Cluster 3: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (Major Cluster)Archived

Students are asked to determine the volume of a rectangular prism by using both a formula and counting cubic units.

Type: Formative Assessment

Students are asked to compare different strategies for finding the volume of a rectangular prism.

Type: Formative Assessment

Students are asked to determine the volume of a rectangular prism in cubic units.

Type: Formative Assessment

Students are asked to find the volumes of solids composed of rectangular prisms.

Type: Formative Assessment

Students determine how many improvised units of volume will fill a large box.

Type: Formative Assessment

Students are asked to determine how a unit cube can be used to measure the volume of a rectangular prism.

Type: Formative Assessment

Students are asked to count unit cubes to determine the volume of a right rectangular prism.

Type: Formative Assessment

Students analyze a rectangular prism that contains one layer of unit cubes and are asked to explain how to determine the volume of the entire prism using only the information given.

Type: Formative Assessment

Students are given the total volume of a rectangular prism and constraints on one dimension and asked to provide dimensions that would fit the constraints.

Type: Formative Assessment

Students are asked to determine the volumes of two right rectangular prisms given the dimensions of one and the base area and height of the other.

Type: Formative Assessment

Students discuss the volume of a prism measured in cubic units with gaps between the unit cubes used to measure its volume.

Type: Formative Assessment

When matter changes state, its properties change, too. In most cases, volume will increase when matter is melted from a solid to a liquid. Water is an exception, as its volume decreases when melted from ice to water. If matter is not added or removed, its mass will remain the same when it changes state. In this lesson, students will use if/then logical thinking to bridge the science and computer science concepts. This is lesson 2 of 3 in the States of Matter Unit.

Type: Lesson Plan

In this technology-rich lesson, students will design a habitat in which a plant or animal can survive. Students will focus on the adaptations that allow certain plants and animals to live in specific habitats.

Type: Lesson Plan

Students will build "apartments" with centimeter cubes by packing boxes (template included).  In addition, they will use centimeter cubes to build a variety of rectangular prisms and record the area of the base (B) and height (h) on a worksheet.  They will use that information to complete the volume formula, V = B x h.  Students will think about how the volume changes as the height and base of rectangular prisms change.

Type: Lesson Plan

This lesson focuses on the application of volume knowledge.  Students will need to add the volumes of individual right rectangular prisms to find total volumes.

Type: Lesson Plan

Students will be able to apply and understand the meaning of volume with shoe boxes and cereal boxes. 

Type: Lesson Plan

Students need to make decisions about the correct bakery box to send cookies through the mail to fill orders. Students need to consider the capacity, dimensions, and volume of the boxes in terms of how many cookies each box will hold.

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 will first review rectangular prisms and the formula for finding the volume of rectangular prisms. After students have determined the volume of a given set of rectangular prisms (aquariums), the students will use that information to help Seymour Phish in determining which aquarium he should purchase for his minnows.

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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This activity was designed for blind learners, but all types of learners can utilize it to investigate volume, mass, and density. The learner will create several boxes with different materials in each. They will then compare the sizes and masses and do the math to figure the densities. Educators could also create a data collection chart for this activity.

Type: Lesson Plan

This lesson provides a hands-on approach to develop the formula for finding the volume of a right rectangular prism. Students will apply the formula. Students will determine the volume of figures composed of two right rectangular-prism solids.  While students will decompose simple 3 D shapes into two rectangular prisms, this decomposition is not required in the standard.  It is used here to help deepened student understanding.

Type: Lesson Plan

In this lesson, students will learn the concept of volume as an attribute of solid figures, using unit cubes in various arrangements with a focus on rectangular prisms.

Type: Lesson Plan

Students will recognize volume as an attribute of solid figures and understand concepts of volume measurement. They will measure volumes by counting unit cubes, using cubic centimeters and cubic inches.

Type: Lesson Plan

In this MEA, students will use problem-solving strategies to rank different parking garages based on given factors. Students will need to apply their knowledge of volume to find the total volume of each parking garage and correctly calculate these values.

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 will review rectangular prisms and the formula for finding the volume of rectangular prisms. Once students have determined the volume of a number of rectangular prisms (cereal boxes), the students will use that information to help a fictitious company in determining which cereal box they should use for their new product.

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 open-ended problem, students will work in teams to determine a procedure for ranking pools to help a customer purchase. Students will need to calculate the size and volume of the pool, make decisions based on a table of data, and write a letter to the customer providing evidence for their decisions. Students will need to tradeoff between the size of the pool, the customer service ranking, the type of pool and the warranty of the pool. The students will have to research on the internet the differences and benefits of a salt water pool versus a chlorinated one.

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

This is the second part of a two-part volume lesson. In the first Building Rectangular Prisms (attached) lesson, foundational volume concepts are taught and students count cubes to find volume. In this lesson, students will discover the volume formulas length x width x height and base x height as they build rectangular prisms. They will use the formulas to find volume in real world situations.

Type: Lesson Plan

In this 5E lesson, the students will explore the concept of volume. The students will build rectangular prisms, identify the dimensions of the prism and discover the volume of the prism.

Type: Lesson Plan

In this open-ended problem, students will work in teams to determine a procedure for ranking shoe closets for a company to purchase. Students will need to calculate the cubic feet of space for the closet, make decisions based on a table of data, and write a letter to the client providing evidence for their decisions.

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 lesson students will learn how to calculate and compare volumes of rectangular prisms.

Type: Lesson Plan

This is the first part of a two-part volume lesson. In this lesson, students will build foundational concepts for volume and count cubes to find volume. In the second part lesson Building Rectangular Prisms Part 2 (attached), students will discover the volume formulas length x width x height and base x height as they build rectangular prisms. They will use the formulas to find volume in real world situations.

Type: Lesson Plan

Students will use situational stories to help them apply the formulas V = l × w × h and V = B × h  to find the volumes of right rectangular prisms with whole-number edge lengths.

Type: Lesson Plan

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

This is a lesson on volume relating specifically to using the formula V = B x h.

Type: Model Eliciting Activity (MEA) STEM Lesson

Help solve the problem of shipping video games and accessories to customers by calculating the volume of the containers needed in this interactive tutorial.

Type: Original Student Tutorial

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

Type: Original Student Tutorial

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume, in this interactive tutorial.

Type: Original Student Tutorial

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Type: Problem-Solving Task

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Students are asked to apply knowledge of volume of rectangular prisms to find the volume of an irregularly shaped object using the principle of displacement.

Type: Problem-Solving Task

This purpose of this task is to help students understand what happens when you scale the dimensions of a right rectangular solid. This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them. These relative volumes can be calculated geometrically, filling the larger box with smaller boxes, or arithmetically using the given dimensions.

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

This lesson is designed to introduce students to the concept of volume and how to find the volume of rectangular prisms. This lesson 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: Teaching Idea

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula. 

Type: Tutorial

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

This Khan Academy tutorial video illustrates measuring volume by counting unit cubes.  Models in this video include composite figure of rectangular prisms although only counting is used to find volume, not an equation.

Type: Tutorial

This Khan Academy tutorial video describes measurement in one, two, and three dimensions.

Type: Tutorial

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