Graphing Stories Writing Equations

Size: px
Start display at page:

Download "Graphing Stories Writing Equations"

Transcription

1 Exploratory Activity Consider the story: Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 ft. apart. Each starts at his or her own door and walks at a steady pace toward each other and stops when they meet. 1. A. What two aspects of their walk should we measure? Distance - y-axis Time - x-axis B. What would their graphing stories look like if we put them on the same graph? Two lines, one starting at 50ft with a negative slope and one starting at zero with a positive slope. 2. When the two people meet in the hallway, what would be happening on the graph? The two lines will intersect (meet). 3. Sketch a graph that shows their distance from Maya s door. S.31

2 Consider the story: Duke starts at the base of a ramp and walks up it at a constant rate. His elevation increases by 3 ft. every second. Just as Duke starts walking up the ramp, Shirley starts at the top of the same 25 ft. high ramp and begins walking down the ramp at a constant rate. Her elevation decreases 2 ft. every second. Understanding the Problem 4. Fill in the chart below to help you understand how quickly Duke and Shirley move and where they start. Duke s Path Time in Seconds Elevation in Feet Shirley s Path Time in Seconds Elevation in Feet 5. Use the extra row in each table to write an expression that describes the elevation pattern. Elevation in Feet The Story of Duke and Shirley Duke: Shirley: Time in Seconds 6. Use the grid above to graph the data for Duke and Shirley. Be sure to finish the legend to help the reader understand your graph. S.32

3 Writing an Equation of a Line The equation of a line can be in the form y= mx+ b, where m represents the slope of the line and b represents the y-intercept. 7. Determine the slope of Duke s line and Shirley s line. Why is one of the slopes negative? Duke s slope: Shirley s slope: 8. What is the y-intercept for each line? Duke s y-intercept: Shirley s y-intercept: 9. Write the equation of Duke s line and Shirley s line. Duke s line: Shirley s line: 10. Where do the two lines intersect? This is the point of intersection. What time do Duke and Shirley pass each other? 11. How could you use the equations to find the point of intersection? The equation you wrote in Exercise 9 are in slope-intercept form or y =mx + b. Point-slope is another very useful form of a linear equation. For point-slope we need any point on the line, not just the y-intercept and the slope of the line. The general form looks like y y 1 = m(x x 1) where (x 1, y 1) is any point on the line and m is the slope of the line. 12. A. Use the points when t = 3 seconds and slope from Exercise 7 with the point-slope equation to get an equation for Duke and Shirley. B. How do these equations compare to the ones you wrote in Exercise 9? The equations are the same. S.33

4 Winter-Wonderland Party! Nancy and Jane want to throw a Winter-Wonderland party. They want to split the cost evenly between them. Nancy owes her parents $30 for the dress she wanted to have for the first day back to school. She must pay them back before she can contribute to the party expenses. Jane has been putting money away all summer and had $66 before she spent $6 on some new songs by her favorite band. Nancy earns $15 each week for keeping up on her chores. Jane earns $18 every week for allowance, but pays her brother half for doing her pooper-scooper duty and cleaning up after their two dogs. It is mid-august and the girls promise to not spend their earnings and plan to save for the party. They each try to figure out how long it will take to have the same amount of savings in order to maximize the party budget. 13. Create a table to help you organize the information you have so far. Then graph your data and include a legend. Does it make sense to connect the points? Finally, write an equation for each girl. Time in Weeks Since Mid-August Nancy s Savings Jane s Savings Money Saved in Dollars Winter-Wonderland Party Time in Weeks n This is where you can write the expression for each girl s saving. S.34

5 14. How many weeks does it take for the girls to have the same amount of money? Check that this answer makes sense on the graph and in each equation. 15 weeks 15. If the girls determine that they need $150 each for the party, which week would they have enough money? Remember that they each have to put in the same amount. Justify your answer using the tables, graph or equations. Week 12 S.35

6 Lesson Summary Linear Equations: If you know the slope and y-intercept you can use the equation y= mx+ b to write an equation for the line. If you have the slope and any point on line you can use the pointslope equation, y y 1 = m(x x 1) where (x 1, y 1) is any point on the line and m is the slope of the line. Example 1: The slope of a line is -3 and the y-intercept is 5. An equation of this line is. Example 2: The slope of a line is ½ and the point (2, 4) is on the line. The equation of this line is. Point of Intersection: The point of intersection is an ordered pair that is a solution to both equations. On a graph this is where the two graphs cross each other. Example: Determine the point of intersection for the graph below. Point of intersection: S.36

