Download Day 1: Triangles and their Angles

Nichole Kurtz
May 7, 2009
Unit Part 2
Full Length Lessons:
1. Day 3
2. Day 4
3. Day 6
4. Day 9
All homework problems will be checked the following day for completion. Students will receive
either full, half or no credit for the assignment.
Day 1: Triangles and their Angles
Individual Project and Class Discussion
Indicator 2: Use standard language to define geometric vocabulary: vertex, face, altitude,
diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
Goal: The students will show that the sum of the angles of any triangle must equal 180 degrees.
The students will classify triangles as right, acute and obtuse.
Beginning (5-7 minutes):
The students will watch a Discovery Channel video that discusses the real-world use of triangles
in construction and other fields.
Middle (40 minutes):
(25 minutes) The students will use Geometer’s Sketchpad to discover that the sum of every
triangle’s angles must equal 180 degrees.
(15 minutes) I will give a short PowerPoint about right, acute and obtuse angles. Then we will
have a class discussion about these types of triangles. For example, is it possible to have two
obtuse angles in one triangle? Why? Is it possible to have two right angles in one triangle? Etc.
End (2-3 minutes):
The students will write in their journals about what they learned and what they still need help
understanding.
Assessment: I will collect the Geometer’s Sketchpad printouts to see who still needs help. I
would also assign a few homework problems about whether the specified angle measures can
form a triangle. I would assign a few problems that ask students to sketch and identify triangles
by their angles.
____________________________________________________________________________
Day 2: Side Lengths and Triangles
Individual Project and Class Discussion
Indicator 2: Use standard language to define geometric vocabulary: vertex, face, altitude,
diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
Nichole Kurtz
May 7, 2009
Unit Part 2
Goal: The students will show that the sum of the two shorter sides must be greater than the
longest side in order to create a triangle. The students will be able to classify triangles as
isosceles, scalene or equilateral.
Beginning (3 minutes):
The students will answer the questions on the board in their journals, which will be review from
the previous day. For example, I would draw three triangles and have them classify the triangles
as right, acute or obtuse. Then, I would have them draw an example of each in their journals.
Middle (40 minutes):
(20 minutes) The students will use Geometer’s Sketchpad to discover that the sum of the two
shorter sides must be greater than the longest side in order to create a triangle.
(20 minutes): I will give a brief PowerPoint about scalene, equilateral and isosceles triangles.
The students will then work in pairs to practice measuring and classifying five pre-cut triangles.
They will record their measurements, triangle names and rationale for naming the triangles on a
worksheet.
End (5-7 minutes):
I would have five different groups volunteer to share their answers on the SMART BOARD
where I would have a copy of the worksheet on the screen.
Assessment: I would collect the Geometer’s Sketchpad worksheets and the triangle naming
worksheets to see if anyone needs help. I would also assign some multiple choice practice
questions about the sum of a triangle’s side lengths and about naming triangles by their sides.
____________________________________________________________________________
Day 3: Triangle Classification
Individual Project
Indicator 3: Use multiple classification criteria to classify triangles; e.g., right, scalene triangle.
NCTM Indicator: Create and use representations to organize, record, and communicate
mathematical ideas.
Previous Knowledge Expected:
For the past two days, the students have learned how to classify triangles by either their sides or
their angles. Today we will put these two methods of classification together.
Objectives:
1. The students will be able to classify triangles by both their angle names and their side
names (e.g., right scalene).
2. Students will build models of all possible triangles (e.g., a right scalene, an acute
isosceles, etc.).
3. Students will explain why some triangles are impossible to build (e.g., an obtuse
equilateral, etc).
Nichole Kurtz
May 7, 2009
Unit Part 2
Materials: math journals, writing utensil, cardstock, rulers, tape and pre-cut straws
Beginning of Lesson (3 minutes):
1. I would have directions on the board for the students to draw an example of a right
triangle, an obtuse triangle, an acute triangle, an equilateral triangle, an isosceles triangle
and a scalene triangle in their journals.
2. I would hope that someone would ask me if he or she could draw three triangles rather
than six because the student would be applying what he already knows.
Middle (40 minutes):
1. I will create a table on the SMART BOARD like the following with directions that I will
also read aloud after I pass out all of the materials: “Use the straws to build a triangle for
each box. Tape the triangles in the appropriate box. If the triangle is impossible to make,
and some of them are, write a sentence that describes why the triangle is impossible to
make in the box where the triangle WOULD BE taped.”
Equilateral
Isosceles
Scalene
Acute
Obtuse
Right
2.
3.
4.
5.
Pass out a piece of cardstock, and a ruler to each student.
Have the students draw the table on the cardstock using rulers.
Pass out the bag of pre-cut straws of varying lengths and tape to each table.
The students need to make a triangle for each possible box out of the pre-cut straws
and tape it to their cardstock.
6. If the triangle is impossible to make, they need to write a sentence that describes why the
triangle is impossible to make in the box where the triangle should be taped (e.g., It is
impossible to make an obtuse equilateral triangle because in order for the sides to be
equal, the angles must all be equal – 60 degrees each).
7. Their projects are due by the end of the block.
End (7 minutes):
1. Have a class discussion about the triangles that were impossible to make and why.
2. Questioning
Questioning:
Which triangles were you able to make? Why?
Nichole Kurtz
May 7, 2009
Unit Part 2
