microsoft word - s1_syllabus.doc€¦ · web viewgrade 11, ma.912.a.3.10, standard 3: linear...

Classroom Interactions

Title of Lesson: Equations of AttackUF Teach Students’ Names: Katelynn DePatie and Karley FreelandTeaching Date and Time: September 27th, 2012 at 10:30-11:20am and 11:55-12:45pmLength of Lesson: 50 minutesGrade / Topic: 11th Grade / Algebra 2Source of the Lesson:

CPALMS: http://www.cpalms.org/RESOURCES/URLresourcebar.aspx?ResourceID=nJhgeJisQt8=D

Appropriateness for High School Students: This lesson gives students the opportunity to play a board game in the algebra classroom, using the skills they have learned, to create linear equations given a point and slope. It involves technology and virtual manipulatives as well which further engages students and allows them to work with the material in a different way.

ConceptsWriting linear equations is a valuable tool because when solving real world problems, it is most likely that the equations will not be given. Instead it will be up to the person to create the appropriate linear equation, and then apply it in the correct manner. Also, linear equations are a great way to represent rates of changes. Many rates of change occur during recreational activities such as riding a bike, swimming, running, etc. Rates of change also occur when driving. Linear equations are an incredibly useful for modeling real-life scenarios and relationships. Grasping the overall picture of the linear equation is crucial for students’ future success in mathematics, such as calculus, and also in science, such as physics. Calculus will apply student’s knowledge about linear equations to the use of the first and second derivatives. Mastering the skill of writing linear equations is just one of the stepping stones to becoming a mathematically literate adult.

Florida State Standards (NGSSS): Grade 11, MA.912.A.3.10, Standard 3: Linear Equations and Inequalities- Write an equation of

a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

o Cognitive Complexity: Moderate

Performance Objectives Students will be able to

1. Write an equation of a line given a point and slope2. Write an equation of a line given two points3. Write an equation of a line given a graph

Materials List and Student Handouts 25 of the following:

o Pre-Assessments (Pg. 15)o Post-Assessments (Pg. 16)o Colored Pencilso Equations of Attack Questions Sheet (Pg. 13)o Writing the Equations of Attack Sheet (Pg. 14)

http://www.cpalms.org/RESOURCES/URLresourcebar.aspx?ResourceID=nJhgeJisQt8=D


14 of the following:o Coins or counterso Rules of the Game (Pg. 11) o 9 x 9 grid (Pg. 12) o Set of slope cards o Zip bloc bags (sandwich size)o Rulers

Advance Preparations Cut out slope cards for each group and place in zip bloc bag Xerox copies for Rules of the Game, 9 x 9 grid, Equations of Attack Questions, Writing Equations of

Attack Set up projector for use of the PowerPoint

Safety There are no safety hazards.

ENGAGEMENT Time: __5 minutes__What the Teacher Will Do Teacher Directions and

Probing QuestionsStudent Responses and Potential Misconceptions

Greet students and have them quickly get seated so that the lesson can begin.

Bring up PowerPoint with pictures of roller coasters on it.

The teacher will point to the incline where the roller coaster would be moving up the tracks towards the top of the Kraken roller coaster.

The teacher will point to the decline where the roller coaster would be moving downwards on the tracks towards the ground.

Who in here enjoys going to or has been to a theme park?Does anyone like going on roller coasters? Which ones?

What do you know about slope, (student name)?

Good job!

Now, if we look at these pictures of Sheikra and Kraken, two popular roller coasters, what can we see when we think of them in relation to slope?

So what about this slope, do you think it would be increasing or decreasing, (student name)? Why?

Right! What about this piece, (student name)? Why?

Exactly.

[Students raise their hands.]

[Students raise their hands and give names of roller coasters.]

[Slope is the rise over run. The rate of change.]The angle of something.Students may not know the answer.

[The tracks have a slope. The tracks are diagonal and have a steep and/or shallow slope.] Answers may vary. Students may not understand.

[Increasing. It is pointing up from the left to the right and the roller coaster goes up the tracks on that part.] Decreasing.

[Decreasing. It is moving downwards towards the ground and is pointing down from left to right.] Increasing.


The teacher will point to the leftmost part of the roller coaster where the car would be going upwards on the track.

Point to the vertical drop on the roller coaster. xxx

The students should know this concept as they have gone over it in the past, but may still be uneasy as to the answer and may need to be refreshed.

Move to the exploration portion

Now, looking at the Sheikra roller coaster, is this piece increasing or decreasing, (student name)?

What about this segment of the roller coasterxx, (student name)?

