Geometry Lesson Plan

Transcription

1 Curriculum/Instructional Strategies: Geometry Lesson Plan This is a geometry lesson plan. Students will calculate the volume and the surface area of some specific objects. Teacher Direct Instruction (TDI) will be used in teaching this lesson. First, students will be provided the objective of the day. If there are multiple objectives, students will be introduced to them one by one. One objective will be fully taught then the class will be moved to the next one. In teaching this lesson TAPPLE will be very useful. TAPPLE stands for teach, ask, pause, pick, listen and echo. This is a very powerful technique in teaching mathematics. There are also plenty of pair share and whiteboard activities in this lesson where supports students engagement. Objective(s): 1. Students will be able to calculate the volume of cylinder 2. Students will be able to calculate the volume of rectangular cube. 3. Students will be able to calculate the surface area of rectangular cube. First objective: Warm up question: (students will have 7 minutes to work on the warm up. Then, they will get an additional 2 minutes to share their answer with a fellow students. After that, using popsicle sticks, students will called on to answer the questions.) 1. High light the radius and indicate its value: Using an arrow mark the height on the following examples.

2 3. Find the area of the following circle. 4 Objective: Students will be able to calculate the volume of cylinder. What is cylinder? (I will explain what cylinder is, and I will project various picture of cylinder on the screen. They also will get the chance to see some cylinder that were cut in foam at Pacific Southwest Container, where I did my SPIE summer intern) (I will ask students to draw a cylinder on their whiteboard and mark the height and the base of their example) What is volume? (I will explain what volume is using an empty cylinder type container. I will start to fill this container with water where students will understand the meaning of volume.) I will then unfold a paper cylinder and I will ask students to name the shapes resulted from unfolding the cylinder on their whiteboard. Students will share their answer with a fellow student.

3 Students will explain what volume is using words or picture on their whiteboard. Students will take notes on the followings. To calculate volume of a cylinder, we need to know the followings: o The height of the cylinder o The area of the base of the cylinder Height : (students now know the reason they were asked to point out the hight in the warm up and I will point to this connection) Height What is the area of the base of the cylinder? Students reviewed the area of the circle in their warm up and I will point out the reason they were asked to calculate the area of the circle in the warm up. 4 Student will take note on the following formula: Volume = Area of the base x height

4 I will model an example first. Then I will give them another example and ask for volunteers to help me solve it. After that, students will get an example and need to answer it on their whiteboard. Then I will ask students to make their own example on their whiteboards and find the volume of their cylinder. For closure: I will show them the pictures I took from the packaging and assembly department of the Pacific Southwest Container company were employees use the concept of volume daily. Then, students will get the cylinders I got from that department. I will divide the students in ten or eleven groups of three and I will have them measure the height and the radius and find the volume of the cylinder. Second objective: Warm up question: (students will have 7 minutes to work on the warm up. Then, they will get an additional 2 minutes to share their answer with a fellow student. After that, using popsicle sticks, students will called on to answer the questions.) 1. Highlight the length and the width of the following rectangle 2. Using the arrow point out the height of the following shape:

5 3. Find the area of the following rectangle Objective: Students will be able to calculate the volume of rectangular cube. What is a rectangular cube? (I will explain what rectangular cube is, and I will project various picture of this shape on the screen. They also will get the chance to see some rectangular cubes that were cut in foam at Pacific Southwest Container, where I did my SPIE summer intern) (I will ask students to draw a rectangular cube on their whiteboard and mark the height and the base of their example) Students will take notes on the followings. To calculate volume of a rectangular cube, we need to know the followings: o The height of the rectangular cube o The area of the base of this shape Height : (students now know the reason they were asked to point out the height in the warm up and I will point to this connection)

6 Height What is the area of the base of the rectangular cube? Students reviewed the area of the rectangle in their warm up and I will point out the reason they were asked to calculate the area of the rectangle in the warm up. I will then unfold a paper rectangular cube and I will ask students to name the shapes resulted and the base from unfolding this rectangular cube on their whiteboard. Students will share their answer with a fellow student. Student will take note on the following formula for the second time: Volume = Area of the base x height I will model an example first. Then I will give them another example and ask for volunteers to help me solve it. After that, students will get an example and need to answer it on their whiteboard. Then I will ask students to make their own example on their whiteboards and find the volume of their rectangular cube.

