Do+exponents+really+exist+in+real+life?

= A Ninth and Tenth Grade Emerging Algebra Unit by Rich Hurley =




 * **// Unit Overview: Exponents //** ||
 * ** Common Core Established Go **** als: **
 * F-IF 1 -Understanding that a function is a set of data ( The graph trend based on input and output)**
 * F-IF 9 -Compare two sets of functions in two different ways (Through visual linear model, questions, through algebra)**
 * FLE 10- Recognize that functions are either polynomial, logarithmic or exponential**
 * S-ID 1- Represent and post data on a number line**
 * RL 1- Initiate + Participate in a range of collaborative discussions (1-1, whole group, teacher led)**
 * RL 4- Present information with findings and supporting evidence** ||
 * ** What Essential understandings are desired? (standards) **

Students will recognize and state


 * how to solve equations over a given domain
 * that graphs are an easy way to show lots of information (like exponential data)
 * the direct connection between exponents and other math sets
 * estimation can be used to judge the reasonableness of an answers
 * how to apply basic algebraic procedures to word problems
 * when to transpose points on a graph || ** What essential questions will be answered? **


 * ** Do exponents really exist in real life? **


 * Given exponential depreciation Is buying a new car a smart financial decision? How apply algebraic procedures to world problems (i.e. buying a car?)


 * How does a certificate of deposit work?

How to **define** in there own words:
 * If I doubled a penny everyday and then doubled that amount would I have a lot of money after a month? ||
 * ** Students Learning outcomes: Students will know **
 * Linear
 * Exponential
 * Y axis
 * X axis
 * Depreciation

[|Merrian Webster Definition]

[|Dictionary.com Definition]

[|Collins Cobuild ELL Definition]


 * Linear function
 * Exponential function
 * Estimation
 * Certificate of deposit

By **producing** these skills
 * How to plot an X and Y axis
 * How to compare and contrast the real number system
 * How to model real world problems
 * What a “rubric” actually is || ** What are the students key knowledge skills to be demonstrated? **


 * distinguish and show how to solve one step algebraic equations


 * sketch multiple data points on one graph with maximum independence


 * appraise and judge increase and decrease of a percent with respect to a car


 * Analyze graph findings and make a prediction as to the value of a car in 4 ,8 and 10 years


 * Answer literal and implied questions based on graph data

//**What __will__ be differentiated in this unit?**//
 * Read and participate in a discussion about exponents ||

__**Process-**__Throughout the supported unit and lessons the process will be differentiate through higher order questions and the use of blooms revised taxonomy to address the students at their thinking level. Students will summarize, map, match and explain the key vocabulary from above. Furthermore they will deconstruct and reconstruct the real number system. We will judge the reasonableness of our answers based on how much a car depreciates. Questions and answers from students may range from shallow and specific to deep and abstract. Other Examples of differentiated process I will use include the utilization of manipulatives and hands-on activities, or using tiered assignments provide examples in which students learn the same skills but proceed through assignments with different levels of support and complexity. I would also be varying the length of time for different groups have to finish a task, or setting up interest centers (anchoring activities - please provide examples_ where students explore pieces of the topic of interest to them. As part of the daily classroom routine I will be developing and following personal agendas so individual students can complete work similar to the rest of the class, or it may be work based on individual needs. Students will have there own folder and will have individual assignments places into their folder based on their ongoing readiness throughout the unit. Their folder may also contain supplemental work or re mediates assignments based on thier IEP goals.

__**Affect-**__ To successfully differentiate for affect I needs to find ways to keep threats, that cause unhealthy stress, absent in the classroom. For example, if a student has a learning disability and cannot read aloud in class confidently than I need to assist the student to feel that he/she has a voice and can contribute to the class. Likewise, if a student has difficulty keeping his/her body still, there may need to be space for movement so the student can avoid frequent reprimands for something that he/she has trouble controlling.

__**Learning Environment-**__ Some ways I will differentiate the learning environment are: (a) to ensure quiet areas within the classroom, (b) invite student collaboration through arrangement of furniture, (c) use materials that reflect a variety of cultures and home situations, (d) match independent work to individual needs by giving assignments based on skill set, readiness, and present level of performance. I will avoid independent assignments for each students that are too lengthy, too wordy or over rely on the same skill. (IE all calculating, all multiple choice, all reasoning. (e) develop procedures for students to follow if unable to access immediate help from the content area teacher. In addition, it is important for students to understand that every learner is different. Some students may need to get out of their seats and move while learning, while others choose to work quietly. I will be mindful, firm and flexible all at the same time.

