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Overview and Background: Unit: Angles and lines
Gerry Wright : Griffin RESA
Mathematics : Middle School Mathematics : 6-8th Patterns and Relationships/Algebra
Third Ward Elementary/Griffin RESA : Grades 6 - 8 : Jan. - Jan.
Title:
Angles and lines
Topics:
various angles, points, lines, planes
Time Frame:
Start Date:
Status:
Date Revised:
Draft
Other Designers: Gerry Wright and Stephanie Sneyd
Summary:
This unit discusses points, lines, planes, and angles. It will take about 1 week to complete.
Print Materials Needed:
Resources:
Resource Attachments:
concept map may be found at link 1.
Internet Resource Links:
Link 1:http://www.griffinresa.net/UBDforms/wright/concept map7.doc
Stage 1: Identify Desired Results
State:
Title:
Standard(s):
GA
pre-algebra
NCTM: Analyze characteristics and properties of two-dimensional figures. GA QCC: 1 Solves
problems, reasons, and estimates throughout mathematics: Selects and uses problem-solving
strategies such as reading the problem, drawing a picture or diagram, using trial and error, making
a table or chart, looking for patterns, making a simpler problem and then generalizing, and working
backwards, etc.
Selects and uses appropriate tools in solving problems.
Uses estimating to check the reasonableness of results.
Solves non-routine problems for which the answer is not obvious.
Relates concepts and skills to practical applications.
ional geometric shapes and develop mathematical arguments about geometric relationship.
9:Selects apropriate measuring instruments and measures accurately length, volume/capacity,
wieght/mass, time, temperature and angles.
10: Measures and classifies angles as right, acute, or obtuse.
20:Identifies physical and symbolic representations of geometric figures, such as points, lines,
planes, line segments, polygons, vertices, rays, sides, angles, and diagonals.
27:Identifies physical and symbolic representations of vertical, supplementary, complementary, and
straight angles; parallel and perpendicular lines; transversals and uses these geometric figures,
properties, and relations to solve problems.
Understandings:
user
The student will understand that there are a variety of angles and geometric figures that have special
names and properties.
Essential Questions:
user
What's my angle?
What is a line anyway?
Why are angles and lines related?
Where can angles and lines be used in real life situations?
Knowledge and Skills:
Students will know the names and properties of various angles and be able to identify them.
Students will know that point, line and plane are undefined, but serve a major purpose in mathematics.
Stage 2: Determine Acceptable Evidence
Assessment Summary:
Task/Prompt: Pick an angle
Type:Performance Task
Topics: various angles and their properties
Summary:
Students will have to sort a group of angles by categories and be able to state the properties of the angles.
Print Materials Needed:
Resources:
Resource Attachments:
Internet Resource Links:
Link 1:
Link 2:
Link 3:
Link 4:
Link 5:
Notes:
Student Directions:
You have been given a bag of angles. (They look like trianges but the angles you are concerned with have been marked). Your task is to
separate them into groups of acute, right, obtuse and straight angles. Be able to state why you have put each angle in the groups. After
you have grouped all angles and recorded which belong to each group, see how many pairs of complementary and supplementary
angles you can find.
Rubric(s)
Rubric: Pick an angle
Summary:
Students are to classify angles and be able to state the properties of the angles.
Trait: Angles
Performance Type: Process.
Level 1: Excellent
Level 2: Good
Level 3: Competent
Level 4: Needs improvement
Student was able to classify all angles correctly.
Student was able to find several pairs of complementary and supplementary angles.
Student was able to explain why each angle was placed in a particular group.
Student was able to classify most angles correctly.
Student was able to find a few pairs of complementary and supplementary angles.
Student was able to explain why most of the angles were placed in a particular group.
Student was able to classify some angles correctly.
Student was able to find one pair of complementary and supplementary angles.
Student was able to explain why some of the angles were placed in a particular group.
Student was not able to classify any angles correctly.
Student was not able to find any complementary or supplementary angles.
Student was not able to explain why any of the angles were in a particular group.
Task/Prompt: Road Map to Geometry
Type:Performance Task
Topics: angle, line, parallel, perpendicular, transversal, vertical angles, adjacent angles, obtuse, right, acute, straight
Summary:
Students will create a road map of a town which includes a visualization of a variety of geometric terms. Students will be able to show
their proficiency of geometric terms through the road map.