7 For closure: I will show them the pictures I took from the packaging and assembly department of the Pacific Southwest Container company were employees use the concept of volume daily. Then, students will get the rectangular cubes I got from that department. I will divide the students in ten or eleven groups of three and I will have them measure the height, the length, and the width of the rectangular cube. After that, they will find the volume of the rectangular cube. Third objective: Warm up question: (students will have 7 minutes to work on the warm up. Then, they will get an additional 2 minutes to share their answer with a fellow student. After that, using popsicle sticks, students will be called on to answer the questions.) 1. Find the area of the following rectangles:

8 Objective: Students will be able to calculate the surface area of rectangular cube. What is surface area? (I will explain what surface area is using a rectangular cube type container. I will start to cover this container with wrapping paper where students will understand the meaning of surface area.) I will then unfold a paper rectangular cube and I will ask students to name the shapes resulted from unfolding this rectangular cube for the second time on their whiteboard. Students will share their answer with a fellow student. Students will take note on the following: Surface area is basically the sum of all the areas of the shapes we get from unfolding the rectangular cube. I will model an example first. Then I will give them another example and ask for volunteers to help me solve it. After that, students will get an example and need to answer it on their whiteboard. Then I will ask students to make their own example on their whiteboards and find the surface area of their rectangular cube. For closure: I will show them the pictures I took from the packaging and assembly department of the Pacific Southwest Container company were employees use the concept of

9 surface area. Then, students will get the rectangular cubes I got from that department. I will divide the students in ten or eleven groups of three and I will have them measure the height, the length, and the width of the rectangular cube. After that, they will find the volume and the surface area of the rectangular cube. Activities: What students will experience from this activity is that they can see the use and the importance of geometry in our world. By seeing the pictures from the Pacific Southwest Container and the geometric concepts employees use daily, students will get the idea of how important is geometry and how actually it s been use every day.

10 Lesson plan Student Performance Pre-requisite skills: How to calculate percentages, averages, and percent increase. Goals: Students use percentages to chart their performance, similar to the way employers record the performance of their employees using Microsoft Excel. Materials: Students will need a computer with Microsoft Excel, a formatted Excel spreadsheet, and a progress report. Procedure: Students will be given a progress report with a record of what they received on each assignment. First students will assign numbers to their homework assignments and quizzes on the progress to be used as a reference number on the spreadsheet. For each week and each assignment each student will enter the points possible and points earned to the spreadsheet provided.. Students will be guided in entering their scores and the formulas to calculate their percentages into Microsoft Excel as a class; they will also use Excel to create charts of their progress. Assessment: Students will be expected to complete their spreadsheet, graph, and answer questions provided on the spreadsheet.

11 Week 1 Week 2 Homework Possible Score Quiz Possible Score Homework Possible Score Quiz Possible Score day day Totals: Percentage: YTD: Totals: Percentage: Percentage: D: YTD: YT Week 3 Week 4 Homework Possible Score Quiz Possible Score Homework Possible Score Quiz Possible Score da y 1 da y Totals: Totals: Percentage: YTD: Percentage: YTD: Percentage: YTD: Percentage: YTD: Week 5 Week 6 Homework Possible Score Quiz Possible Score Homework Possible Score Quiz Possible Score Totals: Totals: Percentage: YTD: Percentage: YTD: Percentage: YTD: % Increase Percentage: YTD:

12 Week Homework Quizzes ) What was the cause of your greatest increases or decreases during the 6 week period? 2) Look at your graph of homework and quizze percentages; do your homework percentages and quiz percentages appear related? 3) If you were to judge your performance only on your homework and quiz percentages what would your grade be?

