Download Exponential Growth By Joe Zakhary Slide 2 Target Audience 10th

Exponential Growth
By Joe Zakhary
Slide 2
Target Audience
10th/11th grade Algebra II
I teach Honors Algebra II and Scholars Algebra II at Ridgefield Park Jr/Sr. High School. My classes are
comprised of, on average, 20-23 students. Each of my classes has students of varied levels of ability.
This lesson is designed for a 42-minute period. My lesson will use the different learning styles and
multiple intelligences.
Slide 3
Goals and Objectives
Students will be able to:
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Model exponential growth and decay.
Tell if a certain equation is growth or decay.
Come up with an equation for growth or decay.
Objectives:
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Students will understand what an exponential graph looks like.
Students will know which graph is correct.
Students will give examples in real life where exponential growth or decay is occurring.
Students will be able to show with their hands what the graph should look like.
Slide 4
This picture shows the effect of doubling an object. When an object doubles, it really does not seem like
a lot at first. Even in the 5th or 6th cycle of the picture, it does not appear to be a lot. However,
eventually the duplication results in many people. This picture also represents the growth of the human
population and how it will become an issue for our planet should it remain unchecked.
Slide 5
Evaluations and Assessments
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Teacher observation during class
Question and Answer
Discussions
Showing with their hands of what the graph should look like
Homework
Quiz
Slide 6
Primacy Recency
Prime Time 1
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Exponential Growth or Exponential Decay
You Tube Video number 1 (first 3 minutes)
You Tube Video number 2 (all)
Explain and model within 10 minutes which equations are growth or decay and what each graph
will look like.
Have students answer the first question by showing with their hands what the graph will look
like
Use TI- Inspire Calculators to check the example that the students modeled with their hands.
Down Time
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Put up on the board 4 questions that get progressively more difficult and have students call you
over as they complete each question.
If a student finishes all the questions before their classmates, have them help their neighbors
Go over the questions
Have students break into groups of 3 or 4 and come up with examples of where exponential
growth or decay are used in real life.
Students need to come up with the name of an endangered animal
Prime Time 2
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Describe how to come up with an equation of exponential growth or decay given two
coordinates.
Have students summarize what they learned and be prepared to be called on.
Have one student explain growth and decay, and have another student explain how to model
the equation.
Slide 7
Sense and Meaning
The YouTube video conveys the concepts of sense and meaning. Students will give examples of where
and how exponential growth is used. Also, during downtime, I collect a name of an endangered animal
and look up how many animals were born in two different years. Based on the information collected, I
come up with an exponential equation that models the population of the animal chosen. We then use
this equation to predict the population of the endangered animal.
Slide 8
Multiple Intelligences
All the multiple intelligences are covered in this lesson.
Intrapersonal- Students will answer questions independently during down time. They will also select an
endangered animal. The intrapersonal learner will also have a set of 5 problems to solve.
Linguistic- Students will write down examples of how exponential growth and decay works in real life.
The linguistic learner will have a chance to talk to his partners in groups about the lesson as they are
coming up with endangered animals or exponential graphs.
Logical/Mathematical- Students will figure out whether the equation represents exponential growth or
decay. The logical learner will need to figure out why one graph grows or decays faster than another of
the same type.
Naturalist- Students will learn that humans cannot sustain exponential growth and that some animals
are becoming extinct because of humans. I will ask students to think of other objects on Earth that are
growing at unsustainable rate.
Spatial- The spatial learner will be engaged with all the different graphs. The students will also have to
compare graphs and determine whether it is increasing or decreasing at a faster rate.
Bodily-Kinesthetic- Students will learn how to use their hands to model the exponential equation given.
Musical- Students will watch the second YouTube video which uses music to help students understand
and remember the concepts of growth or decay.
Interpersonal- Students will engage with each other to discuss where exponential equations are used in
everyday life.
Slide 9
Technology
The YouTube videos in my lesson shows the uses of technology. These two YouTube videos will convey
most of the major concepts to the students in about 6 minutes.
Students will use a TI-Inspire to check the graphs that they found for each one to make sure there are no
errors.
The White Board will be used throughout the lesson to display the concepts and model the graphs.
I will have students come up with an endangered animal list and I will look up these animals while
students are answering questions. If they have an animal that cannot be found, I will use the Amur
Leopard population from wiki. https://en.wikipedia.org/wiki/Amur_leopard
Slide 10
Brainy Bits
Limbic System
The limbic system is located underneath the cerebrum. This system is responsible for higher mental
functions such as learning and forming memories.