What would we call this slope? It’s not increasing OR decreasing.

Right!

So when we have an undefined slope, it means that it is neither increasing nor decreasing; it is a vertical line straight up and down.

What if the line was going straight from left to right, parallel to the ground? What would the slope be then, (student name)?

Right, the slope would be 0, because it is not increasing or decreasing but is not a vertical line either.

So, do you all think we could graph these lines from these segments of the roller coasters?

Would they be linear?

We could, essentially, make an equation for each one of these slopes and graph them if we wanted to practice. Instead, we are going to continue on working with slopes but you all are going to play a game instead.

[Increasing.] Decreasing.

[There is no slope. Undefined.] Increasing, decreasing. Students may not be sure because the angle is 90 degrees from the ground and is neither increasing nor decreasing.

[Undefined.] If students do not understand, go over the concept of an undefined slope.

[The slope would be 0.] Students may not be sure.

[Yes.]

[Yes.]

Classroom InteractionsEXPLORATION Time: 25 minutes

What the Teacher Will Do Teacher Directions and Probing/Eliciting Questions

Student Responses and Misconceptions

The teacher will then transition into the explore activity.

Refer to slide 4 of the PowerPoint.

Refer to Slide 5 of the Ppt.

Now, using what we just discussed about slope, we are going to break into pairs, but not yet, and play a game called “Equations of Attack.”

You will be playing a game using this 9x9 grid (show students a copy) to plot points and graph linear equations. You will each have “ships” which you will plot using circular points and “cannons” which you will plot using x’s. The object of the game will be to “fire” from the cannons a line and try to intersect the “ship” or points in order to “sink” the ship.

Each pair will receive a large 9 x 9 grid like this (show the class the grid), a rules sheet, a zip bloc bag of slope cards, and 2 colored pencils.Let’s take a look at the PowerPoint for an example of how to play the game. Again, remember you will be playing this with a partner.

Please read aloud the first rule of the game, (student name).

Thank you!

Please read rule #2, (student name)

Okay, great. Now, let’s take a look at the PowerPoint to see how we will place the ships on the board.You can see that you and your partner will take turns placing your

[Flip a coin to determine who gets to place the first ship and gets to choose whether he/she gets the even or odd cannons.]

[Each player should choose one color to represent his/her fleet. One player (decided by the coin toss) places the first ship by drawing a large dot on the board. Then, the other player places the second ship. Continue placing ships until each player has ten ships on the board.]





.

color ship on the board until you each have 10 ships. It is totally up to you to decide where to place your ship. Also remember to place your ships on whole number lattice points and not at something like (3.5, 6.25), and do not place them on the y-axis.

Please read rule #3, (student name).

Thank you; now we can see from the PowerPoint exactly how this works.

Please read rule #4, (student name).

[Each player will have five cannons along the y-axis. One player will have all the even cannons (0, 2, 4, 6, 8), and the other player will have the odd cannons (1, 3, 5, 7, 9), as determined by the initial coin toss. Mark your cannons with X’s using your color.]

[It’s time to play! The player with the even cannons goes first. Draw a slope card from the face-down deck. Choose any of your five cannons to shoot from. Draw a line from the cannon you chose in the direction determined by your slope. If you hit an opponent ship (or more than one), the ship is sunk!]

Refer to Slide 9 of the Ppt. So let’s demonstrate this using the deck of slope cards and the PowerPoint.We have drawn a slope (whatever is drawn). We need to choose a cannon then create a line with the slope (whatever is drawn). We know slope is the rise over run, so if we choose the canon on the point (0,3) we will go up ____, and over _____. If we hit an opponent’s ship the ship is sunk. You will be using rulers to ensure that your lines are straight. After you draw the line, you will number it. You will then write the equation of the line with the corresponding number on the Writing Equations Sheet.

Classroom InteractionsLet’s write our line in slope intercept form.What is the slope?Nice!

What is the y-intercept?Fantastic!

Is anyone unclear about the instructions?Great! After you find a partner and scoot your desks together, we will pass around the grid, rules of the game, ruler, activity sheet, and colored pencils.Once you finish playing the game, you will need to each answer the Equations of Attack questions; you can answer them together but you each need to fill one out.You may begin!

[It is (whatever the slope card said).]

[3]

If yes, go over the instructions again and clarify. If not, proceed.

Allow students about 20 minutes for students to play the game. The teacher should walk around the classroom, and help any students that have questions.The teacher may wish to ask students some of the following probing questions while walking around the room.

Is there a ship placement that is totally safe from the cannons? If so, where? If not, why?