Which triangles were you unable to make? Why?
Can anyone sketch for me his or her example of an obtuse isosceles triangle?
Does anyone have an example that looks different?
Can anyone sketch his or her example of an acute equilateral?
Does anyone have anything different?
Is it possible to make any equilateral triangle that is not acute?
Assessment: I would collect their projects. I would also assign some homework problems about
classifying triangles, drawing triangles and deciding whether the specified side lengths and
angles can form triangles.
_____________________________________________________________________________
Day 4: Sorting Shapes and Polygons
Whole Group Discovery
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Previous Knowledge Expected: Students have seen basic shapes in previous school years, but
they may not know that shapes can be classified in more than one way.
Objectives:
1. The students will sort the shapes into groups that make sense to them.
2. The students will discuss properties of those shapes.
Materials: anticipation guide, sorting shapes set for student pairs, worksheet, writing utensil
Beginning (10 minutes):
1. As the students walk in the door, I would hand out an anticipation guide (see the
anticipation guide on the following page).
2. Go over any homework problems that the students did not understand last night.
Middle (35-38 minutes):
1. (25-28 minutes) The students would work in pairs to complete the Sorting Shapes
activity in the Connected Mathematics 2 workbook.
2. Each student would answer questions A, B, C, and D on a worksheet that provides the
questions (see the worksheet on the following page).
3. (10 minutes) I would ask each group to tell the other students how they sorted the shapes
and why. We would talk about the properties they found. I would write down the main
findings on tag board and post them around the room.
End (3 minutes):
1. The students would complete the “End of Class” column and add any comments about
why their opinions changed or did not change in the “Comments” column.
Nichole Kurtz
May 7, 2009
Unit Part 2
2. I would remind the students to study for a quiz on triangles tomorrow.
Assessment: I would collect the anticipation guides and the homework problems.
Anticipation Guide: Write “Agree” or “Disagree” in the “Beginning of Class” column after
reading each statement. We will complete the “End of Class” column after today’s lesson.
Beginning of Class
End of Class
Comments
1. Polygons are shapes that
include rectangles,
squares and circles.
2. I see polygons everyday
outside of school and
math class.
3. Triangles are polygons.
4. The following shape
could be classified as a
parallelogram:
Questions for Sorting Shapes Activity:
A. Sort the polygons in the Shapes Set into groups so that the polygons in each group have or
more properties in common. Describe the properties that the polygons have in common and give
the letters of the polygons in each group.
Nichole Kurtz
May 7, 2009
Unit Part 2
B. Take all the triangles and sort them into two or more groups. Describe the properties you
used to form the groups and give the letters of the triangles in each group.
C. Take all the quadrilaterals and sort them into two or more groups. Describe the properties you
used to form the groups and give the letters of the quadrilaterals in each group.
D. Rose put Shapes R, O and S into the same group. What properties do these polygons have in
common? Would Shape U belong to this group? Explain.
Nichole Kurtz
May 7, 2009
Unit Part 2
_____________________________________________________________________________
Day 5: Quadrilateral Hierarchy Theorem
Teacher-Led Discussion
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Goal: The students will continue yesterday’s lesson by classifying shapes into more than one
category.
Beginning (20 minutes):
(5 minutes) The students will watch the Math’s Mansion video about polygons.
(10-15 minutes) The students will take a short quiz about triangles.
Middle (25 minutes):
Using the worksheets from yesterday, and the properties we have learned about quadrilaterals,
the students and I will construct the Quadrilateral Hierarchy Diagram on page 319 of the
Geometry Part One textbook.
End (3 minutes):
The students will write in their journals about what they learned and what is still unclear.
Assessment: I would grade the quizzes, and I would collect their journals every Friday.
Students would answer question numbers 3-5 on page 17 of the Connected Mathematics book.
_____________________________________________________________________________
Day 6: Parallelograms with Geometer’s Sketchpad
Individual Discovery Learning
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Previous Knowledge Expected: For the past two days, we have been looking at polygons and
their properties. I expect the students know that a parallelogram is a quadrilateral with two
opposite pairs of parallel sides.
Objective:
1. The students will use Geometer’s Sketchpad to show how interior angle measures are
related to parallelograms.
Materials: Geometer’s Sketchpad, computer lab, following worksheet
Nichole Kurtz
May 7, 2009
Unit Part 2
Beginning (5-10 minutes):
1. I would return the quizzes and their journals.
2. We would talk about any problems with which the class struggled.
Middle (30 minutes):
1. Have the students use Geometer’s Sketchpad and the following worksheet I created:
Instructions:
1. Open Geometer’s Sketchpad. Click on Start, then click Programs, then Math, then GSP.
2. Go to my website. Copy and paste the parallelogram into your Geometer’s Sketchpad
screen.
3. Measuring the Angles: Using the arrow tool, select (highlight) points A, then B, then C (order
is very important when measuring angles).
4. Now highlight Measure – Angle from the menu bar. A measurement should appear in the
top left corner.
5. Repeat these steps for the other three angles. *Remember that the letter of the angle you are
measuring should be in the middle. We already measured angle B by measuring  ABC.
This is the same angle as  CBA because B is still in the middle.*
Measure  ABC or  CBA = _________________
Measure  DAB or  BAD = _________________
Measure  DCB or  BCD = _________________
Measure  ADC or  CDA = _________________
What do you notice about the relationships of these angles?
