Virginia Department of Education
Similar Solids and Proportional Reasoning
Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...
Curated OER
SA/V Ratio and Rate of Diffusion
Students calculate the SA/V ratio and volume of phenophthalien agar that are cut into different shapes. They then let ammonia diffuse into the various pieces of agar and determine the effect that SA/V had on the rate of diffusion.
Illustrative Mathematics
Christo’s Building
Hook your charges on how to solve a real-world art problem with mathematics by showing works of Christo. You can find eye-catching images on the Christo and Jeanne Claude webpage. Here, math learners help Jean Claude and Christo prepare...
Neufeld Learning Systems
Concept: Exponents in Formulas
In this volume and surface area worksheet, students use their calculators to find the volume or surface area of a pictured 3-dimensional figure.
Curated OER
The Calculus Whiz Who Owned a Box Company
Students use the relationship between volume and surface area to construct a box out of a piece of paper that maximizes volume using a table and by using graphing and calculus techniques.
Curated OER
A Cylinder Workshop
Students work with given formulas to solve for specific variables. The calculation of the volume of a cylinder and the change in volume when there is a constant surface area is analyzed in this instructional activity.
Curated OER
Changing Twines: Exploring Area and Perimeter
Third graders review formulas for area and perimeter in quadrilaterals. They arrange pre-cut twine on a centimeter graph paper to create non-congruent quadrilaterals. They calculate the perimeter and area of each form.
Curated OER
Pooling Around
Students complete a unit of lessons on computing area and volume. They play a Jeopardy game of basic area formulas, calculate surface area of shapes, develop a Powerpoint presentation, and conduct a simulation of finding the surface area...
Curated OER
Using Nets to Find Surface Area
Eighth graders explore three-dimensional objects (prisms, pyramids, cylinders and cones) to draw nets. They use the understanding of drawing nets to find the surface area of pyramids and cylinders.
Curated OER
How Does Cell Size And Shape Affect Transport of Materials
Tenth graders explore concepts of surface area, volume, and ratios, create spreadsheets to aid organization of data collected and provide graphing capabilities, and use NIH Imaging to enable calculations of microscopic organisms.
Curated OER
Inquiry Unit: Modeling Maximums and Minimums
Young mathematicians explore the maximun area for patio with the added complexity of finding the mimimum cost for construction. First, they maximize the area of a yard given a limited amount of fence and plot width v. area on a...
Curated OER
Geometry, Measurement & Reasoning
Students measure prisms and determine their volume. In this measurement and reasoning lesson, students estimate the volume and area of prisms. They measure given boxes. Students use paper to create prisms and cylinders. They determine...
Curated OER
New Boxes From Old
Middle schoolers find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new,...
Cornell University
Scaling Down: Effects of Size on Behavior
Two activities explore the concept of size, especially small sizes down to the nano. Scholars practice determining volume, mass, and density and calculate exponential increases and decreases. They then predict and test the effect of size...
Curated OER
Cook Me Up Some Equations
Students study a variety of math concepts in the context of cooking up a meal. In this math activity, students calculate surface area and volume. They draw and interpret different types of graphs.
Curated OER
Volume of Spheres
Pupils find the volume of spheres. In this geometry lesson, students measure and derive the formula for each shape and solid. They use the correct terminology and units when solving these problems.
Curated OER
Radius, Diameter and Area
Students identify the radius and diameter of a circle. In this geometry lesson, students calculate the volume and area of a cylinder and circle. They relate the circumference of a circle to Pi.
Teach Engineering
Penny Perfect Properties (Solid-Liquid Interations)
I can get more water to stay on a penny than you can! Collaborative pairs determine the volume of liquids that can be contained on the surface of copper pennies and plastic coins. The pairs analyze their results using graphs and go on to...
Mathematics Assessment Project
Evaluating Statements About Enlargements
Double, toil ,and double linear dimensions. Learners first complete an assessment investigating how doubling linear dimensions affects the area of pizzas and the volume of popcorn containers. They then complete an activity investigating...
Curated OER
Measurement
Students identify and categorize different problem situations or contexts using one of four measurements to solve the problem. Through guided and independent practice, they discover ways to determine which measurement to use when...
Curated OER
Which container holds a larger amount of popcorn?
What does popcorn have to do with math? Seventh grade mathematicians are provided an opportunity to develop a conceptual understanding of the formula for volume and to use it as a tool to solve problems. The lesson begins with a...
Curated OER
Area Explorations
Learners explore the concept of area. For this area lesson, students find the area of irregular shapes with right angles. Learners break down each irregular shape into multiple regular shapes in order to find the area. Students...
Curated OER
Finding the Area & Volume of Buildings Using Architectural Drawings
Fifth graders find the area and volume of buildings. In this architecture lesson plan, 5th graders look at the drawings of three historic Tennessee buildings. They use these to help find the area and volume of the building.
Curated OER
Exploring Volume of Cylinders
Tenth graders investigate the volume of a cylinder. In this geometry lesson, 10th graders create three-dimensional cylinders and use a ruler to determine the dimensions. The lesson progresses to the use of the formula to find...
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