
.Bridges in Mathematics (
Parents and teachers may reproduce for classroom and home use.) ©The Math Learning Center
Grade 5, Unit Three: Geometry & Measurement
In this unit your child will:
• identify and draw specific kinds of angles and line
segments
• identify and draw similar and congruent shapes, as well
as symmetrical shapes
• identify and draw different kinds of polygons
• locate points on a coordinate grid
• flip, slide, and turn different shapes and predict the
results of transformations before completing them
• calculate the area of triangles and quadrilaterals
• measure angles with a protractor
• apply the fact that the angles in every triangle add up to 180º and the
angles in every quadrilateral add up to 360º
• calculate the volume and surface area of 3D shapes
Your child will learn and practice these skills by solving problems like those shown
below. Keep this sheet for reference when you’re helping with homework.
Problem Comments
Find the volume of this building made of
centimeter cubes. Show all your work.
There are 4 cubes in this
slice. The building has 4
slices like this. So
altogether there are 4 x 4 cubes. That’s 16
cubes, so the volume is 16 cubic
centimeters.
Find the surface area of the cube building. Show
all your work.
The faces on the ends are 2by2 squares.
So they are each 4 sq. cm. That’s 8 sq. cm.
The other faces are all 2by4 rectangles.
They are 8 sq. cm each and there are 4 of
them, so that’s 32 sq. cm. Altogether, the
surface area is 8 sq. cm + 32 sq. cm = 40
sq. cm
In later grades, students will apply formulas to
find the volume and surface area of different
threedimensional shapes. (Supplemental
materials are provided with the curriculum
for teachers in districts and states where fifth
graders are expected to learn such
formulas.) For now, it is important for students
to apply their knowledge about volume and
surface area to devise their own methods of
calculating them. When the time comes to
learn formulas, students will be better able to
apply those formulas with understanding and
will remember them more easily.
Bridges in Mathematics (
Parents and teachers may reproduce for classroom and home use.) ©The Math Learning Center
Draw a shape with 2 acute angles, 2 obtuse
angles, and only 1 pair of parallel sides. Label all
of these features in your drawing.
obtuse
acute
acute
obtuse
I circled the two sides that are parallel.
What is the name of the shape you drew? Be as
specific as you can and explain how you know.
It is a trapezoid. I know because it has 4
sides and only 2 of them are parallel.
Students show a deep understanding of
shapes and their properties when they can
draw shapes with specific attributes and
then name them with precise vocabulary.
Although studying geometry requires that
students learn new vocabulary, memorizing
words and their meanings is not the goal of
this unit. Rather, the vocabulary allows
students to express and explore geometric
ideas with greater precision. This unit is far
more than an extended vocabulary lesson: it
is an indepth study of shapes, their
attributes, and the relationships among
them.
Plot these points on the grid and then connect
them.
(5, 1) (5, 6) (1,6)
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7
rectangle
5 x 4 = 20 sq. units
triangle
half of 20
10 sq. units
What is the name of this shape?
right triangle
Find the area of the shape above. Show all your
work.
See work above. The area is 10 sq. units.
Problems like this one integrate many new
skills and concepts, including finding the
area of a triangle. The student found the
area by drawing a rectangle around the
triangle. The area of the triangle is half the
area of that rectangle, in other words, half of
the product of the length and width of the
rectangle. When students have found the
area of triangles this way, the formula makes
good sense to them:
Area of a triangle = 1 x base x height
2
When students understand where formulas
like this come from, they remember them
better and apply them appropriately and
accurately.
Find the number of degrees in each unlabeled
angle below.
30
o
80
o
70
o
45
o
85
o
50
o
To find the measure of the unknown angle in
the first triangle, the student can use the fact
that the angles in any triangle add up to
180º. The labeled angles add up to 100º, so
the third angle must be 80º. The student must
use a protractor to find the angle measures
in the second triangle.
A note about vocabulary in this unit:
Homework assignments include definitions of the
geometric vocabulary words used. You can also print out a list of vocabulary words and their
definitions (including pictures and examples) from the Math Learning Center Web site:
http://www.mathlearningcenter.org/resources/materials/parents/parents5.asp
You can also look up words in your dictionary at home or in any number of online math
dictionaries for students. We recommend