__**Content**-__ Content will be re-mediated, accelerated, or enriched using basic or more complex resources. All students will strategically get more foundations based work but those with higher skills will be accelerated into higher order thinking problems. Students who struggle with the higher order thinking problems may have their work re-mediated or modified. content: - functions, algebraic procedure, graphs etc. Each specific lesson alludes to the specific differentiated content.

A traditional worksheet and poster board display could be used. A power-point presentation addressing the skills in the rubric is an option. A paper comparing two similar car values depreciation over time. A picture book with "own word" definitions and appropriate picture displaying the definition and interview by the teacher
 * __Product__-** There will be many activities in my unit will allow for differentiated products. The formative assessment can be presented by selecting two questions and presenting those questions in the format of your choice.

//**Performance Task Blueprint**//

What criteria and what qualities must students work demonstrate to signify standards and objectives were met?
 * //mathematical accuracy//
 * //Knowledge of Key Vocabulary//
 * //Graphing Accuracy//
 * //Completion of teacher/student rubric//
 * //Completion of multiple tables//
 * //Answering and interaction with literal and implied questions//

What authentic performance task will demonstrate understanding?
 * //Students will create a visual display outlining two table and eight questions. Table will show money accrued and depreciation of a car over 8 years. The visual display will answer the essential questions **Do exponents exist in real life?**//

//What is the criteria by which students are evaluated?//
 * //rubric checklist//
 * //accurate responses with and without accommodations//
 * //other evidence of effective effort and original thought//

Class Profile Matrix

Download my rubric and printed summative assessment below:

Lesson 1: Visual Representation of Positive and Negative Numbers Age/Grade Level 9/10 Date: 6/20/12 Subject: ALGEBRA/MATH Length of Lesson: 40 minutes

To indicate through visual representation positive, negative, decimals and fractions using the human number line
 * TOPIC/GOAL:**


 * CURRICULUM FRAMEWORK**
 * ADDRESSED:**
 * F-IF 1 -Understanding that a function is a set of data ( The graph trend based on input andf output)**
 * F-IF 9 -Compare two sets of functions in two different ways (Through visual linear model, questions, through algebra)**
 * FLE 10- Recognize that functions are either polynomial, logarithmic or exponential**
 * S-ID 1- Represent and post data on a number line**
 * RL 1- Initiate + Participate in a range of collaborative discussions (1-1, whole group, teacher led)**
 * RL 4- Present information with findings and supporting evidence**

To survey that integers can be part of a whole number as well as a negative To subdivide using a different modality to understand positive and negative numbers with exponential growth.
 * OBJECTIVES:**

A good staircase preferable with landings Index cards with printed tiered integers (easy, medium, hard) Calculators
 * MATERIALS:**

Today we are going to show positive, negative, decimal and partial numbers on the staircase. Please grab a card of any number you choose of the back desk and meet me in the hallway outside.
 * INSERT BUILDING, INTRODUCTION:**

The staircase represents a number line. The landing between the floors is zero, since it is level with the ground outside. Below the landing are negative numbers and fractions. Your task is to take your index card and place the card (or yourself) at the appropriate step at the correct level. You many need to adjust your step as other classmates and numbers are added. If you are a decimal or a fraction you are between two steps so you have a choice of sitting on the edge of the step or just placing the card there. Once we go through each card pile once we are done. There will be prompts along the way. If you are unsure of a number you can ask me if you are hot or cold but only up to three times. Good Luck
 * LESSON DEVELOPMENT:**


 * What is differentiated in this particular lesson:**

Emerging students will receive whole numbers while extending students will receive fractions, decimals and percentages.
 * Content-** Different students at different abilities will receive different index card. (see appendix A)


 * Process-** Teacher will use higher order thinking questions to reinforce skills. (I.E. Joe is at -3 and Casey is at -5 that means you (Katie) will be in between -3 and -5. Do you think you are closer to Joe or to Casey? Why do you think that?
 * 1) I will also move the lesson along if students students seem to have stronger readiness in this area.
 * 2) I will slow the lesson down, model and instruct with easier cards if they students begin to struggle.
 * 3) My support staff and myself will be available for direct instruction and we will have agendas posted on the board as well as extension activities ready to go in their folder.

