South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Shots, Standings, and Shopping (Grade 6-8)

Master Teacher

Margaret L. Steele

Time Allotment

Three 60-minute class periods

Overview

Through the activities presented in this lesson, students will define ratios and rates. Using video and the Internet, they will learn how ratios and rates can be used in real-life situations.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

Define rate and ratio;
Write rates and ratios;
Convert rates and ratios to decimal and percent equivalents;
Apply rates and ratios in real-life situations (i.e., mileage and unit rates).

South Carolina Standards

Visit the SC Standards Web site

Grade 6 N.III.A.1 Select appropriate methods and tools to solve problems requiring the addition, subtraction, multiplication, and division of fractions and decimals.

Grade 7 N.I.D.1 Create and write ratios and proportions from applied situations and explain the reasoning used.

Grade 8 N.III.D.1 Analyze and explain each method for solving a proportion (equivalent ratios, unit rates, and cross-multiplying).

Media Components

Video

Math Vantage: Proportional Reasoning, Lesson 1: "Rates and Ratios: Comparisons."

Web Site

NFL.com-NFL Standings

AOL Sports: Columbia Football Stadium Guide

MapQuest: Driving Directions: North America

Materials

trash cans (one for each group
of four students)
deck of Uno cards
balled up paper (students provide)
Sunday grocery ads from four
different stores
transparencies of all Activity Sheets
math notebooks

Equipment

TV
VCR
computers
overhead

Prep for Teachers

Collect one trashcan for each group of four students.
Bookmark all Web sites listed in Steps 2, 3 and 4 of Learning Activities.
Make copies of the three Activity Sheets to distribute.
Make transparencies of all the Activity Sheets.
When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video elements, Web sites or other multimedia elements.

Introductory Activity

This "warm-up" activity is used to gain student interest. The data gathered will be used as part of the Culminating Activity.

Step 1: Divide class into groups of four.

Step 2: Set up a trashcan for each group to be used as the "basket" for "Trashcan Basketball."

Step 3: Instruct each student to draw a card from the deck of Uno cards. This is the number of shots the student will be allowed to take.

Step 4: Each student will use balled up paper (that will be recycled by your Service Learning students) to take their shots.

Step 5: Tell each student to record the number of attempts and shots made on a clean sheet of notebook paper. Tell students to put this in their math notebooks for future use.

Learning Activities

Activity 1

Step 1: Provide a Focus for Media Interaction by asking students to watch and listen for the definitions of ratio and rate, and the three ways to write a ratio. The definition the woman in the video gives of a ratio is "to compare two quantities by division." She defines a rate as "a ratio that uses two different types of measurement units." The three ways to write a ratio are 16 to 15, 16/15, and 16:15. Tell students to write the definitions and the three ways to write a ratio in the notes section of their math notebooks.

Step 2: START the video at the beginning after the Nebraska Mathematics and Science Coalition logo. PAUSE the video after the girl sitting in the stands says, "even coffee cans."

Step 3: Provide students with a Focus for Media Interaction by having them watch and listen for at least one example of a rate or ratio used to compare quantities.

(The examples given in the clip are chicken at $1.25/lb; a gallon of milk with 2% milk fat; a box of pancake mix with a ratio of 2 eggs to 1 cup milk to 1 cup mix; and a bicycle tire inflated to 45 lbs/sq. in.)

Step 4: Have students give some other examples with which they may be familiar. Possible examples might be the cost of gas per gallon, hourly rate for babysitting, miles per hour, cost per ounce.

Step 5: FAST FORWARD the video to the frame where the horse's nose is right up against the camera. You are trying to get to the scene with the refrigerator. The girl in the video will pull several items that use rates or ratios for comparison out of the refrigerator. STOP the video after she pulls the bicycle tire out of the fridge.

Activity 2

Step 1: Pass out Activity Sheet 1. Display the transparency of Activity Sheet 1. Refer to it as needed. Then, provide students with a Focus for Media Interaction by asking them to choose an NFL team and record the team name and division, as well as the statistics listed on Activity Sheet 1.

Step 2: Have students go to the bookmarked Web site NFL.com-NFL Standings . Tell them to choose one team and write the name of the team in the space provided on Activity Sheet 1. Students should also note what division the team chosen is in and record that as well.

Step 3: Instruct students to record the statistics shown in these columns. These correspond to the columns on their Activity Sheets: W (wins), L (losses), T (ties), PCT (winning percentage). Have students use the statistics to set up ratios listed on Activity Sheet 1.

Step 4: Tell students to convert the ratio of wins to total games played to a decimal equivalent and then to a percent in order to verify the PCT column they found in the standings.

Step 5: Next have students follow the example in Step 4 to convert the ratio of losses to total games played and the ratio of wins to losses to decimal and percent equivalents.

Activity 3

Step 1: Provide students with a Focus for Media Interaction by asking them to find the stadium name and address where the team they selected in Step 2 of Activity 2 plays its home games.

