In Lesson 5.1.2, you found that the relationship between the height from which a ball is dropped and its rebound height is determined by a constant multiplier.

Slides:

Advertisements

Similar presentations

Displaying data and calculations  How many trials have been performed?  Were there enough to satisfy the IB Internal Assessment criteria? FYI: IB wants.

Advertisements

 In the 2 scenarios below, find the change in x and the change in y.  What conclusions can you draw? What are the similarities & differences? How would.

ANALYZING SEQUENCES Practice constructing sequences to model real life scenarios.

Real-World Adventures with Representations Quadratic and Exponential functions.

Excellence Justify the choice of your model by commenting on at least 3 points. Your comments could include the following: a)Relate the solution to the.

Exponential Functions

Testing Bridge Lengths The Gadsden Group. Goals and Objectives Collect and express data in the form of tables and graphs Look for patterns to make predictions.

Scientific Method.

So far in this course, you have been investigating the family of linear functions using multiple representations (especially tables, graphs, and equations).

Volume Activity The Relationship between Centimeters Cubed and Milliliters.

Lesson 6.1 Recursive Routines

Welcome to the Summer Institute Day 2 Thursday, August 7 Please sit in lesson study teams Today’s Agenda Homework follow-up Mathematical Modeling Coach’s.

LOGARITHMS Mrs. Aldous, Mr. Beetz & Mr. Thauvette IB DP SL Mathematics.

Many games depend on how a ball bounces. For example, if different basketballs rebounded differently, one basketball would bounce differently off of a.

When is it reasonable to make a prediction? For example, when you know the height of a tree, can you predict the size of its leaves? Or if you know the.

Objectives Compare linear, quadratic, and exponential models.

2. Write an exponential decay function to model this situation.

In Lessons and 4.1.3, you investigated connections between tile patterns, x → y tables, graphs, and rules (equations). Today you will use your observations.

In the bouncing ball activity from Lessons and 5. 1

Look at the tables and graphs below. The data show three ways you have learned that variable quantities can be related. The relationships shown are linear,

In Chapter 2 you looked at multiple representations (such as a table, graph, equation, or situation) of linear functions. In this chapter you will use.

Observation: Brad and Sara were playing at recess with the same type of ball. Brad noticed that when Sara bounced the ball close to the ground, it didn’t.

Pennsylvania Standard B Algebra and Functions Discover and generalize patterns, including linear, exponential and simple quadratic relationships.

Controlling Variables

Internal Assessment Investigation Assessment Criteria.

Teacher Choice Bouncing Ball Pendulum Liquid Assets.

To write exponential equations that model real-world growth and decay data.

Linear, Quadratic, and Exponential Models 11-4

2.1.1 Calling Plans day 3 Unit 2: Linear Relationships SWBAT: Compare calling plans by using graphs, tables, and equations.

What is the graph about? Is it linear? AMSTI-Bouncing Balls.

The Super Ball Project. QUESTION Does a surface effect the bounce of a super ball?

Scientific Method Chapter 1-1. What is Science?  Science – organized way of gathering and analyzing evidence about the natural world  Described as a.

Exponential Hands-on Activity Created and Presented by: Jennifer Weber.

Task 2: The Design A roller coaster can be based on mathematical functions, but they are more likely to be made up of pieces, each of which is a different.

Algebra 1 Warm Up 4,5 April 2012 Find the constant multiplier for each sequence, then find the next 3 terms 1) 16, 24, 36, ___, ___, ___ 2) 100,80,64,

Name the next number in the sequence: a) 1, 3, 9, 27, … b) 1, 5, 25, 125, …

To explore exponential growth and decay To discover the connection between recursive and exponential forms of geometric sequences.

Holt Algebra Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20,

Holt Algebra Linear, Quadratic, and Exponential Models Warm Up Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24).

The Scientific Method involves a series of steps in which scientists answer questions and solve problems.

1 Variables are useful tools for representing unknown numbers. In some situations, a variable represents a specific number, such as the hop of a frog.

Explain the trend the graph shows. Extrapolate the graph to make predictions. Outcomes Draw a line graph with all labels and units. How are these 4 pictures.

Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24). The population of a town is decreasing at a rate of 1.8%

Linear, Quadratic, and Exponential Models

Bell work 1) 3 7 ∙ 5 8 2) ∙ ) ∙ 2 3.

In the last two lessons, you examined several patterns

Lesson 6.2: Exponential Equations

MATH 7174: Statistics & Modeling for Teachers June 11, 2014

Check it out! 3.5.2: Comparing Exponential Functions

Measuring Time June 2018 By the end of the lesson we will have been successful when we have: recapped the units of mass Used our ideas about time.

Linear, Quadratic, and Exponential Models 9-4

Linear, Quadratic, and Exponential Models 11-4

Linear, Quadratic, and Exponential Models

Linear, Quadratic, and Exponential Models 11-4

1.1 Reaction Rates Investigation

Walk In… Take out notebook

2. Write an exponential decay function to model this situation.

4.3 Recursion and Exponential Functions

Learning Targets Students will be able to: Compare linear, quadratic, and exponential models and given a set of data, decide which type of function models.

Todays Lesson: Exponential Functions

Growth rate vs. Decay rate

Linear, Quadratic, and Exponential Models

Objectives Evaluate exponential functions.

Investigation Assessment Criteria

Objectives Compare linear, quadratic, and exponential models.

Linear, Quadratic, and Exponential Models 11-4

Linear, Quadratic, and Exponential Models

Lesson – Teacher Notes Standard:

Presentation transcript:

In Lesson 5.1.2, you found that the relationship between the height from which a ball is dropped and its rebound height is determined by a constant multiplier. In this lesson, you will continue this investigation by exploring the mathematical relationship between how many times a ball has bounced and the height of each bounce.

What was the rebound ratio for the ball your team used? 5-28. Consider the work you did in Lesson 5.1.2, in which you found a rebound ratio. What was the rebound ratio for the ball your team used? Did the height you dropped the ball from affect this ratio? If you were to use the same ball again and drop it from any height, could you predict its rebound height? Explain how you would do this.

5-29. MODEL FOR MANY BOUNCES Imagine that you drop the ball you used in problem 5-19 from a height of 200 cm, but this time you let it bounce repeatedly. As a team, discuss this situation. Then sketch a picture showing what this situation would look like. Your sketch should show a minimum of 6 bounces after you release the ball. Predict your ball’s rebound height after each successive bounce if its starting height is 200 cm. Create a table with these predicted heights. What are the independent and dependent variables in this situation? Graph your predicted rebound heights. Should the points on your graph be connected? How can you tell?

5-30. TESTING THE MANY-BOUNCE MODEL Now you will test the accuracy of the predictions you made in problem 5-29.

5-30. TESTING THE MANY-BOUNCE MODEL Your Task: Test your predictions by collecting experimental data. Use the same team roles as you used in problem 5-19. Drop your ball, starting from an initial height of 200 cm, and record your data in a table. Then compare your experimental data to your predictions using your table and your graph. How do they compare? What might cause your experimental data to be different from your predictions? Do you think that your table and graph model the situation appropriately? Why or why not? These suggestions will help you gather accurate data: Have a spotter catch the ball just as it reaches the top of its first rebound and have the spotter “freeze" the ball in place. Record the first rebound height and then drop the ball again from that new height. Catch and “freeze" it again at the second rebound height. Repeat this process until you have collected at least six data points (or until the height of the bounce is so small that it is not reasonable to continue).

5-31. Compare your graph for the height of successive bounces in problem 5-29 to the graph for drop height versus bounce height that you investigated in Lesson 5.1.2. Can you use the same kind of equation to model the two situations? That is, what family of functions do you think would make the best fit for each data set? Discuss this with your team and be ready to report and justify your choice. Describe how the pattern of growth for successive bounces is the same as or different from other models that you have looked at previously.

5-32 If you continued to let your ball bounce uninterrupted, how high would the ball be after 12 bounces? Would the ball ever stop bouncing? Explain your answer in terms of both your experimental data and your equation.

5-33 Notice that your investigations of rebound patterns in Lessons 5.1.2 and 5.1.3 involved both a linear and an exponential model. Look back over your work and discuss with your team why each model was appropriate for its specific purpose. Be prepared to share your ideas with the class.