EMS 8th Grade Math Department / Pythagorean Theorem / October 26-Nov 5
Math Florida Standard(s)
Benchmarks, Descriptions
and DOK levels / MAFS.8.G.2.6 (DOK 3): Explain a proof of the Pythagorean Theorem and its converse.
Define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a & b, hypotenuse, sides, right angle, converse, base, height, proof.
Identify the legs and hypotenuse of a right triangle.
Explain a proof of the Pythagorean Theorem.
MAFS.8.G.2.7 (DOK 2): Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Recall the Pythagorean Theorem and its converse.
Apply Pythagorean Theorem in solving real-world problems dealing with two and three dimensional shapes.
Solve basic mathematical Pythagorean Theorem problems and its converse to find missing lengths of sides of triangles in two and three dimensions.
MAFS.8.G.2.8 (DOK 2): Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Recall the Pythagorean Theorem and its converse.
Determine how to create a right triangle from two points on a coordinate graph.
Use the Pythagorean Theorem to solve for the distance between the two points.
Learning Goal / Students will understand and be able to apply the Pythagorean Theorem to solve real-world and mathematical problems in 2 and 3 dimensions
Essential Question(s) / · How can the Pythagorean Theorem be applied to the coordinate plane?
Assessments / Pre-Assessments / Class Discussion on Pythagorean Theorem
Formative Assessments / Guided Practice ,Learning Logs
Summative Assessments / Independent Practice, Quizzes, Word Problem Project. End of Chapter Tests
Progress Monitoring/ Feedback Loop / Must show mastery or cannot move on to the next step.
Re test scores under 70
Higher Order Question(s) / How can the Pythagorean Theorem be used in real world situations?
Why does the Pythagorean Theorem work?
How can you create a right triangle from two points on a coordinate graph?
What conclusions can we draw from this?
How can we verify if a triangle is a right triangle?
Key Vocabulary / Pythagorean Theorem, Hypotenuse, Leg, Square Root , Right Angle, Proof, Converse, Pythagorean Triplets
Monday,
Daily Objective / · Teacher Work day
BELL RINGER
( 5 minutes) / ·
I DO: / ·
WE DO: / ·
YOU DO: / ·
Homework / ·
EXIT TICKET:
(5 minutes) / ·
Tuesday, October 27 / Pythagorean Theorem / Rigor Level: DOK 2
6th Period Fills Out PSAT Answer Blank Form
Pre-Algebra Daily Agenda
Daily Objective / · Students will learn to find the lengths of right triangles using the Pythagorean theorem
BELL RINGER
( 5 minutes) / · Introduce personalized learning and explain the reason for it.
I DO: / · Introduce Pythagorean Theorem using the Cornell notes
WE DO: / · Take Cornell Notes and complete guided practice.
YOU DO: / · Rank your progress on Pythagorean theorem
Homework / · Put your Pythagorean Theorem notes in your notebook
EXIT TICKET:
(5 minutes) / · What is Pythagorean Theorem?
Wednesday, October 28 / Pythagorean Theorem / Rigor Level: DOK 2
Pre-Algebra Daily Agenda
Daily Objective / · Students will learn to find the lengths of right triangles using the Pythagorean theorem
BELL RINGER
( 5 minutes) / · Read the daily agenda and decide which route you are going to take.
I DO: / · Pass out folders and monitor the students
WE DO: / · Unpacking the standard.
· Review Cornell notes
· Guided Practice Algebra 1 book Page
YOU DO: / · Self monitor and self pace.
Homework / · Complete anything I have not completed.
EXIT TICKET:
(5 minutes) / · How do I solve for the hypotenuse using Pythagorean Theorem?
Thursday October 29 / Pythagorean Theorem / Rigor Level: DOK 2
Pre-Algebra Daily Agenda
Daily Objective / · Students will learn to find the lengths of right triangles using the Pythagorean theorem
BELL RINGER
( 5 minutes) / · Read the daily agenda and decide which route you are going to take. People behind will go with Mr. Johnson to unpack the standard or do
I DO: / · Pass out folders and monitor the students
WE DO: / · Those not on pace – Rewatch Khan video and stay after to work with Eichelberger OR Work with Mr. Johnson
· Those on pace choose a path.
· A) Independent Practice on Khan Academy ( MUST Show Mastery )
· B) Independent Practice with Worksheet. (Must show 80 % mastery
YOU DO: / · Self monitor and self pace.
Homework / · Complete days tasks that are uncompleted.
EXIT TICKET:
(5 minutes) / · Write an example of a Pythagorean Theorem problem and explain how to solve it.
Friday, October 30 / Pythagorean Theorem / Rigor Level: DOK 3
Pre- Algebra Daily Agenda
Daily Objective / · Students will learn to find the lengths of right triangles using the Pythagorean theorem
BELL RINGER
( 5 minutes) / · Read the daily agenda and decide which route you are going to take. People behind will go with Mr. Johnson work on independent practice
I DO: / · Pass out folders and monitor the students
WE DO: / · Off Pace; Work with Mr. Johnson on unpacking the standard or guided Practice
· Off pace Work with Mrs. Eichelberger on independent practice
· A. On Pace Watch Khan video on Pythagorean Theorem word problems and take Cornell Notes.
· AND
· B)Guided Practice on Pythagorean Theorem Word Problems
YOU DO: / · Self monitor and self pace.
Homework / · Complete tasks that are uncompleted.
EXIT TICKET:
(5 minutes) / · Explain how to pick apart a word problem and use Pythagorean Theorem to solve it.
Note: Learning Scales, Accommodations, and Math Practice Standards are below.
Scale / Learning Goals Scale:Pythagorean Theorem
4.0 / Ø Apply knowledge of the Pythagorean Theorem to real-world situations.
3.5 / In addition to 3.0 skills, I can do some of the 4.0 skills.
3.0
(GOAL)
With no help, I can do all these skills. / Ø Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in three dimensions.
Ø Explain a proof of the converse of the Pythagorean Theorem.
2.5 / In addition to all 2.0 skills, I can do some of the 3.0 skills.
2.0
With no help, I can do all these skills. / Ø Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two dimensions.
Ø Explain a proof of the Pythagorean Theorem.
Ø Apply the Pythagorean Theorem to find the distance between two points on a coordinate plane.
Ø Identify key vocabulary including Pythagorean Theorem, sides, hypotenuse, right angles, base, height, proof, right triangles, square roots, and converse.
1.5 / On my own, I can do some of the 2.0 and 3.0 skills.
1.0 / With help, I can do some of the 2.0 and 3.0 skills.
0.5 / With help, I can do some of the 2.0 skills.
0.0 / Even with help, I have no success.
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 Questioning in Classes
• Costa’s Level 1: Students find the answers right there in the text.
• Costa’s Level 2: Students must figure out the answer from information in the text.
• Costa’s Level 3: Students apply what they have learned or use what they have learned to evaluate or create. / 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.