Standard #: MAFS.6.G.1.1 (Archived Standard)


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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.


General Information

Subject Area: Mathematics
Grade: 6
Domain-Subdomain: Geometry
Cluster: Solve real-world and mathematical problems involving area, surface area, and volume. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Numbers in items must be nonnegative rational numbers. Limit shapes to those that can be decomposed or composed into rectangles and/or right triangles.
    Calculator :

    No

    Context :

    Allowable



Sample Test Items (3)

Test Item # Question Difficulty Type
Sample Item 1

A shape is shown.

What is the area, in square inches, of the shape?

N/A EE: Equation Editor
Sample Item 2

A pentagon is shown.

What is the area, in square inches, of the pentagon?

N/A EE: Equation Editor
Sample Item 3

Mr. Hilton is buying new tile for his kitchen floor. The dimensions, in feet (ft), of the kitchen floor are shown. 

What is the area, in square feet, of Mr. Hilton's kitchen floor?

N/A EE: Equation Editor


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Related Resources

Formative Assessments

Name Description
Swimming Pool Walkway

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

Lost Key

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

Area of Quadrilaterals

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

Area of Kite

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

Area of Triangles

Students are asked to find the area of two different triangles.

Lesson Plans

Name Description
Coding Geometry Challenge 8, 9 & 17

This set of geometry challenges focuses on using area/perimeter as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Coding Geometry Challenge # 16, 18 & 19

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Dream House Project

Students will design a floor plan of their dream house using compositions of basic geometric shapes. They will also calculate the area of the plan to determine flooring costs. Students will conduct research on alternative energy sources and determine the best fit for their dream house location.

 

Breaking Up is Hard to Do

Student will use geoboards to decompose composite figures and polygons into squares, rectangles, and triangles in order to find the total area.

Blown Away

A STEM Engineering Design Challenge

Learning Goals

  • Students will be able to demonstrate an understanding of hazardous weather conditions, specifically hurricanes, and identify ways for humans to protect themselves during those conditions.
  • Students will understand how area of various shapes can enhance the stability of a structure.


Students will create a free-standing structure that can withstand hurricane-force winds. Students will demonstrate their understanding of surface area by constraining to sets of parameters for their structures.

Using Security Camera Angles to Find Area and Calculate Percentages In this lesson, students work individually and then collectively using a real world situation to construct sight lines to see which areas are visible from a security camera. Students then find and compare the area of triangles and quadrilaterals and compare and calculate the percentages and/or fractions of areas.
Area of a Triangle

This lesson is primarily formative in nature and is designed to introduce students to the area of a triangle by having them derive the formula themselves using the relationship between rectangles and triangles. During the lesson the teacher will be facilitating their students as they work with their teams and shoulder partners to solve problems.

Building a Tree House

This MEA will have students determining the safest and most cost effective material to use when building a tree house.They will do this by calculating surface area and determining cost.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Profit Plaza

This lesson requires students to use mathematical data and logic/reasoning to place vendors into retail spaces in a shopping plaza. Students will first rank five vendor types on their profitability (based on average sales and average overhead/upkeep costs), then place the vendor types into the 11-13 retail spaces. They are also required to find the area of each space and calculate the total leasing charges. The plans for the plaza are given on a coordinate plane, so students will need to find the lengths of horizontal and vertical line segments (using the coordinates of the endpoints) to calculate the areas of the rectangular and composite spaces.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Finding Area with Hands-On Measurement

This lesson allows students to apply the area of triangles, quadrilaterals, and trapezoids to composite figures, and gives students a chance to work with classmates to find the area by taking measurements and making the necessary calculations. Students will also see the relationship between the area formulas for rectangles, triangles, trapezoids, and polygons. 

Area of a Right Triangle

Area of a Right Triangle

Enrique's Ruined Carpet

In this activity, students use a house blueprint to find the area of carpeted floor by decomposing composite shapes into rectangles and triangles. As students critique each other's reasoning, they refine their thinking of surface area. 

Original Student Tutorials

Name Description
Area of Triangles

Follow George as he explores the formula for the area of a triangle and uses it to find the area of various triangles in this interactive 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. 

Problem-Solving Tasks

Name Description
Maximizing Area: Gold Rush Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work. At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually. In a whole-class discussion students compare and evaluate the different methods they used. Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen. Finally, students reflect on their work.
Base and Height

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Finding Areas of Polygons, Variation 1

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Painting a Barn

Students are asked to use the given information to determine the cost of painting a barn.

Same Base and Height, Variation 1

This task is a good precursor to students developing the formula for the area of a triangle. The fact that each triangle has the same area can be used to highlight the meaning of the components of the area formula, as well as the meaning of the altitude of a triangle (an issue since the given triangles are not acute.) Students may try to determine the area of each triangle by counting the square units or using the "surround and subtract" method. Students may think that triangle ABC has the largest area because the others appear thinner.

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. They still determine the area of each triangle by counting the square units or using the "surround and subtract" method, but it is a good lead-up for students to think about the formula for the area of a triangle and notice that the length of bases and altitudes are the same. Students who do not analyze the area may think that triangle ABC has the largest area because the others appear thinner.

Student Center Activity

Name Description
Edcite: Mathematics Grade 6

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Tutorials

Name Description
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.

Area of a Parallelogram

This video portrays a proof of the formula for area of a parallelogram.  

Area of a Trapezoid

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Area of Triangle on a Grid

We will be able to find the area of a triangle in a coordinate grid. The formula for the area of a triangle is given in this tutorial.  

Perimeter and Area

Students will learn the basics of finding the perimeter and area of squares and rectangles.  

Virtual Manipulatives

Name Description
Area Builder

This manipulative allows you to create shapes using colorful blocks to explore the relationship between perimeter and area. The game screen challenges you to build shapes or find the area of figures.

Triangle Area This lesson is designed to introduce students to calculating the area of right triangles. This lesson provides links to discussions and activities related to area as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Student Resources

Original Student Tutorials

Name Description
Area of Triangles:

Follow George as he explores the formula for the area of a triangle and uses it to find the area of various triangles in this interactive 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. 

Problem-Solving Tasks

Name Description
Base and Height:

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Finding Areas of Polygons, Variation 1:

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

Student Center Activity

Name Description
Edcite: Mathematics Grade 6:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Tutorials

Name Description
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.

Area of a Parallelogram:

This video portrays a proof of the formula for area of a parallelogram.  

Area of a Trapezoid:

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Area of Triangle on a Grid:

We will be able to find the area of a triangle in a coordinate grid. The formula for the area of a triangle is given in this tutorial.  

Perimeter and Area:

Students will learn the basics of finding the perimeter and area of squares and rectangles.  



Parent Resources

Problem-Solving Tasks

Name Description
Base and Height:

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Finding Areas of Polygons, Variation 1:

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.



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