ALEX Classroom Resource

  

Grade 8 Mathematics Module 7, Topic C: The Pythagorean Theorem

  Classroom Resource Information  

Title:

 Grade 8 Mathematics Module 7, Topic C: The Pythagorean Theorem

URL:

 https://www.engageny.org/resource/grade-8-mathematics-module-7-topic-c-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Module 7, Topic C revisits the Pythagorean Theorem and its applications, now in a context that includes the use of square roots and irrational numbers. Students learn another proof of the Pythagorean Theorem involving areas of squares off of each side of a right triangle (8.G.B.6). Another proof of the converse of the Pythagorean Theorem is presented to students, which requires an understanding of congruent triangles (8.G.B.6). With the concept of square roots firmly in place, students apply the Pythagorean Theorem to solve real-world and mathematical problems to determine an unknown side length of a right triangle and the distance between two points on the coordinate plane (8.G.B.7, 8.G.B.8).

 

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
27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given real-world and mathematical problems that can be represented on a coordinate plane, apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths (distances between points) in right triangles within the problem contexts.
Teacher Vocabulary:
  • Pythagorean Theorem
Knowledge:
Students know:
  • The Pythagorean Theorem.
  • The operations and labeling within a coordinate system.
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 on coordinate planes, 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.
  • Theorems represent general relationships that are true for all shapes that fit certain criteria.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.27.1: Recall how to name points on a Cartesian plane using ordered pairs.
M.8.27.2: Recognize ordered pairs (x, y).
M.8.27.3: Solve problems using the Pythagorean Theorem, with or without a calculator.
M.8.27.4: Identify right triangles.
M.8.27.5: Demonstrate how to find square roots, with or without a calculator.
M.8.27.6: Solve problems with exponents, with or without a calculator.

Prior Knowledge Skills:
  • Define area, special quadrilaterals, right triangles, and polygons.
  • Analyze the area of other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
  • Apply area formulas to solve real-world mathematical problems.
  • Demonstrate how the area of a rectangle is equal to the sum of the area of two equal right triangles.
  • Explain how to find the area for rectangles.
  • Select manipulatives to demonstrate how to compose and decompose triangles and other shapes.
  • Recognize and demonstrate that two right triangles make a rectangle.
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.
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, coordinate system, distance, proof, Pythagorean Theorem, right triangles, threedimensions, twodimensions
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Comments

There are four lessons in this topic.

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  This resource provided by:  
Author: Hannah Bradley
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