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Distance Between Two Points Guided Notes w/ Doodles | Pythagorean Theorem
$4.25
Overview
- Standard: CCSS 8.G.B.8
- Unit: 8th Grade → Unit 6: Pythagorean Theorem, Angles & Volume
- Grade: 8th Grade
Get the Lesson Materials
Distance Between Two Points Guided Notes w/ Doodles | Pythagorean Theorem
$4.25
Learning Objectives
After this lesson, students will be able to:
- Find the distance between two ordered pairs (whole number solutions)
- Find the distance between two points on the coordinate plane (whole number solutions)
Prerequisites
Before this lesson, students should be familiar with:
- Understanding of the concept of right triangles
- Knowledge of the definitions of legs and hypotenuse in a right triangle
- Familiarity with the concept of squares and square roots
Materials
- Pencils
- Colored pencils or markers
- The Distance Between Two Points Guided Notes
Key Vocabulary
- Distance Formula
- Legs
- Hypotenuse
- Pythagorean Theorem
Procedure
Introduction
As a hook, ask students why understanding the distance between two points is important in real-life scenarios. Refer to the last page of the guided notes as well as the FAQs below for ideas.
Use the first page of the guided notes to introduce the concept of finding the distance between two points using the Pythagorean Theorem. Students practice solving for the unknown distance (i.e. hypotenuse) when given the vertical and horizontal lengths (i.e legs). Review the definition of the Pythagorean Theorem and vocabulary terms such as legs and hypotenuse. Then, connect the Pythagorean Theorem to the distance formula.
Use the second page of the guided notes to formally introduce the distance formula. Students then practice finding the distance between two ordered pairs and two points on a coordinate plane.
Based on student responses during the introduction, reteach any concepts that students may need extra help with. If there is a wide range of proficiency levels in the class, consider pulling out students for reteaching while having more advanced students begin engaging with the practice exercises.
Practice
Have students practice finding missing distance by apply the distance formula using the maze activity (pg. 3) in the guided notes resource. Encourage students to work collaboratively and discuss their approach to solving the problems.
Fast finishers can engage with the color by number activity (pg. 4) for additional practice. This will reinforce their understanding of the theorem in a fun and creative way. You can assign the Maze activity as homework to consolidate their learning further.
Real-Life Application
Bring the class back together, and introduce the concept of applying the distance formula in real-world scenarios. Discuss how the distance formula is used in fields like GPS and satellites. Refer to the FAQ for more ideas on how to teach real-life applications of the distance formula.
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for Distance Between Two Points and Pythagorean Theorem, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.
Here’s 1 activity to explore:
Real-Life Math Project
A fun way to wrap this lesson with your students is with one of my real-life math projects. They enable students to see the application of the math in an engaging, extended project:
FAQs
The Pythagorean Theorem can be used in various real-life scenarios, such as measuring distances, construction projects, navigation, and sports field design.
- Determining the diagonal distance of a rectangular field.
- Calculating the height of a ladder leaning against a wall.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
- It helps us find the length of a missing side in a right triangle.
In a right triangle, the two sides that form the right angle are called the legs, and the side opposite the right angle is called the hypotenuse.
- Legs are the sides that form the right angle.
- Hypotenuse is the side opposite the right angle.
Guided notes provide a structured framework for students to follow along during a lesson, helping them take organized notes, identify key concepts, and engage actively in the learning process.
- They keep students focused during the lesson.
- They provide visual aids and examples for better comprehension.
The Pythagorean Theorem is a fundamental principle in geometry, serving as a building block for various geometric concepts and applications in fields such as engineering, architecture, physics, and computer graphics.
- It forms the basis for trigonometry and calculus.
- It is essential for solving complex geometric problems.
- Navigation and Mapping: GPS systems use the distance formula to calculate the shortest path between two points on the earth's surface. This helps in determining the most efficient routes for travel, whether by car, plane, or on foot.
- Computer Graphics and Gaming: In video games and computer graphics, the distance formula is used to calculate the distances between objects, determine how they interact with each other, and render 3D environments in a realistic manner