Volume of a Cylinder (8th grade lesson)

  by Tina Richman hide properties
edit properties Description: Children learn about appropriate social behavior Document Type: Lesson Plan edit page Resources edit Lesson Overview
 After calculating the volume of a cylinder using the formula students will complete the following activities:

Microsoft Excel
-Use Microsoft Excel to input their answers from their calculators and decide the correlation between the numbers already entered in the Excel sheet and how they relate to the volume of a cylinder formula.

-Type in formulas for the other two cylinders.

-Check the values on the spreadsheet against the ones they calculated by hand.

-Alter the radius and volume in the Excel sheet and discuss why doing this is significant.

-Answer comprehension questions individually and then review with the class.

-Answer review questions individual in Microsoft Word and go over as a class.

 

Graphing Calculator

 -Use the graphing calculator handout as a guide to complete the first steps together.

-Work individually to complete the other steps and test their program to see if it works.

-Write another program on your graphing calculator to calculate the area of a rectangle. 

-Write another program on your graphing calculator to calculate the perimeter of a rectangle. 

-Complete some graphing calculator challenges

edit Teaching Techniques and Strategies  Co-Teaching; Alternative Teaching:
I'll work with inclusion students and/or students who need enrichment instruction on more concrete to abstract problems, Ms. Conrad works with the other group of students on more asbstract problems.

Differentiated Techniques/Activities:
-Appointment Calendar
-Math Cube
-Exit Card 

 Inclusion: While other students are working on the Excel spreadsheet part of the lesson. Have these students take a sheet of paper, and roll it up to form a baseless cylinder. Now take another sheet, rotate the paper, and form another baseless cylinder. Think about the volume of each cylinder and make a prediction.

Would the two volumes be equal? Would the short cylinder have greater volume? Would the tall cylinder have greater volume?
Why did you predict as you did?

Tape two sheets of paper to form the two cylinders, one short and one tall (Stiff paper is helpful. I use transparency sheets). Hold the tall cylinder upright in a shallow box and fill with rice. Now fill the shorter cylinder, and compare the two amounts of rice. Was your prediction correct?

Excel spreadsheet: Students will then use their calculators and a handout to guide them to complete an activity using an excel spreadsheet. The steps will be chunked in 3 steps at a time format.

Students will use a different math cube to complete volume activities.

Grouping:
-Individual
-Pairs
-Whole group

 

edit Resources Graphing Calculator    Microsft Excel Volume of a Cylinder sheet    Microsoft Word    Math cube    pg. 106 and 108 of Differentiating Instruction in a Whole-Group Setting 2 sheets of transparency for each inclusion student (where necessary)    Bag of rice    Exit cards    General Ed question: Writing a program for your graphing calculator can be time consuming and difficult. What is the reason for doing it? Inclusion question: Explain one thing you learned about volume today. edit page Details edit Objectives 1. Write and show understanding of a formula in Excel based upon an example. (Blooms, Knowledge and Comprehension)

2. Write a program to calculate the Volume of a Cylinder by following written directions (Blooms, Comprehension)

3. Record answers to comprehension questions (Blooms, Knowledge) 

4. Create at least 2 own programs on their graphing calculators (Blooms, Application and Synthesize)

edit Assessment 1. Execute their written program successfully

 

2. Complete a written program on their graphing calculator

 

3. Answer comprehension questions individually in Word

 

4. Use the Math Cube to select and create at least 2 programs

 

 

 

edit Standards PA Correlated Sets -- PA.M.2.3.8.A  > Develop formulas and procedures for determining measurements (e.g., area, volume, distance). PA.M.2.3.8.D  > Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass and angles. PA.M.2.3.8.E  > Describe how a change in linear dimension of an object affects its perimeter, area and volume. PA.M.2.6.8.F  > Use scientific and graphing calculators and computer spreadsheets to organize and analyze data. PA.SCI.3.7.7.D.5  >--- Apply intermediate skills in utilizing word processing, database and spreadsheet software. if ( typeof sets != 'undefined' ) { sets.push('PA'); } edit Anticipatory Set Time needed: 15 min

Co-Teaching; Alternative Teaching:
I work with inclusion students and/or students who need enrichment instruction on more concrete problems, Ms. Conrad works with the other group of students on more asbstract problems.

My Group will do the following:
The Problem 
Take a sheet of paper, and roll it up to form a baseless cylinder. Now take another sheet, rotate the paper, and form another baseless cylinder. Think about the volume of each cylinder and make a prediction.

A Prediction

Would the two volumes be equal? Would the short cylinder have greater volume? Would the tall cylinder have greater volume?
Explanation Why did you predict as you did?

