# MA.6.GR.2.2

Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.

### Clarifications

Clarification 1: Problem types include finding area of composite shapes and determining missing dimensions.

Clarification 2: Within this benchmark, the expectation is to know from memory a formula for the area of a rectangle and triangle.

Clarification 3: Dimensions are limited to positive rational numbers.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.GR.2.AP.2: Decompose quadrilaterals and composite figures into simple shapes (rectangles or triangles) to measure area.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Swimming Pool Walkway:

Students are asked to solve a problem involving finding the area of a composite plane figure.

Type: Formative Assessment

Lost Key:

Students are asked to find the area of a composite plane figure.

Type: Formative Assessment

Students are asked to find the area of a trapezoid and a parallelogram by composing or decomposing into triangles and rectangles.

Type: Formative Assessment

Area of Kite:

Students are asked to find the area of a kite by composing it into rectangles or decomposing it into triangles.

Type: Formative Assessment

## Lesson Plans

Using Nets to Find the Surface Area of Pyramids:

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Type: Lesson Plan

## Original Student Tutorial

Area of Triangles: Missing Dimensions:

Follow George as he calculates the missing values for the base and height of triangles in this interactive tutorial.

Type: Original Student Tutorial

## Tutorials

Volume through Decomposition:

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula.

Type: Tutorial

Volume: Decomposing a Solid Figure Example:

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

Finding Area by Decomposing a Shape:

This tutorial demonstrates how the area of an irregular geometric shape may be determined by decomposition to smaller familiar shapes.

Type: Tutorial

## MFAS Formative Assessments

Area of Kite:

Students are asked to find the area of a kite by composing it into rectangles or decomposing it into triangles.

Students are asked to find the area of a trapezoid and a parallelogram by composing or decomposing into triangles and rectangles.

Lost Key:

Students are asked to find the area of a composite plane figure.

Swimming Pool Walkway:

Students are asked to solve a problem involving finding the area of a composite plane figure.

## Original Student Tutorials Mathematics - Grades 6-8

Area of Triangles: Missing Dimensions:

Follow George as he calculates the missing values for the base and height of triangles in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Area of Triangles: Missing Dimensions:

Follow George as he calculates the missing values for the base and height of triangles in this interactive tutorial.

Type: Original Student Tutorial

## Tutorials

Volume through Decomposition:

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula.

Type: Tutorial

Volume: Decomposing a Solid Figure Example:

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

Finding Area by Decomposing a Shape:

This tutorial demonstrates how the area of an irregular geometric shape may be determined by decomposition to smaller familiar shapes.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.