Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students will extend their knowledge of volume to find the volume of right prisms, seeing that the volume is the area of the base multiplied by the height.Key ConceptsVolume is measured in cubic units. The area of the base of a prism indicates how many cubic units are in the first unit “layer” of the prism. Multiplying by height gives the number of layers, and therefore the volume.GoalsFind the volume of right prisms.SWD: Some students with disabilities may have difficulty connecting newly introduced information with previously learned concepts. Consider ways to help students with disabilities to make connections between what they have learned in previous lessons about volume and right prisms and finding the volume of right prisms.Consider the prerequisite skills for this lesson. Students with disabilities may need direct instruction and guided practice with the skills, measurement, and concepts needed for this lesson.Students should understand these domain-specific terms:volumeright (domain-specific)prismcubicIt may be helpful to preteach these terms to students with disabilities.ELL: As new vocabulary is introduced, be sure to repeat it several times and allow students to repeat after you as needed. Write the new words as they are introduced, and allow enough time for ELLs to check their dictionaries or briefly consult with another student who shares the same primary language if they wish.