Cluster 1: Solve real-world and mathematical problems involving area, surface area, and volume. (Supporting Cluster)Archived

Students are asked to use a net to find the surface area of a triangular pyramid.

Type: Formative Assessment

Students are asked to use a net to find the surface area of a rectangular prism.

Type: Formative Assessment

Students are asked to determine the number of unit prisms needed to fill a larger prism with fractional dimensions.

Type: Formative Assessment

Students are asked to explain the relationship between two approaches to finding the volume of a right rectangular prism.

Type: Formative Assessment

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Type: Formative Assessment

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Type: Formative Assessment

Students are asked to draw a net of a three-dimensional figure.

Type: Formative Assessment

Students are asked to draw a net of a three-dimensional figure.

Type: Formative Assessment

Students are asked to draw a polygon given the coordinates of its vertices and to determine the length of the polygon’s diagonals.

Type: Formative Assessment

Students are asked to draw a polygon given the coordinates of its vertices and to determine both the lengths of sides and if any sides are parallel.

Type: Formative Assessment

Students are asked to draw a polygon given the coordinates of its vertices and to determine the perimeter of the polygon.

Type: Formative Assessment

Students are asked to draw a polygon given the coordinates of its vertices, and to determine the area of the polygon.

Type: Formative Assessment

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

Type: Formative Assessment

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

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

Type: Formative Assessment

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

Type: Formative Assessment

Students are asked to graph two points given their coordinates and to find the coordinates of two other points so that the four points represent the vertices of a square.

Type: Formative Assessment

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

This is a guided inquiry lesson to help students gain greater understanding of the relationship between 2-dimensional and 3-dimensional shapes. Students create right rectangular and triangular prisms and problem-solve how to find the flat 2-dimensional surface area. Students are asked to figure out how many party favors (prisms) can be painted with a quart of glow-in-the-dark paint.

Type: Lesson Plan

In this lesson students will find the surface area of three-dimensional figures. Students will use nets made up of rectangles and triangles to calculate the surface area of rectangular prisms, triangular prisms, and square pyramids.

Type: Lesson Plan

This set of geometry challenges focuses on creating a variety of polygons 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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

In this Engineering Design Challenge, students will design a terrarium and then monitor the levels of water, gases, and temperature in the environment. The factor being changed will be the layers of plastic wrap covering the terrarium. Students will examine how the thickness of the atmosphere affects the health of the plants in the terrarium. Students will conduct research, work in teams, and then finally create a presentation to the class sharing their findings.

Type: Lesson Plan

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.

Type: Lesson Plan

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

Type: Lesson Plan

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.

Type: Lesson Plan

The students will investigate how radiation from the sun allows us to bake cookie dough. The students will also determine if the volume of the box determines the time it will take for the cookie dough to bake. The students will also create a graph of the data collected while the cookie dough is baking in the solar oven.

Type: Lesson Plan

This lesson introduces the idea of finding volume. Volume in sixth grade math is very "rectangular" (cubes, rectangular prisms) and this lesson brings to light that volume is simply a measure of available space, but can take on many shapes or forms (cylinders for example - graduated cylinders and beakers) in science. Students will be left to design their own data collection and organizing the data that they collect. They will apply the skill of finding volume to using fractional parts of a number (decimals) and finding the product using the volume formula.

Type: Lesson Plan

This lesson is designed to take students from recognizing nets of triangular prisms and finding areas of their individual faces, to finding the surface area of triangular prisms. 

Type: Lesson Plan

This lesson is the first of two in a unit on surface area. This lesson provides a foundation for understanding the concept of surface area by introducing nets of right rectangular prisms. 

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Students will learn what the "net" of a three-dimensional figure is, draw nets of right-rectangular prisms and right-rectangular prisms, accurately calculate the surface area of nets, and put nets together to create an original “person” or “pet.”

Type: Lesson Plan

Students create surface area nets with graph paper and work with manipulative cubes to decide if there is a relationship between surface area and volume in rectangular prisms.

Type: Lesson Plan

In this activity, students will work in groups to evaluate the measurements of shapes that form three-dimensional composite shapes to compute the surface area.

Type: Lesson Plan

This two-day lesson uses a hands-on problem-solving approach to find the volume of a right rectangular prism with positive rational number edge lengths. Students first design boxes and fill with Rubik's Cubes. They create a formula from the patterns they find. Using cubes with fractional edges requires students to apply fractional units to their formulas. 

Type: Lesson Plan

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

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

Type: Lesson Plan

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

Type: Lesson Plan

This activity has students predict the number of one hundred dollar bills that can fit inside the classroom. The students use volume measurements to explain their estimation.

Type: Lesson Plan

In this lesson, students work cooperatively to find the volume of a right rectangular prisms, using whole and fraction units of measurement, using the volume formula, and using manipulatives to count the number of units necessary to fill the prisms, and compare it with the formula results. 

Type: Lesson Plan

In this lesson students will find the surface area of three-dimensional figures. Students will use nets to calculate the surface area of right rectangular prisms and right rectangular pyramids.

Type: Lesson Plan

This is a guided inquiry lesson to help students gain greater understanding of the relationship between 2-dimensional and 3-dimensional shapes. Students create right rectangular prisms and problem-solve how to find the flat 2-dimensional surface area. Students are asked to figure out how many party favors (prisms) can be painted with a quart of glow-in-the-dark paint.