Do you prefer to graph the line first or find the equation of the line first? Why?

[It depends on the slope cards available. For example, if all the possible slopes are positive, then none of the points along the x-axis can ever be hit.]

[I prefer to draw the line first because I can see if I will actually hit a shape that way.]

Classroom InteractionsEXPLANATION Time: _15 minutes__

What the Teacher Will Do Teacher Directions and Probing/Eliciting Questions

Student Responses and Misconceptions

Regroup after the Equations of Attack activity.

Pick up all colored pencils and have students get their desks back in order.

Students should be able to see that both positive and negative slopes were used.

Go over question 4 on the activity sheet as a class. Students should be able to see that by substituting their opponent’s coordinate point into the equation, they can come up with a slope that will sink the ship. Forms that can be used could be: y = mx + b y – y1 = m(x – x1)

So, now that we are done with that activity, let’s go over a few things.

How did you choose which cannons you wanted to use when sinking your opponent’s ships, (student name)?

Right. So the main point of the game was to do what?

When we talk about slopes, what could you say about the different slopes you used, (student name)? Were they all the same?

Did they all look the same?

When did you know when to use a positive slope?

And what about when to use a negative slope?

So, were you able to tell when your equation would sink a ship before you even graphed it, (student name)?

Let’s go over question 4 on your activity sheet. (Read question 4 aloud and change to the slide on the PowerPoint of this page.)

If we were to find out the slope that would connect two points, without simply counting up and over or down and over from the cannon to a given point, how could we do so?

[I picked the slope that would match up so I could draw a line and connect my cannon to his/her ship.] Answers may vary, if student is unsure of the answer, have another student help.[Sink all of my opponent’s ships.]

[No, some were positive and some were negative. Some pointed downwards while others went upwards.]

[No, some were negative and others were positive.]

[When the ship was higher than the cannon.]

[When the ship was lower than the cannon.]

[Yes. No. Sometimes.]

[We could check the slope we drew with the two point we have.] Students may not understand the question or may not immediately see this answer; if so, go over the question on the board by doing an example.


An example could also be done to test two points that do not lie on the same line with a given slope. An example could be: (0,1) and (1,5) with the slope 3.

Let’s go over an example. We can say I have a cannon placed at (0,2) and my opponent’s ship is at (3,5). So if we drew the slope card, 1, how could we check if that would work?

So using the equation: y = mx +b what numbers would we put where?

Right! So would the slope card 1 work in this equation, (student name)?

Another way we could check could be to, assuming I have the same points (0,2) and (3,5), use point slope form. If we wanted to find the slope that connected the two points, how could we use the equation:y – y1 = m(x – x1)?

Exactly! (Finish working out the problem with the students on the board to obtain the slope 1.)

Alright, so could we safely say that there are a few ways to check if both points lie on the same line with a given slope?

Do you prefer to find if a ship was sunk by graphing or would you rather find out algebraically? (ask a few students)Is it easier one way or the other or do they both have pros and cons?

[Plug in the slope and points we have.]

[m = 1 because that is our slope,b = 2 because that is our y intercept, and the x and y would be the point, (3,5).]

[Yes.] No.

[We could plug in both coordinates into point slope form and solve for the slope, m.] Students may not understand the question or may not immediately see this answer; if so, go over the question on the board by doing an example.

[Plug in (0,2) for x and y and then plug in (3,5) for x1 and y1 and solve for m.]

[Yes.]

[Graphing. Algebraically.] Answers may vary.

[Both methods have pros and cons.] Answers may vary.

If time permits, go over parallel and perpendicular lines.

Write the equations on the board that the students tell you (if they have any equations at all that are

Now, looking back at your activity sheets, did anyone end up with any parallel or perpendicular lines?

What were the equation for the lines you had that were parallel, (student name)?

[Yes. No.] Answers may vary.

Answers may vary.


parallel or perpendicular; they may not.)

If no one has any examples, move on to the following example:Find the equation of the line passing through the point (2,5) and parallel to the line: y=3x+4

Move on to the elaboration portion if time permits, otherwise skip to the evaluation.

What about for perpendicular?

What did you notice in common with the parallel lines?

What did you notice about the perpendicular lines?

Let’s try an example. Say we have the point (2,5) and we want to find the equation of the line passing through that point and parallel to the line y=3x+4.

What would the slope of our new line be?

Good! So what would our next step be, (student name)?

What do we do next?

So what would our equation be?

Exactly! And what would we have done differently had we wanted to find the equation of the line perpendicular to the equation y=3x+4?