13 LESSON PLAN: Geometry and Innovation at Frito Lay Curriculum/Instructional Strategies: Direct Instruction Group Problem Solving Jigsaw Objectives: Students will use dimensional analysis to convert units of measurement when solving a complex problem. Students will use ratios to calculate total savings, profit, and payoff time. Students will use the internet to research new terms, conversions, and information relevant to solving the problem. Activities: Students will have a choice of being a part of the Tsunami Project, the Starch Dryer Dilemma, or the Solar Field project. In the Tsunami Project, students calculate the amount of water and money saved by recycling the water used to wash and peel the potatoes. In the Starch Dryer project students have to decide whether replacing the old starch dryer with a larger one would save the company money. In the Solar Field project students have to calculate the number of solar panels needed to produce a set amount of BTU s for the plant. Students will be in groups of 3-4. There will be more than one group working on each project. Warm Ups (attached) will be given to pre-assess student knowledge of dimensional analysis and to directly instruct skills that are weak. Vocabulary research will be given to groups to do at home or online if available (attached) One project description will be given to each group with an advance organizer for written solutions. (attached) Students will present their results to the class via transparencies and white board. Multiple solution methods may arise since several groups will be working on the same project. Assessment: A rubric will be provided to assess their mathematics, presentation, and slogan. Products: Groups will create a slogan in support of their project including the amount of money and resources it will save the company

14 WARM UP: 1. Find the volume of the cylinder. 5 ft. 30 feet 2. Use dimensional analysis to calculate the number of minutes in a year. 3. If a piece of equipment costs $1,000,000, and it saves the company $225,000 per year, in how many years will it be paid off?

15 4. If the lifetime of the same piece of equipment is 15 years, how much money will be saved over that amount of time? VOCABULARY: Use the internet or a dictionary to describe these terms. You may also attach a picture to further define the item. Tsunami Starch BTU Solar Panel Other new words:

16 INTERNET RESEARCH: 1. Search the web using Google to find convert. Write down any conversions you will need below. In your write up, show all steps to your solution. 2. How many gallons are in 1 cubic foot? 3. What is the weight of water per gallon? 4. How many square feet are in an acre? List any other research used to find your solutions.

17 PROJECT DESCRIPTION: Tsunami! Problem: Frito Lay is looking for ways to save water! One way is to recycle the water used to wash the potatoes. By simply adding a chemical to the cleaning water which kills the microbes, water and money will be saved for the company. They need engineers to calculate 1) How much water is in the cylindrical tank, 2) How much water would you save in one week, in one year? and 3) How much money would be saved in a year? Part 1: A cylindrical tank of water used for washing and peeling the potatoes has a radius of 3.5 feet and is 20 feet tall. It is filled ¾ full of water. How many cubic feet of water are in the tank? What is the weight of the water? How many gallons of water is this? Part 2: Facts: The potato peeler uses 80 gallons per minute. The PC (potato chip) 21 Wash Box uses 45 gallons per minute.

18 The PC50 Wash Box uses 70 gallons per minute. The machines operate 24 hours per day, 5.5 days per week for 52 weeks per year How much water would you save in 1 week? In 1 year? Part 3: Facts: 1,000,000 pounds of water costs $2190. The tanks would only need to be refilled once per week instead of every day. How much money would be saved each week? Each year? PROJECT DESCRIPTION: The Starch Dryer Dilemma Frito Lay needs its Engineers to decide whether replacing the old starch dryer with a larger one would save the company money. The engineers need to calculate 1) the amount in pounds of starch per hour saved by using the new dryer 2) How many more dollars per year would the company receive for recycling the starch produced with the new dryer? 3) How much money would be saved per year if the company sent less dirty water down the drain? 4) Find the total savings per year by utilizing the new starch dryer. 5) Find the amount of years it will take the company to recoup their investment in the new starch dryer.

