Education Standards
Surface Area, Volume, and Density Module
Overview
Students will be reviewing and learning surface area, volume, and density over three days. The remaining two days will be used for the students to explore the topics with hands-on material using everyday shapes.
*This work was made possible by the generous support of the National Science Foundation, grant #1755631, and the University of St. Francis Noyce STEM Educators Program
Surface Area, Volume, and Density
Time Frame: 5 days (based on 50 minute class periods)
Objectives:
SWBAT. . .
Calculate the surface area of a 3D figure
Demonstrate a conceptual knowledge of volume
Apply concepts of density based on area and volume
Create volume word problems and associated answer keys
Standards:
CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*
MS-PS1-2. Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred.
TWASAT. . .
Calculate surface area of a 3D figure by checking homework on SA
Apply concepts of density based on area and volume by observing class discussions and checking homework
Create volume word problems by analyzing answer keys
Instructor Overview:
This module consists of students reviewing and learning surface area, volume, and density. One day is allocated to each topic for a total of three days of material. The remaining two days will be used for the students to explore the topics with hands-on material. They will have everyday objects with which they will find surface area, volume, and density. Connections between geometry and chemistry will be made based on substance properties. For each day of material presented, the teacher will present the information using the module PowerPoint attached. Day one’s main goal of the lesson is for students to discover surface area formulas. It will begin with review on two-dimensional area using Google Forms. Connections will be made between area and surface area. Exit slips will be given to assess whether students understand the definition of surface area. Homework will be given to practice computations of different surface area formulas. Day two’s main goal of the lesson is for students to discover volume formulas. It will begin with review on day one’s homework. Distinctions will be made between area and volume. Exit slips will be given to assess whether students understand the definition of volume. Homework will be given to practice computations of different volume formulas. Day three’s main goal is to apply geometric concepts to density. Students will work together to solve problems based on density. Exit slips will assess whether students are able to connect density to a topic outside of mathematics. Homework will be given to further apply density concepts. Day four and five will consist of students using hands-on objects to demonstrate their understanding of the material they learned in the last few days. Students will create their own word problems on volume and density with a peer and associated answer-key to further demonstrate their understanding.
Day 1: Surface Area
The lesson will consist of reviewing previous information on area and presenting on Surface Area using the PowerPoint linked below with assigned problems afterwards. Please see the notes section in the PowerPoint for a guide and feel free to add or remove information. My intended goal is to have material ready for educators to use at their own disposal. Students will begin today’s lesson by reviewing the area. They will read information on a webpage to recall formulas and units. Afterwards, they will take a quick self-assessment to determine whether they understand the information. Instruct the students to let you know when they have finished the self-assessment. Go over any problems they may have missed. The students will then have information presented to them by the instructor. If the presentation finishes early, they can begin their homework problems to go over the next day.
Student Instructions are located here: https://docs.google.com/document/d/1Zvso-1Xi5KqavG38nvNXcRzAl6rbjQcw9OCqph4uum4/edit?usp=sharing
Exit-Slip: https://docs.google.com/document/d/1EaEpy_ACNSG2GdUc0vL0PSvTcfusoW0KsbzH6a1CFKU/edit?usp=sharing
Day 2: Volume
The lesson will consist of reviewing homework problems from day one on Surface Area. Afterwards, the instructor will present material using the PowerPoint attached at the end of this section. Again, my intended goal is to have material ready for teachers to revise and use at their own disposal and preferences. See the notes section in the slides for a guide and feel free to add or remove information. Once the presentation is finished, students can begin their homework problems to be reviewed at the beginning of class the next day.
Student Instructions are located here: https://docs.google.com/document/d/1mozhOogRar4xq-gwRig6imhILT1TQ2IQP7A_3B_-R3k/edit?usp=sharing
Exit-Slip: https://docs.google.com/document/d/1n2yhNidCSVO1dflx3Bu2kfSdqfcRuyFUNvCj9mEXBc/edit?usp=sharing
Day 3: Density (Integrated Unit)
The lesson will consist of reviewing homework problems from day two on Volume. Afterwards, students will read a page from OpenStax on density. From the student instructions, they will then be directed to watch a video connecting volume with density. The instructor will then present material using the PowerPoint attached at the end of this section. The PowerPoint only presents instructions for the students to participate in an online simulator to further their understanding from the reading and video. Again, my intended goal is to have material ready for teachers to revise and use at their own disposal and preferences. See the notes section in the slides for a guide and feel free to add or remove information. Once the presentation is finished, students can begin the interactive simulation. Homework problems will be given at the end of class to be reviewed at the beginning of class the next day.
Student Instructions are located here: https://docs.google.com/document/d/1B8SWkI92DUPDzIlkBFuaMFJqKgzYBGb3ZbvyUPzbdP0/edit?usp=sharing
Exit-Slip: https://docs.google.com/document/d/1nnWSqGHdw1Jflc24_Z5yK00l2z_3yJpOwOGKBjQEHXg/edit?usp=sharing
Day 4 / Day 5: Hands-on Application
These last two days are a hands-on application of the last three days of material. Students will use everyday objects to calculate surface area, volume, and density. Review homework on density at the beginning of Day 4 if necessary.
Materials Needed: calculators, everyday objects (sphere, cylinder, or cone-shaped), rulers, scales
Day 4 (Part 1)
1. Teacher will display sample objects to students (rubber ball, dice, book, etc.)
2. Teacher will ask students what is similar between each object
They should respond that all objects take up space (volume) and have density (mass/volume)
3. Teacher will explain students will be finding the surface area, volume, and density of a few objects (depending on the time)
6. Teacher will pair the students, distribute formula sheet to each student, and distribute objects to each group.
7. Teacher will ask the students to find the SA, volume, and density of each shape
8. Students will find calculations for each using the formula sheet after measuring length, width, and height with a ruler
Day 5 (Part 2) Continuation. . .
1. Teacher will ask the students to create word problems for their peers. Teacher will give examples such as “How many scoops of ice cream will fit in [name of shape]?”
2. Students will create word problems with correct grammar, punctuation, etc. and create an answer key for their problems.
3. Teacher will ask student pairs to exchange them with other pairs.
4. Students will solve each other’s created word problems.
5. Teacher will monitor the work of the students as they create and solve each other’s problems.
6. Teacher will ask students to list the reasons it is important to accurately know the volume of objects. Examples: gas tanks, etc.
7. Students will discuss these reasons with each other.