 Mathematics Grade 6

Strand: GEOMETRY (6.G)

Solve real-world and mathematical problems involving area, surface area, and volume (Standards 6.G.1�4).

Standard 6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

• 24 Unit Squares
The purpose of this activity is to help students think a little more flexibly about the concept of area before studying, generally, the areas of triangles and special quadrilaterals.
• Area
This lesson is designed to help students be able to calculate the area of a random shape on a grid, explain the correlation between the size of the perimeter and the number of different possible areas that can be contained within that perimeter.
• Area Explorations
In this lesson, students will explore the area of irregular shapes to find multiple different methods for calculating area
• Areas of Irregular Shapes: Building Sailboats
Learn how wooden boat builders use a variety of mathematical concepts when custom designing their vessels. This video focuses on how area, volume, and measurements of irregular shapes are used in the engineering process, taking math out of the classroom and into real world problem solving.
• Areas of Right Triangles
This task is intended to help build understanding as students work toward deriving a general formula for the area of any triangle. The purpose of this task is for students to use what they know about area and express regularity in repeated reasoning to generate a formula for area of a right triangle.
The purpose of this task is for students to use what they know about area to find the areas of special quadrilaterals. Depending on previous instruction, methods may include decomposing the figures into right triangles and rectangles, or drawing a rectangle to encircle the figure and subtracting areas of right triangles that are not part of the original figure.
• Base and Height
In this scenario a teacher has given students a task to label the base and height of a triangle and shows 3 students' solutions. Students must then identify which, if any, of the solutions are correct and explain why.
• Chapter 5 - Mathematical Foundations (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Geometry.
• Chapter 5 - Student Workbook (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Geometry.
• Finding Areas of Polygons (6th grade)
This task asks students to find the area of polygons that are best suited for increasingly abstract methods.
• Geometry (6.G) - 6th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 6 - Geometry.
• Grade 6 Math Module 5: Area, Surface Area, and Volume Problems (EngageNY)
In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. Extending skills from Module 3 where they used coordinates and absolute value to find distances between points on a coordinate plane, students determine distance, perimeter, and area on the coordinate plane in real-world contexts
• Grade 6 Unit 5: Area and Volume (Georgia Standards)
In this unit students will: Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals. Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes. Solve real-world and mathematical problems involving area. Decipher and draw views of rectangular and triangular prisms from a variety of perspectives. Recognize and construct nets for rectangular and triangular prisms. Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets.
• Pentagon Puzzles
By deconstructing pentagons into triangles, students in this activity learn how to calculate the area of pentagons.
• Polygons in the Coordinate Plane
The purpose of this task is for students to practice plotting points in the coordinate plane and finding the areas of polygons. This task assumes that students already understand how to find areas of polygons by decomposing them into rectangles and triangles.
• Same Base and Height, Variation 1
This is the first version of a task asking students to find the areas of triangles that have the same base and height, and is the most concrete.
• Same Base and Height, Variation 2
This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.
• Scale Models and Three-Dimensional Scaling in Practice
Students can use this interactive to explore how an object changes when enlarged by a factor of 10. They put this understanding to use in the activity when they compare two cubes of different sizes by volume and surface area. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Sierpinski's Carpet
The purpose of this task is to help motivate the usefulness of exponential notation in a geometric context and to give students an opportunity to see that sometimes it is easier to write a number as a numeric expression rather than evaluating the expression.
• Surface Area , Area and Volume: The Big Sleep
In this video, Bianca is planning a sleepover for friends. She has to figure out how many people she can invite because the floor will only hold so many sleeping bags. She must calculate both the surface area of the floor and the surface area of a sleeping bag. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Surface Area and Volume
An online activity is the focus of this lesson plan to help students understand the concepts of surface area and volume.
• Surface Area of Prisms
In this lesson students will understand surface area and how solve for the surface area of triangular prisms.
• Table for 22: A Real-World Geometry Project
This Teaching Channel video has students apply knowledge of area and perimeter to solve real-world problems. This site provides a lesson plan and student handouts. (13 minutes)
• The Largest Container: Problems Using Volume and Shape
By using a single sheet of paper this interactive leads students to construct shapes, calculate volume, and think about the relationships between different shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Triangle Area
This interactive lesson plan will help students understand how to find the area of a right triangle.
• Triangle Explorer
The applet in this lesson allows students to draw triangles and calculate their area.
• Wallpaper Decomposition
The purpose of this task is for students to experiment with composition and decomposition of polygons to examine shapes in a real world context. To find the area of the wall, students will decompose a pentagon into simpler shapes (for example, a rectangle and a triangle).
• What's Fun About Surface Area?
In this Teaching Channel video an educator helps students construct an understanding of surface area. (7 minutes) http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.