19 Part 1: Facts: The capacity of the old dryer is 550 pounds per hour. The plant produces 800 pounds per hour of starch. How many pounds per hour are saved by using the new dryer? Per year? Part 2: Facts: The company receives $13.75 per 1000 pounds of starch from other companies needing this product. How many more dollars per year would the company receive for recycling the starch produced with the new dryer? Part 3: Facts: 150 pounds of starch produces 100 pounds of dirty water released to the city. The City of Modesto charges companies $ per 1,000 pounds of dirty water produced by manufacturing. How much money would the company save per year if it sent less dirty water down the drain? Part 4: Find the total savings by adding Part 2 and Part 3 Extra Credit Part 5: Facts: The Cost to upgrade to the new Starch Dryer is $770,000. If the Lifetime of the new dryer is 15 years, how much money would the company save by upgrading this dryer? Find the amount of years it will take the company to recoup their investment.

20 PROJECT DESCRIPTION: Solar Field Problem Frito Lay created a field of solar panels to help power their plant. This is where the jingle Sun Chips made by the sun! originated. The company needs engineers to calculate 1) the total amount of power in BTUs collected from the solar field 2) the number of solar panels needed in the field to produce that amount of energy 3) the amount of space in square feet and acres, (excluding walkways) the solar panels take up. Finally you will create a drawing of your solar field. Part 1: Facts: Below is a list of BTUs (in millions) produced each month by the solar field: Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Total What are some generalizations you can make from the table? Calculate the total BTUs generated from the solar field for the year. What is the average amount of BTUs produced per month?

21 Part 2: Facts: Each panel produces 18.5 BTUs per month. How many solar panels are in the field? Part 3: Facts: Each solar panel is 6 ft. by 10 ft. How much space in cubic feet and acres do the solar panels take up (not including walkways)? Part 4: Use graph paper to design a layout for a 3 acres field that fits your solar panels an allows room for walkways in between.

22 PRESENTATION/SLOGAN: The group will put together a short demonstration of their solution to the project using transparencies or the whiteboard. They could also choose to do a short powerpoint. Each member should take part in the presentation and be available to answer questions. The group will also create and demonstrate a slogan in support of their project which highlights the amount of money and/or resources it will save the company.

23 RUBRIC FOR GRADING: Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18. Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18. Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18.

24 Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18. Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18. Name Project Period Attach all 6 components of the project: Warm Up, Vocabulary, Research, Presentation, and Advertising Slogan Completion of all 6 components Work shown Accuracy Total Points received out of 18.

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31 Tenney Norquist, Inc. Curriculum/Instructional Strategies: Algebra Readiness is a course designed to give teachers the flexibility and time to rebuild foundational skills and concepts that may be missing from earlier grades. Teachers are given the freedom to address student needs and fill in gaps in the child s mathematical knowledge. While the course outline lists chapters in sequential order, concepts can be addressed to meet individual needs. Topics to be covered include whole numbers, variable expressions, solving equations, decimal operations, fractions, exponents, fraction operations, ratios, percents, integer operations, inequalities, two-step equations and square roots. Students will work through a series of problems involving measurements involving fractions. They will need to read a diagram of a reduction unit and determine the length and width of the piece of sheet metal to fabricate the piece. They will then work in small cooperative learning groups using the measurements they have made to put together the different pieces each student would have in order to complete the project. Objectives: Activities: Assessment: Products: 1) Students will correctly add and subtract fractions with like denominators. 2) Students will correctly add and subtract fractions with unlike denominators. 3) Students will correctly assemble the four pieces of the project. 1) Review of addition and subtraction of fractions with like and unlike terms using white boards. 2) Students work on measurements from individual pieces in order to determine the correct size of sheet metal. 3) Students work in cooperative groups to assemble their project. 4) Students present their final project to the class. If the pieces are assembled correctly, measurements will have been correctly calculated. The correctly (or incorrectly) assembled project will be the product of the lesson.