ALEX Classroom Resource

  

Grade 8 Mathematics Module 2, Topic D: Pythagorean Theorem

  Classroom Resource Information  

Title:

 Grade 8 Mathematics Module 2, Topic D: Pythagorean Theorem

URL:

 https://www.engageny.org/resource/grade-8-mathematics-module-2-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Optional Module 2, Topic D begins the learning of the Pythagorean Theorem. Students are shown the “square within a square” proof of the Pythagorean Theorem. The proof uses concepts learned in previous topics of the module, i.e., the concept of congruence and concepts related to degrees of angles. Students begin the work of finding the length of a leg or hypotenuse of a right triangle using a2 + b2 = c2. Note that this topic will not be assessed until Module 7. 

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
26. Informally justify the Pythagorean Theorem and its converse.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use mathematical reasoning and vocabulary to verbally explain the Pythagorean Theorem and its converse.
Teacher Vocabulary:
  • Pythagorean Theorem
  • Converse
Knowledge:
Students know:
  • the Pythagorean Theorem
Skills:
Students are able to:
  • Use mathematical reasoning and vocabulary to verbally explain a proof of the Pythagorean Theorem and its converse.
Understanding:
Students understand that:
  • theorems represent generalizations about geometric relationships that are used to solve problems.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.26.1: Define a right angle, Pythagorean Theorem, converse, and proof.
M.8.26.2: Recognize examples of right triangles.
M.8.26.3: Demonstrate how to find square roots.
M.8.26.4: Solve problems with exponents.

Prior Knowledge Skills:
  • Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
  • Discuss strategies for solving mulit-step problems and equations.
  • Identify all types of angles.
  • Identify right angles and straight angles.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.26 Identify vertical angles given two parallel lines cut by a transversal.
Mathematics
MA2019 (2019)
Grade: 8
28. Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications
Unpacked Content
Evidence Of Student Attainment:
Students: Given real-world and mathematical problems in two and three dimensions,
  • Apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths in right triangles within the problem contexts.
Teacher Vocabulary:
  • Pythagorean Theorem
Knowledge:
Students know:
  • The Pythagorean Theorem.
  • Appropriate labeling of a right triangle, leg and hypotenuse.
Skills:
Students are able to:
  • Solve equations involving one variable and square root.
  • Represent real-world and mathematical contexts involving right triangles in a variety of formats (drawings, equations).
  • Justify solutions and solution paths using conceptual understandings and vocabulary related to the Pythagorean Theorem (right angle, hypotenuse).
Understanding:
Students understand that:
  • the properties of right triangles can be used to solve problems.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.28.1: Discuss strategies for solving real-world and mathematical problems.
M.8.28.2: Solve problems using the Pythagorean Theorem, with or without a calculator.
M.8.28.3: Identify right triangles.
M.8.28.4: Demonstrate how to find square roots, with or without a calculator.
M.8.28.5: Solve problems with exponents, with or without a calculator.

Prior Knowledge Skills:
  • Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
  • Compute a numerical expression with exponents, with or without a calculator.
  • Restate exponential numbers as repeated multiplication.
  • Choose the correct value to replace each variable in the expression (Substitution).
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.27 Use the pythagorean theorem to find the hypotenuse when given the measures of two legs in a real-world context. Limit to Pythagorean triples.
Tags: converse, length, Pythagorean Theorem, right triangles, side, threedimensions, twodimensions
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Comments

There are two lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. 

  This resource provided by:  
Author: Hannah Bradley
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