Unit 11 Geometric Relationships

Pre-Algebra
EMS 8th Grade Math Department / Unit 11: Geometric Relationships / Dates: March 7th – March 18th
Math Florida Standard(s)
Benchmarks, Descriptions
and DOK levels / MAIN STANDARD
*MAFS.8.G.1.5 (DOK 3): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For examples, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
REVIEW STANDARD
MAFS.8.EE.3.7 (DOK 2): Solve linear equations in one variable.
a. Solve linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show these possibilities is the case by successively transforming the given equation into equivalent forms, using algebraic properties.
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.
Learning Goal / Students will use exploration and deductive reasoning to determine relationships that exist between a) angle sums and exterior angle sums of triangles, b) angles created when parallel lines are cut by a transversal, and c) the angle – angle criterion for similarity of a triangle.
Essential Question(s) / How are geometric figures and properties of parallel lines used to solve problems involving logical reasoning? How do you classify angles of parallel lines crossed by a transversal? How do you justify the exterior angles of a triangle?
Assessments / Pre-Assessments
Formative Assessments
Summative Assessments
Progress Monitoring/ Feedback Loop
Higher Order Question(s) / Why is the figure similar? Why are the angles congruent? How can you describe the image? Why does the sum of a triangle’s interior angles equal 180 degrees? How do you know the figures are congruent?
Key Vocabulary / Similar Figures, Transversals, Parallel Lines, Perpendicular Lines, Corresponding Sides, Corresponding Angles, Perpendicular Lines, Alternate Interior Angles, Alternate Exterior Angles, Adjacent Angles.
Coefficient, Variable, Algebraic Expression, Constant, Evaluate, Substitute, Product, Quotient, Sum, Difference, Equation, Inverse Operation
Monday, March 7th, 2016 / Review Systems of Equations / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will review for system test using KaHoot it.

BELL RINGER
( 5 minutes) /
  • 4 system sample problems

I DO: /
  • Assess and Monitor student tasks

WE DO: /
  • Review for system test using Kahoot it

YOU DO: /
  • Study notes for system test

EXIT TICKET:
(5 minutes) /
  • What is the skill you have the most trouble with on the system test? How can you master it?

Tuesday, March 8th, 2016 / Assess Systems / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students take the system test and demonstrate their knowledge of the system unit

BELL RINGER
( 5 minutes) /
  • A system problem

I DO: /
  • Assess and Monitor student tasks

WE DO: /
  • System Discussion
  • System test

YOU DO: /
  • Monitor yourself on the learning scale

EXIT TICKET:
(5 minutes) /
  • Relax new nit coming

  • How did you do on the system test?

Wednesday, March 9th, 2016 / Computer Practice for FSA / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will take the practice FSA which explains questions and the different ways to answer them in the computer lab using computers

BELL RINGER
( 5 minutes) /
  • None

I DO: /
  • Read the instructions

WE DO: /
  • Follow the instructions and practice the practice test

YOU DO: /
  • Pay attention

EXIT TICKET:
(5 minutes) /
  • None

  • DO I need to go over anything on the practice test?

Thursday, March 10th, 2016 / Unpack Standards and Pre-Assess / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will unpack the standard in the geometric relationship unit

BELL RINGER
( 5 minutes) /
  • What do you know about angles? Complete a circle map and write three sentences

I DO: /
  • Assess and monitor

WE DO: /
  • Unpack the standards on the Circle map.
  • Reviewed Angles relationships learned earlier in the year

YOU DO: /
  • Monitor yourself on the learning scale

EXIT TICKET:
(5 minutes) /
  • What is the unit going to be about?

Friday, March 11th, 2016 / Parallel Lines Cut by a Transversal / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will review geometric relationships when two parallel lines are cut by a transversal. They will review the angle pari names, and the congruent and supplementary angles

BELL RINGER
( 5 minutes) /
  • What is a transversal?

I DO: /
  • Monitor and assess

WE DO: /
  • Discuss geometric relationships
  • Worksheet on geometric relationships

YOU DO: /
  • Assess and monitor yourself on the learning scale

Homework /
  • Study geometric relationships

EXIT TICKET:
(5 minutes) /
  • Illustrate a pair of geometric relationships and tell me what you know about it.

Monday , March 14 / Parallel Lines Cut by a Transversal / DOK 3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will put algebraic equations into geometric relationships to solve for x and determine the angles measure using Cornell notes, guided practice and independent practice.

BELL RINGER
( 5 minutes) /
  • Sample problems one congruent and one supplementary

I DO: /
  • Assess and Monitor

WE DO: /
  • Class Discussion on geometric relationships
  • Guided practice on geometric relationships

YOU DO: /
  • Rank yourself on the learning scale

Homework /
  • Independent practice on geometric relationships

EXIT TICKET:
(5 minutes) /
  • How do you set up an equation using geometric relationships. Explain and illustrate

Tuesday, March 15 / Justify the Triangle Sum theorem / DOK 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will justify triangle sum theorem and use ti to determine the interior measures of an unknown angles in a triangle using Cornell Notes, guided practice, and independent practice They will also learn the to use the exterior angle theorem.

BELL RINGER
( 5 minutes) /
  • Why do all the angles in a triangle equal 180 degrees.