Print Materials Needed:
Resources:
Resource Attachments:
Internet Resource Links:
Link 1:
Link 2:
Link 3:
Link 4:
Link 5:
Notes:
A great way to have students label their maps is to put a letter at each intersection and then write what the letter
represents on the back of the map. For example: At A you will find a set of Vertical Angles.
Another way to label is to have the students write a sentence for each of their terms. For example: Parallel Ave. and
Staight Rd. are parallel to each other.
Student Directions:
Students will create a road map of an imaginary town where the following items must be included (but are not limited to):
A Town Name
4 buildings
2 sets of parallel lines
2 sets of perpendicular lines
2 transversals
2 right angles
2 acute angles
2 obtuse angles
1 straight angles
2 sets of vertical angles
2 sets of adjacent angles
All of the roads should be named and each of the elements of the map should be identified. Your map should be accurate and show
your knowledge of geometry vocabulary terms.
Rubric(s)
Rubric: Road Map to Geometry
Summary:
This rubric will measure the students proficiency in geometric terms, their use of measuring tools, and their ability to follow directions
while using their creativity.
Trait: Geometry Vocabulary
Performance Type: Display.
Level 1: Excellent
Level 2: Good
Level 3: Competent
Level 4: Needs Improvement
All information is included.
Shows proficiency in knowledge of geometry terms.
Uses appropriate tools (ruler, protractor, etc.) to create a neat map and accurate measurements.
Creative town name.
All roads and intersections are labelled accurately.
All information is included.
Shows knowledge of terms with few mistakes.
Uses appropriate tools with few measurement mistakes.
Roads and intersections are labelled with few mistakes.
Some of the necessary information is missing.
Roads and intersections are not labeled accurately.
Mistakes were made with measurement.
Not all necessary information is present.
Lack of labels for intersections and roads.
Tools were not used for measurement or neatness.
Other assessment evidence to be collected:
Stage 3: Plan Learning Experiences and Instruction
Learning Activities:
Word splash with the names of the various types of angles, using all kinds that are mentioned in the standards above
After discussing them, have the students draw an angle that represents each of the words on the word splash. Do a
pair and share, to allow each student explain his/her drawing to a partner.
Give a handout with various measurements for one or two angles on it, and have the students state the type of
angle(s) depicted. For example: 25 degrees would be an acute angle. 35 degrees and 55 degrees would be
complementary angles.
Have the students draw the various angles.
Discuss the difference between line, ray and line segment. Discuss parallel, perpendicular and intersecting lines. Have
the students find pictures of the different kinds of lines in magazines and around the building.
Talk about complementary, supplementary and vertical angles. Have the students identify these angles around the
room.
Have students draw examples of complementary, supplementary, vertical, adjacent, corresponding, and right angles
using lines cut by a transversal.
Draw several angles and have students estimate the degrees based on the definitions for acute, obtuse, right, and
straight angles.
Group students into partners and give each set of partners a geometry vocablulary word (point, line, plane, ray, line
segment, angle, supplementary, complementary, vertical angles, adjacents angles, parallel, perpendicular,
transversal). Each group will define their word using a 3-dimensional piece of artwork, a role-playing episode, a
story, etc. Have the students use their creativity. Eg. two students stand directly next to each other without touching
to represent parallel lines. They should explain what parallel lines are and give some main points about them.
Have students practice using complementary and supplementary angles and determining the missing angle if given
the measure for one angle and knowing that the two angles are complementary or supplementary.
Help students differentiate between complementary and supplementary. Allow them to come up with a mnemonic
device of their own; e.g. supplementary angles make Straight angles (notice the S's.)
Give students a list of at least 10 angle measures: 180, 90, 75, 45, 110, 30, 150, 175, 60, 10 for example and have
them create a drawing using each of the angles at least once. They must use a protractor to draw the anlges in order
to make their drawing neat. This is a good way to determine their proficiency with measuring and drawing angles.
Try to have them stay away from drawing houses to allow their creative genius to flow.
Demonstrate how to add angles and how the rotation of geometric figures can show addition. Relate this activity to
complementary and supplementary angles.
Notes:
Conceptmap7
What's my
angle?
Process
Angles and
lines
undef ined terms
undef ined terms
angles
points
names by size
word splash on
angles
names of angles
draw angles
line
of perpendicular
lines
angles and lines
plane
of parallel lines
cut by
transv ersal
of intersecting
lines