Microsoft Word - Differentiated Learning Plan (Parallel and Perpendicular lInes).docxName: Taylor Brockhaus
Unit Topic/Theme: Parallel and Perpendicular Lines
Prentice Hall Mathematics Geometry
Unit Plan Sketch – Part One: Develop KUDo’s for your unit. Use correct format and be comprehensive
in content.
• MA 11.2.1.e Analyze and graph linear functions and inequalities (point-slope form, slope-intercept form, standard form, intercepts, rate of change, parallel and perpendicular lines, vertical and horizontal lines, and inequalities).
• MA 11.3.1.a Know and use precise definitions of ray, line segment, angle, perpendicular lines, parallel lines, and congruence based on the undefined terms of geometry: point, line and plane.
• MA 11.3.1.b Prove geometric theorems about angles, triangles, congruent triangles, similar triangles, parallel lines with transversals, and quadrilaterals using deductive reasoning.
• MA 11.3.1.c Apply geometric properties to solve problems involving similar triangles, congruent triangles, quadrilaterals, and other polygons.
• MA 11.3.2.b Use coordinate geometry to analyze linear relationships to determine if lines are parallel or perpendicular.
• MA 11.3.2.c Given a line, write the equation of a line that is parallel or perpendicular to it.
Know:
• Flow proof
• Isosceles triangle
• Obtuse Triangle
• Parallel Line
• Perpendicular Line
• Transversal
Understand:
• Relationships between angles and lines can be proven using various rules and theorems.
• Geometry can be used to interpret and assess the world around us.
Do:
• Determine the type of triangle and solve for its angles.
• Discover that the three angles of a triangle add up to 180 degrees.
• Write and graph equations of lines in slope-intercept form, point-slope form, and standard form.
• Use algebra to determine whether lines given in standard form are parallel or perpendicular.
• Prove geometric relationships using definitions and theorems.
Unit Plan Sketch - Part Two: Write a short paragraph that explains EVERY teaching day of your unit.
Incorporate any of the differentiated strategies or techniques we have discussed in class or read about
in your textbook as you see fit. You are NOT required to demonstrate differentiation on every day of
your unit, but I should see multiple examples.
Students will complete a pre-assessment for the unit, which will be a tic-tac-toe board. The tic-tac-toe
boards will be tiered. Based on observations of my students throughout the semester thus far, they will
be given a tic-tac-toe board that has differentiated content to test for their readiness. Students will need
to complete one diagonal and one vertical/horizontal line.
Day One: 3.1 Properties of Parallel Lines & 3.2 Proving Lines Parallel: Students will work in mixed-
ability groups in order to complete a Patty Paper Investigation on Special Angles Formed by Parallel
Lines (http://mrthompsonmath.weebly.com/uploads/5/1/5/3/5153251/lesson_2.6.pdf ). This lab activity will introduce students to the term covered in 3.1 (alternative interior angles, same-side angles,
corresponding angles). After completion of the lab, students will receive problems from the textbook to
work through with their group.
Day Two: 3.2 Proving Lines Parallel & 3.3 Parallel Lines and the
Triangle Angle-Sum Theorem: Whole class work through example
problems of solving for missing angles. Next, students will work in
groups by readiness to solve missing angles created on their desks. All
students will be solving to find the same angles. Groups needing extra
support will be given additional information and solve for fewer angles.
Groups needing a challenge will be given the least amount of
information needed to solve the missing angles. (Adapted from
http://middleschoolmathman.blogspot.com/2016/02/angles-triangles-
and-start-of-geometry.html)
After each group solves their missing angles, we will share as a class to see if everyone got it correct. If
groups have varying answers, groups will determine who is right and explain why they have the correct
answer.
