microsoft word - s1_syllabus.doc€¦ · web viewin a word problem, the initial starting value at...

Step 1/2: Explorations in Mathematics and Science Teaching

Title of Lesson: Dot your I’s and cross your intercepts at a constant paceUFTeach Students’ Names: Sarah Burkhardt and Sarah GoldTeaching Date and Time: Tuesday, October 29, 2013Length of Lesson: 50 minutesGrade / Topic: 8th Grade Algebra I Honors/ Slope, x-intercepts, and y-interceptsSource of the Lesson: http://www.mathsisfun.com/definitions/y-intercept.html, http://cs.selu.edu/~rbyrd/math/intercept/ , http://www.purplemath.com/modules/slope.htm

Appropriateness for Middle School Students: The students work individually as well as in groups throughout the lesson. Students will apply their understanding that the initial amount (at the x value of zero) is the y intercept. They will be interested in the real life application of earning more money each week is more beneficial in the long run than starting with more money. Students will walk across the tape, allowing learners to volunteer to demonstrate the different speeds and the relationship with slope. Students will draw on the smart board, visually displaying the intercepts and slopes. Students who do not understand the form of the equation can also draw the graph from the equation to bridge the connection to the parts of the equation and the graph. This paragraph is much better than in your draft. You submitted your lesson before class on Thursday. Perhaps after seeing the list of topics to cover in this section you will understand even better what could be included in this section.

Concepts: Finding the y-intercept, x-intercept, and slope of positive linear functions. (Your previous statement is not a sentence. It is more a prepositional phrase.) The y-Intercept is the point where the line crosses the y-axis of a graph, (where x=0). Solve for the y-intercept by substituting zero (Substitute into what?) in for x and solving for y. A y-intercept will always have a zero x-coordinate. There can be only one y-intercept of a function. A x-Intercept is the point where the line crosses the x-axis of a graph, (where y=0). Solve for the x-intercept by substituting zero in for y and solving for x (Substitute where?). A x-intercept will always have a zero y coordinate. If the graph crosses the origin the y and x-intercept is (0,0). The slope of a line is a number that measures its "steepness", denoted by the letter m in an equation of a line. Slope is the change in y values for every one x value. The larger the absolute value of the slope, the steeper the line. A negative slope can be steeper than a positive slope. m represents the slope and the b represents the y-coordinate of the y-intercept (Where? You forgot the sentence, “ You can use the form y = mx + b to find the equation of a line given two points on a line.) In a word problem, the initial starting value at zero x units is the y-intercept. The amount of money being earned or any constant change in y for each x unit is the slope.Better. For lesson 4 be sure to research the concept and just don’t rely on your previous knowledge.

Definition from: http://www.mathsisfun.com/definitions/y-intercept.htm

Florida State Standards (NGSSS) with Cognitive Complexity:

Benchmark Number Benchmark Description Cognitive Complexity

M.A.912.A.3.9 Determine the slope, x-intercept, and y-intercept of a line given the graph, its equation, or 2 points on a line

Moderate

Performance Objectives:

http://www.mathsisfun.com/definitions/y-intercept.htm

http://www.purplemath.com/modules/slope.htm

http://cs.selu.edu/~rbyrd/math/intercept/

http://www.mathsisfun.com/definitions/y-intercept.html


Students will be able to draw a graph of a line given its slope and y-intercept Students will be able to determine for the x-intercept given an equation Students will be able to relate slope to the steepness of a graph

Materials List and Student Handouts Colored tape Stop watch 22 Exploring worksheets 22 Notes worksheets 22 Pre-Evaluations 22 Post-Evaluations 22 Who Won the Bet Worksheets

Advance Preparations Power Point made to supplement instruction Students will be in their normal groups of 4

Safety There are no specific safety concerns

5E Lesson:Engagement Time: 10 minutesWhat the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible

MisconceptionsGreet students as they come in the room (worksheets will be sitting faced down in center of groups)Pre-evaluations will be on each individual desk

Good morning class. Please leave the papers in the center of your desks faced down.Go ahead and begin the pre-evaluation found on your desk. Please work individually. Raise your hand when you are finished.

Display PowerPoint slide 1 on the board with the objectives

Today we will be using graphs, equations, and 2 points on a line to determine slope, x-intercepts, and the y-intercept.

Display slide 2.Teacher will walk across room from one piece of tape to the other at a moderate constant pace

I am going to walk at a moderate constant pace from one piece of tape to the other while Ms. Gold will be recording the time it takes from start to finish

Display slide 3.Will display what a possible line on a graph would look like representing a moderate walking pace

It took Ms. Burkhardt __ seconds to reach the finish marker. If we assume she walked at a constant moderate pace, this line would represent her pace.

