Download Model Mathematics Curriculum Unit Implementation

Model Mathematics Curriculum
Unit Implementation Plan
UNIT COVER SHEET
Name:
_​
Kayleen Loch​
_____
Unit Title:
Math 1 Unit 2: Geometry Lesson 2 Theorems of Lines & Angles
Dates of Instruction:
Grade Level: _​
Geometry​
__
_____​
late September- early October​
_________
Timeframe (Add lessons and space as needed):
Unit Timeframe:
____​
6 - 7 class periods​
__________________________________
Lesson 1 Title:
Lesson 2 Title:
_​
Let’s Move​
__________
_​
Let’s Move​
__________
Lesson 3 Title:
Vocab Graphic Organizer Timeframe: ____​
1 day​
_______
Lesson 4 Title:
_​
Build Your Own City​
___ Timeframe: ____​
1 to 3 days​
___
Lesson 5 Title:
_​
Build Your Own City​
___ Timeframe: ____​
1 to 3 days​
___
Lesson 6 Title:
Lesson 7 Title:
_​
Build Your Own City​
___ Timeframe: ____​
1 to 3 days​
___
_​
Assessment_______​
___ Timeframe: ____​
1 day _____​
___
Timeframe: ____​
1 to 2 days​
____
Timeframe: ____​
1 to 2 days​
____
Standards Alignment
Content Standards:
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent.
Standards for Mathematical Practice:
*MP 1: Make sense of problems and persevere in solving them. ​
Students will use experiences in their lives to
visualize examples of key vocabulary.
*MP 3: Construct viable arguments and critique the reasoning of others.​
Students will provide non-examples
of key vocabulary.
MP 5: Use appropriate tools strategically. ​
Students will use rulers, protractors, and/or Geogebra to help
make connections between angles, parallel lines, and their transversals.
*MP 6: Attend to precision.​
Students will be mathematically concise in their definitions, pictures, examples,
and non-examples.
MP 7: Look for and make use of structure. ​
Students will construct and manipulate lines to gain insight on how
their intersections form special angles.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson __________​
1​
___________
Objectives
Students will deepen their understanding and reasoning regarding lines and angles
kinesthetically.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line,
and distance around a circular arc.
MP 3: Construct viable arguments and critique the reasoning of others. Students
will look at various pre-images and images and identify key vocabulary words that
correspond to them.
Painters tape & numbers on small pieces of paper, student note
sheet(Let’s Move)
Mathematical
Practices
Materials
Preparation
Using the masking tape, create two parallel lines and a transversal on the
floor. Tape the small pieces of paper into each of the angles.
Lesson Activities
1.Call out the items listed in the teacher notes and ask students to stand in the
different locations. Ask students to persevere by seeing if they can identify the
angles without telling them what they are. After students have modeled the items
and a discussion has been held, ask them to return to their seats and fill out the
table.
2.Lead the discussion about what transformations prove the different angles are
congruent.
3.Put students into pairs/groups to complete the information for the second
diagram. Emphasize the sum of supplemental angles is 180 degrees.
4.Lead the discussion on the conclusion questions. Let the students brainstorm their
ideas before discussing it as a whole class (this is a pre-view of parallelograms still to
come).
Assessments
Discussion- group and class; Let’s Move
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will look at various pre-images and images and identify key vocabulary words that correspond to them.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson __________​
2​
___________
Objectives
Students will deepen their understanding and reasoning regarding lines and angles
kinesthetically.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
MP 3: Construct viable arguments and critique the reasoning of others. Students
will look at various pre-images and images and identify key vocabulary words that
correspond to them.
Painters tape & numbers on small pieces of paper, student note
sheet(Let’s Move)
Mathematical
Practices
Materials
Preparation
Using the masking tape, create two parallel lines and a transversal on
the floor. Tape the small pieces of paper into each of the angles.
Lesson Activities
1.Call out the items listed in the teacher notes and ask students to stand in the
different locations. Ask students to persevere by seeing if they can identify the
angles without telling them what they are. After students have modeled the items
and a discussion has been held, ask them to return to their seats and fill out the
table.
