Geometric Figures
Geometric Figures
Objectives
In this unit, students will draw and identify lines and angles and also classify shapes based on the properties of these geometric constructs. Students will:
- draw points, lines, line segments, rays, and angles.
- categorize angles (acute, right, obtuse) and lines (parallel, perpendicular).
- classify two-dimensional figures based on the figures’ lines and angles.
- recognize and draw lines of symmetry.
Essential Questions
How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems?
How can geometric properties and theorems be used to describe, model, and analyze situations?
How can patterns be used to describe relationships in mathematical situations?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
- How can patterns be used to describe relationships in mathematical situations?
- How can recognizing repetition or regularity assist in solving problems more efficiently?
- How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations to solve problems?
- How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
- How can geometric properties and theorems be used to describe, model, and analyze situations?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
Geometry: An Introduction to Terms
http://math.about.com/library/weekly/aa031503a.htm
Basic Geometry
http://www.basic-mathematics.com/basic-geometry.html
Plane Geometry
http://www.mathsisfun.com/geometry/plane-geometry.html
Introduction to Basic Geometry Concepts
http://mathandreadinghelp.org/basic_geometry.html
Classification of Triangles and Angles
http://math.about.com/od/geometry/ig/Angles-and-Triangles/
Classifying Triangles
https://www.mathopenref.com/triangleclassify.html
Classifying Quadrilaterals
http://www.mathsisfun.com/quadrilaterals.html
Classification of Quadrilaterals (Detailed)
http://www.cut-the-knot.org/Curriculum/Geometry/Quadrilaterals.shtml
EAI Catalog (Miras)
http://www.eaieducation.com/category.aspx?categoryID=82
- EAI Catalog (pattern blocks)
http://www.eaieducation.com/category.aspx?categoryID=71 - Line Symmetry Worksheets
http://www.superteacherworksheets.com/symmetry.html
Formative Assessment
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View
Multiple-Choice Items:
1. Which of the following terms describes the geometric figure shown below?
A
Angle
B
Line
C
Line segment
D
Ray
2. Which statement describes two parallel lines?
A
Two lines that cross.
B
Two lines that make a right angle.
C
Two lines that never cross.
D
Two lines that, if they continued forever, might cross.
3. Which of the following describes the angle shown below?
A
Acute angle
B
Obtuse angle
C
Right angle
D
Straight angle
4. Which of the following shapes does not have two sets of parallel lines?
A
Parallelogram
B
Rectangle
C
Square
D
Trapezoid
5. How many right angles are there in a right triangle?
A
0
B
1
C
2
D
3
6. Which of the following is not a property of a square?
A
Two sets of parallel lines.
B
Four right angles.
C
All the sides are the same length.
D
At least one obtuse angle.
7. Which shows a shape reflected across a line?
A
B
C
D
8. Which figure has more than one line of symmetry?
A
B
C
D
9. Which figure makes a letter of the English alphabet when it is reflected across the line of symmetry?
A
B
C
D
Multiple-Choice Answer Key:
1. D
2. C
3. B
4. D
5. B
6. D
7. C
8. C
9. D
Short-Answer Items:
- In the figure below, identify how many points, lines, and perpendicular lines there are. Also, classify each of the three angles inside the triangle as acute, right, or obtuse.
- For the shape shown below, explain how you know whether the shape is each of the following: square, rectangle, parallelogram, and trapezoid.
3. Draw all the lines of symmetry for the figure shown below.
Short-Answer Key and Scoring Rubrics:
1. In the figure below, identify how many points, lines, and perpendicular lines there are. Also, classify each of the three angles inside the triangle as acute, right, or obtuse.
Sample Answer: There are three points, three lines, and two perpendicular lines. There are two acute angles and one right angle.
Points
Description
2
The student correctly identified and counted all of the required geometric constructs.
1
The student correctly identified at least half of the required geometric constructs.
0
The student correctly identified less than half of the required geometric constructs.
2. For the shape shown below, explain how you know whether the shape is each of the following: square, rectangle, parallelogram, and trapezoid.
Sample Answer: The shape is not a square because it does not have four right angles. The shape is not a rectangle because it does not have four right angles. The shape is a parallelogram because it has two sets of parallel sides. The shape is not a trapezoid because it has two sets of parallel sides.
Points
Description
2
The student provided 4 valid mathematical statements, one about each of the possible categorizations.
1
The student provided 2 or 3 valid mathematical statements about the possible categorizations.
0
The student provided fewer than 2 valid mathematical statements about the possible categorizations.
3.Draw all the lines of symmetry for the figure shown below.
Points
Description
2
The student correctly drew all 6 lines of symmetry with no additional incorrect lines.
1
The student correctly drew 3, 4, or 5 lines of symmetry with 1 or no additional incorrect lines.
0
The student correctly drew 0, 1, or 2 lines of symmetry.
Performance Assessment:
Have students design a tile mosaic using the shapes covered in the unit. The mosaic doesn’t necessarily need to be repeating but should cover an entire page and contain at least 12 shapes (some of them may be repeated). Mosaics should include at least two different quadrilaterals and one type of triangle. Students should color their mosaics by classifying all the shapes and coloring each type the same color. (For example, all squares should be colored red, all rectangles should be colored blue, and so on.)
Students should trade mosaics with one another. For each mosaic, students should create a legend that can be used to determine which shape is which color. The legend should show each unique shape in the mosaic and should include all colors in the mosaic.
Performance Assessment Scoring Rubric:
Points
Description
4
- The student created a mosaic that incorporates at least two different quadrilaterals.
- The student’s mosaic incorporated at least one type of triangle.
- The student colored the mosaic based on a coloring scheme associated with the types of shapes used.
- The student correctly created a legend to show the colors associated with each type of shape in a classmate’s mosaic.
- The student showed an advanced understanding of geometric shapes.
3
- The student correctly completed 3 of the 4 tasks detailed above.
- The student showed a good understanding of geometric shapes.
2
- The student correctly completed 2 of the 4 tasks detailed above.
- The student showed a limited understanding of geometric shapes.
1
- The student correctly completed 1 of the 4 tasks detailed above.
- The student showed a very limited understanding of geometric shapes.
0
- The student did not correctly complete any of the tasks detailed above.
- The student showed no understanding of geometric shapes.
- In the figure below, identify how many points, lines, and perpendicular lines there are. Also, classify each of the three angles inside the triangle as acute, right, or obtuse.
Final 06/07/2013
