Lesson 2: Day 3
1. Descriptive Data
Teacher: _____Asra Khan____ Date: December 14, 2011
Grade Level/Course: ___9th grade/ Algebra____
Topic: ___Functions___ Time Required: __45 min__
2. Standards and Objectives
Illinois State Core Standards
Objectives:
Students will be able to:
3. Rationale
The Domain and Range of define the practicality of any function. Looking at a function can mean anything or nothing. However, once we have defined what its limits are and analyze it, we will have a better understanding of what the function actually means. Therefore, it is essential to teach students how to find the Domain and Range of a function.
4. Materials and Resources
Pencils, notebooks, erasers, and Overhead
(worksheets are attached to the lesson plan)
5. Instructional Procedure
5 minutes. Introduction: During the last class, we had a discussion on Function notations and Algebraic generalization. Now that the students are familiarized what a Function is, I will introduce the Domain and Range of a function. I will have a few examples written on the board before the students even walk-in. Once they walk in and are settled down, I will get their attention to the functions I have written.
15 minutes. Lecture/Discussion on Domain: I am hoping to have a classroom where I will either have a smart board where I can switch between slides or a room with multiple white boards like the one in our SCED 301 classroom. In such case, I will have the definition of Domain written on one the boards:
-If the students answer yes, I will ask them to plug in -4 and see if they are able to solve it.
-Of course they will be able to solve it because plugging in -4 hands back sqrt(3) which is solvable.
-Therefore, this function does NOT have the same domain as the last one.
-Each function has a unique domain.
- We will plug in a couple more numbers to see if they work. For example, let’s plug in -8. It hands back sqrt(-1) which has no solution where as plugging in -7 hands back 0 which is solvable. Therefore, the domain of this functions is all numbers x such that x>= -7
-What numbers can we plug in for x that will give us a solution? (We have to remember that the denominator cannot equal to 0).
-So for what values of x does (x^2 – 4) equal to 0? (2 and -2)
-Thus, the domain for this functions is all number except for x=2 and x=-2.
15 minutes - Lecutre/Discussion on Range: I will then lead the class discussion into Range:
5 minutes - Notation for Domain and Range: Now that I have told them what the Domain and Range are, I will explain to them how to write in so that when they are finding the Domain and Range of a function, they know how to write it properly. They will also be able to read it correctly when seen somewhere else.
5 minutes. Closure: I will close the discussion by giving a function as an exit slip for which the students will be asked to find the Domain and Range. Students will work on this exit slip individually. Meanwhile, I will pass out homework. I will also tell the students that now that we are familiar with what Domain and Range of a function are, we are going to learn how to graph functions. Knowing the Domain and Range of the functions will help us visualize and construct what the graph should look like.
6. Assessment
Students with assessed informally throughout the lecture when they assist me in finding the Domain and Range for given examples. At the end, the exit slip will allow me to assess if they understood topic. They will also be assessed on homework.
7. Modifications
Suppose there is a LD/ED student(s) in my class room. I will Omit objective number three or pair students with a higher level learner to help her/him with lessons. I will Provide notes, study guide and/or outline of the lesson ahead of time so the students will know what the lesson is about before hand. I will use a variety of sensory strategies for learning: audio tapes, visuals such as the overhead or pictures, have the notes on the overhead as I go through the lesson. In my classroom, I will make sure that these students are seated up front and near me, so I can check progress and keep student on task. Distractions should be kept at a minimal with seating near students who are not behavior problems, away from computer screens, trash can, pencil sharpener, and window and doors.
Additional Documents:
1. Descriptive Data
Teacher: _____Asra Khan____ Date: December 14, 2011
Grade Level/Course: ___9th grade/ Algebra____
Topic: ___Functions___ Time Required: __45 min__
2. Standards and Objectives
Illinois State Core Standards
- CC.K-12.MP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
- CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Objectives:
Students will be able to:
- Have a better understanding of what Domain and Range of a function are
- Define Domain and Range of a function
- Interpret what the Domain and Range say about a function
- Write domain and range with proper notation
3. Rationale
The Domain and Range of define the practicality of any function. Looking at a function can mean anything or nothing. However, once we have defined what its limits are and analyze it, we will have a better understanding of what the function actually means. Therefore, it is essential to teach students how to find the Domain and Range of a function.
4. Materials and Resources
Pencils, notebooks, erasers, and Overhead
(worksheets are attached to the lesson plan)
5. Instructional Procedure
5 minutes. Introduction: During the last class, we had a discussion on Function notations and Algebraic generalization. Now that the students are familiarized what a Function is, I will introduce the Domain and Range of a function. I will have a few examples written on the board before the students even walk-in. Once they walk in and are settled down, I will get their attention to the functions I have written.
- One function I have written is y = sqrt(x).
- If the function is given a 9, it hands back a 3.