7 Homework Problem Set 1. Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 ft. apart. Each starts at his or her own door and walks at a steady pace toward each other and stops when they meet. Suppose that Maya walks at a constant rate of 2 ft. every second and Earl walks at a constant rate of 4 ft. every second starting from 50 ft. away. Create equations for each person s distance from Maya s door and determine exactly when they meet in the hallway. How far are they from Maya s door at this time? Let y = distance from Maya s door in feet Let x = time in seconds 2. Suppose two cars are travelling north along a road. Car 1 travels at a constant speed of 50 mph for two hours, then speeds up and drives at a constant speed of 100 mph for the next hour. The car breaks down and the driver has to stop and work on it for two hours. When he gets it running again, he continues driving recklessly at a constant speed of 100 mph. Car 2 starts at the same time that Car 1 starts, but Car 2 starts 100 mi. farther north than Car 1 and travels at a constant speed of 25 mph throughout the trip. A. Sketch the distance-versus-time graphs for Car 1 and Car 2 on a coordinate plane at the right. Be sure to include a legend. B. Approximately when do the cars pass each other? C. Tell the entire story of the graph from the point of view of Car 2. (What does the driver of Car 2 see along the way and when?) S.37

8 3. Challenge Problem A. Write linear equations representing each car s distance in terms of time (in hours). Note that you will need four equations for Car 1 and only one for Car 2. B. Use these equations to find the exact coordinates of when the cars meet. 4. Suppose that in Problem 2 above, Car 1 travels at the constant speed of 25 mph the entire time. A. Sketch the distance-versus-time graphs for the two cars on a graph below. B. Do the cars ever pass each other? Explain. C. What is the linear equation for Car 1 in this case? S.38

9 5. The graph at the right shows the revenue (or income) a company makes from designer coffee mugs and the total cost (including overhead, maintenance of machines, etc.) that the company spends to make the coffee mugs. A. How are revenue and total cost related to the number of units of coffee mugs produced? Dollars Units Produced and Sold Total Cost Revenue B. What is the meaning of the point (0, 4000) on the total cost line? C. What are the coordinates of the intersection point? What is the meaning of this point in this situation? S.39

10 6. Challenge Problem Consider the story: May, June, and July were running at the track. May started first and ran at a steady pace of 1 mi. every 11 min. June started 5 min. later than May and ran at a steady pace of 1 mi. every 9 min. July started 2 min. after June and ran at a steady pace, running the first lap 1 mi. in 1.5 min. She maintained this 4 steady pace for 3 more laps and then slowed down to 1 lap every 3 min. A. Sketch May, June, and July s distance-versus-time graphs on a coordinate plane below. Be sure to label your axes, put a title on your graph, and include a legend. B. Write linear equations that represent each girl s mileage in terms of time in minutes. You will need two equations for July since her pace changes after 4 laps (1 mi.). C. Who was the first person to run 3 mi.? D. Did June and July pass May on the track? If they did, when and at what mileage? E. Did July pass June on the track? If she did, when and at what mileage? S.40

3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation?

3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation? Classwork Exploratory Challenge 1. Watch the first 1:08 minutes of the video below and describe in words the motion of the man. Elevation vs. Time #2 [http://www.mrmeyer.com/graphingstories1/graphingstories2.mov.

More information

3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation?

3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation? J Hart Interactive Algebra 1 Classwork Exploratory Challenge 1. Watch the first 1:08 minutes of the video below and describe in words the motion of the man. Elevation vs. Time #2 [http://www.mrmeyer.com/graphingstories1/graphingstories2.mov.

More information

Lesson 18: There Is Only One Line Passing Through a Given Point with a Given Slope

Lesson 18: There Is Only One Line Passing Through a Given Point with a Given Slope There Is Only One Line Passing Through a Given Point with a Given Slope Classwork Opening Exercise Examine each of the graphs and their equations. Identify the coordinates of the point where the line intersects

More information

8th Grade. Data.

8th Grade. Data. 1 8th Grade Data 2015 11 20 www.njctl.org 2 Table of Contents click on the topic to go to that section Two Variable Data Line of Best Fit Determining the Prediction Equation Two Way Table Glossary Teacher

More information

Vocabulary. Page 1. Distance. Displacement. Position. Average Speed. Average Velocity. Instantaneous Speed. Acceleration

Vocabulary. Page 1. Distance. Displacement. Position. Average Speed. Average Velocity. Instantaneous Speed. Acceleration Vocabulary Term Definition Distance Displacement Position Average Speed Average Velocity Instantaneous Speed Acceleration Page 1 Homer walked as follows: Starting at the 0,0 coordinate, he walked 12 meters

More information

x 2 = (60 m) 2 + (60 m) 2 x 2 = 3600 m m 2 x = m

x 2 = (60 m) 2 + (60 m) 2 x 2 = 3600 m m 2 x = m 3.1 Track Question a) Distance Traveled is 1600 m. This is length of the path that the person took. The displacement is 0 m. The person begins and ends their journey at the same position. They did not

More information

(Lab Interface BLM) Acceleration

(Lab Interface BLM) Acceleration Purpose In this activity, you will study the concepts of acceleration and velocity. To carry out this investigation, you will use a motion sensor and a cart on a track (or a ball on a track, if a cart

More information

2.5. All games and sports have specific rules and regulations. There are rules about. Play Ball! Absolute Value Equations and Inequalities

2.5. All games and sports have specific rules and regulations. There are rules about. Play Ball! Absolute Value Equations and Inequalities Play Ball! Absolute Value Equations and Inequalities.5 LEARNING GOALS In this lesson, you will: Understand and solve absolute values. Solve linear absolute value equations. Solve and graph linear absolute

More information

1. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?

1. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit? Chapter Problems Motion at Constant Speed Class Work. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?. During the first 50 s a truck traveled at constant speed of 5 m/s.

More information

8.5 Training Day Part II

8.5 Training Day Part II 26 8.5 Training Day Part II A Solidify Understanding Task Fernando and Mariah continued training in preparation for the half marathon. For the remaining weeks of training, they each separately kept track

More information

Homework Helpers Sampler

Homework Helpers Sampler Homework Helpers Sampler This sampler includes s for Algebra I, Lessons 1-3. To order a full-year set of s visit >>> http://eurmath.link/homework-helpers Published by the non-profit Great Minds. Copyright

More information

a. Sketch the path of the diver by plotting the vertex, y-intercept, and additional points as needed.

a. Sketch the path of the diver by plotting the vertex, y-intercept, and additional points as needed. Algebra Applications of quadratic functions Name: 1. The path of a diver off a springboard is modeled by the function h( x) ( x 3) 3, where h is the height of the diver and x is the distance of the diver

More information

1.6 Sketching a Piecewise Function

1.6 Sketching a Piecewise Function 1.6 Sketching a Piecewise Function Now that we understand qualitative descriptions of graphs, we can use that information to sketch graphs of a function or give a verbal description of an already sketched

More information

MATH GRADE 6 UNIT 6 RATE ANSWERS FOR EXERCISES

MATH GRADE 6 UNIT 6 RATE ANSWERS FOR EXERCISES MATH GRADE 6 UNIT 6 RATE FOR EXERCISES LESSON 2: PRICE AS A RATE 1. $6.25 2. $.625, or $.63 3. $5.25 4. $.3125, or $.31 5. a. $2.5 b. $13.75 6. a. Amount (pt) 1 2 3 4 5 6 Cost non-organic ($) $.75 $1.5

More information

Physics 2204 Worksheet 6.5: Graphical Analysis of Non- Uniform Motion D-T GRAPH OF NON-UNIFORM MOTION (ACCELERATING) :

Physics 2204 Worksheet 6.5: Graphical Analysis of Non- Uniform Motion D-T GRAPH OF NON-UNIFORM MOTION (ACCELERATING) : Physics 2204 Worksheet 6.5: Graphical Analysis of Non- Uniform Motion D-T GRAPH OF NON-UNIFORM MOTION (ACCELERATING) : The d-t graph for uniformly Accelerated motion is definitely not the same as a d-t

More information

Lesson 14: Modeling Relationships with a Line

Lesson 14: Modeling Relationships with a Line Exploratory Activity: Line of Best Fit Revisited 1. Use the link http://illuminations.nctm.org/activity.aspx?id=4186 to explore how the line of best fit changes depending on your data set. A. Enter any

More information

Interpreting Slope and Intercepts. What s My Meaning?

Interpreting Slope and Intercepts. What s My Meaning? Name: What s My Meaning? Cut apart the What s My Meaning Cards. Match the appropriate equation or graph card with each of the following situations and attach the cards in the appropriate spaces. Determine

More information

Lesson 22: Average Rate of Change

Lesson 22: Average Rate of Change Student Outcomes Students know how to compute the average rate of change in the height of water level when water is poured into a conical container at a constant rate. MP.1 Lesson Notes This lesson focuses

More information

STAAR Practice Test #1. 2 (2B) What is the equation in standard form of the line that

STAAR Practice Test #1. 2 (2B) What is the equation in standard form of the line that STAAR Practice Test #1 TEKS 2 (Linear Equations) 1. (2B) The population of Webb County, Texas, from the year 2000 through 2010 is shown in the graph. If the trend shown in the graph continues, what will

More information

Grade: 8. Author(s): Hope Phillips

Grade: 8. Author(s): Hope Phillips Title: Tying Knots: An Introductory Activity for Writing Equations in Slope-Intercept Form Prior Knowledge Needed: Grade: 8 Author(s): Hope Phillips BIG Idea: Linear Equations how to analyze data from

More information

Ball Toss. Vernier Motion Detector

Ball Toss. Vernier Motion Detector Experiment 6 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would

More information

ACTIVITY: Drawing a Box-and-Whisker Plot. a. Order the data set and write it on a strip of grid paper with 24 equally spaced boxes.