______________________________________________________________________________
______________________________________________________________________________
6. Using the pointer arrow, highlight all four angle measures.
7. Select Graph – Tabulate from the menu bar. A table with all four angle measures should
appear in the top left corner.
8. Changing the Parallelogram: Using the arrow, click on a blank spot on the screen to make
sure nothing is selected.
9. Highlight point A and drag it to a new spot. Drop it there.
What happens to the shape of your parallelogram?
Nichole Kurtz
May 7, 2009
Unit Part 2
______________________________________________________________________________
______________________________________________________________________________
What happens to the angles of your parallelogram?
______________________________________________________________________________
______________________________________________________________________________
What happens to the relationship of the angles in my parallelogram?
______________________________________________________________________________
______________________________________________________________________________
*Print your drawing to turn in with this worksheet.*
Extension:
10. Select Graph – Grid Form – Square Grid. Predict what will happen if you rotate your
parallelogram by 90 degrees:
________________________________________________________________________
11. Highlight all four edges and all four points on your parallelogram. Select Transform —
Rotate. Click Enter. What happened? Was your prediction correct?
________________________________________________________________________
________________________________________________________________________
End (10 minutes):
1. The class will discuss what they learned about interior angles of parallelograms.
2. We will especially discuss question numbers 5, 9 and 11 from the Geometer’s Sketchpad
worksheet.
Assessment:
1. I would collect and grade the Geometer’s Sketchpad printouts.
2. The students would answer questions 13-16 on pages 19-20 in the Connected
Mathematics book.
Research: Kerchner, J. Area of a parallelogram. http://faculty.kutztown.edu/schaeffe/GSP/
Kerchner_GSP.pdf.
_____________________________________________________________________________
Day 7: Marshmallow Quadrilaterals
Individual Project
Nichole Kurtz
May 7, 2009
Unit Part 2
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
NCTM Indicator: Create and use representations to organize, record, and communicate
mathematical ideas.
Goal: The students will classify the quadrilaterals by their sides and angles.
Beginning (5 minutes):
We will review the Quadrilateral Hierarchy Diagram that we made as a class on Day 5. I will
pass out the directions for the assignment, the card stock, the toothpicks and the marshmallows.
Middle (40 minutes):
I will give the students two large pieces of cardstock taped together. First, the students should
write the heading “Quadrilaterals” at the top of the page. They will work individually
constructing their six quadrilaterals out of toothpicks and marshmallows. These will include a
square, a rectangle, a rhombus, a parallelogram, a kite and a trapezoid. By the end of the day, all
six shapes should be constructed and taped down in an order similar to the Quadrilateral
Hierarchy Diagram.
End (3 minutes):
We will discuss the rest of the project, which will be finished tomorrow. The rest of the project
requires that three sentences be written next to each shape. One sentence will describe the
angles, one sentence will describe the sides and one sentence will describe why the shape is
connected to other shapes.
Assessment: I would walk around and ensure that the students are on the right track.
_____________________________________________________________________________
Day 8: Marshmallow Quadrilaterals continued
Individual Project continued
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Goal: The students will classify the quadrilaterals by their sides and angles.
Beginning (3-5 minutes):
We will review the requirements for the sentences, and I will give an example. For the square: A
square has four congruent, 90-degree angles. A square also has four congruent sides. The
square is also a rhombus because the rhombus has four congruent sides. The square is also a
rectangle because the rectangle has four congruent, 90-degree angles.
Middle (40 minutes):
Nichole Kurtz
May 7, 2009
Unit Part 2
Any students who have not finished making their shapes need to finish quickly. Then they will
write their sentences for each shape NEATLY.
End (3 minutes):
The students will write in their journals about what they still do not understand about polygons
and what they enjoyed about the unit so far.
Assessment: I would collect the projects.
____________________________________________________________________________
Day 9: Coordinate Geometry
Discovery Learning
Indicator 4: Identify and define relationships between planes; i.e., parallel, perpendicular and
intersecting.
Previous Knowledge Expected: I expect that the students know properties of quadrilaterals and
triangles. Today we are going to continue with this by using an electronic Geoboard.
Objective:
1. The students will draw and identify which figures are parallel, perpendicular and
intersecting.
Materials: computer lab, electronic Geoboard, paper for KWL, markers
Beginning (3-5 minutes):
1. The students will make a KWL chart in groups of two or three to show what they know,
what they want to learn and (later) what they have learned.
Middle (40 minutes):
1. The students will create three-sided figures on the electronic Geoboard and compare them
those of another student.
2. Have the students discuss similarities and differences among the figures.
Virtual Geoboard Example
Nichole Kurtz
May 7, 2009
Unit Part 2
3. As a class, discuss the properties common to each figure.
4. Students should work in pairs for this lesson. Each student should receive a worksheet.
Student Worksheet:
1. Create a four-sided figure and compare it with the one their partner made.
2. Write down the similarities and differences between your figures.
Similarities
Differences
3. Use two rubber bands on the Virtual Geoboard to make a set of parallel line segments.

