Activities
All Lessons Are Based Off a 75 min period. Time spent for each part of the lesson is tentative and should be based off student understanding.
Lesson 1 Introduction
Objectives
Students will identify and understand number facts/relationships for numbers 1-10. They will be expected to apply these number relationships to scientific notation in order to become more familiar with the concept. Finally, students will utilize scientific notation to understand basic astronomy concepts. They will also be the time that the mass of the Sun along with the distance of a light year are introduced to serve as a example of how using Scientific Notation make our lives more simple.
Warm up (10 min)
Students will enter the classroom and answer the following question: How long would it take you to count to 1 million? 1 billion? 1 trillion? Once the students have answered the questions in their notebook, the teacher will ask them share out their answers. The answers shared with the class will stimulate a discussion about place value and order of magnitude. During this time the teacher will explain the meaning of place value along with order of magnitude and its application to Astronomy.
Direct Instruction (15 min)
A discussion will be held following the warm up question to explain the different strategies used to find their solution. The students will share their answers with the class by demonstrating their strategies on the board. Following that, the teacher will break down the concept by elaborating on the estimation that is involved in answering this type of question. They will understand how accurately estimating is dependent on the amount of leading digits used. Next the teacher will provide the examples of the mass of the Sun and distance of a light year to emphasize the importance of estimation. It will then be explained to the students how learning this idea will be useful to them in the future.
Guided Practice (20 min)
At this point students will be introduced to the commonly known number facts for numbers 1-10. The students will then identify various number relationships as the teacher demonstrates the processes on the board. Students will then be asked to create their own number facts with the groups at their table. The students will then be asked to reflect the same facts using Cuisenaire Rods. To build on their understanding they will also be asked to use the rods to create new number facts and relationships on their own. The students will then share out the examples with the class and on the board. One student from each group will come to board and produce the fact/relationships they created with their groups. Included in their explanation will be a description of how they created their relationships with and without the rods. This section of the lesson will conclude with the students discussing the implications of the relationships with their groups. (20 min)
Independent Practice (25 min)
Students will then begin their independent work by identifying something a million seconds old, billion, and trillion seconds old. They will also be asked to convert all results to days and years. This section will conclude with the answers being explained to students to check that they are understanding the concepts.
Closing (5 min)
Students will be asked during the conclusion of the lesson to think about more examples that exemplify the importance of using scientific notation and how efficient it is at expressing numbers neatly. An example of this question may be to have the students identify anything else that uses trillions to describe its value. It should also be reiterated that mastering number relationships will make it easier for the students to grasp scientific notation as they progress through the unit.
Homework
See Appendix for scientific notation worksheet to accompany this lesson.
Lesson 2 Luminosity, Temperature, Size
Objective
During this lesson students will be expected to apply the scientific notation to the luminosity, temperature, and size of a star. Additionally, students will compare and contrast orders of magnitude and understand its implications when describing the qualities of stars.
Warm Up (10 min)
Students will enter the classroom and begin their introductory question for the day's lesson. At the point students should be more comfortable with scientific notation due to extensive practice they will have had prior to this lesson. Accordingly, students should handle the following question rather easily: If the star Proxima Centauri's temperature is 3,000 K, how much cooler is it than the star Bellatrix with a temperature of 22,000 K. Express values using scientific notation and explain what we can hypothesize about the star's qualities based on the values given.
