The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

This simulation allows students to explore the gas laws. Variables that can be manipulated are volume, temperature, pressure, amount of a gas, and relative mass.

Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume formulas for solids. The student materials consist of the student pages for each lesson in Module 3. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This activity has students calculating how any boxes of Girls Scout Cookies can fit into the back of a hatchback.

This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to a situation requiring decomposition of the volume into two pieces, to one where a height must be calculated using the Pythagorean theorem.

How many cubes will fit? This 3 Act Task by Graham Fletcher begins with a picture of an empty cube and one unifix cube inside it. First students make observations and estimates to begin determining how many unifix cubes would fit in the empty cube. Students can then use images with the dimensions of the cube and unifix cube to determine how many unifix cubes fit into the cube. Students are estimating, visualizing, measuring, adding and multiplying fractions and whole numbers to determine the volume of the cube.

In this 25-day module, students work with two- and three-dimensional figures.  Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms.  The second half of the module turns to extending students’ understanding of two-dimensional figures.  Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths.  They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes.  This module fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volume and area.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life.  Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two.  Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions.  Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line.  They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line.  Students compare linear functions and their graphs and gain experience with non-linear functions as well.  In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Students' eyes are opened to the value of creative, expressive and succinct visual presentation of data, findings and concepts. Student pairs design, redesign and perform simple experiments to test the differences in thermal conductivity (heat flow) through different media (foil and thin steel). Then students create visual diagrams of their findings that can be understood by anyone with little background on the subject, applying their newly learned art vocabulary and concepts to clearly communicate their results. The principles of visual design include contrast, alignment, repetition and proximity; the elements of visual design include an awareness of the use of lines, color, texture, shape, size, value and space. If students already have data available from other experiments, have them jump right into the diagram creation and critique portions of the activity.

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

Students teams determine the size of the caverns necessary to house the population of the state of Alabraska from the impending asteroid impact. They measure their classroom to determine area and volume, determine how many people the space could sleep, and scale this number up to accommodate all Alabraskans. They work through problems on a worksheet and perform math conversions between feet/meters and miles/kilometers.

Students learn about geotechnical engineers and their use of physical properties, such as soil density, to determine the ability of various soils to offer support to foundations. In an associated activity, students determine the bulk densities of soil samples, and assess their suitability to support foundations.

Students determine the mass and volume of soil samples and calculate the density of the soils. They use this information to determine the suitability of the soil to support a building foundation.

While learning about volcanoes, magma and lava flows, students learn about the properties of liquid movement, coming to understand viscosity and other factors that increase and decrease liquid flow. They also learn about lava composition and its risk to human settlements.

Students learn about porosity and permeability and relate these concepts to groundwater flow. They use simple materials to conduct a porosity experiment and use the data to understand how environmental engineers decide on the placement and treatment of a drinking water well.

The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

This lesson focuses learners on the concept of 1,000,000. It allows learners to see firsthand the sheer size of 1 million, while at the same time providing learners with an introduction to sampling and its use in mathematics. Learners use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This Check Your Readiness Assessment is used in conjunction with the Illustrative Mathematics Curriculum. It breaks down identifying the Essential Standard associated. This assessment should be utilized with the uploaded rubric to determine levels of prerequisite skills when beginning a new unit and allow for placement of interventions.