6th Grade Math Practice 7 Script
Look for and make use of structure.
Highlighted Problem – Christo’s Buildings
In this highlighted problem, students are asked to find the volume and surface area
of a large building using a scale model. Use of formulas, however, is not emphasized.
Instead, students are guided to visualize the real-world building as a model made
with ½-inch cubes and to derive the volume and surface area based on the structure
of the prism presented. Also, students are asked to compose and decompose the
scale model of the building into ½-inch unit cubes. It is by modeling and using
composition/decomposition that students look for and make use of structure to
calculate surface area and volume.
Area and Perimeter “Follow Me” Cards
This Area and Perimeter Follow Me activity supports students as they develop
fluency in calculating area and applying their understanding of the patterns and
structure of area calculations.
To begin, distribute one card to each student. Start the game by saying "I am a
square with a side length of 12 centimeters." The student with the answer on his or
her card will respond and then read the clue on his/her card. This process continues
until all cards have been used.
Cutting Up
The activity below, Cutting Up, guides students through the decomposition of plane
figures in order to determine area. Includes teacher notes and videos showing how
students work to develop an understanding of area by making sense of structure.
Geoboard
This geoboard is a National Library of Virtual Manipulatives Applet and helps
students visualize the patterns and structure of composition and decomposition of
plane figures. It presents students with an irregular shape on a geoboard and
encourages decomposition to find area. It is suitable for teacher and student use.
Click instruction button at the top right corner of the applet for more information on
how to use this applet.
Triangle Problem
The Triangle Problem, is a challenging problem that can be used to encourage
critical thinking about decomposition/composition of plane figures and area.
Tangrams
This module shows how tangrams can be decomposed and composed into plane
figures and helps to answer for students the question, "What does it mean to
6th Grade Math Practice 7 Script
compose and decompose plane figures?" Also, the derivation of the formulas for
area of trapezoid, kite, and parallelogram using decomposition are addressed.
Conceptual Foundations
In this document, you will see illustrated examples of composition and
decomposition, as well as sample items involving area and volume of cubes with
fractional side lengths. Included are connections to previous grade level content and
helpful teacher tips for supporting student concept development.
Composite Shapes PPT
In this activity (PPT) students explore the area of polygons. By cutting up of
notecards, students are able to derive the formulas for the area of parallelograms,
triangles, trapezoids, and circles.
Composite Activity
This PDF contains the problems from the Composite Shapes PPT.
Composite Shapes PDF
This PDF contains the answers to the Composite Activity pdf.
Exploring Area PPT
In this PPT students find the perimeter and areas of composite two-dimensional
figures, including non-rectangular figures (such as semicircles) using various
strategies.