ACTIVITY: Drawing a Box-and-Whisker Plot. a. Order the data set and write it on a strip of grid paper with 24 equally spaced boxes. 2. Box-and-Whisker Plots describe a data set? How can you use a box-and-whisker plot to ACTIVITY: Drawing a Box-and-Whisker Plot Work with a partner. The numbers of first cousins of the students in an

More information

Bicycle Rental Costs straight lines on a graph are called

Bicycle Rental Costs straight lines on a graph are called 1 Walking Rates In Variables and Patterns, you read about a bicycle touring business. You used tables, graphs, and equations to represent patterns relating variables such as cost, income, and profit. You

More information

1/6

1/6 Chapter 3 (5570063) Current Score: 0/59 Due: Tue Oct 7 2014 11:59 PM PDT Question Points 1 2 3 4 5 0/12 0/12 0/12 0/11 0/12 Total 0/59 1. 0/12 points UWAPreCalc1 3.P.001. [2125213] This exercise emphasizes

More information

9/30/2016 Assignment Previewer

9/30/2016 Assignment Previewer Chapter 3 (8415640) Due: Tue Oct 11 2016 11:58 PM PDT Question 1 2 3 4 5 1. Question Details UWAPreCalc1 3.P.001. [2125213] This exercise emphasizes the "mechanical aspects" of circles and their equations.

More information

1/7

1/7 Chapter 3 (13383712) Due: Tue Oct 9 2018 11:58 PM PDT Question 1 2 3 4 5 1. Question Details UWAPreCalc1 3.P.001. [3944502] This exercise emphasizes the "mechanical aspects" of circles and their equations.

More information

Figure 1. The distance the train travels between A and B is not the same as the displacement of the train.

Figure 1. The distance the train travels between A and B is not the same as the displacement of the train. THE DISTANCE-TIME RELATIONSHIP Q1. A train travels from town A to town B. Figure 1 shows the route taken by the train. Figure 1 has been drawn to scale. Figure 1 (a) The distance the train travels between

More information

Coimisiún na Scrúduithe Stáit State Examinations Commission. Junior Certificate Examination Mathematics

Coimisiún na Scrúduithe Stáit State Examinations Commission. Junior Certificate Examination Mathematics 2018. S34 Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination 2018 Mathematics Paper 1 Higher Level Friday 8 June Afternoon 2:00 to 4:30 300 marks Examination Number

More information

University of Colorado-Boulder MATH 1300 Homework 1

University of Colorado-Boulder MATH 1300 Homework 1 Turn in the following problems: 1. Consider the following mathematical statements. Determine if the statements are always true, sometimes true, or never true. (a) (x + 2) 4 = x 4 + 16 (b) x 4 + 8x 2 +

More information

Relations & Functions Practice Test

Relations & Functions Practice Test Relations & Functions Practice Test 1. Consider the relation represented b this graph. Represent the relation as a set of ordered pairs. Distance (km) 11 1 9 8 7 6 5 3 1 Distances Jogged in a Da Josh Koko

More information

MATH IN ACTION TABLE OF CONTENTS. Lesson 1.1 On Your Mark, Get Set, Go! Page: 10 Usain Bolt: The fastest man on the planet

MATH IN ACTION TABLE OF CONTENTS. Lesson 1.1 On Your Mark, Get Set, Go! Page: 10 Usain Bolt: The fastest man on the planet MATH IN ACTION TABLE OF CONTENTS LESSON 1 WORLD RECORD SPEEDS LINEAR FUNCTIONS WITH PROPORTIONAL RELATIONSHIPS Focus on: SLOPE Lesson 1.1 On Your Mark, Get Set, Go! Page: 10 Usain Bolt: The fastest man

More information

Tying Knots. Approximate time: 1-2 days depending on time spent on calculator instructions.

Tying Knots. Approximate time: 1-2 days depending on time spent on calculator instructions. Tying Knots Objective: Students will find a linear model to fit data. Students will compare and interpret different slopes and intercepts in a context. Students will discuss domain and range: as discrete

More information

Algebra 2 Unit 1 Practice

Algebra 2 Unit 1 Practice Algebra 2 Unit 1 Practice LESSON 1-1 Use this information for Items 1. Aaron has $65 to rent a bike in the cit. It costs $15 per hour to rent a bike. The additional fee for a helmet is $ for the entire

More information

Extending the Number System

Extending the Number System 1 Extending the Number System In your study of numbers, you have focused on operations (+, -,, and 4) with whole numbers, fractions, and decimals. In this unit, you will learn about some important new

More information

Movement and Position

Movement and Position Movement and Position Syllabus points: 1.2 plot and interpret distance-time graphs 1.3 know and use the relationship between average speed, distance moved and 1.4 describe experiments to investigate the

More information

CHAPTER 1. Knowledge. (a) 8 m/s (b) 10 m/s (c) 12 m/s (d) 14 m/s

CHAPTER 1. Knowledge. (a) 8 m/s (b) 10 m/s (c) 12 m/s (d) 14 m/s CHAPTER 1 Review K/U Knowledge/Understanding T/I Thinking/Investigation C Communication A Application Knowledge For each question, select the best answer from the four alternatives. 1. Which is true for

More information

Functions 6 Identifying Key Information from the Graph

Functions 6 Identifying Key Information from the Graph 1. Functions 6 Identifying Key Information from the Graph Warm-up 1 For each of the following, highlight the regions of the graphs that correspond to different graph shapes (constant, increasing, or decreasing).