Table groups of 4 (mixed ability): Envelope with one of each different type of triangle (equiangular,
acute, right, obtuse). Students will work through the investigation on the Sum of Three Angle Measures
on page 131 in the book (similar to this
http://www.miamiseniorhigh.org/ourpages/auto/2015/8/27/46099032/lgp04bad.pdf) to discover that
the three angles always add to 180 degrees no matter what kind of triangle. Students will then create
their own triangle and complete the investigation on page 133, which looks at exterior angles of
triangles. Students will discover that the exterior angle of the triangle is equal to the sum of two
nonadjacent interior angles. End with a whole class discussion on the findings and example problems
with students working out on the board.
Day Three: 3.4 Polygon Angle-Sum Theorems: Students can choose
between three groups to learn today’s lesson (learning profile):
Group one works individually or with a partner on the polygon angle-
sum investigation. This method reaches the kinesthetic learners in the
class. https://betterlesson.com/lesson/resource/2610693/polygon-
sum-conjecture-investigation?from=lessonsection_narrative.
Group two works with the students to walk through the content.
Students are given the option to use the handout (pictured) to help
organize their notes. (http://atwood202.blogspot.com/2014/01/its-
Group three watches a video that explains the polygon angle-sum
theorem (https://youtu.be/H4akM87VZm8) using EdPuzzle where
students will have to work out problems alongside the video and submit their answers so I can receive
feedback on what they understand and where they still have questions. Providing a video option
reaches the audio and visual learners.
Introduce Polygon Exterior Angle-Sum Theorem as a whole class. Provide students problems to work on
ClassKick where peers can help answer questions, and I can also guide students and answer questions.
ClassKick allows me to see the student’s individual progress as they work so I can note which areas are
causing struggle.
Day Four: 3.5 Lines in Coordinate Plane & 3.6 Slopes of Parallel and Perpendicular Lines: Groups based
off of readiness will work through the lessons via the class-website
(http://mathwithmsbrockhaus.weebly.com). The purple page is for the students needing extra support,
the yellow page is for the students on target, and the blue page is for the students needing a challenge.
The pages are tiered by readiness and content. The pages include videos, graphics, examples and
definitions walking the students through the sections working to reach the various learning profiles in
the classroom. It includes practice problems that the students will be expected to turn in following the
completion of the webpage. Groups are expected to work together to get an answer making sure
everyone in the group understands the content.
Day Five: Finishing up working through the webpage. Introduce the final project, which requires
designing a layout of a city either in pairs or alone. If the student chooses to work with a partner, they
will be expected to have more parts to their city. During the work time, I will be holding times where
groups of students can come alongside with me to work through the areas they may be struggling
together. During this time, I would make the struggling students come and meet with me during these
times, while other students can take advantage of this opportunity if they would like. Students will also
have the option to use a template scaffold to help guide their designing of the city.
Day Six: Workday on final project
Day Seven: Evaluate each other’s final projects.
Concordia University Long Form Lesson Plan
Grade Level: 9 th
• MA 11.2.1.e Analyze and graph linear functions and inequalities (point-slope form, slope-intercept form, standard form, intercepts, rate of change, parallel and perpendicular lines, vertical and horizontal lines, and inequalities).
• MA 11.3.2.b Use coordinate geometry to analyze linear relationships to determine if lines are parallel or perpendicular.
• MA 11.3.2.c Given a line, write the equation of a line that is parallel or perpendicular to it.
Name of Lesson: 3.5 Lines in Coordinate Plane & 3.6 Slopes of Parallel and Perpendicular Lines
I. Goal: Students will use point-slope formula, standard form of a line, and slope-intercept form to graph and write equations of parallel and perpendicular lines.
Required Adaptations/Modifications:
II. Objectives:
In tiered groups, students will solve problems on graphing and equations of parallel and perpendicular lines with 90% proficiency.