Direct Instruction (25 min)
Students will spend this part of the lesson sharing and discussing their answers from the introductory question. Then, the teacher will explain the answer by describing the relationship that exists between the qualities of a star and its temperature. Two particular qualities affected by a star's temperature include a star's luminosity and size. The students should recognize how prominent the relationship between a star's luminosity, temperature, and size is and discuss the implications with their groups. During their discussion the teacher can facilitate by clarifying misconceptions. For example, a student may wonder how scientists know these answers so accurately. This would provide a perfect opportunity to elaborate on the estimation techniques used in science and particularly astronomy. Then, the teacher would explain how scientific notation enhances the accuracy of a value by focusing on a few leading digits. Thus, making the estimation almost as accurate as it could possibly be. With time permitting the teacher could expound on the concept by explaining to the students the efficiency of using 1-3 leading digits in Scientific notation. Again, understanding how the leading digits determine accuracy should enlighten the students. The 1 st leading digit puts you within 10% accuracy which is considered to be moderately good accuracy. Using 2 leading digits puts you within 1% accuracy, which is considered quite good accuracy. Finally, three leading digits puts you within .1 % accuracy which is considered to be very good accuracy. (This concept may take an extended amount of time to complete, therefore is to the teacher's discretion on much of the information to include in the lesson) Following that the teacher will reiterate the importance of scientific notation and connect the all the ideas learned to the HR Diagram.
Guided Practice (10 min)
Students will receive a copy of their own HR diagram to look over as the teacher models how to read and interpret the diagram. They will then be asked to compare luminosities to each other using scientific notation as their values. They will analyze these values with their groups and indentify the implications of increased and decreased luminosity in regards to temperature and size.
Independent Practice (25 min)
After the students have completed their group work they will share their results with the teacher and class. The correct results will be explained in detail leading the their complete understanding. Accordingly, students will then perform independent work by answering several word problems given by the teacher. The questions associated with this part of the lesson can be found in the appendix.
Closing (5 min)
The teacher will provide answers to the students while the students explain how they obtained their answers.
Homework
Students will complete HR Diagram worksheet given to them to be discussed the next day in class.
Lesson 3 Currency
Objectives
The students will expected to compare and contrast orders of magnitude with currency in practical and sometimes impractical terms. They will also be expected to apply scientific notation when representing currency values.
Warm Up (10 min)
This lesson can be expected to be completed towards the end of the unit and thus the students should have a strong understanding of scientific notation. Students will enter the classroom and begin the lesson with this introductory question: If the country, Zimbabwe in Africa, has a currency value of 10 - 1 7 when compared to the American dollar, how much money would you have if you went there with 10 dollars?
Direct Instruction (15 min)
The teacher will then explain the introductory question to the students as they break down the significance of the answer. To answer the problem they will understand that all that needs to be done is to move the decimal over 17 times to the right. This profound number will have the students in awe bringing them to understand deeper concepts about the answer. Understanding the implications behind the number might lead the students to ask more questions. The teacher can capture that moment use it as a 'teachable moment' and discuss the national deficit in conjunction with other huge numbers all along tying it back to scientific notation.
Guided Practice (20 min)
Students will then be given currency order of magnitude charts. The teacher will model how to read the chart and interpret its meaning. It will be particularly interesting to witness how our consumer interest compare with the different orders of magnitude of currency (i.e. cars, home, planes, etc.). Following that discussion students will identify several significant values and compare them to each other.
Independent Practice (25 min)
The students will group together and discuss the gaps and differences in currency magnitude. Then they will move on to other "money issues" that concern orders of magnitude and scientific notation. Students will be given problems asking them to compare Gross National Product (GNP) of countries with GNP per capita. Another 'money issue' considers income distribution and calculating the total range. The students will solve these problems and others with their groups.
Closing (5 min)
Students will attempt to capture concepts of the day by discussing its relevance to their lives. It should be evident how scientific notation makes it easier to understand and calculate numbers such as the ones used in the lesson.
Homework
The students will receive the following 3 questions to be completed by themselves at home. The results of the homework will be discussed the next day in class:
1) If everyone earned the median wage, what would be the total payroll of the country? How does that compare with this compare with the total earned income? Explain the difference in value.
2) Compare the national debt to GNP. How long would it take us to pay off the debt if we put all our income towards it?
3) How many Billionaires would it take to buy Philadelphia if the total value of all real estate in Philadelphia was $115 x 10 9?
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