More information

Add this important safety precaution to your normal laboratory procedures:

Add this important safety precaution to your normal laboratory procedures: Student Activity Worksheet Speed and Velocity Are You Speeding? Driving Question What is speed and how is it related to velocity? Materials and Equipment For each student or group: Data collection system

More information

Lesson 4: Describing the Center of a Distribution

Lesson 4: Describing the Center of a Distribution : Describing the Center of a Distribution In previous work with data distributions, you learned how to derive the mean and the median (the center) of a data distribution. In this lesson, we ll compare

More information

Name Date. Solving Equations and Inequalities with Two Variables: Discovering Slope Independent Practice

Name Date. Solving Equations and Inequalities with Two Variables: Discovering Slope Independent Practice Name Date Solving Equations and Inequalities with Two Variables: Discovering Slope Independent Practice 1. Jeff Mordon drives 140 miles in 4 hours. Part A: What is his rate of change? Part B: Represent

More information

Lesson 5.3 Interpreting and Sketching Graphs Exercises (pages )

Lesson 5.3 Interpreting and Sketching Graphs Exercises (pages ) Lesson 5.3 Interpreting and Sketching Graphs Exercises (pages 281 283) A 3. a) Bear F has the greatest mass because it is represented by the point on the graph farthest to the right and the horizontal

More information

Practice Exam for Algebra II Module 1

Practice Exam for Algebra II Module 1 Practice Exam for Algebra II Module 1 1. Frank swam 50 laps at the pool at a constant speed of 300 feet per minute. Which of the following describes a varying quantity in this situation? a. The speed Frank

More information

Lesson 19: Comparison Shopping Unit Price and Related Measurement Conversions

Lesson 19: Comparison Shopping Unit Price and Related Measurement Conversions : Comparison Shopping Unit Price and Related Measurement Analyze tables, graphs, and equations in order to compare rates. Classwork Example 1: Creating Tables from Equations 1. The ratio of cups of blue

More information

The purpose of this experiment is to find this acceleration for a puck moving on an inclined air table.

The purpose of this experiment is to find this acceleration for a puck moving on an inclined air table. Experiment : Motion in an Inclined Plane PURPOSE The purpose of this experiment is to find this acceleration for a puck moving on an inclined air table. GENERAL In Experiment-1 you were concerned with

More information

A Study of Olympic Winning Times

A Study of Olympic Winning Times Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ A Study of Olympic Winning Times Objective: Students will graph data, determine a line that models

More information

Describing a journey made by an object is very boring if you just use words. As with much of science, graphs are more revealing.

Describing a journey made by an object is very boring if you just use words. As with much of science, graphs are more revealing. Distance vs. Time Describing a journey made by an object is very boring if you just use words. As with much of science, graphs are more revealing. Plotting distance against time can tell you a lot about

More information

Be sure students get all the combinations that add to , 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0

Be sure students get all the combinations that add to , 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Lesson: Ten Lap Challenge Grades: K-1 Skills: Ways to make 10, number sense Time: 20 minutes What to do: Tell students they have two days to run ten laps in the gym. Have them use the worksheet on the

More information

Piecewise Functions. Updated: 05/15/10

Piecewise Functions. Updated: 05/15/10 Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ Objectives: Students will review linear functions and their properties and be introduced to piecewise

More information

Section 1. Objectives:

Section 1. Objectives: Chapter 2 Motion Objectives: Section 1 Use a frame of reference to describe motion Differentiate between Speed and Velocity Calculate the speed of an object Use graphs to describe speed Observing Motion

More information

SPEED, VELOCITY, ACCELERATION, & NEWTON STUDY GUIDE - Answer Sheet 1) The acceleration of an object would increase if there was an increase in the

SPEED, VELOCITY, ACCELERATION, & NEWTON STUDY GUIDE - Answer Sheet 1) The acceleration of an object would increase if there was an increase in the SPEED, VELOCITY, ACCELERATION, & NEWTON STUDY GUIDE - Answer Sheet 1) The acceleration of an object would increase if there was an increase in the A) mass of the object. B) force on the object. C) inertia

More information

CHANGES IN FORCE AND MOTION

CHANGES IN FORCE AND MOTION reflect CRACK! That s the sound of a bat hitting a baseball. The ball fl ies through the air and lands over the fence for a home run. The motion of a batted ball seems simple enough. Yet, many forces act

More information

Tyler Runge and Kelly McCaffrey. The Dynamic Relation between String Length and Height with a Set Mass

Tyler Runge and Kelly McCaffrey. The Dynamic Relation between String Length and Height with a Set Mass The Dynamic Relation between String Length and Height with a Set Mass Introduction: The purpose of this experiment was to find the relation between string length and height while keeping the mass constant

More information

Chapter 11 Motion. Section 1

Chapter 11 Motion. Section 1 Chapter 11 Motion Objectives: Section 1 Use a frame of reference to describe motion Differentiate between Speed and Velocity Calculate the speed of an object Use graphs to describe speed 1 Observing Motion

More information

Mini-Golf Course Description. 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants.

