PA Multi-Region Mathematics And
PA Multi-Region Mathematics and
Science STEM Partnership
UNIT #_1_
TITLE OF UNIT: / Use of Visual Data and Imaging in Exploring Deep SpaceTARGET GRADE(S): / 7-12
SUBJECT AREA(S): / Math/Science
KEYWORD SEARCH: / Mirrors, light, electromagnetic waves, images, telescopes, red shift
UNIT SUMMARY: / This unit deals with the math and science behind visual imaging and how red shift is used in the study of deep space. How mirrors form images is discussed as well as mathematical and graphical methods in determining image location and size. A lab is also performed to investigate curved mirrors and images. The use of visual data in determining distances in space is applied through red shift and through movements of planets around stars. All of this is done in the context of how telescopes such as the Hubble gather light from objects in space and form images of the universe.
DEVELOPED BY: DISTRICT/SCHOOL:
Team Contact Person:
Gerald Rabatin / Uniontown Area/High School
Team Members:
Rian Davis / Uniontown Area/Ben Franklin MS
Cindy Gallick / Southmoreland/Middle School
REGION:_____West______
Unit #_1_ Overview
Top of Form
GRADE LEVEL(S):7-12
APPLICABLE PA CORE OR NEXT GENERATION STANDARDS:
Science- HS. Waves and Electromagnetic Radiation
- PS4-5: Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.
Math - M07.D-S.2.1 Use statistical measures to compare two numerical data distributions.
M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability. CC.2.4.7.B.2 Draw informal comparative inferences about two populations.
M07.A-R.1.1 Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.
M07.C-G.2.2 Determine circumference, area, surface area, and volume.
M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.
M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.
M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
M07.B-E.2.3.1 Determine the reasonableness of an answer(s), or interpret the solution(s) in the context of the problem.
BIG IDEA(S): (RTOP #6, #7, #8)
(Develop at least one big idea that will enable students to make sense of seemingly isolated facts and learning experiences.)
Visual data such as images formed by telescopes and red shift can be used to determine distance through the use of mathematical expressions.
ESSENTIAL QUESTION(S):
(Develop at least two essential questions that focus learning toward the big idea and fosters critical thinking and deeper understanding.)
How do mirrors and utilize the behavior of light to form images?
What is the relationship between the location and size of the object and the location and size of the image?
How is red shift used in determining distances in space?
How are mathematical expressions utilized in visual imaging?
UNIT GOAL(S):
1. To describe how different types of mirrors produce images.
2. To analyze the characteristics of the types of images.
3. To tell how telescopes such as the Hubble utilize different mirrors to explore deep space.
4. To apply mathematical relationships between object/image distances and to draw those relationships with ray diagrams.
5. To apply red shift and visual data to determine distance in space.
MATERIALS AND/OR RESOURCES NEEDED FOR UNIT DELIVERY:
(Include technology, NASA resources, etc…)
1. Videos of the Hubble Deep Field and Edwin Hubble
2. Handouts of the Hubble Space Telescope from hubblesite.org.
3. Projector
4. Demonstration mirrors
5. Concave mirrors, meter sticks, light sources, index cards, candles, calculators, and graph paper for lab
6. Worksheet from Spacemath.com
7. Algebra Planet Blaster
ASSESSMENT/EVALUATION: (authentic student products, assessment methods)
Formative:
Question and answer sessions Various worksheets
Self-assessment, “ticket out the door”
Class discussions
Summative:
Lab write-up
Section on quiz dealing with unit material
Bottom of Form
ACCOMMODATIONS FOR STUDENTS WITH SPECIAL LEARNNG NEEDS(Choose an important anchor assessment from the unit, and tell how would you modify for a student with a learning disability.)
M07.A-R.1.1 Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.
This can be accomplished through the use of group/peer instruction and/or working with a higher academic partner. This also can be accomplished through the utilization of a learning support teacher with pull-out sessions to practice. Less intervention and support may be tried as the student becomes more adept with the concepts, especially the math.
Lesson Plan #_1_ of Unit #_1_
TOPIC/TITLE OF LESSON / Visual imaging – Mirrors and reflectionAUTHOR(S) / Gerald A. Rabatin
GRADE LEVEL(S) / 9 - 12
APPLICABLE PA CORE OR NEXT GENERATION STANDARDS:
HS. Waves and Electromagnetic Radiation
- PS4-5: Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.
LESSON OBJECTIVES: / ASSESSMENT(S) EVALUATE
(formative and/or summative)
1. To describe how different types of mirrors produce images.
2. To analyze the characteristics of the types of images.
3. To tell how telescopes such as the Hubble utilize different mirrors to explore deep space. / 1. Homework problems
2. Feedback from class discussion
3. Follow up with a lab on concave mirrors and images
4. Eventual quiz/test section dealing with mirrors and images
ACTIVATION OF PRIOR KNOWLEDGE (RTOP #1) ENGAGE
This lesson comes after a unit on the behavior of mechanical waves which includes reflection. Students are asked to recall wave reflection and the law of reflection which will enhance their understanding of the new material being presented dealing with the reflection of light, mirrors, and images.
TEACHING AND LEARNING APPROACHES EXPLORE, EXPLAIN, EXTEND
WHAT IS THE TEACHER DOING?
RTOP (# 2-10; #9-12; #21-25 / WHAT ARE STUDENTS DOING?
RTOP (#11-19)
1. Show video dealing with the Hubble Deep Field (from hubblesite.org).
2. Give handouts dealing with the Hubble Space Telescope.
3. Lead class discussion about video and handouts.
4. Lead notes/discussion/demos of the different types of mirrors and images formed by each.
5. Lead notes/discussion on object-image relationships using both ray diagrams and quantitative approaches using mirror equations.
6. Walk around and monitor student progress and understanding. / 1. Watch video of the Hubble Deep Field.
2. Read handouts of the Hubble Space Telescope from hubblesite.org. The handouts should be focused on the utilization of mirrors by the Hubble to form images.
3. Participate in discussion of video and handouts.
4. Write notes, participate in discussion, and observe with small hand-held mirrors the types of images formed by each.
5. Write notes of how to do ray diagrams and to use mirror equations to locate images.
6. Work in groups on various example problems that utilize ray diagrams and mirror equations to locate and describe images. Problems include given data on object location and size, focal length of the mirror, and type of mirror. Students are to calculate image size and location through calculation and the use of ray diagrams and to describe the image accordingly.
WRAP UP RTOP (#14) EXTEND
Wrap up by summarizing the main points of the lesson. Give insight to the follow-up lesson which will be a lab dealing with curved mirrors and images.
Assign various homework problems from text to reinforce the concepts covered in this lesson.
Refer to the RED text in the headings to see how the 5 E’s correspond to the lesson plan components. It is the teacher’s prerogative where extension activities are addressed.
Rubric for Lesson Plan #_1_ of Unit #_1_
Instruction: Use the rubric below to review your lesson against the indicators listed below. Consider how someone unfamiliar with your unit would rate your work. Place a checkmark in the appropriate rating box.
RTOPIndicator / Indicator Description / Thoroughly
Addressed / Adequately Addressed / Some Evidence / No Evidence
_ / Aligned with PA Core or Next Generation Science Standards / x
_ / Strong correlation between lesson objectives and assessment methods / x
_ / Incorporates NASA content and/or resources within the lesson / x
_ / Integrates available technology / x
#1 / Provides opportunities to help students to activate prior knowledge / x
#2 / Structures lesson to engage students as members of a learning community / x
#4, #5 / Utilizes a problem based/inquiry learning model in which students make predictions, estimations and /or hypotheses with a means for testing them / x
#12, 14 / Describes structured activities requiring student exploration, self-assessment, elaboration and reflection / x
#11, 16 / Indicates how students will use a variety of means to represent phenomena / x
#10 / Connects with other content discipline and/or real world phenomena / x
Incorporates the use of modeling, guided practice and independent practice / x
Identifies and/or provides an authentic real-world problem relevant to the students for them to solve / x
Addresses each of the 5 E’s—engage, explore, explain, extend, and evaluate / x
Lesson Plan #_2_ of Unit #_1_
TOPIC/TITLE OF LESSON / Visual imaging: Concave mirrors and reflection lab activity. Designed as a follow up to the previous lesson on the Hubble Space Telescope and concave mirrors and images.AUTHOR(S) / Gerald A. Rabatin
GRADE LEVEL(S) / 9 - 12
APPLICABLE PA CORE OR NEXT GENERATION STANDARDS:
HS. Waves and Electromagnetic Radiation
- PS4-5: Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.
LESSON OBJECTIVES: / ASSESSMENT(S) EVALUATE
(formative and/or summative)
1. To describe how concave mirrors produce different images.
2. To analyze the characteristics of the types of images through observation.
3. To apply mathematical relationship between object/image distances and to draw those relationships with ray diagrams. /
1. Lab on concave mirrors and images
2. Eventual quiz/test section dealing with mirrors and images
ACTIVATION OF PRIOR KNOWLEDGE (RTOP #1) ENGAGE
This lesson comes after a lesson on the Hubble Space Telescope and how mirrors are utilized to observe images. The students will be asked to recall the types of images discussed and how curved mirrors form the different types of images.
TEACHING AND LEARNING APPROACHES EXPLORE, EXPLAIN, EXTEND
WHAT IS THE TEACHER DOING?
