Lesson Topic: Volume of Cylinders Grade: 7 Subject: Math 7 Student Teacher: Jordan Hunt

Transcription

1 Lesson Topic: Volume of Cylinders Grade: 7 Subject: Math 7 Student Teacher: Jordan Hunt Virginia Standards of Learning Objective Standard 7.5a & 7.5b Strand: Measurement Grade Level 7 a) Describe volume and surface area of cylinders. b) Solve practical problems involving the volume and surface area of rectangular prisms and cylinders. Lesson Objective By the end of this lesson the students will have learned new vocabulary relating to finding volume, recognize practical uses of finding volume, and the formula for finding volume of a cylinder. The students will demonstrate their understanding of the lesson in a few ways: o Applying the volume formula when given different cylinders in different problems, including word problems o Independent practice o Ticket to leave o Short quiz Task Analysis Essential understandings, knowledge, and skills: o Find the volume of a cylinder. o Solve practical problems that require finding the volume of a cylinder. Do the students know what volume means? o Yes, students will know what volume means in the context of rectangular prisms. This knowledge should lead them to understanding what volume is in the context of cylinders. Do the students know what a cylinder is? o The students may not know what a cylinder is. A definition and examples will be given at the beginning of the lesson. Are students proficient in the topic of 2D measurement; i.e. finding the area a rectangle and a circle, finding circumference and perimeter, etc.? o Yes, students should have an understanding of this since a review was given during the volume of a rectangular prism lesson. Do students know properties of basic shapes?

2 o Yes, students should know the properties of basic shapes. Do the students know how to find the volume of the most basic 3D shape, a rectangular prism? o Yes, students should know this very well since it was the last lesson taught. Key Terms (Teacher Input) Volume- The volume of a solid is the measure of space occupied by it; the amount of liquid or solid that will fill a 3D object. Cylinder- A three-dimensional figure with two parallel congruent circular bases. Diameter- The distance across a circle through its center. Radius- The distance from the center of a circle to any point on the circle. Pi ( )- Mathematical constant that is the ratio of any circle s circumference to its diameter. In this lesson, students will only need to understand that pi is approximately 3.14 or. Units Cubed- What volume is measured in; ex. cubic centimeters (cm 3 ) or cubic inches (in 3 ). Sequence of Lesson Anticipatory Set: o Students will immediately begin their warm-up activity that is on the board. This is a review of their past lesson on finding the volume of rectangular prisms. Therefore, it will activate prior knowledge and allow them to recall what volume is. There will be 4 problems, one on each slide, which students will work on individually. The slides will be on a timer, so the PowerPoint will automatically switch slides to the next problem. When the students have completed all of the problems, ask for volunteers to come up to the board and teach the class how to do the problem. If there are not enough volunteers to present each question, use popsicle sticks to randomly call on students. If a student had trouble with one and is called on, allow them to have one pass. However, if they are called on again, they must go up to the board. (warn them of this beforehand.) Teacher Input o After the warm-up, start the PowerPoint. Tell students that they should fill in their notes outline as we go through the PowerPoint. Be sure to remind students that everything they need to fill in on their outline will be written in red in the

3 PowerPoint. Also, when the slides come up that students need to fill something in on their outlines, be sure to mention in orally. Introduce the topic of finding volume of a cylinder to the students. Define cylinder within the first slide After the first slide, let the second slide prompt a review of what volume is. The second slide, entitled Remember will prompt an experiment, led by the teacher with class participation. Take a sheet of paper and join the top and bottom edges to form a "base-less" cylinder. The edges should meet exactly, with no gaps or overlap. With another sheet of paper the same size and aligned the same way, join the left and right edges to make another cylinder. Stand both cylinders on a table. One of the cylinders will be tall and narrow; the other will be short and stout. We will refer to the tall cylinder as cylinder A and the short one as cylinder B. Mark each cylinder now to avoid confusion later. Now pose the following question to the class: "Do you think the two cylinders will hold the same amount? Or will one hold more than the other? If you think that one will hold more, which one will that be?" Have them record their predictions, with an explanation. Place cylinder B in a large flat box with cylinder A inside it. Fill cylinder A. Ask for someone to restate his or her predictions and explanation. With flair, slowly lift cylinder A so that the filler material falls into cylinder B. (You might want to pause partway through, to allow them to think about their answers.) Since the filler material does not fill cylinder B, we can conclude that cylinder B holds more than cylinder A. Ask the class: "Was your prediction correct? Do the two cylinders hold the same amount? Why or why not? Can we explain why they don't?" (Note to the teacher: because the volume of the cylinder equals r 2 h, r has more effect than h [because r is squared], and therefore the cylinder with the greater radius will have the greater volume.) *Experiment adapted from When the experiment is over and meaningful discussion has ensued, turn to the next slide and prompt students to take out their SOL formula sheet