What is the important property of parallel lines?
________________________________________________________________________

How are parallel lines used in the environment and in art?
________________________________________________________________________
________________________________________________________________________
4. Use two rubber bands on the Virtual Geoboard to make intersecting lines.

What happens to the two intersecting lines?
________________________________________________________________________

How do intersecting lines compare with parallel lines?
________________________________________________________________________
5. Use two rubber bands on the Virtual Geoboard to make perpendicular lines.

What is special about perpendicular lines?
________________________________________________________________________

How are perpendicular lines and parallel lines different?
________________________________________________________________________
________________________________________________________________________
Nichole Kurtz

May 7, 2009
Unit Part 2
Why is it important to know the properties of perpendicular and parallel lines?
________________________________________________________________________
________________________________________________________________________
6. Make a quadrilateral with one set of parallel lines, two acute angles, and two obtuse angles.

What is name of your figure, and how does it differ from other quadrilaterals?
________________________________________________________________________
________________________________________________________________________

Describe the properties of your figure.
________________________________________________________________________
______________________________________________________________________
7. Ask students to make a quadrilateral that has two sets of parallel lines.

What is the name of your shape? _____________________________

Describe the properties of your shape and explain how it differs from other quadrilaterals.
________________________________________________________________________
______________________________________________________________________
8. Make a shape that has five sides.

What is the name of this figure? _____________________

How many vertices does it have? ____________________

How does it compare with other figures we have made?
________________________________________________________________________

Why is it important to know the properties of these figures compared with the figures
studied previously?
________________________________________________________________________
9. Repeat with a figure with six sides.

What is the name of this figure? __________________

How many vertices does it have? _________________
Nichole Kurtz

May 7, 2009
Unit Part 2
How does it compare with other figures we have made?
________________________________________________________________________
10. Repeat with a figure with eight sides.

What is the name of this figure? __________________

How many vertices does it have? _________________

How does it compare with other figures we have made?
________________________________________________________________________