I DO: /
  • Assess and Monitor

WE DO: /
  • Justify the Triangle Sum theorem
  • Cornell notes on triangles
  • Guided practice finding the angle measure

YOU DO: /
  • Monitor yourself on the learning scale

Homework /
  • Independent practice finding the angles measure

EXIT TICKET:
(5 minutes) /
  • Create a triangle with an unknown angle measure and find the measure.

Wednesday, March 16 / Algebraically Find the Missing Triangle Measure / DOK 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to find the measure of an angles when they are expressed with algebraic expressions.

BELL RINGER
( 5 minutes) /
  • 2 triangle problems

I DO: /
  • Assess and Monitor

WE DO: /
  • Class Discussion on solving angles with algebraic expressions
  • Guided practice on solving angles with algebraic expressions

YOU DO: /
  • Assess and monitor yourself on the learning scale

Homework /
  • Independent practice on solving angles with algebraic expressions

EXIT TICKET:
(5 minutes) /
  • How do you set up an equation when the interior angles in a triangle are expressions? How do you solve them?

Thursday, March 17 / Angle Angle Criterion / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will study the angle angles criterion and see how it affects similar triangles using Cornell notes, guided practice, and independent practice. .

BELL RINGER
( 5 minutes) /
  • Sample problems of triangles and parallel lines cut by a transversal

I DO: /
  • Assess and Monitor

WE DO: /
  • Cornell Notes Angle Angle Criterion
  • Guided Practice with Angle Angles Criterion

YOU DO: /
  • Assess and monitor yourself on the learning scale

Homework /
  • Independent practice on Angle Angle Criterion.

EXIT TICKET:
(5 minutes) /
  • How does angle angle criterion help us determine angle and side lengths? Describe and illustrate.

Friday, March 18th, 2016 / Test Geometric Relationships / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will show their mastery on the geometric relationship unit by taking a pencil and paper test.

BELL RINGER
( 5 minutes) /
  • 3 same questions

I DO: /
  • Assess and monitor

WE DO: /
  • Class discussion on Geometric relationships

YOU DO: /
  • Assess and monitor yourself on the learning scale

Homework /
  • Have a great spring break

EXIT TICKET:
(5 minutes) /
  • How did you do on the geometric relationship unit

Note: Learning Scales, Accommodations, and Math Practice Standards are below.

Learning Goal Scale
Level / Date / Skill
4 / □I can apply geometric relationships of angles and triangles to real-world situations.
3 / □I can justify that the sum of interior angles of a triangle equals 180 degrees.
□I can justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.
□I can use the angle-angle criterion to probe for similarity among triangles.
2 / □I can algebraically find the missing angle measure of a triangle.
□I can algebraically find the measure of angles created when a parallel line is cut by a transversal.
1 / □I can define similar triangles.
□I can define and identify transversals.
□I can identify and name angles created when a parallel line is cut by a transversal.
WICR Strategies used during each unit.
Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process Writing
• using a rubric as evaluation
On-Demand/Timed-Writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective Writing
• students write about what they have learned and what they still need / Higher-Level Questioningin Classes
• Costa’s Level 1: Studentsfind the answers right therein the text.
• Costa’s Level 2: Studentsmust figure out the answerfrom information in thetext.
• Costa’s Level 3: Studentsapply what they havelearned or use what theyhave learned to evaluate orcreate. / Think Pair Share
Sharing Ideas With a Partner or in a Group
Carousel or Gallery Walk
Problem Solving in Groups
Projects in Groups / Before Reading Activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During Reading Activities
• marking the text
• Cornell notes
• graphic organizers
After Reading Strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
  • Read directions for the student
  • Check for understanding
  • Allow to leave class for assistance
  • Extra time for exams
  • Daily agenda
/
  • Allow student time to step out to de-escalate
  • Testing in small groups
  • Use of a planner/binder for organization
  • English Language Dictionary
/
  • Extended time on assignments =1 day
  • Preferential seating
  • Written direction given
  • Break directions into chunks
/
  • Read Aloud to Students
  • Visual manipulatives
  • Cooperative Learning,
  • Vocabulary, Description, Introduction,
.
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make Sense of Problems and Persevere in Solving Them
• Make a plan! • Try different approaches when your problem is hard. • Solve your problem in more than one way. • Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason Abstractly and Quantitatively
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.
MAFS.K12.MP.3.1 Construct Viable Arguments and Critique the Reasoning of Others.
• Explain both what to do and why it works. • Work to make sense of others’ mathematical thinking.
MAFS.K12.MP.4.1 Model with Mathematics
• Apply math to real-world situations. • Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate Tools Strategically
• Choose appropriate tools for your problem. • Use mathematical tools correctly and efficiently. • Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to Precision
• Communicate your mathematical thinking clearly and precisely. • Use the level of precision you need for your problem. • Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and Make Use of Structure
• Find, extend, analyze, and create patterns. • Use patterns and structures to solve problems.
MAFS.K23.MP.8.1 Look for and Express Regularity in Repeated Reasoning
• Use patterns and structures to create and explain rules and shortcuts. • Use properties, rules, and shortcuts to solve problems. • Reflect on your thinking before, during, and after you solve a problem.