2.Lead the discussion about what transformations prove the different angles are
congruent.
3.Put students into pairs/groups to complete the information for the second
diagram. Emphasize the sum of supplemental angles is 180 degrees.
4.Lead the discussion on the conclusion questions. Let the students brainstorm
their ideas before discussing it as a whole class (this is a pre-view of parallelograms
still to come).
Assessments
Discussion- group and class; Let’s Move
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will look at various pre-images and images and identify key vocabulary words that correspond to them.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson ___​
3​
__________________
Objectives
Students will deepen their understanding of key vocabulary in a real-world
context.
Content
Standards
Materials
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line,
and distance around a circular arc.
*MP 1: Make sense of problems and persevere in solving them. Students
will use experiences in their lives to visualize examples of key vocabulary.
*MP 3: Construct viable arguments and critique the reasoning of others.
Students will provide non-examples of key vocabulary.
*MP 6: Attend to precision. Students will be mathematically concise in
their definitions, pictures, examples, and non-examples.
Vocabulary Graphic Organizer
Preparation
Copy Vocabulary Graphic Organizer
Lesson Activities
1. Pass out “Vocabulary Graphic Organizer”.
2. Go through an example together and give students time to work
independently.
Discussion-group and in class; Vocab Graphic Organizer
Mathematical
Practices
Assessments
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will use experiences in their lives to visualize examples of key vocabulary. Students will provide
non-examples of key vocabulary. Students will be mathematically concise in their definitions, pictures, examples, and
non-examples.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson ______​
4​
_______________
Objectives
Students will make connections about parallel lines, transversals and
angles using visuals (drawings, diagrams, Geogebra) as tools.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line,
and distance around a circular arc.
MP 5: Use appropriate tools strategically. Students will use rulers,
protractors, and/or Geogebra to help make connections between angles,
parallel lines, and their transversals
MP 6: Attend to precision. Students will need to make sure their design
meets ALL of the requirements by making modifications and additions as
necessary
MP 7: Look for and make use of structure. Students will construct and
manipulate lines to gain insight on how their intersections form special
angles
“Build Your Own City”
Geogebra OR Art Supplies
Mathematical
Practices
Materials
Preparation
Copy “Build Your Own City”, layout art supplies or secure access to a lab
for Geogebra
Lesson Activities
1. Students should be familiar with Dynamic Geometry Software. If not,
give them a day to play around with it.
2. If you are not using technology, than provided students with the
necessary materials to design their city.
3. Distribute the “Build Your Own City” sheet and explain the process.
4. Use the “Build Your Own City – Sample Key” as an example to clarify
directions.
5. Depending on how creative students take, this could easily last up to 3
class periods.
6. As students work, monitor their progress and point out areas they may
want to re-evaluate. Remind the students to include all the necessary
landmarks. Students may want to check them off as they complete them.
7. Have students print off cities and display them around the room (with
the directions) – these will need to be covered or removed during the
assessments.
Discussion, Cities(projects) themselves (Did the students properly place
objects?
Assessments
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will use rulers, protractors, and/or Geogebra to help make connections between angles, parallel lines, and
their transversals. Students will need to make sure their design meets ALL of the requirements by making
modifications and additions as necessary. Students will construct and manipulate lines to gain insight on how their
intersections form special angles.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson ______​
5​
_______________
Objectives
Students will make connections about parallel lines, transversals and
angles using visuals (drawings, diagrams, Geogebra) as tools.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
MP 5: Use appropriate tools strategically. Students will use rulers,
protractors, and/or Geogebra to help make connections between
angles, parallel lines, and their transversals
MP 6: Attend to precision. Students will need to make sure their design
meets ALL of the requirements by making modifications and additions
as necessary
MP 7: Look for and make use of structure. Students will construct and
manipulate lines to gain insight on how their intersections form special
angles
“Build Your Own City”
Geogebra OR Art Supplies
Mathematical
Practices
Materials
Preparation
Copy “Build Your Own City”, layout art supplies or secure access to a
lab for Geogebra
Lesson Activities
1. Students should be familiar with Dynamic Geometry Software. If not,
give them a day to play around with it.
