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

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

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

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

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 two different triangles.

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.

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.

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.

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

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.

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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

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. 

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. 

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

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

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

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.

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.

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.

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

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

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

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.  

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

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.

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. 

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

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

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

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.

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

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

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

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.  

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

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

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

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