Why is it important to know the properties of these figures compared with other figures?
________________________________________________________________________
________________________________________________________________________
End (5-7 minutes):
Call on several students to make the shapes on the SMART BOARD. Have the students discuss
similarities and differences. Have the students fill out the last column in their KWL charts.
Assessment: Have students answer numbers 34-36 on page 22 of the Connected Mathematics
workbook.
Research: NCTM Illuminations. http://illuminations.nctm.org/LessonDetail.aspx?ID=L555
_____________________________________________________________________________
Day 10: Problem Solving
Group Work
NCTM Indicators: Build new mathematical knowledge through problem solving. Recognize
reasoning and proof as fundamental aspects of mathematics. Develop and evaluate mathematical
arguments and proofs
Goal: The students will solve real-world problems and prove their answers.
Beginning (3-5 minutes):
Students will answer a few questions on the board in their journals to review from yesterday.
Middle (40 minutes):
Students will work in pairs to solve three or four real-world math problems that use geometry
and coordinate geometry. Examples of questions and scenarios can be found in the Geometry
Section of the Internet 4 Classrooms website.
End (5 minutes):
Nichole Kurtz
May 7, 2009
Unit Part 2
The students will write in their journals about what they learned and what they still need help
learning. The homework assignment is to fill out the study guide for Tuesday’s test.
Assessment: I will collect the problems and grade them based on understanding.
Research: Internet 4 Classrooms. http://www.internet4classrooms.com/skills_6th_math.htm
____________________________________________________________________________
Day 11: Review Day
Teacher-Led Review
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Indicator 2: Use standard language to define geometric vocabulary: vertex, face, altitude,
diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
Indicator 3: Use multiple classification criteria to classify triangles; e.g., right, scalene triangle.
Indicator 4: Identify and define relationships between planes; i.e., parallel, perpendicular and
intersecting.
Goal: The students will review the information they have learned over the last two weeks in
order to prepare for the test.
Beginning (3-5 minutes):
I will walk around and see who completed the study guide as a homework check. I will pass out
any remaining projects and/or papers.
Middle (40 minutes):
I will lead a game of Jeopardy. The students will be on two teams. The winning team will get
two bonus points on their test.
End (5 minutes):
The students will have a few minutes to review or ask me any questions before tomorrow’s test.
Assessment: I will observe while we play the review game.
____________________________________________________________________________
Day 12: Test Day
Individual Assessment
Nichole Kurtz
May 7, 2009
Unit Part 2
Indicator 1: Classify and describe two-dimensional and three-dimensional geometric figures and
objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides,
congruent angles/sides.
Indicator 2: Use standard language to define geometric vocabulary: vertex, face, altitude,
diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
Indicator 3: Use multiple classification criteria to classify triangles; e.g., right, scalene triangle.
Indicator 4: Identify and define relationships between planes; i.e., parallel, perpendicular and
intersecting.
Goal: The students will demonstrate what they have learned over the past two and a half weeks.
Beginning (2 minutes): Any final questions?
Middle (45 minutes): The test
End (if any time left): Students can work on puzzles and other problem solving games.
____________________________________________________________________________
Assessments:
Traditional Test
Alternative Assessment
Nichole Kurtz
May 7, 2009
Unit Part 2
Traditional Test:
Directions (3 pts each):
Questions # 1-2: Determine whether the following side lengths can form a triangle. Write “Yes”
or “No” on the line. Then EXPLAIN why or why not!
1. 6 ft, 9 ft, 3 ft