Required Adaptations/Modifications:
IV. Integrated Technology:
Computers/Tablets for groups to work through the Website (preferably one device per student) PowerPoint SlidesàSMART Board
Required Adaptations/Modifications:
V. Materials:
Computer/Tablet Paper Pencil PowerPoint with Examples of Slope SMART Board
Required Adaptations/Modifications:
VI: Procedure:
Set / Hook: Using the SMART Board, project slides with examples of slope in the world. Students will create a “+” sign with their arms if the slope is positive, or a “-“ sign with their arms if it is negative. (This will be a quick review of positive and negative slope. The purpose of this activity is to engage the students in examples of slope in the real world.) **PowerPoint can be viewed on class website home page**
Required Adaptations/Modifications:
**While they are separate groups, I encourage them to ask the other groups if they have a question** Purple (extra support):
Transition “Today and tomorrow we will be working in our Blue, Purple, and Yellow groups to work through the content for sections 3.5 and 3.6. On the board I have listed your group members, please find your groups. Once you have found your group members, go to our class website and find group’s webpage and work through the content together as a group. Each member should work out each practice problem on a piece of paper that they will be turning in at the end of these sections.” Main Lesson: Students will be working in tiered groups for the content of 3.5 and 3.6. I have created a website http://mathwithmsbrockhaus.weebly.com that has the content each group will be working through. Groups have been tiered by readiness and content. The websites include a variety of pictures, videos, and examples to reach the different learning profiles in the class. Transition “Let’s pause on our progress on the websites, and look back at the pictures we looked at the beginning of class and see if we can determine the slope of the object in the picture.” Conclusion: Show the pictures from earlier. Add a grid overlay over the pictures. Have one student come up and solve for the slope while others try to work it out on their paper. Have another student use one of the equations they worked with today to write an equation of the line while the others work it out at their desk. On the way out the door have students turn in their work for the problems they got completed in class.
Group 1 Group 2
The other 12 students (split into three groups of 4)
Blue (challenge):
Scott Emma Samantha Brock Liz
VII. Assessment: Teacher observation Collecting their work for the problems they completed in class (I can see if some students look confused in some areas, how far students got on their websites, and which groups I might need to support more tomorrow)
Required Adaptations/Modifications:
Create the Teaching Tools: Copy/Paste/Create student teaching tools required for the long form lesson
plan day.
See http://mathwithmsbrockhaus.weebly.com
Create the Assessments: Copy/Paste/Create two forms of assessment below. The assessments can
come from any day in your unit plan sketch.
Circle two angles that
Complete this
y=2x-5 & y-2x=3
angle a
y=3/2x+2 & y= -2/3+7
How many triangles are formed by this
polygon?
Complete this
equation: < d= < ? +< ?
Find the slope of the line
(4, -6) (7,2). Is the slope positive
or negative?
missing angle?
polygon?
to each other.
y=2x-5.
of 2.
Write a line with a slope perpendicular
to y=3/2x+2
polygon. (Hint: find how many
triangles there are)
1 2 3 4
5 6 7 8
Build Your Own City
You’ve been elected Mayor! Your goal is to design your own city. You may draw it on graph paper, or create it out of any material of your choice. You can design your city digitally using Dynamic Geometry software such as Geogebra®, Desmos®, or Geometer’s Sketchpad®.
First create a rough draft on graph paper. The rough draft should include the angle measures of every angle. Please include your work. Approve your rough draft with the teacher and begin your final copy.
*On a separate sheet of paper, write a paragraph that summarizes the angle measure relationships between pairs of corresponding angles, same-side interior angles, alternate interior angles, alternate exterior angles, and same-side exterior angles created when parallel lines are cut by a transversal. For example, you know that corresponding angles are congruent when parallel lines are cut by a transversal. Use correct spelling and grammar. (If done with a partner, each student needs to submit his or her own paragraph)
Include the following in your city:
• A city name. • Give each street a name. • Give each location a name (ex. campground named Lake Forest) • Write the equation of street lines (one equation per street) on each street • At least 5 streets must be parallel. • At least 5 streets must be transversals.
o The city inspector says one MUST be perpendicular to your parallel streets.
•  4 Stop Signs at vertical angles. • A Gas station that is at the alternate interior angle of a restaurant. • A church at a corresponding angle with a school. • 4 campgrounds at 4 adjacent interior angles. • A forest or lake at 2 surrounding exterior angles adjacent to the campgrounds. • A shopping center that is at a supplementary angle with a movie theater. • A post office at the alternate exterior angle of a shipping company. • A courthouse and police station at vertical angles.