A Demonstration Tape two sheets of paper to form the two cylinders, one short and one tall (Stiff paper is helpful. I use transparency sheets). Hold the tall cylinder upright in a shallow box and fill with rice. Now fill the shorter cylinder, and compare the two amounts of rice. Was your prediction correct?

The Calculation Calculate both volumes. (You may need these formulas)

Circumference = 2(pi)(r) Volume = (pi)(r^2)h
 

V=      V=       

Ms. Conrads group will do the following:
Turn up the 'Volume!' 

Use a calculator and the formula V=(3.14)r2 h to calculate the volume for each cylinder below. Copy the table below and paste it into Microsoft Word and put your answers into the correct cells. Radius

Height

 Volume

  

 

 

1.2

 5

  

4

 23

  

 

  

  

 

 

 

 

 

 

Drag the Microsoft Excel file "Cylinder Lab" from the Outbox into your niche and open. You should see the same chart as above. We are going to have Excel do the calculations we just did by hand. What does "=Pi*B9*B9*C9" mean? How does it correlate to the volume of a cylinder formula? If you know the answers to these questions, you should be able to type in formulas for the other two cylinders. Do that now. Now check the values on you Excel spreadsheet against the values you calculated by hand at the beginning of the lab. Are they the same? If they are not, figure out where the mistake was made. Make note of what your mistakes were in Word document. Click on one of the radius's and change it to anything you want. Notice what happens to the volume. Try the same thing with one of the heights. Think about why this is significant. Read the questions section and think about the answers. We will discuss together.
edit Purpose The purpose of the activities today are for students to learn volumes of a cylinder, advantages of using an excel sheet, and understanding the reasons for using their graphing calculator to write a program since it can be time consuming and difficult.

edit Procedure Time Needed: 2    -45 minute class periods

1. Announce to the students that they will be learning about the Volume of a Cylinder today using hands-on activities. The first two activities will be divided into two groups.

2. Complete the Anticipatory Set

3. Once the Anticipatory set is finished my group will do the following:
Turn up the 'Volume!' 

Use a calculator and the formula V=(3.14)r2 h to calculate the volume for each cylinder below. Copy the table below and paste it into Microsoft Word and put your answers into the correct cells. Radius

Height

 Volume

  

 

 

1.2

5

 

4

23

 

 

 

 

 

 

 

 

 

 

Drag the Microsoft Excel file "Cylinder Lab" from the Outbox into your niche and open. You should see the same chart as above. We are going to have Excel do the calculations we just did by hand. What does "=Pi*B9*B9*C9" mean? How does it correlate to the volume of a cylinder formula? If you know the answers to these questions, you should be able to type in formulas for the other two cylinders. Do that now. Now check the values on you Excel spreadsheet against the values you calculated by hand at the beginning of the lab. Are they the same? If they are not, figure out where the mistake was made. Make note of what your mistakes were in Word document. Click on one of the radius's and change it to anything you want. Notice what happens to the volume. Try the same thing with one of the heights. Think about why this is significant. Read the questions section and think about the answers. We will discuss together
Once the Anticipatory set is finished Ms. Conrad's group will do the following:

Graphing Calculator:

Together as a class we will follow steps 1-2, 3-4, 5 on the attached sheet "Getting Started: Volume of a Cylinder" taken from the owners manual for your graphing calculator. Now complete 6-9 on your own When you are finished, test your program with the same values from the beginning of the lab. Check to see you get the same values. Read the questions section and TYPE your answers in Microsoft Word. We will discuss together.
4. Once all students are finished they will meet with their 4:00 appointments and complete 1 to 2 Math cube excercises together.

Enrichment/ Inclusion may do any color coded yellow and green activties. 
General Ed. may do any color coded green and blue activities.

          -Experiment with volume of an irregular shaped object(yellow)
          -Calculate the volume of 3 more cylinders using the teachers Excel worksheet (yellow)
          -Calculate the volume of 3 more cylinders using an Excel worksheet you created (green)
          -Write a program on your graphing calculator following the step by step guide OR Write another program on your graphing   
            calculator to calculate the area of a rectangle. (green)
          -Write another program on your graphing calculator to calculate the perimeter of a rectangle. (blue)
          -Write a program on your graphing calculator for the quadratic formula.(blue)
         

5. Hand out exit cards: 
               General Ed question: Writing a program for your graphing calculator can be time consuming and difficult. What is the reason 
                for doing it? 
               General Ed/Inclusion question: Explain one thing you learned about volume today.