_____________________________________________________________________
2. 5 in, 1 ft, 8 in
_____________________________________________________________________
Questions # 3-4: Determine whether the following angle measures can form a triangle. Write
“Yes” or “No” on the line. Then EXPLAIN why or why not!
3. 36 degrees, 102 degrees, 42 degrees
______________________________________________________________________
4. 45 degrees, 50 degrees, 90 degrees
______________________________________________________________________
Question #5: Use a ruler to draw the following three triangles in the space provided. Label the
sides in inches. Be sure to use hash marks to show which sides are equal!
Right Isosceles
Acute Equilateral
Obtuse Scalene
Directions True/False (3 pts each): Write the full word (i.e., TRUE or FALSE) on the line in
front of each question. If the question is FALSE, re-write the statement underneath it to make it
TRUE.
_____________ 6. A polygon is a straight-edged, closed figure with more than two sides.
Nichole Kurtz
May 7, 2009
Unit Part 2
_____________ 7. It is possible to have more than one 90-degree angle in a triangle.
_____________ 8. It is possible to construct a triangle with angles measuring 79 degrees, 14
degrees and 89 degrees.
_____________ 9. The double yellow lines in the middle of the road are parallel lines.
_____________ 10. A triangle with two equal sides and one angle greater than 90 degrees
would be classified as an obtuse isosceles triangle.
_____________ 11. It is possible for a triangle with three equal sides to have three different
angle measures.
_____________ 12. Every rectangle is a parallelogram, but not every parallelogram is a
rectangle.
_____________ 13. Every rectangle is a square, but not every square is a rectangle.
_____________ 14. Train tracks are an example of perpendicular lines.
_____________ 15. Most architects construct bridges with squares in their design because
squares provide a sturdy and predictable framework.
Nichole Kurtz
May 7, 2009
Directions Multiple Choice (3 pts each): Circle the letter of the correct response.
16. Which of the following images best represents intersecting lines?
A.
B.
C.
D.
17. Which of the following triangles is a right scalene triangle?
A.
B.
C.
Unit Part 2
Nichole Kurtz
May 7, 2009
D.
18. Which of the following is NOT true about triangles?
A.
B.
C.
D.
They are polygons.
The sum of their angles must be less than or equal to 180 degrees.
The sum of the two shorter sides must be greater than the longest side.
They should be classified by both their side lengths and angle measures.
19. Which of the following is an example of a polygon you might see everyday?
A.
B.
C.
D.
A clock
A wheel
A flower
A yield sign
20. Which of the following is NOT a quadrilateral?
A.
B.
C.
D.
A square
A pentagon
A rectangle
A trapezoid
21. Is it possible for a scalene triangle to have two angles with the same measure?
A.
B.
C.
D.
No because then two side lengths would be the same also.
No because that would make it an equilateral triangle.
Yes because “scalene” only has to do with side lengths.
Yes because scalene triangles always have two angles that are the same.
22. Choose the following TRUE statement.
A.
B.
C.
D.
Every rhombus is also a square.
A rectangle is a parallelogram with four congruent angles.
A trapezoid is a parallelogram with four congruent angles.
A quadrilateral is a closed figure with more than two straight edges.
23. Which of the following could NOT also be labeled a parallelogram?
Unit Part 2
Nichole Kurtz
A.
B.
C.
D.
May 7, 2009
Unit Part 2
A square
A rhombus
A trapezoid
A square
24. What does the term “regular polygon” mean?
A.
B.
C.
D.
It means that every side of the polygon is the same length.
It means basic polygons like squares and rectangles.
It means a polygon that I see everyday outside of math class.
None of the above
25. What is the difference between a ray and a line?
A.
B.
C.
D.
Lines can curve and rays cannot.
A ray has two endpoints or vertices.
A line continues forever in one direction.
A ray continues forever in one direction.
Shape Identification Directions (5 pts each): Write the correct shape (or shapes) under each
statement. NOTE: Some shapes can be used more than once, and some may not be used at all!