Mini-Golf Course Description. 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. Algebra 1 Mrs. Blake B256 Mini-Golf Course Description Guidelines for your creation: 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. 2. On the graph paper

More information

LINEAR AND ANGULAR KINEMATICS Readings: McGinnis Chapters 2 and 6 DISTANCE, DISPLACEMENT, SPEED, VELOCITY, AND ACCELERATION:

LINEAR AND ANGULAR KINEMATICS Readings: McGinnis Chapters 2 and 6 DISTANCE, DISPLACEMENT, SPEED, VELOCITY, AND ACCELERATION: LINEAR AND ANGULAR KINEMATICS Readings: McGinnis Chapters 2 and 6 1 DISTANCE, DISPLACEMENT, SPEED, VELOCITY, AND ACCELERATION: How far? Describing change in linear or angular position Distance (Scalar

More information

Ch. 2 & 3 Velocity & Acceleration

Ch. 2 & 3 Velocity & Acceleration Ch. 2 & 3 Velocity & Acceleration Objective: Student will be able to Compare Velocity to Speed Identify what is acceleration Calculate velocity and acceleration from an equation and from slope of a graph.

More information

time v (vertical) time

time v (vertical) time NT4E-QRT20: PROJECTILE MOTION FOR TWO ROCKS VELOCITY AND ACCELERATION GRAPHS II Two identical rocks are thrown horizontally from a cliff with Rock A having a greater velocity at the instant it is released

More information

Motion Graphing Packet

Motion Graphing Packet Name: Motion Graphing Packet This packet covers two types of motion graphs Distance vs. Time Graphs Velocity vs. Time Graphs Describing the motion of an object is occasionally hard to do with words. Sometimes

More information

Gabe represents his mystery number with the variable f.

Gabe represents his mystery number with the variable f. Mystery Numbers Home Link 7- Gabe and Aurelia play Number Squeeze. Gabe represents his mystery number with the variable f. - a. Represent each of the two Number Squeeze clues with an inequality. Describe

More information

How can I use the graph to figure out which racer is faster? How can we find the unit rate for each racer?

How can I use the graph to figure out which racer is faster? How can we find the unit rate for each racer? Common Core Standard: 8.EE.6 How can I use the graph to figure out which racer is faster? How can we find the unit rate for each racer? What if the line does not pass through (0, 0)? CPM Materials modified

More information

Absolute Value. Domain 1 Lesson 4. Getting the Idea. Example 1. Strategy Step 1. Step 2 Count the number of units from 27 to 0.

Absolute Value. Domain 1 Lesson 4. Getting the Idea. Example 1. Strategy Step 1. Step 2 Count the number of units from 27 to 0. Domain 1 Lesson 4 Absolute Value Common Core Standards: 6.NS.7.c, 6.NS.7.d Getting the Idea The absolute value of a number is its distance from 0 on a number line. Since a distance must be either a positive

More information

Predator Prey Lab Exercise L3

Predator Prey Lab Exercise L3 Predator Prey Lab Exercise L3 Name Date Objective: To compare predator and prey populations over time in a small ecosystem. Introduction: In 1970 the deer population of a small island forest preserve was

More information

Section 4.2 Objectives

Section 4.2 Objectives Section 4. Objectives Determine whether the slope of a graphed line is positive, negative, 0, or undefined. Determine the slope of a line given its graph. Calculate the slope of a line given the ordered

More information

4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2.

4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Warm Up 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Objectives Find rates of change and slopes. Relate a constant rate of change to the slope of

More information

Student Exploration: Distance-Time and Velocity-Time Graphs

Student Exploration: Distance-Time and Velocity-Time Graphs Name: Date: Student Exploration: Distance-Time and Velocity-Time Graphs [NOTE TO TEACHERS AND STUDENTS: This lesson was designed as a follow-up to the Distance-Time Graphs Gizmo. We recommend you complete

More information

Math 10 Lesson 3-3 Interpreting and Sketching Graphs

Math 10 Lesson 3-3 Interpreting and Sketching Graphs number of cards Math 10 Lesson 3-3 Interpreting and Sketching Graphs I. Lesson Objectives: 1) Graphs communicate how two things are related to one another. Straight, sloped lines indicate a constant change

More information

Unit 6, Lesson 1: Organizing Data

Unit 6, Lesson 1: Organizing Data Unit 6, Lesson 1: Organizing Data 1. Here is data on the number of cases of whooping cough from 1939 to 1955. a. Make a new table that orders the data by year. year number of cases 1941 222,202 1950 120,718

More information

Sample Grade 7 End-of-Unit Assessment: Proportional Reasoning

Sample Grade 7 End-of-Unit Assessment: Proportional Reasoning Sample Grade 7 End-of-Unit Assessment: Proportional Reasoning Name: Date: I can determine unit rates and scale factors. 1. Find the unit rate: 40 feet in 1 minute. 1 point. Find the unit rate: $8.40 for

More information

Los Angeles Unified School District. Student Test Booklet

Los Angeles Unified School District. Student Test Booklet Office of Curriculum, Instruction, and School Support INTERIM ASSESSMENT Common Core Math 7 Fall Semester 2014-2015 Student Test Booklet Directions: Answer all multiple choice questions and selected response

More information

Chapter : Linear Motion 2

Chapter : Linear Motion 2 Text: Chapter 2.5-2.9 Think and Explain: 4-8 Think and Solve: 2-4 Chapter 2.5-2.9: Linear Motion 2 NAME: Vocabulary: constant acceleration, acceleration due to gravity, free fall Equations: s = d t v =

More information

Note! In this lab when you measure, round all measurements to the nearest meter!