Step 2: Pass out Activity Sheet 2. Display the transparency of Activity sheet 2. Refer to it as needed. Tell the students to go to the bookmarked Web site AOL Sports: Columbia Football Stadium Guide. Students will find the division they recorded on Activity Sheet 1 and click the drop down arrow to select their team. This will take them to their team's stadium home page. Students will record the stadium name and complete address on Activity Sheet 2.

Step 3: Provide students with a Focus for Media Interaction by asking them to find the driving directions from their home addresses to their team's stadium.

Step 4: Have students go to the bookmarked Web site MapQuest and tell them to click on the driving directions icon. Then ask them to enter their home address as the starting location. Next have students enter their team's stadium address as the ending location.

Step 5: Next students will scroll down and click on "get directions." Students will record the mileage distance from home to the stadium on Activity Sheet 2.

Students will record the total estimated drive time in hours and minutes on Activity Sheet 2.

Step 6: Students will scroll down through the driving directions, reading the directions from their home and looking at the map of the United States that marks the route.

Students will print the directions and the map.

Students will round the drive time to the nearest hour and the mileage distance to the nearest mile.

Students will set up a rate to find the average miles per hour needed to accomplish the trip in the estimated time given.

Step 7: Lead a discussion with the following questions.

0 Do you think the drive time is reasonable?

0 Have you ever taken a long trip with your family?

0 What kinds of things did you need to think about before you started the trip?

(Note to Teacher: Encourage students to consider whether or not eating and "potty" breaks were included in the drive time given, as well as whether driving speed is a constant. They should come to the conclusion that more time is probably needed, and that if they actually took a trip like this, they might need to stay in a hotel one or more nights.)

Culminating Activity/Assessment

(Note to Teacher: Students will turn in the work from the Culminating Activity as part of their Assessment of this lesson.)

Step 1: Remind students of the data they recorded during the trashcan basketball activity. They should still have the paper they used during the trashcan basketball activity. Discuss the fact that each "score" could be recorded as a ratio. Lead students to write their scores as ratios of shots made to shots attempted. They will need to record all information on the notebook paper from the opening activity.

Step 2: Tell the students to convert their individual ratios to decimal and percent equivalents to find out who is the best shot in each of their groups of four.

Step 3: The best shot from each group will stand and give his/her original ratio and percentage. Record these on the board or overhead.

Step 4: Lead students in a discussion of the ratios and percentages given by the best shots. Encourage students to notice that 4 out of 8 and 1 out of 2 (for example) will both have an equivalent percentage of 50 percent. Who do they think is really the better shot?

If "good" comparisons aren't offered by the best shots, solicit ratios from other students in the room. The goal is to help the students see how different ratios can yield the same percentage and put a spin on who is a good shot and who just happened to make good use of a low number of attempts.

Step 5: Pass out Activity Sheet 3.

Step 6: Pass out grocery store ads from the Sunday newspaper. Make sure each student in a group of four gets a different grocery listing.

Step 7: Display the transparency of Activity Sheet 3. Refer to it as needed. Students will use the sales paper to find the cost of the items listed on Activity Sheet 3. Students will complete guided handout to calculate unit rates therefore finding the best deal on each of the items listed.

Students should try to compare the same product (name brand and size) where possible, but may compare two different name brands if needed to see which is cheaper and justify why based on the unit rate. For example, one student may calculate the unit rate on 6 Pepsis and another the unit rate on 12 Cokes.

Student groups will decide based on the unit rates found which of the stores represented has the lowest prices for the same products or lower prices for similar products.

Step 8: Generate a class discussion about comparison shopping and how unit rates can help shoppers find the best deal. Inform students that many unit rates are calculated for them on the shelf tags at the grocery store.

Cross-Curricular Extensions

English/Language Arts and Social Studies: Write a road trip diary. Be sure to incorporate some of the sites and scenery along the way. The map of the United States and a little time spent researching the sites along the route would make this a great activity.

Social Studies/History: Research historical sites along the route given on the map of the United States. Make a list of places you would like to visit.

Art: Draw your team's logo or create your own team name and design a logo for it.

Community Connections

Ask the high school football coach to come and discuss how ratios are used to calculate many of the statistics used in the game of football. He may also want to discuss other vital statistics, the importance of education, hard work, determination, and discipline.
Do a taped interview with the meat department manager at a local grocery store. Interview the manager on site and ask him to demonstrate or discuss how meat prices are calculated. He may also want to discuss the importance of math in the workplace.
Invite a travel agent to the classroom. The travel agent may want to discuss how rates for trips are calculated in various forms of transportation. He may also want to discuss how to go about finding and calculating the best deal before you travel. For example, what are the things you need to consider to make a trip economically a good idea?
As an extra credit idea, ask students to attend a local school game, college game or professional game, record some statistics and use ratios to report their findings.

Student Materials

pencils
scratch paper (for paper balls)
Activity Sheets 1, 2, and 3
calculator (optional)