I will have quiet area available as needed for students who are multi-sensory reactive. I will have a procedure and plan for students who are having difficulty accessing my activity or for students I will have a procedure for students who finish early and show mastery I will make sure there hallway is quiet for instruction I will use numbers that are in the students environment (i.e money)
 * Learning Environment:**

I will monitor for threats and safety/ space violations. I monitor for comments made about other students performance,
 * Affect:**

If a student is struggling with the follow up assignment The teacher will have the student flip the paper over and make a number line with numbers given by the teacher. This will hopefully conclude naturally when you run out of cards. If the students begin to struggle I will begin to model. “Bob is at the first step so he must be one since he is above the landing. Does everyone agree that Bob is one?
 * Product:**
 * CONCLUDING LESSON:**

Algebra with PIZZAZ riddles math positive and negative numbers. This assignment can be done individually, in groups of two or as an entire class This assignment will be modified, extended, remediated based on readiness of the students
 * FOLLOW UP ASSIGNMENT:**



Ease and efficiency of the task Completion and accuracy Class participation
 * EVALUATION:**

Lesson 2: Visual Representation of Combining Like Terms

Date: 6/20/12 Subject: ALEBRA/MATH Length of Lesson: 40 minutes

Students will understand the difference between squared and cubed variables and how to combine like terms to perform various operations.
 * TOPIC/GOAL:**

Students will conceptualize that squared and cubed variables cannot be combined, a common misconception.
 * OBJECTIVES:**

Textbook Visual representations of technology Calculators Smartboard/chalkboard
 * MATERIALS:**

(Before you begin I need to have a firm grasp on technology so I can make the connection to the students directly) Here are three IPODS what are the similarities and differences between them.
 * INSERT BUILDING, INTRODUCTION:**

Teacher displays three pictures of video game systems or apple products (i.e. PlayStation one. PlayStation two PlayStation 3) and asks the simple question: Are these video games systems exactly the same? Can i play a PlayStation 1 game in a PlayStation 3?)Lets attach a variable representation for PlayStation one and call it P; lets call PlayStation 2 "p squared" and PlayStation 3 "p cubed" Can i add two video game systems together and magically get a new one? Of course not! They are all different and variables are the same way. Even those these video games are similar in a lot of ways they are not alike. You cannot play a new video game in a old system even though it is made by the same company. You cannot add "p to the first power to p to the second power and get P to the third power". The following demo below shows a similar visual display with IPODS.
 * LESSON DEVELOPMENT :**

Check for clarification/ students should be writing their answers down Model and scaffold 3 - 4 problems as a class
 * CONCLUDING LESSON:**

Algebra with Pizzaz 1.8
 * FOLLOW UP ASSIGNMENT:**

Algebra with PIZZAZ 1.8 This assignment can be done individually, in groups of two or as an entire class This assignment will be modified, extended, remediated based on readiness of the students

Lesson 3 : Visual Representation of Decimals and percent Age/Grade Level 9/10 Date: 6/20/12 Subject: ALGEBRA/MATH Length of Lesson: 40 minutes

Students will convert decimals and fractions to a whole or parts of a whole number.
 * TOPIC/GOAL:** Students will understand the correlation between the price tag of an item and its actual percentage in dollar representation.


 * CURRICULUM FRAMEWORK**
 * ADDRESSED:** 10.n.1;10.n.2;10.n.3;10.p.3;10.p.4;10.p.6;10.g.8;10.m.1;10.m.2


 * OBJECTIVES:** Convert decimals to percent, Convert percent to decimals and apply correctly across various problems

Textbook smartboard / chalkboard
 * MATERIALS:** Change - pennies, nickels, quarters, dimes dollar bill (not to exceed 5 dollars total)

Today we are going to interact with decimals and percents using real money and some real life problems
 * INSERT BUILDING, INTRODUCTION:**

Teacher will demonstrate the correlation between the price tag if an item and an actual percentage in dollar representation. ( for example a .50cent pack of gum represents 50% of a dollar and $2.12 box of cereal is 212% of a dollar.) Teacher will show several items from the local dollar store. Teacher will show the students how much percent of a dollar is represented in pennies.(20)Teacher will then show 2% represented in pennies. Teacher then explains that 20 pennies is 20 percent and 2 pennies is 2 percent. Teacher will place an index card next to each pile of pennies that says 20% is 20 pennies and 2 percent is 2 pennies. Teacher will call out dollar amounts like $1.25, .47 and .05 and ask students to the students to count out the about and call out the appropriate percentages. A fair amount of modeling and instructing is used.
 * LESSON DEVELOPMENT :**

Use ticket to leave Teacher will ask random students to demonstrate 5 dollar amounts as a percentage and a written integer. When five students answer in a row class is dismissed.
 * CONCLUDING LESSON:**

Tiered assignments based on PLEP Emerging Students assignment: Find the message
 * FOLLOW UP ASSIGNMENT:**


 * [[image:EPSON015.JPG width="460" height="596"]]

Extending Students assignment: Code Alamode

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