LEARN NC

K–12 teaching and learning · from the UNC School of Education

Mathematics — Grade 8

Goal 2: Measurement - The learner will understand and use measurement concepts.

Objective 2.01. Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

Additional related resources

We’re in the process of aligning our content for students to the Standard Course of Study. As we do, you’ll find it here.

General resources

Aligned lesson plans

Woodworkers and finishers: Working with area
In CareerStart lessons: Grade eight, page 3.6
In this lesson, students participate in a furniture-finishing scenario in which they draw and calculate the area of a set of tabletops with different shapes.
Format: lesson plan (grade 6–8 Mathematics)
By Valerie Davis, Sonya Rexrode, and Monika Vasili.
Modeling volume
This activity helps the students see how the volume of something includes the third dimension (width or depth) which is different from area. This activity also helps the students "prove" that the volume formula actually works. Students will already know that the volume of a rectangular prism is found by multiplying the object's length, width, and height. By using the blocks as models of volume, the students should come to realize that volume can be calculated simply by multiplying the area of the base by the height of the rectangular prism. Thus, they will come to realize that there is no need to try and fill the entire box with the tiny 1cm cubes, they can simply fill the bottom (to see how many cubes are there) and figure out how many rows there will be and multiply.
Format: lesson plan (grade 6–8 Mathematics)
By Erin Foerster.
A hula hoop is like a racetrack: Calculating the circumference, radius, and area of a circle
In On track learning: Safety through technology and design, page 10
In this lesson, students will use hoops of different sizes to explore geometry concepts such as circumference, area, and radius. They will also use indirect measurement and calculate percent of error.
Format: lesson plan (grade 7–10 Mathematics)
By Roxanne Moses.
Graphic designers: Working with scale
In CareerStart lessons: Grade eight, page 3.3
In this lesson, students will create a design on centimeter graph paper and enlarge it by creating a grid on a piece of poster board. Students will learn discuss the use of scale factor in the careers of graphic artists.
Format: lesson plan (grade 7–9 Mathematics)
By Valerie Davis, Sonya Rexrode, and Monika Vasili.
Giving meaning to volume and surface area
This lesson is designed to help students give meaning to volume and surface area by solving problems using a meaningful situation rather than formulas.
Format: lesson plan (grade 7–8 Mathematics)
By Grayson Wheatley.
Discovering perimeters
By using string, students will discover a formula for finding the perimeter of a rectangle.
Format: lesson plan (grade 6–12 Mathematics)
By Jenny Crumpler.
Commercial and industrial designers: Working with volume
In CareerStart lessons: Grade eight, page 3.7
In this lesson, students calculate the volume of a variety of boxes, and calculate the change in volume that would result from a change in the boxes' dimensions.
Format: lesson plan (grade 7–8 Mathematics)
By Valerie Davis, Sonya Rexrode, and Monika Vasili.
Calculating slope of a ramp
In On track learning: Safety through technology and design, page 9
In this lesson, students build a ramp and calculate its slope at different heights. They will also test cars to see how the height of the ramp affects speed.
Format: lesson plan (grade 7–10 English Language Arts, Mathematics, and Science)
By Roxanne Moses.

Resources on the web

Shops at the Mall
Students develop number sense in and around the shopping mall. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Scaling away
In this Illuminations lesson, students measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Learning about length, perimeter, area, and volume of similar objects using interactive figures: Side length and area of similar figures
This two-part example illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length and Area of Similar Figures, the user can manipulate the side lengths of one of two... (Learn more)
Format: lesson plan (grade 8 Mathematics)
Provided by: Illuminations
Finding the balance
In this lesson for middle grades students, one of a multi-part unit from Illuminations, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and... (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Finding our top speed
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. (Learn more)
Format: lesson plan (grade 8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Fill'r up
In this lesson, one of a multi-part unit from Illuminations, students can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships between edge lengths and volumes. (Learn more)
Format: lesson plan (grade 7–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Discovering the area formula for triangles
In this lesson, one of a multi-part unit from Illuminations, students learn the area formula for a triangle. Students find the areas of rectangles and squares and compare them to the areas of triangles derived from the original shape. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Cylinders and scale
In this lesson, students learn about the extreme limits of scale. This lesson is designed to build upon students' ability to build structures and to learn about mathematical and engineering relationships like length, area, and volume. Once students have... (Learn more)
Format: lesson plan (grade 7–8 Mathematics)
Provided by: Science Netlinks
Cubes everywhere
In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through real-life applications. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Collecting the rays
In this lesson, students explore how variations in solar collectors affect the energy absorbed. They make rectangular prisms that have the same volume but different linear dimensions. Students investigate relationships among the linear dimensions, the area,... (Learn more)
Format: lesson plan (grade 7–8 Mathematics)
Provided by: Illuminations