Thalamus – “All incoming sensory information (except smell) goes first to the thalamus. From here it is
directed to other parts of the brain for additional processing. The cerebrum and the cerebellum also
send signals to the thalamus, thus involving it in many cognitive activities, including memory.” (Sousa,
2011). Basically, your Thalamus serves as the computer motherboard of your brain; it connects your
brain to the other parts of the brain. The Thalamus filters out all the information around you and
determines what is important and what should be ignored. In my classroom I maintain an environment
that is friendly and without distractions. This helps my students focus on learning and helps me to focus
on my teaching.
Hypothalamus- The hypothalamus monitors the internal systems of the body. A student needs the
internal systems to be at homeostasis for learning to be able to occur. If the student is hungry, tired, too
hot or too cold they will perseverate with learning. I try and make sure my room is not too hot or too
cold. I let students move around the room if they are too cold or too hot.
Hippocampus- The Hippocampus consolidates learning and transfers it into working memory. Longterm personal memory is also based in the Hippocampus. If the lesson makes sense, it might be stored
by the hippocampus. When I am teaching this lesson I will explain why population or spending left
unchecked cannot continue indefinitely. I will also explain that there usually is carrying capacity for any
species.
Amygdala- It is commonly accepted that memory and emotion are stored in the Amygdala. The
memories of what I teach are stored and remembered. I believe that some of the information is
memorable because I come up with unusual sayings and make them funny for my students to
remember. My students often come up to me during the next school year and tell me that they
remember the saying and it helps them to remember the lesson.
Lobes of the Brain
The brain is comprised of four lobes beginning with the prefrontal cortex and frontal lobe.
Frontal Lobes- The Frontal Lobes of the brain controls the rational and executive control of the brain.
The frontal lobe helps with logic and higher order thinking. The frontal lobe is used to make sense of an
exponential function to determine if it is growth or decay.
Temporal Lobes- The Temporal Lobes of the brain deals with object recognition, long-term memory, and
auditory information. The YouTube videos with music, lecture, and the shape of exponential graphs will
engage this system by hopefully converting the information into long-term memory.
Occipital lobes- The Occipital Lobes of the brain processes visual information. YouTube videos, graphs,
and motion during class will keep this part of the brain engaged.
Parietal Lobes- The Parietal Lobes of the brain is exercised when students make a table and draw the
graphs according to the respective intended scale.
Motor Cortex- The Motor Cortex and Cerebellum deal with motion and body movement. When a person
moves, this part of the brain visualizes it and pictures the person doing the same motion. This part of
the brain is being used when students show me with their hands if the function is growth or decay.
Slide 11
Brainy Bits 2
Cerebrum- “Thinking, memory, speech, and muscular movement are controlled by areas in the
cerebrum.” (Sousa, 2011) This whole lesson is engaged for this part of the brain to be used. From
working in groups to thinking about the graphs to showing what an exponential graph looks like with
movement, the Cerebrum is exercised.
Cerebellum- Most of the neurons of the brain are located in the Cerebellum. This part of the brain helps
us complete handshakes and make more complex motions. This region of the brain will be engaged to
help remember the movements of the learning of an exponential curve.
Neurons – Neurons are cells which collect signals and pass them through dendrites to the part of the
brain where the memory is stored. The more connections and reinforcement of a topic, the better the
chances the memory will be stored.
Slide 12
Works Cited
http://www.stephenbolwell.com/?tag=exponential-growth (2/13/16)
http://www.slideshare.net/bigkelt12/35-36-explog-models-1314 (2/13/16)
https://www.youtube.com/watch?v=45l6wbdC2H0 (2/20/16)
https://www.youtube.com/watch?v=aDkRHY16Py4 (2/21/16)
http://questgarden.com/96/85/8/120318091157/ (2/27/16)
https://www.pinterest.com/pin/224898575118979837/ 2/29/16
http://avexdesigns.com/responsive-youtube-embed/ 2/28/16
https://www.ifixit.com/Wiki/TI-Nspire_Calculator_Troubleshooting 2/29/16
http://www.altaconservation.org/files/2012/05/Hanka-kohisemas_5.06.10-credits-MaajaKitsing-e1344504990791.jpg 2/29/16
http://dryeraseboard.com/multi-section-markerboard.html 2/29/16
Difference between Cerebrum and Cerebellum | Major Differences 2/29/16
https://askabiologist.asu.edu/neuron-anatomy 2/29/16
Sousa, D. (2011). How the Brain Learns. (4th ed.). Thousand Oaks, CA. Corwin Press