Note! In this lab when you measure, round all measurements to the nearest meter! Distance and Displacement Lab Note! In this lab when you measure, round all measurements to the nearest meter! 1. Place a piece of tape where you will begin your walk outside. This tape marks the origin.

More information

Motion and Speed Classwork Classwork #1

Motion and Speed Classwork Classwork #1 Motion and Speed Classwork Classwork #1 8 th Grade PSI 1. Define motion. 2. When you look at the ground, you seem to be at rest. Why is this? Why does someone in space see you moving in a circle? 3. Define

More information

4-3 Rate of Change and Slope. Warm Up Lesson Presentation. Lesson Quiz

4-3 Rate of Change and Slope. Warm Up Lesson Presentation. Lesson Quiz 4-3 Rate of Change and Slope Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up 1. Find the x- and y-intercepts of 2x 5y = 20. x-int.: 10; y-int.: 4 Describe the correlation

More information

Functional Skills Mathematics Assessment Level 2

Functional Skills Mathematics Assessment Level 2 Sample Paper Assessment Task Sheet Functional Skills Mathematics Assessment Level 2 Learner name Run ID Learner signature Centre Assessment Date NOCN USE ONLY Available marks Task 1 Q1 10 Q2a 5 Q2b 3 Task

More information

Physics 2048 Test 1 Name: Dr. Jeff Saul

Physics 2048 Test 1 Name: Dr. Jeff Saul Physics 248 Test 1 Name: Dr. Jeff Saul Group: Spring 22 Date: READ THESE INSTRUCTIONS BEFORE YOU BEGIN Before you start the test, WRITE YOUR NAME ON EVERY PAGE OF THE EXAM. Calculators are permitted, but

More information

UNIT 2 End-of-Unit Test REVIEW

UNIT 2 End-of-Unit Test REVIEW Name: Date: Page 1 of 7 UNIT 2 End-of-Unit Test REVIEW 1. The Bridgeport Bluefish management discovered that the profit they make on their concession stands may be found by using the formula P = 5A 500,

More information

MHF 4U Unit 2 Rational Functions Outline

MHF 4U Unit 2 Rational Functions Outline MHF 4U Unit Rational Functions Outline Day 1 Lesson Title Specific Epectations Rational Functions and Their Essential Characteristics C.1,.,.3 (Lesson Included) Rational Functions and Their Essential Characteristics

More information

A position graph will give the location of an object at a certain time.

A position graph will give the location of an object at a certain time. Calculus 3.4 Notes A position graph will give the location of an object at a certain time. At t = 4, the car is 20 miles away from where it started. A position function is usually written as or. If the

More information

NAME DATE PERIOD SCORE

NAME DATE PERIOD SCORE NAME DATE PERIOD SCORE Chapter 1 Test 1. Miriam buys 24 petunia plants and 40 azalea plants. She wants to plant an equal number of flowers in each row of her garden. Each row will contain only one type

More information

Compare the scalar of speed and the vector of velocity.

Compare the scalar of speed and the vector of velocity. Review Video QOD 2/14/12: Compare the scalar of speed and the vector of velocity. What are the equations for each? Feb 14 6:51 AM 1 Imagine that you are a race car driver. You push on the accelerator.

More information

Monday Tuesday Wednesday Thursday

Monday Tuesday Wednesday Thursday Name: Weekly Math Homework - Q1:1 Teacher: Monday Tuesday Wednesday Thursday Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of

More information

When it is 80 degrees he will sell about 42 ice creams.

When it is 80 degrees he will sell about 42 ice creams. What are some of the ways Functions are represented? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 4, Lesson

More information

EXSC 408L Fall '03 Problem Set #2 Linear Motion. Linear Motion

EXSC 408L Fall '03 Problem Set #2 Linear Motion. Linear Motion Problems: 1. Once you have recorded the calibration frame for a data collection, why is it important to make sure the camera does not shut off? hat happens if the camera automatically shuts off after being

More information

Where are you right now? How fast are you moving? To answer these questions precisely, you

Where are you right now? How fast are you moving? To answer these questions precisely, you 4.1 Position, Speed, and Velocity Where are you right now? How fast are you moving? To answer these questions precisely, you need to use the concepts of position, speed, and velocity. These ideas apply

More information

Chapter 11: Motion. How Far? How Fast? How Long?

