Mathematics Success – Level C
T825
LESSON 29: Quadrilateral Attributes
[OBJECTIVE]
The student will be able to identify different types of quadrilaterals based on attributes
and draw examples of quadrilaterals that do and do not belong to subcategories.
[PREREQUISITE SKILLS]
knowledge of polygons and quadrilaterals
[MATERIALS]
Student pages S276 – S283
Transparencies T836, T839, T841, and T843
Transparency cutouts of T838
Copy Master T838 (1 per student pair)
Scissors
Glue
[ESSENTIAL QUESTIONS]
1. Explain the difference between a rectangle and a square.
2. How do you know if a quadrilateral is a parallelogram?
3. Sketch an example of a quadrilateral that is not a rectangle, square,
parallelogram, rhombus, or trapezoid.
[WORDS FOR WORD WALL]
quadrilateral, attributes, congruent, right angles, parallel sides, rectangle, square,
parallelogram, rhombus, trapezoid
[GROUPING]
Cooperative Pairs (CP), Whole Group (WG), Individual (I)
*For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to
students. This allows each student to be responsible for designated tasks within the
lesson.
[LEVELS
OF
TEACHER SUPPORT]
Modeling (M), Guided Practice (GP), Independent Practice (IP)
[MULTIPLE REPRESENTATIONS]
SOLVE, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete
Representation
T826
Mathematics Success – Level C
LESSON 29: Quadrilateral Attributes
[WARM-UP] (5 minutes – IP, WG, I) S276 (Answers on T835.)
• Have students turn to S276 in their books to begin the Warm-Up. Students will
identify different polygons. Monitor students to see if any of them need help
during the Warm-Up. Give students 3 minutes to complete the problems and then
spend 2 minutes reviewing the answers as a class. {Verbal Description, Pictorial
Representation}
[HOMEWORK] (5 minutes)
Take time to go over the homework from the previous night.
[LESSON] (60 minutes – M, GP, IP, CP, WG)
SOLVE Problem
(3 minutes – WG, GP) T836, S277 (Answers on T837.)
Have students turn to S277 in their books, and place T836 on the overhead. The
first problem is a SOLVE problem. You are only going to complete the S step with
students at this point. Tell students that during the lesson they will learn how to
classify quadrilaterals based on attributes. They will use this knowledge to complete
this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer}
Classifying Quadrilaterals - Concrete
(17 minutes – M, CP, WG, IP, GP)
Copy Master T838
10 minutes – M, WG, GP, CP: Distribute sticky notes and colored pencils to each
pair. Have students work in partners and designate
Partner A and Partner B. {Verbal Description,
Concrete Representation, Pictorial Representation}
Mathematics Success – Level C
T827
LESSON 29: Quadrilateral Attributes
MODELING
Classifying Quadrilaterals – Concrete
Step 1: Group students in your class by the color of shirt they are wearing,
without revealing the characteristic you are using and have them guess
how they are sorted.
Step 2: Choose another characteristic such as boys/girls, shirt/pants or hair color
and group students again. Have students guess which characteristic was
used to group them.
Step 3: Have students cut out the shapes on Copy Master T838. The shapes
should not be cut directly on the sides, but just cut apart. (Students
need to be able to see the congruent marks on the shapes.) When they
are finished, Partner A should put a set aside and use Partner B’s shapes
to do the activity.
Step 4: Tell students that they can use the characteristics of the shapes to sort
and organize them.
• Partner A, describe one characteristic that could be used to sort the
shapes. (Ex: right angle or no right angle, congruent sides, parallel
sides, etc.)
• Partner B, describe another characteristic that could be used to
sort the shapes. (Ex: right angle or no right angle, congruent sides,
parallel sides, etc.)
T828
Mathematics Success – Level C
LESSON 29: Quadrilateral Attributes
5 minutes – IP, CP:
Have students work with their partners to sort their
quadrilaterals into groups. Tell them that Partner
A should choose one quadrilateral and explain its
characteristics. Partner B needs to try to find a
quadrilateral that would go in the same category,
and explain why. Monitor closely to make sure
students are using the appropriate vocabulary.
{Verbal Description, Concrete Representation}
2 minutes – WG:
Have students come back together as a class
and share their results. They should explain and
justify why they placed certain quadrilaterals in
the same category. Use the transparency cutouts
to put the quadrilaterals on the overhead, and
ask other students if they think the quadrilaterals
belong together. {Verbal Description, Concrete
Representation}
Defining Attributes
(10 minutes – WG, M, CP, GP) T836,
S277 (Answers on T837.)
10 minutes – M, WG, GP, CP: Have students turn to S277 in their books, and
place T836 on the overhead. {Verbal Description,
Pictorial Representation}
MODELING
Defining Attributes
Step 1: Direct students’ attention to the shapes they used for the first activity.
Step 2: Explain to students that each of the shapes is a quadrilateral.
• Ask partners to make up a definition for quadrilateral based on their
observations. (a closed figure that has four sides) Record.
