Analyze two- and three-dimensional figures by using distance and angle.
Number: MA.8.G.2
Title: BIG IDEA 2
Type:
Big Idea
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 8
Body of Knowledge: Geometry
Related Benchmarks
This cluster includes the following benchmarks
| Code |
Description |
| MA.8.G.2.1: | Use similar triangles to solve problems that include height and distances. |
| MA.8.G.2.2: | Classify and determine the measure of angles, including angles created when parallel lines are cut by transversals. |
| MA.8.G.2.3: | Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles and the sum of angles in polygons. |
| MA.8.G.2.4: | Validate and apply Pythagorean Theorem to find distances in real world situations or between points in the coordinate plane. |
Related Access Points
This cluster includes the following access points.
Independent
| Access Point Number |
Access Point Title |
| MA.8.G.2.In.a: | Identify triangles that are the same shape but different size (similar) using physical and visual models. |
| MA.8.G.2.In.b: | Form intersecting lines and identify the angles as acute, obtuse, or right angles by matching to a model. |
| MA.8.G.2.In.c: | Distinguish angles within triangles as acute, obtuse, or right angles using a right angle as a model. |
| MA.8.G.2.In.d: | Locate the right angle and the side opposite the right angle (hypotenuse) in a right triangle. |
Supported
| Access Point Number |
Access Point Title |
| MA.8.G.2.Su.a: | Match triangles that are the same shape but different size (similar) using physical models. |
| MA.8.G.2.Su.b: | Identify angles formed by lines that cross (intersecting lines). |
| MA.8.G.2.Su.c: | Identify the angles within a triangle. |
| MA.8.G.2.Su.d: | Locate the right angle within a right triangle. |
Participatory
| Access Point Number |
Access Point Title |
| MA.8.G.2.Pa.a: | Recognize a triangle. |
| MA.8.G.2.Pa.b: | Recognize corners and angles in two-dimensional shapes, including rectangles and triangles. |
| MA.8.G.2.Pa.c: | Recognize the longest side (hypotenuse) of a right triangle. |
Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Educational Software / Tool
| Name |
Description |
| Glossary: | This resource is an online glossary to find the meaning of math terms. Students can also use the online glossary to find words that are related to the word typed in the search box. For example: Type in "transversal" and 11 other terms will come up. Click on one of those terms and its meaning is displayed. |
Image/Photographs
| Name |
Description |
| Angles (Clipart ETC): | This large collection of clipart contains images of angles that can be freely used in lesson plans, worksheets, and presentations. |
| Clipart: Geometric Shapes: | In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes. |
Lesson Plans
| Name |
Description |
| The Ins and Outs of Polygons: | In this lesson, students will explore how to find the sum of the measures of the angles of a triangle, then use this knowledge to find the sum of the measures of angles of other polygons. They will also be able to find the sum of the exterior angles of triangles and other polygons. Using both concepts, students will be able to find missing measurements. |
| Bike Club Trip: | In this activity the students will rank different locations for a bike club's next destination. In order to do so, the students must use Pythagorean Theorem and well as analyze data of the quantitative and qualitative type.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom. |
| How Many Degrees?: | This lesson facilitates the discovery of a formula for the sum of the interior angles of a regular polygon. Students will draw all the diagonals from one vertex of various polygons to find how many triangles are formed. They will use this and their prior knowledge of triangles to figure out the sum of the interior angles. This will lead to the development of a formula for finding the sum of interior angles and the measure of one interior angle. |
| Alas, Poor Pythagoras, I Knew You Well! #2: | Using different activities, students will find real life uses for the Pythagorean Theorem. |
Presentation/Slideshow
| Name |
Description |
| Pythagoras' Theorem: | This resource can be used to introduce the Pythagorean Theorem to students. It provides sketches, applets, examples and easy-to-understand visual proofs as well as an algebra proof for the theorem.
It also includes interactive multiple choice practice questions on solving for a side of a right triangle, and applications involving right triangles, as well as a hands-on activity for students to do that allows them to create their own proof. |
Problem-Solving Task
| Name |
Description |
| It's Raining!!! (Compare areas of wiped windshields): | In this problem-solving task, students are challenged to determine whether the windshield wipers on a car or a truck allow the drivers to see more area clearly. To solve this problem, students must apply the Pythagorean theorem and their ability to find area of circles and parallelograms to find the answer. Be sure to click the links in the orange bar at the top of the page for more information about the challenge. From NCTM's Figure This! Math Challenges for Families. |
Text Resource
| Name |
Description |
| The Pythagorean Theorem: | This overview of the Pythagorean Theorem covers its purpose, equation, application, and validity. The site also provides a number of illustrations which help students visualize the theorem, and links to related resources for further understanding. |
Virtual Manipulatives
| Name |
Description |
| Angles: | This lesson is designed to introduce students to different types of angles including acute, obtuse, and right. The lesson also introduces ways to compare angles such as alternate interior, corresponding, and many others. This lesson provides links to discussions and activities related to angles as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. |
| Demonstrate the Pythagorean Theorem: | Representation to illustrate the Pythagorean Theorem. |
Student Resources
Vetted resources students can use to learn the concepts and skills in this topic.
Educational Software / Tool
| Title |
Description |
| Glossary: | This resource is an online glossary to find the meaning of math terms. Students can also use the online glossary to find words that are related to the word typed in the search box. For example: Type in "transversal" and 11 other terms will come up. Click on one of those terms and its meaning is displayed. |
Problem-Solving Task
| Title |
Description |
| It's Raining!!! (Compare areas of wiped windshields): | In this problem-solving task, students are challenged to determine whether the windshield wipers on a car or a truck allow the drivers to see more area clearly. To solve this problem, students must apply the Pythagorean theorem and their ability to find area of circles and parallelograms to find the answer. Be sure to click the links in the orange bar at the top of the page for more information about the challenge. From NCTM's Figure This! Math Challenges for Families. |
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
Educational Software / Tool
| Title |
Description |
| Glossary: | This resource is an online glossary to find the meaning of math terms. Students can also use the online glossary to find words that are related to the word typed in the search box. For example: Type in "transversal" and 11 other terms will come up. Click on one of those terms and its meaning is displayed. |
Image/Photograph
| Title |
Description |
| Clipart: Geometric Shapes: | In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes. |