2. If you are not using technology, than provided students with the
necessary materials to design their city.
3. Distribute the “Build Your Own City” sheet and explain the process.
4. Use the “Build Your Own City – Sample Key” as an example to clarify
directions.
5. Depending on how creative students take, this could easily last up to
3 class periods.
6. As students work, monitor their progress and point out areas they
may want to re-evaluate. Remind the students to include all the
necessary landmarks. Students may want to check them off as they
complete them.
7. Have students print off cities and display them around the room (with
the directions) – these will need to be covered or removed during the
assessments.
Discussion, Cities(projects) themselves (Did the students properly place
objects?)
Assessments
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will use rulers, protractors, and/or Geogebra to help make connections between angles, parallel lines, and
their transversals. Students will need to make sure their design meets ALL of the requirements by making
modifications and additions as necessary. Students will construct and manipulate lines to gain insight on how their
intersections form special angles.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson ______​
6​
_______________
Objectives
Students will make connections about parallel lines, transversals and
angles using visuals (drawings, diagrams, Geogebra) as tools.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
MP 5: Use appropriate tools strategically. Students will use rulers,
protractors, and/or Geogebra to help make connections between
angles, parallel lines, and their transversals
MP 6: Attend to precision. Students will need to make sure their design
meets ALL of the requirements by making modifications and additions
as necessary
MP 7: Look for and make use of structure. Students will construct and
manipulate lines to gain insight on how their intersections form special
angles
“Build Your Own City”
Geogebra OR Art Supplies
Mathematical
Practices
Materials
Preparation
Copy “Build Your Own City”, layout art supplies or secure access to a
lab for Geogebra
Lesson Activities
1. Students should be familiar with Dynamic Geometry Software. If not,
give them a day to play around with it.
2. If you are not using technology, than provided students with the
necessary materials to design their city.
3. Distribute the “Build Your Own City” sheet and explain the process.
4. Use the “Build Your Own City – Sample Key” as an example to clarify
directions.
5. Depending on how creative students take, this could easily last up to
3 class periods.
6. As students work, monitor their progress and point out areas they
may want to re-evaluate. Remind the students to include all the
necessary landmarks. Students may want to check them off as they
complete them.
7. Have students print off cities and display them around the room (with
the directions) – these will need to be covered or removed during the
assessments.
Discussion, Cities(projects) themselves (Did the students properly place
objects?)
Assessments
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will use rulers, protractors, and/or Geogebra to help make connections between angles, parallel lines, and
their transversals. Students will need to make sure their design meets ALL of the requirements by making
modifications and additions as necessary. Students will construct and manipulate lines to gain insight on how their
intersections form special angles.
Model Mathematics Curriculum
Unit Implementation Plan
DAILY PLAN For Lesson _________​
7​
____________
Objectives
The focus is to assess student mastery of reasoning and proof in regards
to lines and angles.
Content
Standards
G.CO.9​
Prove theorems about lines and angles. ​
Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent;
G.CO.1​
Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line,
and distance around a circular arc.
Mathematical
Practices
Materials
MP 3: Construct viable arguments and critique the reasoning of others.
Students will provide reasoning for angle relationships of parallel lines
and transversals
MP 6: Attend to precision. Students will be exact in identifying angle pairs
given any diagram/picture
Lesson 2 Assessment
Preparation
Copy Lesson 2 Assessment
Lesson Activities
1. Distribute the Lesson 2 Assessment. Explain expectations and allow
students ample time to complete the assessment.
Ensure that the directions are not a factor in the students’ success.
Instructional practices should mirror the language and rigor of the
assessment practices.
Assessments
Lesson 2 Assessment
In what ways will you intentionally emphasize the development of student mathematical practices
through this lesson?
Students will provide reasoning for angle relationships of parallel lines and transversals. Students will be exact in
identifying angle pairs given any diagram/picture.