Chapter 11: Motion. How Far? How Fast? How Long? Chapter 11: Motion How Far? How Fast? How Long? 1. Suppose the polar bear was running on land instead of swimming. If the polar bear runs at a speed of about 8.3 m/s, how far will it travel in 10.0 hours?

More information

Physics: Principles and Applications, 6e Giancoli Chapter 3 Kinematics in Two Dimensions; Vectors. Conceptual Questions

Physics: Principles and Applications, 6e Giancoli Chapter 3 Kinematics in Two Dimensions; Vectors. Conceptual Questions Physics: Principles and Applications, 6e Giancoli Chapter 3 Kinematics in Two Dimensions; Vectors Conceptual Questions 1) Which one of the following is an example of a vector quantity? A) distance B) velocity

More information

Mathematics. Leaving Certificate Examination Paper 1 Higher Level Friday 10 th June Afternoon 2:00 4:30

Mathematics. Leaving Certificate Examination Paper 1 Higher Level Friday 10 th June Afternoon 2:00 4:30 2016. M29 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2016 Mathematics Paper 1 Higher Level Friday 10 th June Afternoon 2:00 4:30 300 marks Examination number

More information

Answer C. It must be straight and through Origin (0,0)

Answer C. It must be straight and through Origin (0,0) STUDY GUIDE UNIT 2 You will need a straightedge for this assessment. 1. Which graph represents a proportional relationship? Answer C. It must be straight and through Origin (0,0) 2. The graph shows the

More information

Fall 2008 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton

Fall 2008 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton Fall 2008 RED Barcode Here Physics 105, sections 1 and 2 Exam 1 Please write your CID Colton 2-3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.

More information

Homework: Turn in Tortoise & the Hare

Homework: Turn in Tortoise & the Hare Your Learning Goal: After students experienced speed in the Runner s Speed Lab, they will be able to describe how different speeds look like on a graph with 100% accuracy. Table of Contents: Notes: Graphs

More information

CHAPTER 3 TEST REVIEW

CHAPTER 3 TEST REVIEW AP PHYSICS Name: Period: Date: DEVIL PHYSICS BADDEST CLASS ON CAMPUS 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response AP EXAM CHAPTER TEST

More information

Final Exam review Course II

Final Exam review Course II Class: Date: Final Exam review Course II Short Answer 1. Mrs. Richland planted 12 tulip bulbs in her garden. All 12 bulbs bloomed the first year. The second year, 15 tulip blooms appeared, and the third

More information

Although many factors contribute to car accidents, speeding is the

Although many factors contribute to car accidents, speeding is the 74 Measuring Speed l a b o r at o ry Although many factors contribute to car accidents, speeding is the most common kind of risky driving. Unsafe speed is involved in about 20% of fatal car accidents in

More information

Motion in 1 Dimension

Motion in 1 Dimension A.P. Physics 1 LCHS A. Rice Unit 1 Displacement, Velocity, & Acceleration: Motion in 1 Dimension In-Class Example Problems and Lecture Notes 1. Freddy the cat started at the 3 meter position. He then walked

More information

HONORS PHYSICS One Dimensional Kinematics

HONORS PHYSICS One Dimensional Kinematics HONORS PHYSICS One Dimensional Kinematics LESSON OBJECTIVES Be able to... 1. use appropriate metric units and significant figures for given measurements 2. identify aspects of motion such as position,

More information

Hitting Your Marks on the Drag Strip

Hitting Your Marks on the Drag Strip By Ten80 Education Hitting Your Marks on the Drag Strip STEM Lesson for TI-Nspire Technology Objective: Collect data, analyze the data using graphs, and use the results to determine the best driver. Frameworks:

More information

Create a bungee line for an object to allow it the most thrilling, yet SAFE, fall from a height of 3 or more meters.

Create a bungee line for an object to allow it the most thrilling, yet SAFE, fall from a height of 3 or more meters. Student Names:,, OBJECTIVE: Create a bungee line for an object to allow it the most thrilling, yet SAFE, fall from a height of 3 or more meters. Each group gets their own object, a meter stick, and 7 new

More information

7)A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there?

7)A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there? Systems of Equations 1)A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot dogs and 4 bags of potato chips for

More information

June x. 2. x. 3. x. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 8.NS.1 8.NS.1 8.NS.1 8.NS.1 8.NS /3 + 1/9 2.

June x. 2. x. 3. x. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 8.NS.1 8.NS.1 8.NS.1 8.NS.1 8.NS /3 + 1/9 2. June 2018 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Father s Day 24 25 26 27 28 29 30 1. 1/3 + 1/9 2. 1 8/9 + 3 2/3 3. 9 6/7 +

More information

PATTERNS & FUNCTIONS

PATTERNS & FUNCTIONS PATTERNS & FUNCTIONS University of Houston Central Campus September 23, 2006 1 Warm-up Activity Test your knowledge by answering the following questions. No calculations or finger counting allowed. Good

More information