• Are all the shapes on the paper quadrilaterals? (Yes.) Record.
• Explain why each of the shapes is a quadrilateral. (Each shape has
four sides and is a polygon.)
Mathematics Success – Level C
T829
LESSON 29: Quadrilateral Attributes
Step 3: Read the paragraph below Question 2 together and explain that there
are many different types of quadrilaterals. Students are going to learn
how to classify them using their attributes. Explain that attributes are
what help you distinguish the shapes from each other.
Step 4: Tell students that one of the attributes you will be looking at is congruent
sides.
• Partner A, look at Figure A. Figure A has 4 congruent sides. Based
on that information, what does it mean if sides are congruent? (The
sides are the same length or equal.) Record.
• Have students look at the shapes in front of them.
• Partner B, identify any markings on Figure A. (the little line on each side)
• Partner A, infer what those little lines could mean. (The sides that have
the same number of lines through them in a shape are congruent.)
• Have students look at Figure D. How many sides are congruent? (all
of them)
• Have students look at Figure I. How many sides are congruent? (Two
different sets or pairs of sides – the sides with one line are congruent to
each other, and the sides with two lines are congruent to each other.)
Record.
Step 5: Tell students that another attribute that some quadrilaterals have is right
angles.
• Partner B, identify a quadrilateral on your paper that has a right angle.
(A, C, I, J)
• Partner A, explain how you know that the quadrilateral has a right
angle. (It makes an “L” shape and has a square inside of it.) Record.
• Have partners take a corner of their piece of paper, which is a right
angle and see if it fits perfectly into a corner of Shape A. (Yes.)
• Tell the students that this is one way to check to see if an angle is a
right angle. (The corner of a regular piece of paper should fit into it
exactly.)
• Have partners discuss other ways they could check an angle to see if
it is a right angle. (The corner should form a perfect capital letter L.
You could put a corner of a sticky note or an index card in it.)
• Have students draw a right angle for Question 6.
• Tell students that they show a right angle using a square in the corner
of the figure.
T830
Mathematics Success – Level C
LESSON 29: Quadrilateral Attributes
Step 6: Tell students that the last attribute you will look at in quadrilaterals is
parallel sides.
• Have partners discuss possible meanings for parallel sides. (sides that
could on forever and will never touch or intersect) Record.
• Explain to students that the two sides of railroad or roller coaster
tracks always have to be the same distance apart.
Classifying Quadrilaterals – Pictorial
(15 minutes – WG, M, GP, CP, IP)
T839, S278 (Answers on T840.)
10 minutes – M, GP, CP, WG: Have students turn to S278 in their books,
and place T839 on the overhead. Students
will be using one set of shapes and working in
cooperative pairs. Have Partner A put their set
of shapes away and work in Partner B’s book
for this activity. {Verbal Description, Graphic
Organizer, Pictorial Representation}
MODELING
Classifying Quadrilaterals - Pictorial
Step 1: Direct students’ attention to the graphic organizer on S278. Explain to
students that the graphic organizer shows them how to sort quadrilaterals
based on the attributes we have talked about in this lesson.
Step 2: • Partner A, determine which of the shapes are quadrilaterals. (all of
them)
• Partner B, explain why all of the shapes are quadrilaterals. (All are
closed, 4-sided shapes.)
Mathematics Success – Level C
T831
LESSON 29: Quadrilateral Attributes
Step 3: Direct students’ attention to the box that says parallelogram. Read the
attributes of a parallelogram.
• Partner A, explain how you can identify congruent sides. (Look for the
lines on the sides to show that they are congruent.)
• Partner B, explain how many sets or pairs of parallel sides a quadrilateral
needs in order to be categorized as a parallelogram. (two)
• Partner A, separate the shapes that have two sets of congruent lines.
(A, C, D, E, G, I)
• Partner B, determine if the pairs of congruent sides are also parallel.
Explain how you know. (Yes, I can put my pencils over the sides, and
they could go forever and never cross, like railroad tracks.)
• Partner A, justify the placement of these shapes. (Place them around
the box that says parallelogram because they have two sets of parallel
and congruent sides.)
• Partner B, determine if these shapes are also still quadrilaterals.
Justify your answer. (Yes, they all have 4 sides.)
*Teacher Note: Some good questions to ask students would be:
1. Are all parallelograms quadrilaterals?
2. Are all quadrilaterals parallelograms?
Have students explain their answers.
Step 4: Direct students’ attention to the box that says rectangle. Read the
attributes of a rectangle.
• Partner A, explain which shapes we should look at to determine if
they are rectangles. (We need to consider only the parallelograms
because it says that rectangles are parallelograms.)
• Partner B, explain which shapes you think are rectangles. Why? (C, I,
A, because they are parallelograms with four right angles.)
• Partner A, justify how these rectangles are still parallelograms. (They
have two sets of parallel and congruent sides.)