RTOP (# 2-10; #9-12; #21-25 / WHAT ARE STUDENTS DOING?
RTOP (#11-19)
1. Give students lab papers dealing with concave mirrors and image formation.
2. Break class into groups of two for the lab.
3. Provide needed materials for the lab. Materials include small concave mirror, meter stick, meter stick supports, index card, card holder, candle with holder for mounting on meter stick.
4. Walk around and monitor lab. / 1. Look over lab papers.
2. Choose a partner for the lab.
3. Gather lab materials.
4. Perform lab. Students will gather data on object and image locations for three trials.
5. Work on lab write-up which includes ray diagrams and calculations utilizing the mirror equations to find the focal length of the mirror.
WRAP UP RTOP (#14) EXTEND
Have students evaluate the results of the lab and to confirm that they follow the object/image relationships as shown in the lens/mirror equation.
Rubric for Lesson Plan #_2_ of Unit #_1_
RTOPIndicator / Indicator Description / Thoroughly
Addressed / Adequately Addressed / Some Evidence / No Evidence
_ / Aligned with PA Core or Next Generation Science Standards / x
_ / Strong correlation between lesson objectives and assessment methods / x
_ / Incorporates NASA content and/or resources within the lesson / x (from Lesson 1)
_ / Integrates available technology / x
#1 / Provides opportunities to help students to activate prior knowledge / x
#2 / Structures lesson to engage students as members of a learning community / x
#4, #5 / Utilizes a problem based/inquiry learning model in which students make predictions, estimations and /or hypotheses with a means for testing them / x
#12, 14 / Describes structured activities requiring student exploration, self-assessment, elaboration and reflection / x
#11, 16 / Indicates how students will use a variety of means to represent phenomena / x
#10 / Connects with other content discipline and/or real world phenomena / x
Incorporates the use of modeling, guided practice and independent practice / x
Identifies and/or provides an authentic real-world problem relevant to the students for them to solve / x
Addresses each of the 5 E’s—engage, explore, explain, extend, and evaluate / x
Lesson Plan #1 – Unit #1
TOPIC/TITLE OF LESSON / The Hubble Telescope Story and Calculating Red Shift.AUTHOR(S) / Cindy M Gallick
GRADE LEVEL(S) / 7
APPLICABLE PA CORE OR NEXT GENERATION STANDARDS:
M07.D-S.2.1 Use statistical measures to compare two numerical data distributions.
M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability. CC.2.4.7.B.2 Draw informal comparative inferences about two populations.
LESSON OBJECTIVES: / ASSESSMENT(S) EVALUATE
(formative and/or summative)
To create a histogram then will tally up the different galaxies within a specified red shift. To calculate the average red shift galaxy. To find the median and the mode of all the red shift galaxies within a picture from the hubble deep space gallery. / 1. Create a histogram.
2. Calculate mean, median, and mode.
3. Turn in either a recent image taken from Hubble or one of the latest discoveries from an on-line source such as hubblesite.org..
ACTIVATION OF PRIOR KNOWLEDGE (RTOP #1) ENGAGE
This lesson combines the student’s knowledge on creating a histogram, calculating mean, median, and mode, then making inferences. A brief review of the concepts is conducted.
TEACHING AND LEARNING APPROACHES EXPLORE, EXPLAIN, EXTEND
WHAT IS THE TEACHER DOING?
RTOP (# 2-10; #9-12; #21-25 / WHAT ARE STUDENTS DOING?
RTOP (#11-19)
1. Teacher will give a brief description of the beginnings of the Hubble Telescope and its mission.
2. Teacher will introduce to the Hubble Telescope website and will watch a brief video about Edwin Hubble and Red shift.
3. Provide: Worksheet obtained from SpaceMath.com Problem 54.
4. Online Red shift calculator at Wolfram-Alpha / 1. Students will watch a video on the Hubble Telescope. They will then be given a short lecture on the background of the Hubble telescope and its purpose.
2. Student will create a histogram then will tally up the different galaxies within a specified red shift.
3. The student will also be able to determine the largest red shift galaxy and the least red shift galaxy.
4. Student will then calculate the average red shift galaxy and find the median and the mode of all the red shift galaxies within a picture from the hubble deep space gallery.
5. Students will also use the online red shift galaxy calculator from Wolfram-Alpha to determine look back time.
6. From these calculations students will be able to determine the longest look back time and how long after the Big Bang that this galaxy took to form
7. Finally they will be given the worksheet on Exploring Distance Galaxies. SpaceMath.com Problem 54.
WRAP UP RTOP (#14) EXTEND
After students have been given time to complete the worksheet they will be given time to discuss, ask questions and reflect upon their results.
Rubric for Lesson Plan #_1_ of Unit #_1_