Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: Geometric Constructions
Subject/Course:
Topic: Introduction to Constructions Grade(s): 7th
Pre-Algebra (2006-07)
Designer(s): Angela Gilliam
Stage 1 – Desired Results
Established Goal(s)
o
M7G1. Students will construct plane figures that meet given conditions.
o Perform basic construction using both compass and straight edge, and appropriate technology.
Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting
an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
Enduring Understanding(s)
Essential Question(s)
Students will understand that...
1. Knowledge of constructions will further
develop and apply the student’s
understanding of plane and solid figures
through the use of constructions.
1. What is an angle bisector?
2. Can you draw geometric constructions with
a straight edge and a compass?
2. Knowledge of constructions will further
develop the student’s understanding of
properties of plane figures.
Q
Students will know...
Students will be able to...(Bloom’s Verbs)
1. A compass is a tool used to make circles.
1. Construct geometric figures using a
straight edge and compass.
2. A protractor is an instrument used to
measure angles.
3. A straight edge is a ruler, with or without
numbers or units.
4. Parallel lines are lines that never intersect.
5. Perpendicular lines are lines that intersect to
form right angles.
2. Inspect / evaluate own work product based
on the specified construction techniques
and requirements, and prior established
knowledge of geometric properties.
3. (Extension): Devise more advanced
constructions based on the techniques
learned through the lesson.
6. Right angles have a measure of 90° degrees.
4. Identify and use tools needed for
geometric constructions.
7. Acute angles have a measure less than 90°
degrees.
5. Establish familiarity with vocabulary for
geometric constructions.
8. Obtuse angles have a measure greater than
90° degrees.
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
9. Angle bisector is an angle divided into two
equal angles.
10. A vertex is the common endpoint of the two
rays that serve as the sides of an angle.
11. A ray begins at a point and goes off forever
in one direction.
12. An angle is represented by two line
segments or two rays that have a common
endpoint.
13. An arc is the curve between two points on a
circle.
Stage 2 – Assessment Evidence
Performance Task(s) Summary in G.R.A.S.P.S. form
1. Students will be evaluated based on using correct techniques and correct constructions.
2. Students will be required to demonstrate good listening skills.
3. Students may receive additional credit based on pace of understanding and application of these
skills to more advanced constructions
Key Criteria:
Students will demonstrate proficiency in geometric constructions by displaying the ability to
duplicate the procedure and the ease with which the procedure can be communicated.
Other Evidence
o Teacher observation of students working on tasks
o Assess understanding through class conversation and questioning.
o Ask students for their interpretation of the Essential Question.
o Cooperative groups will problem solving methods.
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Stage 3 – Learning Plan
Learning Activities Consider the W.H.E.R.E.T.O. elements.
Introduction:
1. Review the use of the protractor with students.
2. Review the types of angles.
3. Distribute Angle Practice Worksheet for students to use protractor to measure and draw
angles. (Provides practice in measurement of given angles, drawing angles for given
degree measure.
(Activity sheets available at:
http://www.coreknowledge.org/CK/resrcs/lessons/82K_Geometric.pdf )
4. Present and demonstrate “new” terms (parallel, perpendicular, congruent).
5. Practice using the compass by making circles with different diameters.
6. Show a web-based movie clip of an angle bisector. Clip is found at:
http://regentsprep.org/Regents/math/construc/bisect.htm
Given: angle BAC
Task: Bisect angle BAC.
Directions:
1. Place the point of the compass on the vertex of angle BAC (point A).
2. Stretch the compass to any length so long as it stays ON the angle.
3. Swing an arc with the pencil that crosses both sides of angle ABC. This will create two
intersection points with the sides of the angle.
4. Place the point on one of these intersection points created on the sides of the angle BAC. If
needed, stretch your compass to a sufficient length to place your pencil well into the interior of the
angle. Stay between the sides (rays) of the angle. Place an arc in this interior - you do not need to
cross the sides of the angle.
5. Without changing the width of the compass, place the point of the compass on the other
intersection point on the side of the angle and make the same arc. Your two small arcs in the
interior of the angle should be crossing.
6. Connect the point where the two small arcs cross to the vertex A of the angle.
You have now created two new angles that are of equal measure (and are each 1/2 the measure of
angle BAC.)
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/