
HEX = 6
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?
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?
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!
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.
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.
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…
There are many different 3-D geometric solids.
These all have
faces,
edges,
and vertices.
Can you name
some of these?
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.
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
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.
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.
Now you try some.
4 rows & 2 columns
3 rows & 2 columns
____ equal sections
5 rows & 4 columns
____ equal sections
____ equal sections
Let’s do some more.
3 rows & 5 columns
4 rows & 3 columns
____ equal sections
5 rows & 6 columns
____ equal sections
____ equal sections
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.
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.
Now you try some. Make your line from
12 to 6 and another line from 9 to 3.
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.
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.
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.
½
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.
Now it is your turn to practice.
If you need help look at the examples.
These are all different ways you can cut or partition
a rectangle into 4 equal parts.
You have probably helped cut a pizza into equal sections.
Try to cut this pizza into 4 equal slices or sections.
12
3
9
6
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!
Your pizza should have looked like this.
Now partition this clock into
4 equal sections.
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
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?
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
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.
When the number on the top of the line is the same as the
number under the line then you shaded the whole thing.
4/4 = 1 whole
3/3 = 1 whole
2/2 = 1 whole
If I cut a pizza into 3 equal pieces and I eat all 3 pieces
then I ate the WHOLE thing!
3/3 = 1 whole
If I cut a pizza into 4 equal pieces and I eat all 4 pieces
then I ate the WHOLE thing!
4/4 = 1 whole
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
This is a 2 X 5. But if you flip it over it becomes a 5 X 2.
2
X
5
These can be written as addition sentences.
2 + 2 + 2 + 2 + 2 = 10
or
5 + 5 = 10
5
X
2
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
Use an addition sentence to tell how many
objects are in each rectangular ARRAY.
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.
1X8=8
or
8X1=8
4 X 2=8
or
2 X 4 = 8
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.
Label and solve each picture array.
Rows X Columns = ?
___ X ___ = ___
____ X ____ = ____
____ X ____ = ____
Label and solve each picture array.
Write the addition sentences that go with each array.
2
+2
+2
+2
8
4 +4=8
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.
Joannie arranges 15 penguins into a rectangular array as shown
below. Write two different equations to represent
her arrangement.
Mark arranges 12 ice cream cones into a rectangular array
as shown below. Write two different equations to represent
his arrangement.
Keith arranges triangles into a rectangular array as shown
below. Write two different equations to represent
his arrangement.
Look at each building
array. Write two
equations to represent
each array.
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
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
c. sphere
b. triangle
d. trapezoid
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
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
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
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
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
Melanie arranges 8 ice cream cones into a rectangular array
as shown below.
Which equation represents her arrangement?
a.
b.
c.
d.
2+2+2+4
4+4=8
8–4=4
4+2+2=4
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?
a. halves
b. thirds
c. fourths
d. whole
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
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?
a. one half
b. two halves
c. three thirds
d. four fourths
Lillian made a pie with her mother.
She cut the pie into equal pieces as pictured.
How can the whole pie be described?
a. one half
c. two halves
b. four fourths
d. three thirds
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
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?
a. whole
b. halves
c. thirds
d. fourths
Hunter uses partitioned baby plates
when he serves dinner to his little brother.
What do we call the way
this plate is partitioned?
a. one whole
b. one half
c. halves
d. thirds
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
Ian has been assigned an art project.
He must create a work of art using
only shapes with 5 sides and 5 angles.
Can
you draw
his shape
here?
What is the name of the shape
he will be using?
a. pentagon
b. rhombus
c. trapezoid
d. triangle
Dylan designed a sign for his lemonade stand.
The shape of the sign has
6 sides and 6 angles. What shape is his sign?
a. rectangle
c. hexagon
b. pentagon
d. trapezoid
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?
a. size of the faces
b. number of sides, vertices and angles
c. color of the edges
d. number of sharp corners
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
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
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?
a.
c.
b.
d.
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? _______________________
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.
b.
c.
d.
pentagon
octagon
hexagon
rhombus
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?
a.
b.
c.
d.
fourths
halves
thirds
fifths
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
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?
a.
b.
c.
d.
42
50
52
100
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.
b.
c.
d.
one half
one third
two halves
four fourths
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?
a.
b.
c.
d.
one half
two halves
two thirds
three thirds
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?
a. whole
b. halves
c. thirds
d. fourths
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?
a. 8
b. 10
c. 12
d. 15
Which equation describes this
rectangular array?
a.
b.
c.
d.
4 + 4 + 4 + 4 = 16
2+2+2+2+2+2 = 16
16
8+4+4
Which cake is partitioned into equal fourths?
a.
c.
b.
d.
MATH SECOND GRADE
GEOMETRY
CATS
DOGS