This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Who's Your Match?: | 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. |
| Who's Your Match?: | 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. |
| How Much Paint Will It Take?: | 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. |
| Surface Area of Prisms and Pyramids: | 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. |
| Coding Geometry Challenges #1-7, 14 & 15: | 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.
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| 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. |
| Amazing Insulating Atmosphere: | 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. |
| 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.
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| 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.
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| Solar Oven Bakery: | 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. |
| Sound Is Not The Only Place You Hear About Volume!: | 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. |
| Wrapping Up Geometry (Surface Area of Triangular Prisms) : | 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. |
| Wrapping Up Geometry (Lesson 1 of 2): | 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. |
| 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. |
| Netty People and Pets: | Students will learn what a "net" is, draw nets of three dimensional shapes, accurately calculate the surface area of their nets, and put them together to create an original person or pet. |
| Hands-On! Rectangular Prisms: | 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. |
| What's on the Surface?: | 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. |
| How Many Rubik's Cubes Can You Pack?: | 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. |
| Who's Your Match?: | 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. |
| 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. |
| The Classroom Money Vault: | 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. |
| Fill to Believe!: | 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. |
| Surface Area of Prisms and Pyramids: | 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. |
| How Much Paint Will It Take?: | 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. |
| Box It Up, Wrap It Up (Surface Area of Rectangular Prisms): | 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 :) |
| How Many Small Boxes?: | 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. |
| Plotting Rectangles: | 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. |
| 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. |
| Plotting Polygons with GeoGebra: | 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. |
| How much can it hold?: | 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.
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| Area of a Right Triangle: | Area of a Right Triangle |
| Wrapping Up Geometry (Lesson 2 of 2): | 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.
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| Lola's Landscaping MEA: | 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. |
| 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. |
| Formula Detective: Finding the Surface Area of a 3D Figure: | This lesson allows students to derive the formulas for 3D figures by having them build models for nets. |
| Analyzing Polyhedra: | Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula. |
| Boxing Candles: | This lesson is designed for 7th grade students and is best suited for advanced students. It can be used (with modifications) in the general education classroom for 7th grade or in an advanced 6th grade classroom. 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. |
| Plotting Polygons: | 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. |
| The Mystery of Crop Circles...on a coordinate plane: | 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).
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| What's on the Surface?: | 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. |
| 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. |
| Banana Bread: | 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. |
| Base and Height: | Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle. |
| Christo’s Building: | 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. |
| 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. |
| Surface Area and Volume: | 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. |
Vetted resources students can use to learn the concepts and skills in this topic.
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
