Lesson 1.1.4Concept: Representing Data

Vocabulary:

rounding- to express an approximate value of a number that is exact to a given place value.

(for example: round to the hundreds place, or round to the thousandths place.)

A famous frog-jumping contest takes place each May in Calaveras County, California.  For more than 80 years, contestants have been entering large bullfrogs into the contest.  The frogs measure at least 4 inches long!  The purpose of the contest is to see which frog can move the farthest in three hops.  Each year, people travel from around the country (and sometimes the world) to see the frogs jump.

I n this lesson, scientists have come to the fair to study the frogs.  You will ask questions and analyze data about some of the frogs in the contest.  As you work, you will choose a strategy for organizing the information.  You will try to find a good way to show the patterns.  As a team, you will share ideas about how to represent the data and will

work together to describe it as completely as you can. 

1-24. JUMPING FROG JUBILEEWhen it is time to compete in the Jumping Frog Jubilee, the frog is put on a starting pad.  The frog hops three times.  Then the distance is measured from the center of the starting pad to the end of the third hop.  This measurement is the official jump length. 

The chart below shows data about the 8th-place frogs in 2008 and 2009.  Later, your teacher will show you a chart of data with all eight of the best frogs from each of those years.

Frog NameJump Lengths

(inches)Year

Dr. Frog 185.25 2009

Delbert Sr. 216.5 2008

1-24. JUMPING FROG JUBILEEWhen it is time to compete in the Jumping Frog Jubilee, the frog is put on a starting pad.  The frog hops three times.  Then the distance is measured from the center of the starting pad to the end of the third hop.  This measurement is the official jump length. 

The chart below shows data about the 8th-place frogs in 2008 and 2009.  Later, your teacher will show you a chart of data with all eight of the best frogs from each of those years.

Frog NameJump Lengths

(inches)Year

Dr. Frog 185.25 2009

Delbert Sr. 216.5 2008

a. Before you look at the rest of the data, think about what else you could learn about the frogs and their jumps from the numerical data.  With your team, brainstorm questions that you could use the numbers (data) to answer.  For example, you might ask, “What was the longest

jump?”  Use the following bullet points to help your team come up with as many questions as you can (at least four).

1. What could the numbers tell us about all of the frogs as a group?2. What could the numbers tell us about the frogs in just 2008 or just 2009?3. What could we ask to compare frogs from 2008 to frogs from 2009?4. What could we ask to compare individual frogs?

b. As a class, discuss the different questions each study team wrote.  Ask Mrs. Rigsbee for a contest data sheet. Look over the data and decide which questions you

can answer using the data and which you cannot.

c. With your team, choose two of the class questions to answer.  Follow the guidelines below as you choose.

• Choose one that requires using all of the numbers to answer the question.• Choose one that can be answered using just some of the data.

Think carefully about how to organize the data in order to find the answer.  Write your conclusions in complete sentences.

1-25. Different ways of presenting data can tell you different things.  For example, some of your questions might have been easy to answer with an organized table of data.  However, other questions can be easier to answer if the data is arranged in a different way, such as in a histogram like the one shown below.

Look carefully at the graph.  Use it to try to answer the questions below.

a. Between which two numbers on the graph did the most frogs jump?

b. Typical frogs jump between what two jump lengths?

c. Were there any unusually long or short jumps?

d. How many frogs are represented on this histogram?

e. Half the frogs jumped less than how many inches?

1-26. In the book, If You Hopped Like a Frog, written by David M. Schwartz and illustrated by James Warhola, the author shares that when he was a child, he wondered how far he could hop if he hopped like a frog.  In his letter to the reader at the front of his book, he wrote, “I imagined soaring through the air with grace and ease, landing gently on my big, springy legs.  How far could I jump?”

a. Obviously, people and frogs are different sizes and have different jumping abilities.  But imagine if you had the hopping muscles of a bullfrog but were still the same size you are now.  With your team, explore how far you could jump:

b. Estimate how far you might be able to jump if you were a giant frog competing in the Jumping Frog Jubilee.  (Think about how the information from problem 1-1 could help you.)Justify your estimate.

Use pictures and/or words to help explain your thinking.The book assumes that a 3-inch frog can jump about 60 inches in one hop. 

Does this estimate seem reasonable when looking at the data from problem 1-25?  Why or why not?

1-34. Rowena and Polly still cannot agree about who has more of the other’s item.  Rowena is still sure that Polly got more of her raisins, and Polly is sure that Rowena got more of her peanuts.  In order to make sense of what happened, they decided to try a simpler experiment.Rowena got a cup of 10 red beans, and Polly got a cup of 10 white beans.  Polly gave 3 white beans to Rowena, and Rowena stirred them into her red ones.  Then she closed her eyes and chose 3 beans from her mixture at random to give back to Polly.  The girls then examined each cup.

a. Try their experiment a few times with a partner.  What happens each time?  Work with your team to find a way to explain why your results make sense.

b. Would you have gotten similar results if you had exchanged 5 beans?  6 beans?  20 beans?  Be ready to explain your thinking.

c. With your team, consider whether your ideas about Rowena’s raisins and Polly’s peanuts have changed.  If so, write and explain your new conjecture.  If not, explain why you still agree with your original conjecture.  Be sure to include anything you think will be convincing as you write down your ideas.  Be prepared to share your ideas with the class. 

Tonight’s homework is… Review & Preview, page , problems #28 to #32.

• Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 1.1.4)

•Show all work and justify your answers for full credit.

Daily Closure:

1.Return Group folder to the math box.2.Return your individual Concept Notebook to the math section of your binder.3.Return the group supply box to the cart after making sure all supplies have been stored in the box and the lid is secured.4.Record Review/Preview in student planner.