- If the function is give a 2, it hands back approximately 1.4
- However, what if the function is handed a -4? Taking a square root of a negative number is impossible.
15 minutes. Lecture/Discussion on Domain: I am hoping to have a classroom where I will either have a smart board where I can switch between slides or a room with multiple white boards like the one in our SCED 301 classroom. In such case, I will have the definition of Domain written on one the boards:
- Definition: the domain of a function is all the numbers that it can successfully act on. Put another way, it is all the numbers that can go into the function.
- So the domain of y = sqrt(x) is x>=0 because it can’t perform on any number smaller than 0.
- On each board/slide, I will have a function written (maximum of three).
- Y = sqrt(x+7)
-If the students answer yes, I will ask them to plug in -4 and see if they are able to solve it.
-Of course they will be able to solve it because plugging in -4 hands back sqrt(3) which is solvable.
-Therefore, this function does NOT have the same domain as the last one.
-Each function has a unique domain.
- We will plug in a couple more numbers to see if they work. For example, let’s plug in -8. It hands back sqrt(-1) which has no solution where as plugging in -7 hands back 0 which is solvable. Therefore, the domain of this functions is all numbers x such that x>= -7
- I will remind the students that there are two mathematical operations that are not allowed: first, we cannot take the square root of a negative number. Second, we cannot divide anything by 0. This will lead us into our second example.
- Y = 1/(x^2 -4)
-What numbers can we plug in for x that will give us a solution? (We have to remember that the denominator cannot equal to 0).
-So for what values of x does (x^2 – 4) equal to 0? (2 and -2)
-Thus, the domain for this functions is all number except for x=2 and x=-2.
- Next, I will have 3 more problems written on another board that I want students to tell me the domain for.
- Y= 1/x
- Y= 1/x-3
- Y= Sqrt(x-3)/x-5
- Once we are done I will have a sheet with a table with these functions, their domains and explanations. (The sheet is attached to the lesson plan.)
15 minutes - Lecutre/Discussion on Range: I will then lead the class discussion into Range:
- If the Domain of the function is the possible values of x that you can put into that function, what do you think the Range of a function is students? (I will wait for them to answer.)
- I will then have the definition of Range written on one of the boards/slides:
- Definition: The range of function is all the numbers that it may possibly produce. Put another way, it is all the numbers that can come OUT of the function. Thus it is the possible values of f(x) or y.
- To Illustrate this, we will return to our example y=sqrt(x+7).
- Recall that we said the domain of this function was all numbers x such that x>=-7. In other words, we are allowed to put any number greater than or equal to -7 into this function.
- Then, what numbers might come out of this function?
- If we plug in -7, it will produce a 0.
- If we plug in -6, it will produce a 1.
- Thus, as we increase the value of x, the value of y increases. It never decreases. Hence, the range of this function is all number y such that y>= 0.
- This means that the function is capable of handing back 0 or any positive number but it will never hand back a negative number.
- Instead of presenting students with new problems, we will find the range for each of the examples we found the Domain for. This will help them understand the relationship between Domain and Range.
5 minutes - Notation for Domain and Range: Now that I have told them what the Domain and Range are, I will explain to them how to write in so that when they are finding the Domain and Range of a function, they know how to write it properly. They will also be able to read it correctly when seen somewhere else.
- Parentheses () mean “an interval is starting or ending here, but NOT INCLUDING this number”
- Square brackets [] mean “an interval is starting or ending here, INCLUDING this number.
- I will then explain it with the examples we did. I will write down the Domain and Range of each example in proper notation.
- I will also hand out a sheet with some sample notations. (The sheet is attached to the lesson plan)
5 minutes. Closure: I will close the discussion by giving a function as an exit slip for which the students will be asked to find the Domain and Range. Students will work on this exit slip individually. Meanwhile, I will pass out homework. I will also tell the students that now that we are familiar with what Domain and Range of a function are, we are going to learn how to graph functions. Knowing the Domain and Range of the functions will help us visualize and construct what the graph should look like.
6. Assessment
Students with assessed informally throughout the lecture when they assist me in finding the Domain and Range for given examples. At the end, the exit slip will allow me to assess if they understood topic. They will also be assessed on homework.
7. Modifications
Suppose there is a LD/ED student(s) in my class room. I will Omit objective number three or pair students with a higher level learner to help her/him with lessons. I will Provide notes, study guide and/or outline of the lesson ahead of time so the students will know what the lesson is about before hand. I will use a variety of sensory strategies for learning: audio tapes, visuals such as the overhead or pictures, have the notes on the overhead as I go through the lesson. In my classroom, I will make sure that these students are seated up front and near me, so I can check progress and keep student on task. Distractions should be kept at a minimal with seating near students who are not behavior problems, away from computer screens, trash can, pencil sharpener, and window and doors.
Additional Documents: