Problem Context: How Does the Time Change When Different Students Drive the Tekbot Through

Problem Context: How does the time change when different students drive the TekBot through a maze?

About SPIRIT Lessons: This is a sample Lesson developed within the SPIRIT Project to help students examine mathematics concepts related to angles, speed, and graphing. SPIRIT lessons are currently in "building block" format, which is in essence an educational activity that might be later turned into a more formal classroom lesson by a creative teacher. These SPIRIT “lesson building blocks” will soon be up on the web for the potential use by teachers as they prepare more formal educational lessons using the TekBot robotics platform.

I. Concepts Covered

Mathematics

• Build a Tally Table and graph the results
• Find and compare mean, median, and mode

Science

• Distance and time for the motion of a TeKBot
• Data collection and analysis

II. Applicable Standards

Mathematics

National Council of Teachers of Mathematics, K-2

Activities for pre-kindergarten through grade 2 should enable all students to apply appropriate techniques, tools, and formulas to:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another
• Analyze change in various contexts
• Understand measurable attributes of objects and the units, systems, and processes of measurement
• Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
• Develop and evaluate inferences and predictions that are based on data
• Make and investigate mathematical conjectures
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Science

National Science Education Standards, K-4

As a result of activities in grades K-4, all students should develop the

• Ability to do scientific inquiry
• Understanding of position and motion of objects
• Understanding about science and technology

III. Learning Activity Context

Context: X Moving TekBot __Building a TekBot __ Programming a TekBot

Activity A: Whole Class Activity

Students will make a tally table from information gathered during time trials using the TekBot to run a maze. Students will then make a colored bar graph using the table.

Students will use the TekBot to run through a short maze while being timed by the teacher. After all students have had a turn, and are told their time, they will write their name correctly on the chart (longer than 2 minutes red side and shorter than 2 minutes blue side). Students will then create a Tally Table using the information. They will then color a bar graph using the data collected from the time trials on the Tally Table. (Longer than 2 minutes, redbar, shorter than 2 minutes bluebar).

Activity B: Group Activity

After an introduction to the concepts of mean, mode, and median, and giving the opportunity for students to practice using the TekBot remote control, students will work in teams (5 to a team) with each student taking the TekBot through a maze while the teacher times how long it takes. The students record their times.

The maze can be constructed using masking tape with a start and finish line made from construction paper. Students follow the TekBot directing it to run through the maze as the other students watch.

IV. Teacher and Student Suggestions/Tips

Anticipatory Set A: Whole Class Activity

Arrange the desks or tables in the classroom around a center area to be used for the maze. Students can then sit in their seats as they watch their classmates drive the TekBot through the maze.

Call all students to the floor to explain that we are going to be using the TekBot to help us understand Tally Tables and Graphs. Explain that each student will get a turn at using the Tekbot to get through the maze that is outlined with tape on the floor. Explain that they will be responsible for writing their name on either the red side of the chart or the blue side depending on how long it takes them to drive the Tekbot through the maze.

Anticipatory Set B: Group Activity

Use a corner of the classroom to create the maze for the group activity. Since students will be working in groups with the TekBot this arrangement will help avoid distraction as the other groups are completing other classroom tasks.

Make sure students have had ample lessons using the terms mean, median, and mode, and that students were given opportunity to practice showing results. While the teacher is timing each group, have other activities going on in the classroom usingother adult supervision support.

V. Teacher Questions

Activity A: Whole Class Activity

After completing their graph they will answer these questions:

1. Which group had the most students? ______How many were there? _____

1. Which group had the fewest students? ______How many were there?_____

1. How many more students did the group in question 1 have? ______

1. How many fewer students did the group in question 2 have? ______

1. How many students were in BOTH groups? ______

Activity B: Group Activity

After collecting the group data answer these questions:

1. What time occurred the most?
   Record that time as the Mode: ______
   
2. List the times from shortest to longest
   and eliminate times from each end.
   Record the timeleft asthe Median: ______
   
3. Add all the numbers together using
   a calculatorand divide by the
   number of times. Record the Mean: ______

VI. Assessment Ideas

Formal assessments with written answers about each mathematical term could be usedhowever it may be enough to do visual and oral assessment by asking the students questions and comparing and recording their responses.

VI. Other Information

After the data collection, bring the students together on the floor and answer them questions. Ask probing questions like like:

• How did the boys do?
• How did the girls do?
• Did it help to go faster?
• What problems were there?
• What other information could the Tally Table tell us?
• If you practice driving the TekBot more, what will happen to the times?
  Try it in a week or so and find out!

Theseare difficult concepts for many first graders to grasp.It is hoped that this activity will engage the students and show them that doing an activity while using the TekBot can make math FUN!

These are photos of the practice run before the actual time trial. Look at the other students and how interested they are in what is going on. It is so fun to see kids get excited about learning.

VII. Materials

TekBotMasking Tape

StopwatchPencils/Pens

Notebook or paper for a data sheetColored Markers

Meter Stick or Yard Stick/ RulerCalculator

VIII. Student Templates or Worksheets

Activity A: Whole Class Activity

This table should be constructed on poster paper. Use red and blue markers. Use red for less than 2 minutes and blue for greater than 2 minutes.

Activity B: Group Activity

This table should be constructed by the student on writing paper. Each group will record the data for students in their group. Data will be analyzed for mean, median, and mode.

IX. Expected Results

Activity A: Whole Class Activity

Students will write their names on either side of the class data table using red for less than 2 minutes and blue for greater than 2 minutes. Thebar graph of the results might look like the one shown below.

Activity B: Group Activity

The table below illustrates the times for a group of 5 students to complete the maze. Each group will record the data for students in their group. The teacher would have the option of which times to give to the students. Data can be analyzed for mean, median, and mode.

A stop watch will give times in minutes and seconds which can be used to sort the times to determine the median (middle number) or count the times to determine the mode (occurs most often). To find the mean, students will need the time in just seconds or the time in just minutes. Students will use a calculator to add up all 5 times and divide by 5 to get the mean (average).

The data will need to be arranged by time so that the mode can be determined.The data sorted by time is shown below.

Median:Akshay, 1:58

Mode:Diego, Quentin 2:04

Mean:1:57, or 117 seconds, or 1.94 minutes

X. Additional Links

Sorting Through Spiders: A lesson used to introduce data collection and analysis

Sound Walk: Listening on an outdoor walk provides data to be organized

Clock It!: A lesson that uses student sleep and wake times