Learning Objectives
Graph distance and time for fast CAT
Find speed
Grade Levels
Grades 6-7
Common Core Standard
NC Essential Standards for Science 7.P.1.4 Interpret distance versus time graphs for constant speed and variable motion.
NGSS Crosscutting Concept 3. Scale, Proportion, and Quantity. Middle School. Proportional relationships (e.g. speed as the ratio of distance traveled to time taken) among different types of quantities provide information about the magnitude of properties and processes.
CCSS.MATH.CONTENT.6.EE.C.9 Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Materials Needed
Web-enabled device and projection to show the video of Fast CAT
AKC TV fast CAT video from Eukanuba Performance Games
Chart of breeds and their respective Fast CAT times
Lesson
Introduction
Prior to this lesson students should already have done work with ratios and proportions and have been introduced to unit rates.
- Fast CAT is a new American Kennel Club sport that lets you find out how fast your dog really is. CAT stands for Coursing Ability Test, and it is basically a 100 yard dash for dogs. Show students the video of Fast CAT from the Eukanuba Performance Games. Dogs chase after a lure, sometimes a white cloth or plastic bag, as fast as they can.
- Ask students to guess how fast the fastest human can run, and how fast they think the dogs can run.
- Usain Bolt, currently the fastest human, has been clocked at almost 28 mph. Dogs have been known to reach speeds of 35-45 mph.
Explicit Instruction/Teacher Modeling
- Write “miles per hour” on the board, in the form of a fraction, with the word “per” in a rectangle, forming the fraction bar. “Miles” is the numerator and “Hour” is the denominator.
- Explain to students that miles per hour means how many miles a person (or car or dog) can go in ONE hour, so it is a unit rate. The answer to the miles per hour division problem is the person’s speed.
- Ask students to create an equation using the words distance, time and speed (or the letters d, t and s) as variables. (example: d=st)
- Discuss their ideas.
- Ask students to tell their table partner what they think the independent and dependent variables are in this relationship (distance versus time). Remind them that the dependent variable depends on the independent variable. One changes because of the other. This concept can be tricky for middle schoolers because it can change based on your perspective. How far you run depends on how long you run, but how long you run also can depend on how far you run. If students are struggling, encourage them to think about which part of the FastCat run was the same for each dog, and which part changed depending on the dog’s ability.
- Discuss student responses.
- Students will be creating graphs to show the relationship between distance and time, and determining each dog’s speed. Ask students which variable should go on the x-axis and which on the y-axis. (x-axis is independent, distance, and y-axis is dependent, time).
- Discuss student responses.
Independent Working Time
- Given various dogs’ times, students will create graphs to show the relationship between distance and time, and will determine each dog’s speed as a unit rate.
- Remind students that each dog ran 100 yards.
- Give students the sheet listing dogs’ times to complete the Fast CAT and allow them to work alone or with partners to create graphs for each dog.
- Remind students to label both axes and to determine the speed of each dog using what they know about unit rate.
- For an extra challenge: Give students the table with the top 20 dogs’ speeds from Fast CAT events in 2019 (see Fast CAT Top 20). The speeds are written in miles per hour. Students can determine how many yards per second each dog ran, and then find out how to graph that information in 1 second intervals, to the nearest tenth place).
Review and Closing
- Discuss student responses. Talk about how to label each dog’s speed (yards per second). Ask students why it’s not written seconds per yard instead.
- Remind students to label both axes and to consider the scale they use when marking intervals on each axis.
Resources
Sept. 6, 2019. Fast Cat Top 20 Fastest Dogs By Breeds. Retrieved from https://www.apps.akc.org/apps/fastcat_ranking/index.cfm?display
n.d. Fast CAT. Retrieved from https://www.akc.org/sports/coursing/fast-cat/