If completing with a partner, include the above list plus the following:
• Add five more streets (can be parallel, perpendicular, or transversal) • A school and your house at complementary angles. • A library and recreation center at alternate exterior angles. • A swimming pool at a right angle. • An airport at a same-side exterior angle to a parking garage.
Adapted from: https://1ntegrationbyparts.files.wordpress.com/2014/10/projectcity.pdf http://www.peoriapublicschools.org/cms/lib2/IL01001530/Centricity/Domain/4566/Build%20Your% 20Own%20City.pdf
Name: _______________________________
Streets:
___ City includes at least 5 parallel streets (5 pts.) ___ A correct equation is written for each street (10 pts.)
___ City includes at least 5 transversal streets, one of which is perpendicular (5 pts.)
Locations: (5 pts. each)
___ 4 Stop Signs at vertical angles.
___ A Gas station that is at the alternate interior angle of a restaurant.
___ A church at a corresponding angle with a school.
___ 4 campgrounds at 4 adjacent interior angles.
___ A forest or lake at 2 surrounding exterior angles adjacent to the campgrounds.
___ A shopping center that is at a supplementary angle with a movie theater.
___ A post office at the alternate exterior angle of a shipping company.
___ A courthouse and police station at vertical angles.
Other:
___ Your city must be titled with a name (1 pts.) ___ All streets and buildings must be clearly labeled (5 pts.) ___ Your city must be neat and be colored (4 pts.)
___ Every angle measure is recorded (15 pts.) ___ Paragraph is written summarizing angle measure relationships (15 pts.)
___ Total 100 pts.
Individual
Name: _______________________________
Streets:
___ City includes at least 5 parallel streets (5 pts.) ___ A correct equation is written for each street (10 pts.)
___ City includes at least 5 transversal streets, one of which is perpendicular (5 pts.)
___Add five more streets (can be parallel, perpendicular, or transversal) (5 pts.)
Locations: (5 pts. each)
___ 4 Stop Signs at vertical angles.
___ A Gas station that is at the alternate interior angle of a restaurant.
___ A church at a corresponding angle with a school.
___ 4 campgrounds at 4 adjacent interior angles.
___ A forest or lake at 2 surrounding exterior angles adjacent to the campgrounds.
___ A shopping center that is at a supplementary angle with a movie theater.
___ A post office at the alternate exterior angle of a shipping company.
___ A courthouse and police station at vertical angles.
___A school and your house at complementary angles.
___A library and recreation center at alternate exterior angles.
___A swimming pool at a right angle.
___An airport at a same-side exterior angle to a parking garage.
Other:
___ Your city must be titled with a name (1 pts.) ___ All streets and buildings must be clearly labeled (5 pts.) ___ Your city must be neat and be colored (4 pts.)
___ Every angle measure is recorded (15 pts.) ___ Individual paragraph is written summarizing angle measure relationships (15 pts.)
___ Total 125 pts.
With a partner
(Keep this included in your final submission)
KUDo’s follow correct format, provide clear direction for the unit, and are comprehensive.
/10
The unit plan sketch offers a clear understanding of content, teaching strategies, and varied uses of differentiation. Brief paragraphs are included for each teaching day.
/10
The lesson plan includes all listed components with a clear connection from standard to objective to assessment. Instructional plans are age appropriate, strategic, and engaging.
/10
The lesson plan/unit sketch demonstrates differentiated techniques that addresses specific learning populations.
• The needs of the gifted and high achievers were addressed. • The needs of the students with IEPs were addressed. • The needs of the 5 low performing students were addressed. • The needs of the student with average skills/varied profile were
addressed.
/20
All teaching tools required to teach the long form lesson plan day are included and are professionally prepared/shared.
/10
Two assessments were created to address learner growth and/or proficiency. The evaluations include two different aspects of either pre-assessment, formative assessment, and/or summative assessment.
/10