Ask for a volunteer to walk at a slower constant pace. Record elapsed time

Who will come up and walk at a slower constant pace?

[I will]Student walks at a slower pace


It took (student’s name) __ seconds to walk from start to finish

Student will draw the line on the same graph representing (student’s name) pace

Who will display on the graph what (student’s name) line would look like, assuming that his/her pace is constant?

[I will]Student will draw line with a smaller slope

Ask for volunteer to walk at a faster constant pace. Record elapsed time

Who will come up and walk at a faster constant pace?

[I will]Student walks at a faster pace

It took (student’s name) __ seconds to walk from start to finish

Student will draw the line on the same graph representing (student’s name) pace

Who will display on the graph what (student’s name) line would like, assuming that his/her pace is constant?

[I will] Student will draw graph on smart board

Ask students whose line on the graph has the greatest slope

Whose line on the graph has the greatest slope?

(2nd student’s name) walked faster so they have a greater slope

Do not tell student’s correct answer. Ask students to think about it throughout the lesson

Think about the relationship between the slope and steepness of the line as we progress through the lesson

Exploration Time: 20 minutesWhat the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible

MisconceptionsTeamwork:Students will work in their groups of 4 on the “Exploring X-intercepts, Y-intercepts, and Slope” worksheet. Display slide 4

Go ahead and pick up the worksheet in the middle of the desks that is called “Exploring X-intercepts, Y-intercepts, and Slopes”.

You will be working in your groups of 4 to complete the exploring worksheet

Students will work on the first section of the worksheet titled, “Graphs”

Begin working on the “Graph” portion of the worksheet and stop working when you are finished

What’s the difference between x and y intercept?(What prompted this question? Is this a student’s question or your question? Either way, where’s the answer?)

Circulate around room and ask probing questions to students to make sure they’re on task and can clear up any misconceptions

How did you find the slope? [rise/run][the difference between 2 y-values divided by the difference between 2 x-values][(y2-y1)/(x2-x1)]


What is similar about the two graphs? [y-intercepts are the same]What is the x-intercept for that graph? [Graph 1: (-2,0)

Graph 2: (-1,0)]What is the x-value for all y-intercepts? Why?

[0][All y-intercepts are determined when x=0]

What is the y-intercept for that graph? [Graph 1 and 2 are both (0,1)]

Is the line increasing or decreasing? [increasing]How do you know that? [We know the line is

increasing because the slope is positive][The line is moving up and to the right]

Does the line cross the origin? [no]If the graphs did cross the origin, what would be the x and y intercept?

[(0,0)]

How are the graphs different? [The x-intercepts and slopes are different]

Students will stop working and focus attention to the front of the room

Put your pencils down and focus your attention on us.

Students will share their answers to the “Graph” portion of the worksheetA volunteer will share their answer to the first two questions

Who will tell us what the y-intercepts of the graphs are?

[1: (0,1)2: (0,1)]

Circle y-intercepts on the graphs after student gives answer

A volunteer will share their answer for questions 3 and 4

Who will tell us what the x-intercepts of the two graphs are?

[1: (-2,0)2: (-1,0)]

Circle x-intercepts on the graphs after student gives answerA volunteer will share their answer for questions 5 and 6

Who will tell us what the slopes are for the two different graphs?

[1: ½ 2: 1]

A volunteer will share their answer for question 7

Which graph has a larger slope? [Graph 2]

A volunteer will share Which graph is steeper? [Graph 2]


their answer for question 8

Why? [Both slopes are positive and Graph 2 has a larger positive slope]

Can a line with a negative slope be steeper than a line with a positive slope?

[Yes]

Who will give me an example of a negative slope of a line which is steeper than the slope of positive 2?

[-3, -8,etc.]

See Explanation 1Students will get back in their groups and finish the rest of the worksheet

Go ahead and take back out your exploring worksheet. You will have 7 minutes to finish the rest of the worksheet.

Raise your hands if you have any questionsCirculate around room and ask probing questions to students to make sure they’re on task and can clear up any misconceptions

What is the y-intercept? [Equation a: (0,14)Equation b: (0,8)]

What is the x-intercept? [Equation a: (-2,0)Equation b: (-4,0)]

What is the slope of the equation? [Equation a: 7Equation b: 2]

How did you solve for the y-intercept? [I plugged in 0 for X][I graphed the line and found where the line passed through the y-axis]

Can a function have more than one y-intercept?