Type: Lesson Plan

In this introductory lesson to surface area, students will make connections between area of two-dimensional figures and calculating the surface area of rectangular prisms using nets, within the context of wrapping birthday presents! Math is Fun :)

Type: Lesson Plan

In this lesson students will extend their knowledge of volume from using whole numbers to using fractional units. Students will work with adding, multiplying, and dividing fractions to find the volume of right rectangular prisms, as well as, determining the number of fractional unit cubes in a rectangular prism.

Type: Lesson Plan

Students are challenged to plot coordinates on a graph in order to create a rectangle, and then find the length of its horizontal and vertical sides using the coordinates to calculate the area and perimeter. 

Type: Lesson Plan

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. 

Type: Lesson Plan

This introductory lesson guides students through the process of graphing polygons on the coordinate plane and finding vertical and horizontal side lengths. Explicit instructions are given for teachers who are new to GeoGebra. A detailed summative assessment includes extensions and an answer key is provided.

Type: Lesson Plan

This lesson uses a discovery approach to exploring the meaning of volume. The students will work with cubes as they construct and analyze the relationship between the length, width, and height to the total amount of cubes. Students will be able to apply this concept to real world applications of other right rectangular prisms and compare them to determine which will hold the most volume. 

Type: Lesson Plan

Area of a Right Triangle

Type: Lesson Plan

This lesson is 2 of 2 and is primarily formative in nature, but includes a summative assessment for students to take during the following class period. 

During the lesson, students will be reviewing for their assessment on the surface area formula for a right rectangular prism. 

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students are asked to develop a procedure to fit the most amount of rectangular prism plant packages on one sheet of cardboard, using nets and surface area.

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.

Type: Lesson Plan

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. 

Type: Lesson Plan

This lesson allows students to derive the formulas for 3D figures by having them build models for nets.

Type: Lesson Plan

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula. 

Type: Lesson Plan

In this MEA, students select jars for candles based on a variety of factors and then design boxes to contain the jars.

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.

Type: Lesson Plan

Students are challenged to plot coordinates on a graph, in order to create a mystery polygon, and find the length of its horizontal and vertical sides using the coordinates.

Type: Lesson Plan

In this lesson, students will use their knowledge of plotting points on quadrant I of the coordinate plane to figure out other coordinate pairs within quadrants II, III, and IV. Students are challenged to match description cards to the matching "map" (four-coordinate grid). 

Type: Lesson Plan

In this activity, students will work in groups to evaluate the measurements of shapes that form three-dimensional composite shapes to compute the surface area.

Type: Lesson Plan

Explore the coordinate plane in an epic Capture the Flag tournament with this interactive tutorial.

This is part 1 in a two-part series:

• Open "Capturing Flags on the Coordinate Plane Part 1"
• Open "Capturing Flags on the Coordinate Plane Part 2"

Type: Original Student Tutorial

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. 

Type: Original Student Tutorial

Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.

This is part 3 in a three-part series. Click below to open the other tutorials in the series.

• Volume Part 1
• Volume Part 2

Type: Original Student Tutorial

Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.

This is part 2 in a three-part series. Click below to open the other tutorials in the series.

• Volume Part 1
• Volume Part 3

Type: Original Student Tutorial

Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.

This is part 1 in a three-part series. Click below to open the other tutorials in the series.

• Volume Part 2
• Volume Part 3

Type: Original Student Tutorial

Type: Original Student Tutorial

<p>Blaze a trail when you utilize laser technology to make art.</p>

Type: Perspectives Video: Professional/Enthusiast

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.

Type: Problem-Solving Task

The purpose of this task is two-fold. One is to provide students with a multi-step problem involving volume. The other is to give them a chance to discuss the difference between exact calculations and their meaning in a context. It is important to note that students could argue that whether the new pan is appropriate depends in part on how accurate Leo's estimate for the needed height is.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

Students are asked to draw a scale model of a building and find related volume and surface areas of the model and the building which are rectangular prisms.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

In this activity, students adjust the dimensions of either a rectangular or triangular prism and the surface area and volume are calculated for those dimensions. Students can also switch into compute mode where they are given a prism with certain dimensions and they must compute the surface area and volume. The application keeps score so students can track their progress. This application allows students to explore the surface area and volume of rectangular and triangular prisms and how changing dimensions affect these measurements. This activity also includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Problem-Solving Task

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.

Type: Student Center Activity

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

Type: Tutorial

In this video, discover another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism.

Type: Tutorial

This video shows how to solve a word problem involving rectangular prisms.

Type: Tutorial

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

Students will graph the given coordinates of three of the polygon vertices, then locate and graph the fourth vertex. 

Type: Tutorial

This video demonstrates using a net to find surface area.

Type: Tutorial

In this example, students are given the coordinates of the vertices and asked to construct the resulting polygon, specifically a quadrilateral.  

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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.  

Type: Tutorial

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

Type: Tutorial

In these two 50-minute lessons, students will work in pairs or small groups to design cartons that can contain specifically sized candies. Upon completion of these lessons, students will have selected appropriate mathematical models for an unstructured problem, identified constraints and variables, and worked with two and three dimensional shapes to solve a problem involving capacity and surface area.

Type: Unit/Lesson Sequence

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.

Type: Unit/Lesson Sequence

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

This lesson is designed to develop students' understanding of volume and ability to find volumes of triangular prisms. It provides links to discussions and activities related to volume 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.

Type: WebQuest