4 they received last lesson. Help them locate the formula for find volume of a cylinder. The next slide will be a review of key terms like diameter, radius, and pi. Modeling o The next two slides of the PowerPoint introduce very basic problems involving finding the volume of a cylinder. Walk the students through these problems. (Use SmartBoard to model) o After the basic problems, the next two slides introduce word problems involving finding the volume of a cylinder. Check for Understanding o At the conclusion of the first four slides containing problems of finding volume of cylinders, do a quick check for understanding. Use index cards that students will have on their desk. Have students hold up the green card if they understand everything to the point where they could teach someone else, yellow if the student is still has some confusion or just feels like he/she needs more practice, and red if the student has a lot of confusion. o Take note of any yellows and reds and be sure to pay particular attention to them during independent practice. Guided Practice o The next 4 slides will contain questions that students will work on with their elbow buddy. We will use think-pair-share to work through these problems. Students will be given about two minutes to work on the problem individually. When teacher rings bell, the student should turn to their elbow buddy to discuss the problem. If there are differences in their answers, the students should discuss the problem and find the best answer together. Again, give about two minutes then ring the bell. After students have talked to their elbow buddy about the problem, the teacher will give the answer. Check to make sure every pair got the answer by simply asking Who got this answer. If the teacher sees a pair who didn t raise their hands, the teacher should go over the problem step by step on the board. Independent practice o When the PowerPoint is finished, students will use laptops for independent practice.

5 Students will sign into teacher s homepage on studdyladder.com ( then they will find their name on the right hand side of their screen and simply type in the password that was given to them (passwords and names should have been set up by teacher ahead of time, so all teacher will have to do is tell the student their password have list out and write password on a sticky note and give to each student) See screen shot below for a view of the homepage. Once students are logged in, they click on tasks within the toolbar, scroll down to mathematics and there should be an interactive activity on finding the volume of cylinders on their screen. See screen shot below.

6 Students should start game and have their yellow, green, and red cups stacked on their desks. If a student is a little stuck, but doesn t urgently need help, he/she will have a yellow cup on top. If he/she is making good progress and doing well, he/she will have a green cup on top. If a student really needs help and is really stuck, he/she will have a red cup on top. Teacher should walk around and watch student progress. Be aware of cup colors. Be sure to note that the last question on the activity is tricky and students should pay close attention to the units. Differentiation o Bodily/Kinesthetic learners will find satisfaction in the beginning warm-up activity, when they can come up to the board. o Auditory learners will most likely learn best from listening to the lesson and recognizing what they need to fill in on their notes outline. Learning from their peers during the warm up will also benefit the auditory learners. o The discussion about which cylinder will hold more in the beginning of the lesson, the warm-up, and working with elbow buddies will appeal to interpersonal learners whereas intrapersonal learners will more likely enjoy working out problems on their own on whiteboards and using the laptops for independent practice. o Visual learners will learn best from the teacher-led experiment.

7 o Logical/mathematical learners will most likely be the students who conceptualize the experiment and capitalize on the questions and prompts derived from that discussion. Closure o Students will demonstrate what they have learned with a ticket to leave. On the ticket to leave, ask the students to write, in their own words, what they have learned today about finding the volume of a cylinder and give an example of a cylinder that they see in everyday life on a piece of paper. Encourage them to use pictures, words, charts, whatever works best for them. o Ask students to hand their cardstock to the teacher as they leave the classroom. Assessment o The pre-assessment for this lesson will be the warm-up activity where students work on finding the volume of rectangular prisms. o Formative Assessments: The ticket to leave will also serve as a form of informal assessment; to see how deep of an understanding they have of the concepts discussed in class. Also, when students complete the activity on studyladder.com, the grades are immediately reported to the teacher automatically. This will give the teacher instant feedback of who in their class is understanding the topic and who isn t. o Ask students to study since they should expect a quiz on finding volume of rectangular prisms and cylinders next class. This will be a summative assessment for this lesson. Materials o Two 8 1/2" by 11" pieces of paper (for experiment) o A filler--rice krispies, popcorn, birdseed, cheerios etc. (for experiment) o Warm-up o PowerPoint o Notes Outline o Yellow, green, and red index cards o Laptops o Yellow, green, red cups Technology Integration o PowerPoint will be used to give students a visual of cylinders. 3-D objects are difficult to effectively and accurately draw on a whiteboard.

8 o Utilizing SmartBoard technology, the teacher will be able to underline, circle, or add to sentences and pictures to better student understanding of finding volume of cylinders. Also, students will be able to utilize the SmartBoard during the warm-up. o Laptops will be used for independent practice. Student and teachers will get instant feedback. Also, this will allow students to go at their own pace and if they get a question wrong, the activity explains how to solve the problem for them. Reflection

9 Math 7 Notes- Volume of Cylinders Name: Date: Block: A is a three-dimensional figure with two parallel congruent circular bases. Formula for volume of a cylinder: o r: radius o h: height Diameter is the distance across a circle through its. Radius is the distance from the of the circle to any point on the circle. ( the diameter) Pi ( ) = or. EXAMPLES 1. Find the volume of this cylinder: 2. Rodolfo is designing a new, cylindrical 4 cm drinking glass. If the glass has a diameter of 8 cm and a height of 12.8 cm, how much liquid can it hold? 11 cm