You all seem to have the concept of making equations down pretty well. We are going to move on to the next activity.

Answers may vary.

[They had the same slope.]

[Their slopes were the negative reciprocal of each other. Their slopes were flipped and had the opposite sign of each other.]

[3] -1/3

[Plug in the slope of 3 and the point (2,5) into point slope form.] Answers may vary.

[Distribute the 3 to the x and the 2 and then add the 5.]

[y = 3x – 4]

[We would have used the slope -1/3 instead of 3.]

Classroom InteractionsELABORATION Time: 15 minutes

What the Teacher Will Do Probing/Eliciting Questions Student Responses and Misconceptions

The teacher will allow students to play a game on the computer in which they will get to practice writing linear equations.Use the following website: http://hotmath.com/hotmath_help/games/kp/kp_hotmath_sound.swf

;

EVALUATION Time: _5 minutes___What the Teacher Will Do Assessment Student Responses

Hand out the Post-Assessment to students after they have cleared their desks and allow them to work on it until the bell rings.

Please clear your desks and I will hand out the post-assessment.

This is to be worked on alone, not in groups. You have until the bell rings to finish it; I will collect them all when you all are finished.

Classroom InteractionsRules of the Game… Equations of Attack!

1. Flip a coin to determine who gets to place the first ship and gets to choose whether he/she gets the even or odd cannons.

2. Each player should choose one color to represent his/her fleet. One player (decided by the coin toss) places the first ship by drawing a large dot on the board. Then, the other player places the second ship. Continue placing ships until each player has ten ships on the board.

a. Note: Ships can only be placed at lattice points (where both the x- and y-coordinates are integers). For example, you can place a ship at (4, 5) but you can’t place a ship at (4.5, 5) or (4, 5 1

3). Also, ships cannot be placed along the y-axis.

3. Each player will have five cannons along the y-axis. One player will have all the even cannons (0, 2, 4, 6, 8), and the other player will have the odd cannons (1, 3, 5, 7, 9), as determined by the initial coin toss. Mark your cannons with X’s using your color.

4. It’s time to play! The player with the even cannons goes first. Draw a slope card from the face-down deck. Choose any of your five cannons to shoot from. Draw a line from the cannon you chose in the direction determined by your slope. If you hit an opponent ship (or more than one), the ship is sunk!

a. IMPORTANT: Number each of the lines you draw, and then write the equation of each line you draw with the corresponding number on the equations sheet.

5. Play alternates until 5 of one player’s ships are sunk. The first player to sink at least 5 opponent ships is the winner!


Player A’s Name: ___________________ Color: _________________

Player B’s Name: ___________________ Color: _________________

**Remember to number the lines that you draw, and write the equation of that line on the corresponding number of the Writing Equations of Attack! sheet.

Classroom InteractionsEquations of Attack! NAME ___________________________

Questions

1. If you did not sink all of your opponent’s ships, write equations that would sink the ships that are still afloat.

2. Explain the strategy you used for choosing your cannons. Do you think your strategy is the best possible strategy? Why?

3. Explain how you could tell that your equation would sink an enemy ship without graphing.

4. Do you notice any parallel lines on your grid? If so, write down the equations of those lines that you believe are parallel. What do the equations of parallel lines have in common?

5. Do you notice any perpendicular lines on your grid? If so, write down the equations of those lines that you believe are perpendicular. What do equations of perpendicular lines have in common?

Resources for Teaching Math © 2008 National Council of Teachers of Mathematics http://illuminations.nctm.org

Classroom InteractionsWriting Equations of Attack!

Name: _____________________________ Color: ________________________________Write your equations in y=mx+b form.

1) 13)

2) 14)

3) 15)

4) 16)

5) 17)

6) 18)

7) 19)

8) 20)

9) 21)

10) 22)

11) 23)

12) 24)


Pre- Assessment

1. What is the slope and y-intercept of the following equation?y = 5x + 7

2. Given the points (1,3) and (2,4) find the equation of the line and write the equation of the line in slope-intercept form.

Pre- Assessment

1. What is slope and y-intercept of the following equation?y = 5x + 7

2. Given the points (1,3) and (2,4) find the equation of the line and write it in slope-intercept form.

Classroom InteractionsPost- Assessment

1. Refer to the graph below to answer the following questions.

(a) What is the equation in slope-intercept form that would connect the cannon to the ship and sink it?

(b) What is the equation in point-slope form?

microsoft word - s1_syllabus.doc€¦ · web viewgrade 11, ma.912.a.3.10, standard 3: linear...

Documents