The Building Blocks of Geometry
The Building Blocks of Geometry
Objectives
This unit covers the essential terminology of geometry from lines, segments, and rays to how we define (and calculate) distance in geometric terms. At the end of this unit, students will:
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define, draw, and find real-world examples of basic geometric forms.
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classify shapes using a variety of criteria (sides, angles, faces, etc.)
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find the distance between two points (on a map or a Cartesian plane).
Essential Questions
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How can we identify and classify shapes and structures that we see in our everyday lives, what are their properties, and how can we use information about those shapes to discover things about them that are not immediately obvious?
Related Unit and Lesson Plans
Related Materials & Resources
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Materials haven't been entered into the unit plan.Formative Assessment
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Multiple Choice Items:
Use the following map to answer questions 1–3.
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1. Which word best describes
? -
A
Line
B
Line Segment
C
Ray
D
Point
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2. Which word best describes the intersection of Oak Street and Washington Avenue?
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A
Line
B
Line Segment
C
Ray
D
Point
3. Which streets are parallel?
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A
Oak Street and Washington Avenue
B
Broadway Street and Pine Street
C
Maple Drive and Washington Avenue
D
Maple Drive and Birch Road
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4. Which term most accurately describes a quadrilateral with only one pair of parallel sides?
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A
Parallelogram
B
Square
C
Trapezoid
D
Kite
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5. Which attribute most accurately describes a parallelogram?
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A
It has three sides.
B
It has two pairs of parallel sides.
C
All four of its angles are congruent.
D
All four of its sides are congruent.
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6. Which statement most accurately describes the relationship between rectangles and squares?
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A
All squares are rectangles.
B
Some squares are rectangles.
C
All rectangles are squares.
D
No rectangles are squares.
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7. To get from the library to the supermarket, one walks 6 blocks north and 8 blocks west, usingthe sidewalks. One can also take a path that is a straight line from the supermarket to the library. How long is the path?
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A
8 blocks
B
10 blocks
C
14 blocks
D
50 blocks
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8. What is the distance between (2, 2) and (5, 6)?
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A
3 units
B
4 units
C
5 units
D
7 units
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9. From the origin (0, 0), Student 1 walks 1 unit west and 3 units north. From the same point (0, 0), Student 2 walks 4 units east and three units south. What is the shortest distance between the two students?
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A
unitsB
10 units
C
25 units
D
Multiple Choice Answer Key:
1. B
2. D
3. D
4. C
5. B
6. A
7. B
8. C
9. A
Short Answer Items:
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10. Draw line l perpendicular to line segment AB through point k with segment AB contained in plane R, and line l not contained in plane R.
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11. Compare and contrast a square and a rhombus with a visual representation.
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12. Plot two points on a grid. Describe in detail two methods to find the distance, and then find the distance.
Short-Answer Key and Scoring Rubrics:
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10. Draw line l perpendicular to line segment AB through point k with segment AB contained in plane R, and line l not contained in plane R.
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The difference is that a line continues in both directions forever, while a line segment has a point at its beginning and end.
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Points
Description
2
Student correctly describes both a line and a line segment.
1
Student correctly describes either a line or a line segment.
0
Student does not correctly describe a line or a line segment.
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11. Compare and contrast a square and a rhombus with a visual representation.
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Possible answers: They have four sides; they are both parallelograms; they have four angles; they have four congruent sides.
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Points
Description
2
Student correctly identifies two similarities.
1
Student correctly identifies only one similarity.
0
Student does not correctly identify any similarities.
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12. Plot two points on a grid. Describe in detail two methods to find the distance, and then find the distance.
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The distance formula and the Pythagorean theorem.
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Points
Description
2
Student identifies both methods.
1
Student identifies only one of the methods.
0
Student does not identify either method.
Performance Assessment:
Use the following list of shapes/lines to complete this section of the assessment:
square
rectangle
parallelogram
trapezoid
pentagon
right triangle
equilateral triangle
kite
rhombus
isosceles triangle
line
line segment
ray
parallel lines
perpendicular lines
circle
prism
cone
pyramid
cylinder
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1. Find an example from the real world of ten different shapes from the list. Take a picture of each shape (with a camera) or find a picture online and print it out.
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2. Design a poster or other way to display the pictures. For each picture, identify the shape that is represented and describe at least one attribute of the shape that is portrayed by the object. Students should answer this question: What shape do I see in this picture, and how do I know it’s that shape?
Performance Assessment Scoring Rubric:
Points
Description
4
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Student presents ten pictures of ten different objects representing ten different shapes.
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Objects are easily identified as the shape they represent.
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Well-written explanation is given for each picture.
- Project is presented in a neat and organized fashion.
3
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Student presents ten pictures of ten different objects representing ten different shapes.
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Some objects may not clearly be identified as the shape they represent.
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Explanations are given for each picture, though some may not be well written or clear.
- Project is neatly presented.
2
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Student presents ten pictures of ten different objects representing ten different shapes.
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Many objects are not clearly identified as the shape they represent.
- Explanations are not clear, or some explanations are missing.
1
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Student is missing some pictures or has multiple pictures representing the same shape.
- There are few explanations.
0
- Project is mostly or completely incomplete or incorrect.
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DRAFT 08/31/2011