[No]

Why? [You can only have one output(y value) for every input (x value)]

How did you solve for the x-intercept? [I set the equation equal to 0][I graphed the line and found where the line passed through the x-axis]

Tell students to put Put your pencils down and focus your


pencils down and focus attention on the board

attention to the front of the room


Who will tell us the y-intercepts of the equations?

[a: (0,14)b: (0,8)]

A volunteer will share their answers for questions 3 and 4

Who will tell us the x-intercepts of the equations?

[a: (-2,0)b: (-4,0)]


Who will tell us the slopes of the equations?

[a: 7, b:2]

Ask students which graph had the greater slope

Who will tell us which graph had the greatest slope?

[Graph of equation a]

Ask students to share which equation would have a steeper slope when graphed

When graphed, which graph would be steeper?

[Graph of equation a]

Why? [Both graphs have a positive slope and graph a would have a larger positive slope]

See Explanations 2Explanation Time: 10 minutesWhat the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible

MisconceptionsExplanation 1Tell students to follow along on their notes sheet.

Take out the paper labeled Notes and remember to follow along as we go through the information

Display slide 5. Ask students what a y-intercept is

Who will tell us the definition of a y-intercept?

Yes, (student’s name)

[Where the line goes through the y-axis]

Display definition of y-intercept

A y-intercept is the point where the line crosses the y-axis of a graph (x=0)

Display graph that shows y-intercept

Who will tell us the y-intercept of this graph?

(0,1) is the y-intercept of this graph

Students will find the y-intercept on their notes worksheet

Go ahead and find the y-intercept on the graph on your notes worksheet

Students work on notes worksheet

Explanation 2Display slide 6.Ask students what a x-intercept is

Who will tell us the definition of x-intercept?

[Where line crosses x-axis]

Display definition of x-intercept

A x-intercept is the point where the line crosses the x-axis of a graph (y=0)]


Students will find the x-intercept on their notes worksheet

Find the x-intercept on your Notes worksheet

Students work on notes worksheet

Display slide 7.Ask students what the definition of slope is

Who will tell me the definition of slope? [Rise/run][Change in the values of y over the change in the values of x][Steepness of the line]

Display definition of slope The slope of a line is a number that measures its "steepness", denoted by the letter m in an equation for a line. It is the change in y values for every one x value

Display slide 8 Who will tell me how to solve for the y-intercept given an equation?

[I do not know how to solve for the y-intercept]

Be sure to indicate throughout the lesson plan when you are calling on a particular student. The reader of the lesson plan shouldn’t think that you are accepting shout outs.

Who will give me an example of a y-intercept?

[(0,7)]

Who will tell me what the x-coordinate is always going to be in a y- intercept?

[0]

What number would you substitute for X in the equation Y=5X+3 to find the Y-intercept?

[0]

Who will tell me the y-intercept of the equation?

[(0,3)]

Display slide 9 Who will tell me how to solve for the x-intercept given an equation?

[I do not know how to solve for the x-intercept]

Who will give me an example of an x-intercept?

[(5,0)]

Who will tell me what the y-coordinate is always going to be in the x-intercept?

[0]

Is the x-coordinate different among x-intercepts?

[Yes]

Why? [The x-coordinate of the intercept depends on where the line crosses the x-axis]

What number would you substitute for Y in the equation Y=5X+3 to find the X-intercept?

[0]


Who will tell me the X-intercept of the equation?

[(-3/5,0)]

Display slide 10 Slope is the coefficient in front of x which is represented by the letter m in an equation for a lineIn this given equation, what would the is the slope be?

[m=5]

How did we use an equation to find the y-intercept?

[We substituted 0 in for x]

If we substitute 0 in for x in the equation y=mx+b, what would be the y-intercept?

[(0,b)]

As you can see, the b in the equation y=mx+b will always be the y value of the y-intercept You are telling the students something they should be telling you. Ask students to summarize what the m and b represent in the equation y = mx + b. Then tell students that this is why it is called the slope-intercept form of a linear equation.

Elaboration Time: 10 minutesWhat the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible

Misconceptions

We will distribute “Who Won The Bet” papers to students

Since you all were so quick at learning the information, we have an extra worksheet for you, titled Who Won The Bet.

You may work with your group on this worksheet

Raise your hands if you have any questionsEvaluation Time: 5 minutesWhat the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible

MisconceptionsTo evaluate how well the learning objectives were learned, a post-evaluation will be distributed to all students to work on individually. This will be distributed to students 5 minutes before class ends.

Please clear your desks.Now you are going to show us what you have learned.

Be sure to put your name at the top of the paper.

You will be working individually, so keep your eyes on your own paper.


Students will raise hands when finished When you are finished, turn your paper

over and raise your hand and we will come over and collect your paper.

