This short video and interactive assessment activity is designed to teach fifth graders about visually finding weight in compound units.

This short video and interactive assessment activity is designed to give fifth graders an overview of comparison of weights (metric units).

This is a hands-on activity to show that air takes up space even though you cannot see it.The goal is to understand that gas occupies space and relate it to real situations that prove it.

This activity is an inquiry investigation where students gather data on why the Cartesian diver sinks or floats. They then develop a new question and then conduct a new investigation by changing one variable and repeat the altered experiment and record their conclusions.

Students will be able to use their knowledge of volume and surface area through this fun, hands-on activity.

This short video and interactive assessment activity is designed to teach fifth graders about single object length (english units).

The earth’s atmosphere may seem thick when compared to something like your height—but it’s surprisingly thin when compared to the earth’s radius. Here, you can find out exactly how thin, using strips of plastic to model the correctly scaled thickness of the atmosphere on a globe.

During this problem-based blended learning module students will be designing their dream bedroom as well as creating a scale drawing of the items they chose to be in their bedroom.  The launch activity introduces the students to Scale City, which is a video that explores scale models in the real world. Students are then given dimensions for a fictional bedroom to furnish with items of their choosing. Price is not considered in this module, but a budget could be introduced as an extension of the module.  Students will then spend time researching items that they would want to place in their bedroom with the area constraints given. Students will have the opportunity to provide each other peer feedback on their bedroom designs.  Once students have a rough idea of their bedroom design, they will spend some time creating a scale drawing of their bedroom on graph paper. This will give students the opportunity to use a scale factor to create a scale drawing. Students will again be provided feedback on their designs and be given time to reflect and redesign as needed.  If students need extra time to practice using a scale factor and creating scale models, a station rotation lesson has been included as an optional resource.

Learn to create mobiles in the style of artisans at the Hsu Studios.

In this problem-based learning module, students will work collaboratively to improve the accessibility or safety of their school or community. For example, students could identify that accessibility ramps need to be added to the school property or additional sidewalks need to be created/repaired to increase the safety of students as they walk to school. Students would work together to create models of these improvements and create a communications plan that informs the stakeholders of the materials needed to create these improvements (i.e. using volume to determine the amount of concrete, using angles to determine measurements for ramps, etc..).

Kent Treadgold's 7th grade science class uses a hands-on project to learn the abstract concept of density. They measure the mass and volume of different cylinders, create their own computerized spreadsheets for data, and enter the formula to calculate density. By the end of the project, they're able to conclude on their own that density will not change as the shape and size of an object changes, as long as the material it's made of stays the same.

This is a three-credit course which covers topics that enhance the students’ problem solving abilities, knowledge of the basic principles of probability/statistics, and guides students to master critical thinking/logic skills, geometric principles, personal finance skills. This course requires that students apply their knowledge to real-world problems. A TI-84 or comparable calculator is required. The course has four main units: Thinking Algebraically, Thinking Logically and Geometrically, Thinking Statistically, and Making Connections. This course is paired with a course in MyOpenMath which contains the instructor materials (including answer keys) and online homework system with immediate feedback. All course materials are licensed by CC-BY-SA unless otherwise noted.

Topics List for this Lesson: Points, Lines, Planes, and AnglesTriangles Plus Similarity and ProportionsPerimeter, Area, and CircumferenceVolume and Surface Area

This sections has two activities, a 2D and 3D activity. Students will explore area in a real-life situation in the 2D project. They will also learn how to calculate a prospective budget proposal for a paint project, and how to write up a formal proposal email. Students will explore surface area and volume in the 3D project. They will be able to create a 3D object in TinkerCad and determine the amount of material needed to create that object.

Surface Area and Volume

Type of Unit: Conceptual

Prior Knowledge

Students should be able to:

Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights.
Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices.
Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units.
Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.

Lesson Flow

The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.

Lesson OverviewStudents revise their packing plans based on teacher feedback and then take a quiz.Students will use their knowledge of volume, area, and linear measurements to solve problems. They will draw diagrams to help them solve a problem and track and review their choice of problem-solving strategies.Key ConceptsConcepts from previous lessons are integrated into this assessment task: finding the volume of rectangular prisms. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply your knowledge of the volume of rectangular prisms.Track and review your choice of strategy when problem-solving.

Lesson OverviewStudents explore nets—2-D patterns that can be folded to form 3-D figures. They start by examining several patterns and determining which nets form a cube. Then, they sketch nets for rectangular prisms. They also find the surface area of the rectangular prisms.ELL: Remind students of the units used to measure area and volume. Use this opportunity to reinforce why square units are used for area (2-D) and cubed units are used for volume (3-D).MathematicsA net is a 2-D pattern that can be folded to form a 3-D figure. In this lesson, the focus is on nets for rectangular prisms. There are many possible nets for any given prism. For example, there are 11 different nets for a cube, as shown below.The surface area of a prism is the area of its net.Goals and Learning ObjectivesIdentify nets for cubes.Sketch the net of a rectangular prism.Find the surface area of a rectangular prism.

Lesson OverviewStudents build prisms with fractional side lengths by using unit-fraction cubes (i.e., cubes with side lengths that are unit fractions, such as 13 unit or 14 unit). Students verify that the volume formula for rectangular prisms, V = lwh or V = bh, applies to prisms with side lengths that are not whole numbers.Key ConceptsIn fifth grade, students found volumes of prisms with whole-number dimensions by finding the number of unit cubes that fit inside the prisms. They found that the total number of unit cubes required is the number of unit cubes in one layer (which is the same as the area of the base) times the number of layers (which is the same as the height). This idea was generalized as V = lwh, where l, w, and h are the length, width, and height of the prism, or as V = Bh, where B is the area of the base of the prism and h is the height.Unit cubes in each layer = 3 × 4Number of layers = 5Total number of unit cubes = 3 × 4 × 5 = 60Volume = 60 cubic unitsIn this lesson, students extend this idea to prisms with fractional side lengths. They build prisms using unit-fraction cubes. The volume is the number of unit-fraction cubes in the prism times the volume of each unit-fraction cube. Students show that this result is the same as the volume found by using the formula.For example, you can build a 45-unit by 35-unit by 25-unit prism using 15-unit cubes. This requires 4 × 3  × 2, or 24, 15-unit cubes. Each 15-unit cube has a volume of 1125 cubic unit, so the total volume is 24125 cubic units. This is the same volume obtained by using the formula V = lwh:V=lwh=45×35×25=24125.15-unit cubes in each layer = 3 × 4Number of layers = 2Total number of 15-unit cubes = 3 × 4 × 2 =  24Volume = 24 × 1125 = 24125 cubic units Goals and Learning ObjectivesVerify that the volume formula for rectangular prisms, V = lwh or V = Bh, applies to prisms with side lengths that are not whole numbers.