73 – 84 Rates, Ratio, and Unit Rates

Lesson Focus / Number and Operations Standard.Studentswill use ratios and proportions to represent quantitative relationships and solve problems involving scale factors, using ratios and proportions.
Materials / TI-73 Explorer™ or TI-84 graphing calculator
TI-Navigator™
Student Activity sheets
Stop Watch or Timer (one per group)
Tape Measures (one per group)
Grouping / Pairs and individuals
Prerequisite Knowledge and Skills / Students should have knowledge about rates, ratios, and unit rates. Students should also be familiar with entering items in the List function of the TI-73.
Overview of the lesson / In Activity I, students willuse the Text Editor and List function of the TI-73 to analyze and compare rates, ratios, and unit rates to determine who the fastest TI-“Texter” is. In Activity II, students will examine ratios to test for proportionality.
Time / Suggested time for Introduction and Activity 1:
Activity 2:

Introduction:

  1. Open TI-Navigator and Start Class. Have students log in to NavNet.
  1. Introduce the activity by providing students with recent statistics regarding texting in the United States.Statistics show that the average teenager sends or receives approximately 1,500 texts per month.An average of 4.1 billion daily text messages were sent or received in the US in 2009. Pedro Matias, the 2010 Guinness World Record holder for text strokes per minute, can text 264 characters in 1 minute 59 seconds. How many characters can he type per second?
  1. Using the Quick Poll feature, ask the students the following questions:

4.Discuss student responses.

Activity I

Procedure:

Begin the activity with students logged into TI-Navigator. Students will be exploring rates, ratios, and unit rates by simulating texting on their cell phones with the text Editor feature of the TI-73.

1.Have students exit to the Homescreen. Review using the Text Editor Feature to type text.

2.Students will use their knowledge of ratio, rates, unit rates, and the Test Editor Function of the TI-73 to determine who the fastest “TI-Texter” is in the class.

3. Distribute Student Activity Sheet, How Fast Can You TI-Text?, and guide students to complete the activity.

How fast can you TI-Text?Student Activity Sheet

Name: ______Class: ______

Instructions: Create 5 sentences/phrases which are no more than 16 characters/keystrokes long and write them in the chart below. Then complete the tasks/questions that follow.

Example: I_<3_MATHEMATICS (I Love Mathematics)

16 keystrokes

**The space bar (_), if needed,is a command and therefore must be included in your keystroke count. You may incorporate SMS Language (texting) into any or all of your sentences/phrases.**

Phrase/Sentence / Number of Keystrokes: / Time in Seconds: / Rate:
1) / ______
2) / ______
3) / ______
4) / ______
5) / ______
Average
Rate:

Task:

  1. Working with a partner or small group, use the provided timer to determine how long it takes to enter each phrase (one at a time) you created for the chart above.
  1. Record the time for each trial in the appropriate column.
  1. Complete the last column in the chart above by writing a ratio of keystrokes to seconds.
  1. Calculate your averagerate and record it above.

Extension:

On the cell phone screen below createa typical text (school appropriate) that you wouldsend to a friend. Using your rate from above,predict how long it would take you to type thenecessary keystrokes. (Remember spaces, symbols,and numbers count as a character because it takesa keystroke to access their command.)

Activity II

Procedure:

Students will collect data and examining lists to determine whether a proportional

relationship exists.

  1. Ask students to work with a partner to measure their arm span and height in inches. Have students record the information on a piece of scrap paper.
  1. OpenActivityCenter Select Edit, Clear All Data.

3.Select Contribute:Form and configure as shown below.

4.Click on the List Tab.

5.Start the Activity and instruct students to enter the prompted information.

Students will select from the TI-Navigator Home screen, 1:ActivityCenter.

6.Students will see the class collection of data on the ActivityCenterscreen. Point out that L1 displays their arm span in inches and L2 displays their height in inches.

7.Stop the activity. Select Contribute:List and Configureto configure as shown below. Be sure to select Start With: Existing Activity List.

8.Select StartActivity. Students will receive the class list. Stop the activity. CloseActivityCenter and use Screen Capture to display and ensure all students have received the class lists.

9.Lead discussion with the students to see the relationship between the class’ two pieces of data. Instruct students to compare them by calculating the ratio of one to the other and recording it as a single number. Ask questions such as:

  • How do we write ratios?
  • How can we take a ratio that is written as a fraction and turn it into a single number?
  • Based on your data, will our number be less than or greater than 1?
  • What does this mean in terms of arm length and height?
  • What pattern do you think we might see?
  • What might the pattern reveal?
  • Using these two lists, what formula might we use to find the ratio?

10.Students should exit ActivityCenter by selecting  (Quit) and exit the TI-Navigator home screen by pressing  (Exit) and press  to view the class list of data.

11.Have students create a dependent list in List 3 using the formula “L1/L2” to calculate the

ratio for Arm Span and Height.

Keystrokes:

  • Arrow over and up (, , ) to highlight L3.
  • Press , select the quotation mark, then press and done 
  • Press (STAT), select1:L1, ÷, (STAT), select 2:L2, 
  • No need to enter right quotation mark.

12.RefreshScreen Capture and instruct students to look for a pattern. Questions to ask:

Are the students’ ratiosof arm span to height similar?

What does the pattern reveal?

Proportionality exists if the ratios form equivalent decimals. Are they close?

13.Instruct students to find the average ratio of arm span to height. From the TI-73 home screen calculate the average of the arm span-to-height ratios displayed in List 3.

Keystrokes:

  • Press  (STAT),,  (to MATH)
  • Select 3:mean(
  • Select  and select 3:L3, 

14.Repeat steps 3 – 13 to test proportionality with other pieces of data. For example: distance from the top of the head to the bottom of the chin compared to height (Leonardo Da Vinci’s Vitruvian Man/Golden Ratio = 1.618034), shoe size to foot length, age to height, forearm length to foot length, hand span to foot length, etc.

Extension:

From ActivityCenter, select Configure Plots and configure as shown. Then select the Graph Tab and set the x and y max to 100. Discuss how students can use ordered pairs created by the two terms of each ratio to determine proportionality. If proportionality exists,the pairs will form a straight line going through the origin of the graph.

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