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


    • 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 3-D 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


    Find the surface area of the cube building. Show

    all your work.

    The faces on the ends are 2-by-2 squares.

    So they are each 4 sq. cm. That’s 8 sq. cm.

    The other faces are all 2-by-4 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

    three-dimensional 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.





    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 in-depth study of shapes, their

    attributes, and the relationships among


    Plot these points on the grid and then connect


    (5, 1) (5, 6) (1,6)








    0 1 2 3 4 5 6 7


    5 x 4 = 20 sq. units


    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


    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


    When students understand where formulas

    like this come from, they remember them

    better and apply them appropriately and


    Find the number of degrees in each unlabeled

    angle below.













    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:


    You can also look up words in your dictionary at home or in any number of online math

    dictionaries for students. We recommend