Grades 6-8
Station 1
Geometry
3N8 – Teacher Copy
Activity 1
Materials Needed: Graph paper
Students will draw 5 different rectangles and 2 squares on a sheet of graph paper.
They will determine the area of each rectangle and square by counting the number of
blocks. Students may write inside or outside of each figure: A = ___ square units.
Grades 6-8
Station 2 5M6 – Teacher Copy
Geometry
Activity 1
Materials Needed: Graph paper
On graph paper, students will create two columns of different sized squares. The first
column is a review of the area of squares: A = bh. The second column requires
students to cut the squares in half by drawing a line from vertex to vertex. They are
now finding the area of the triangle. The object is for the student to determine that the
area of a triangle is half of the area of its corresponding square. Therefore, since the
area of a square is A = bh, then the area of a triangle is A = ½ bh.
Grades 6-8
Station 3 5M6 – Teacher Copy
Geometry
Activity 1
Materials Needed: Graph paper
Students will use the area of a rectangle or square to determine the area of a
parallelogram. They will do this by creating a parallelogram, cutting out the triangular
portion and reattaching the triangular piece to the other side of the parallelogram. This
will create a rectangle with area, A = bh. Since the area was not altered, the area of a
parallelogram is A = bh.
Grades 6-8
Station 4 7M6 – Teacher Copy
Geometry
Activity 1
Materials Needed: Handout
Students will cut out the congruent trapezoids and place them together, creating a
rectangle. Using the area formula for a rectangle, students will create an area formula
for the two trapezoids then divide in half for the area of one trapezoid.
The students will use drawings and formulas to show the proof of the area of a
trapezoid in their math journal.
Activity 2 (Abstract*)
Materials Needed: Handout
Students will draw each step shown in their math journal. The area of the trapezoid will
be derived from the two triangles created by drawing a line from vertex to vertex. When
the areas for each triangle are added together it creates the formula for the area of a
trapezoid.
Grades 6-8
Station 5 8M9 – Teacher Copy
Geometry
Activity 1
Materials Needed: Graph paper
Students will create a house on graph paper using triangles and squares or rectangles.
They will find the surface area of the 3 drawings using the formulas and by counting the
squares.
Activity 1 Station 1 Geometry
3N8
Draw 5 different rectangles and 2 squares on a sheet of graph paper. Determine the
area of each rectangle and square by counting the number of blocks. Write the area as
shown below.
Area = 12 square units
Activity 1 - Station 2 Geometry
5M6
On graph paper create two columns of different sized squares as shown below.
A = bh
A=
A=bh
A=
A=bh
A=
Next, find the area of each of the squares in the FIRST COLUMN ONLY. You can find
the area by counting the squares.
Draw a line from vertex to vertex on the squares in the SECOND COLUMN ONLY.
Shade half of the square as shown. Find the area of the un-shaded piece (a triangle).
A = bh
A=
A=bh
A=
A=bh
A=
Compare the area of each square to the area of its corresponding triangle. What is the
pattern? Based on what you’ve found, how should we write the area of a triangle?
Activity 1 – Station 3 Geometry
5M6
The area of a rectangle or square is base times height: A = bh. This can be shown
using graph paper and by counting the squares. But what is the area of a
parallelogram?
Using graph paper, draw a parallelogram with the dimensions shown.
Count the squares to determine the area of this figure. A = ________ units 2
Draw a dotted line as shown below. Cut the parallelogram along the dotted line. The
cut-out shape is a triangle. Move the triangle to the other side of the parallelogram and
attach it.
What is this new shape? ________________________________________________
By counting the squares, what is the area of the new shape? The areas of the figure
are the same, because the figure still has the same total amount of space.
If the area of a square and rectangle equals bxh, then the area of a parallelogram must
be A = ______. The height is the length of the dotted line that creates a right angle.
Activity 1 – Station 4 Geometry
7M6
A trapezoid is a quadrilateral with one set of sides parallel. What is the
area of a trapezoid? To show this, you will first create a trapezoid with
bottom base b1 and top base b2. The height, h, is on the left.
b2
h
b1
Next cut out the same trapezoid below that has been flipped over (reflected
twice), and place it next to the first trapezoid.
b1
h
b2
The two should slide together like this. The two trapezoids combine to
create a ___________________________.
The rectangle’s dimensions are shown below. Verify these dimensions
with the original 2 trapezoids.
b2
b1
h
b1
b2
Since this is a rectangle, we know that the area of a rectangle is
A = _______.
So, that would mean that the area of our figure (2 trapezoids placed
together) is
A = bh
A = (b1 + b2) h
This can be rewritten: A = h (b1 + b2).
But we only want the area of one trapezoid. Since both trapezoids are the
same, you can divide the area in half to get the answer.
A = ½ h (b1 + b2)
In your math journal, use pictures and area formulas to prove the area of a
trapezoid:
A = ½ h (b1 + b2).
Activity 2 – Station 4 Geometry
7M6
In mathematics, proof is everything. Being able to problem solve and see
problems from different aspects is important. Now we will look at the area
of a trapezoid in a different way. Draw each step in your math journal.
First, draw a trapezoid in your math journal like the one below. Remember
that the height is the dotted line from the vertex at the top to the base at the
bottom and it must create a right angle.
b2
h
b1
The height will remain there, but we are not going to show it in the next
picture. Instead, we will cut the trapezoid from vertex to vertex.
b2
b1
The area of the trapezoid is equal to the area of the two triangles added
together. The area of a triangle is A = ½ bh.
Area of Trapezoid = (½ bh) + (½ bh)
= (½ b1 h) + (½ b2 h)
= ½ h (b1 + b2)
In your math journal, use pictures and area formulas to prove the area of a
trapezoid: A = ½ h (b1 + b2).
Activity 2 – Station 5 Geometry
8M9
Surface area: the total area of the surfaces on the outside of a 3D object
On the graph paper, create a house net like the one below made of squares and
triangles. Ensure all squares are the same size and all triangles have the same base
and height. Find the surface area of each house using 2 different methods: count the
total squares and check your answer using the formulas for area and addition.