Word Bank:
Kite
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
26. This figure has (or these figures have) four congruent sides.
27. This figure has (or these figures have) four congruent angles.
28. This figure has (or these figures have) only ONE OPPOSITE pair of parallel sides.
29. This figure has (or these figures have) TWO congruent pairs of ADJACENT sides.
30. This figure has (or these figures have) TWO OPPOSITE pairs of congruent sides, but
NOT ALL FOUR SIDES ARE CONGRUENT.
Nichole Kurtz
May 7, 2009
Unit Part 2
Answer Key:
Fill In:
1. No because 3 ft + 6 ft = 9 ft, which is not greater than 9 ft.
2. Yes because 8 in + 5 in = 13 in, which is greater than 1 ft.
3. Yes because 36 + 42 + 102 = 180 degrees.
4. No because 45 + 50 + 90 is greater than 180 degrees.
5. Answers will vary
True/False:
6. True
7. False – It is impossible to have a triangle with more than one 90-degree angle.
8. False – It is possible to construct a triangle with angles measuring 80 degrees, 90 degrees
and 10 degrees.
9. True
10. True
11. False – It is impossible for a triangle with three equal sides to have three different angles.
12. True
13. False – Every square is a rectangle, but not every rectangle is a square.
14. False – Train tracks are an example of parallel lines.
15. False – Most architects construct bridges using triangles in their design because triangles
provide a sturdy and predictable framework.
Multiple Choice:
16. D
17. C
18. B
19. D
20. B
21. A
22. B
23. C
24. A
25. D
Shape Identification:
26. Rhombus and Square
27. Rectangle and Square
28. Trapezoid
29. Kite
30. Parallelogram and Rectangle
Nichole Kurtz
May 7, 2009
Unit Part 2
Alternative Assessment: Marshmallow Quadrilaterals
Due Date: End of Class Tomorrow
Materials: Each student needs one large piece of cardstock, marshmallows, toothpicks, a writing
utensil and tape.
Directions Day One:
1. Write “Quadrilaterals” or “Marshmallow Quadrilaterals” at the top of your cardstock.
2. Construct the following six quadrilaterals with toothpicks and marshmallows. Be sure
that the edges of your figures are STRAIGHT. If the vertices should be 90 degrees, make
sure that they are!
A.
B.
C.
D.
E.
F.
Kite
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
3. Once you have all six shapes, lay them down on the cardstock in a way that is similar to
the Quadrilateral Hierarchy Chart that we learned in class. Tape them onto the paper
NEATLY. You may need to refer to your notes.
Directions Day Two:
4. Once you have all six shapes taped down, draw a line from the shapes on the first level
that could also be classified as the shapes on the second level, from the shapes on the
second level to the third level, etc. You may refer to your chart.
5. Next to EACH shape, write ONE succinct sentence about the shape’s sides (e.g., A
parallelogram has two opposite pairs of parallel sides).
6. Next to EACH shape, write ONE succinct sentence about the shape’s angles (e.g., A
square has four congruent angles).
Nichole Kurtz
May 7, 2009
Unit Part 2
Rubric for Marshmallow Quadrilaterals:
Six
Quadrilaterals
10
7
All of your
figures are
represented
perfectly!
You are
missing a
shape OR your
sides/angles
are sloppy.
4
1
You are
missing a
shape AND
your
sides/angles
are sloppy.
You have
connected
more than
two shapes
that are
incorrect.
You are
missing more
than one
shape.
You have few
or no lines
drawn.
Shapes are
randomly
placed.
Quadrilateral
Hierarchy
You have
Your lines are
connected two
drawn
shapes that do
correctly from
not share
level to level.
characteristics.
Sentences
about Angles
and Sides
All of your
descriptions
are accurate!
One or two of Three of your
More than
your
descriptions
three of your
descriptions
are
descriptions
are inaccurate. inaccurate. are inaccurate.
Grammar/
Spelling
Your spelling
and grammar
is perfect!
You have one
or two words
misspelled.
You have
three words
misspelled.
You have
more than
three words
misspelled.
Neatness/
Overall
Impression
I would use
this chart to
Your chart is
teach
fairly neat, but
someone
you need to fix
about
a few items.
quadrilaterals!
You have a
little work to
do on this
project.
You should
have spent
more time on
the quality of
your work.
Total
/ 50