T832
Mathematics Success – Level C
LESSON 29: Quadrilateral Attributes
Step 5: Direct students’ attention to the box that says rhombus. Read the
attributes of a rhombus.
• Partner B, explain which shapes we should look at to determine if
they are rhombuses. (We need to consider only the parallelograms,
because it says that a rhombus is a parallelogram.)
• Partner A, determine which shapes are rhombuses. Justify your
answer. (D and A, because they are both parallelograms with four
congruent sides)
• Partner B, explain how this rhombus is still a parallelogram. (We still
have two sets of parallel and congruent sides.)
Step 6: Direct students’ attention to the box that says square. Read the attributes
of a square.
• Partner A, explain which shapes we should look at to determine if they
are squares. (We need to consider only the parallelograms because it
says that a square is a parallelogram.)
• Partner A, determine which shapes are squares. Justify your answer.
(A, because it is a parallelogram with four congruent sides and four
right angles.)
• Partner B, explain how this square is still a parallelogram. (We still
have two sets of parallel and congruent sides.)
• Partner A, explain how this square is still a rectangle. (It is a
parallelogram with two sets of congruent sides and 4 right angles.)
• Partner B, explain how this square is still a rhombus. (It is a
parallelogram with four congruent sides.)
Step 7: Direct students’ attention to the box that says trapezoid. Read the
attributes of a trapezoid.
• Partner A, explain which shapes we should look at to determine if they
are a trapezoid. (We need to consider only the shapes that were not
parallelograms because a trapezoid has only one set of parallel sides.)
• Partner B, identify which shapes are trapezoids. Justify your answer.
(B, H, J, because they have one set of parallel sides.)
• Partner A, are the trapezoids still quadrilaterals? (Yes, because they
have 4 sides.)
• Partner B, are the trapezoids rectangles? (No, because they do not
have 4 right angles and two sets of congruent sides.)
Mathematics Success – Level C
T833
LESSON 29: Quadrilateral Attributes
Step 8: Direct students’ attention to the quadrilateral area.
• Partner A, determine if there are any shapes still in the quadrilateral
area. (Yes, K and F.)
• Partner B, make a speculation about what this means. (That they are
quadrilaterals because they have four sides, but do not fit in any of
the other categories.)
Step 9: Explain to students that since the shapes all started at the top they are
all quadrilaterals. As the arrows move down, so do the shapes. Some
that moved down to parallelograms did not stop there. They also moved
down to rectangle, rhombus, or square. Some of the shapes have a lot
of names. The best name for a shape is the category that it ended up
in, although it can be called anything that was connected with an arrow
above it.
5 minutes – IP, CP:
Pass out glue and have Partner A’s get their shapes back
out. They should use Partner B’s graphic organizer to put
the shapes in the correct spot. Both partners should then
glue the shapes to the graphic organizer. Monitor closely to
make sure students are gluing the shapes in the appropriate
place. {Verbal Description, Pictorial Representation, Graphic
Organizer, Concrete Representation}
Classifying Quadrilaterals - Abstract
6 minutes – IP, CP:
(8 minutes – WG, CP, IP) T841, S279
(Answers on T842.)
Have pairs fill in their chart using their graphic organizer
and answer Questions 1-3. Partner A and Partner B should
take turns filling in each row. {Verbal Description, Graphic
Organizer, Pictorial Representation, Concrete Representation}
2 minutes – WG:
Go over the answers to the chart and three questions as
a whole group. Students should explain and justify why
they placed certain quadrilaterals in the same category.
{Verbal Description, Pictorial Representation, Graphic
Organizer}
T834
Mathematics Success – Level C
LESSON 29: Quadrilateral Attributes
SOLVE Problem
(5 minutes – WG, GP) T843, S280 (Answers on T844.)
Remind students that the SOLVE problem is the same one from the beginning
of the lesson. Complete the SOLVE problem with your students. Ask them for
possible connections from the SOLVE problem to the lesson. (Students will be
working with identifying quadrilaterals.) {SOLVE, Pictorial Representation, Verbal
Description, Graphic Organizer}
If time permits…
(10 minutes – IP, CP) S281 (Answers on T845.)
Have students work in partners to complete Problems 1-8.
[CLOSURE] (2 minutes)
To wrap up the lesson, go back to the essential questions and discuss them with
students.
• Explain the difference between a rectangle and a square. (The rectangle has two
separate pairs of congruent sides, and a square has all four sides congruent.)
• How do you know if a quadrilateral is a parallelogram? (A quadrilateral is a
parallelogram if it has two pair of congruent parallel sides.)
• Sketch an example of a quadrilateral that is not a rectangle, square, parallelogram,
rhombus, or trapezoid. (Answers will vary, but should not have any parallel sides.)
[HOMEWORK] Assign S282 and S283 for homework. (Answers on T846 and T847.)
[QUIZ ANSWERS] T848–T850
The quiz can be used at anytime as extra homework or to assess how students
progress on identifying quadrilaterals.