Pre-Evaluation

1. Draw the graph of a linear function with a y-intercept at (0,4) and with a slope of 1/3.


2. Given the equation y=3x+5, determine the x-intercept.

3. How does the slope of a line affect the steepness of the graph of the line, assuming the slopes are is positive? In your lesson be sure to talk about the greater the positive slope the steeper the line – the closer the line lies to the y-axis.

Pre-Evaluation Answer Key

1. Draw the graph of a linear function with a y-intercept at (0,4) and with a slope of 1/3.

Where’s your graph?


2. Given the equation y=3x+5, determine the x-intercept? 3x+5=03x=-5 or -3x=5x=-5/3

3. How does the slope of a line affect the steepness of the graph of the line, assuming the slopes are positive?

As the value of the positive slope increases, the steepness of the line increases.Perfect, be sure students hear this in your lesson.

Name: Date:

Exploring Y-Intercepts, X-Intercepts, and Slopes

Graphs


Graph 1:

Graph 2:

1. What is the Y-Intercept of graph 1?(0,1)

2. What is the Y-Intercept of graph 2?(0,1)

3. What is the X-Intercept of graph 1?(-2,0)


4. What is the X-Intercept of graph 2?(-1,0)

5. What is the slope of graph 1?1/2

6. What is the slope of graph 2?1

7. Which graph has the larger slope?Graph 2 has a larger slope.

8. Which graph is steeper? Why?Graph 2 because it has a larger slope

Equations

a. Y= 7x+14 b. Y= 2x+8

1. What is the Y-Intercept of the graph given equation a?(0,14) Y=7(0)+14

2. What is the Y-Intercept of the graph given equation b?(0,8) Y=2(0)+8

3. What is the X-Intercept of the graph given equation a?(-2,0) 0=7X+14

4. What is the X-Intercept of the graph given equation b?(-4,0) 0=2X+8

5. What is the slope of the graph given equation a?7

6. What is the slope of the graph given equation b?2

7. Which graph given by the equations has the larger slope?Graph of equation a

8. If you were to graph the equation, which graph would be steeper? Why?


Graph of equation a because it has a larger slope

Notes NAME____________________________DATE________

A Y-Intercept is ______________________________________________________.

Please write the coordinate points of the Y-Intercept.

Y-Intercept: ( _ , _ )

A X-Intercept is ____________________________________.

Please write the coordinate points of the X-Intercept.

X-Intercept: ( _ , _ )


A Slope is __________________________________________________.

Solve for Y-Intercept by setting ______equal to zero

Solve for X-Intercept by setting ______equal to zero

The slope is the number in front of____. It is represented by the letter___.


Post-Evaluation

1. Draw the linear function with a y-intercept at (0,-3) and with a slope of 4.

2. Given the equation y=2x-1 determine the x-intercept.

3. How does the slope affect the steepness of a graph?


Post-Evaluation Answer Key

1. Draw the graph of a linear function with a y-intercept at (0,-3) and with a slope of 4.

Where’s your graph?

2. Given the equation y=2x-1 determine the x-intercept.2X-1=0

2X=1 or -2x=-1

X=1/2

3. How does the slope affect the steepness of a graph, assuming the slope is positive? As the value of the positive slope increases, the steepness of the line increases.


Who won the bet?

Julia and Carlos made a bet on who would have the most money in their account after 8

weeks. They both began working on the same day. Julia started out with $40 in her bank

account. She began working at the mall and earned $120 per week. Carlos started out with

$85 in his bank account. When he got his job at Target, he earned $115 per week. After 8

weeks, who had more money in their bank account?

1. Underline the y-intercepts.

2. Put a circle around the slopes.

3. Write two equations to represent how much money Julia and Carlos have.

4. How much did Julia have in her bank account after 8 weeks?

5. How much did Carlos have in his bank account after 8 weeks?

6. Who won the bet?


Who won the bet? (answer Key)

Julia and Carlos made a bet on who would have the most money in their account after 8

weeks. They both began working on the same day. Julia started out with $40 in her bank

account. She began working at the mall and earned $120 per week. Carlos started out with

$85 in his bank account. When he got his job at Target, he earned $115 per week. After 8

weeks, who had more money in their bank account?

1. Underline the y-intercepts.

2. Put a circle around the slopes. (will circle)

3. Write two equations to represent how much money Julia and Carlos have.

Y=120X+40, Y=115X+85

4. How much did Julia have in her bank account after 8 weeks?

$1000

5. How much did Carlos have in his bank account after 8 weeks?

$1005

6. Who won the bet?

Carlos won the bet

microsoft word - s1_syllabus.doc€¦ · web viewin a word problem, the initial starting value at...

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