How Did I Move
Unit: Movement with Functions
6th to 8th,High School
Create a set of index cards for each group of three students,
with a different position at time 0 on each card. Each group should
have unique set of index cards. Each group member will be assigned a
different role on the football field for each of the three tasks. If a
football field is not readily available, a hallway or other space can
be used. Students should have a simple method for measuring their
distance (e.g., number of blocks on the wall, tiles on the floor, etc.)
so that they focus on the concept of movement as a rate of change
rather than spending time measuring distance. Use the following
criteria to create the three index cards for each group:
An example set of index cards is shown below.
How Did I Move? Activity Sheet
Distribute page 1 of the How Did I Move? Activity Sheet, which includes a drawing of the field. Read the
instructions on the page with students. Stress that students can only
run from left to right, and they must begin at the field position
specified on their index card. Inform students that they must move in a
forward direction; they cannot run forward and then back again. Also,
let them know that the remaining pages of the activity sheet will have
them analyze the data they collect on the football field. Allow
students to ask questions to clarify the tasks. When all student
questions have been answered, take them to the football field.
At the field, provide each group with a set of 3 index cards, a
stopwatch, and a pencil. Ask students to rotate through the roles of
football player, recorder, and timer. Each player should run or act out
the situation that corresponds to the data provided on his or her index
card. When groups complete their tasks, distribute the remaining pages
of the activity sheet. Students can either work on this at the field
or, when all students have finished gathering their data, back in the
Students should work together in their groups to complete
pages 2 and 3 of the activity sheet. Circulate among groups and help
them with any difficulties they may have.
By the end of the activity, students should be able to relate yards per second to their movement (m) and their beginning position (b) to their position at time 0. Clarify for students that m does not stand for movement and b does not stand for beginning. This is just a mnemonic for remembering the role slope and y-intercept play in the equation y = mx + b.
Coleman's Touchdown Activity Sheet & Answer Key
In the Coleman's Touchdown Activity Sheet,
students are presented with 7 questions that help to reinforce the
concepts from the previous activity. They predict when Coleman will
score a touchdown, and discover — either visually or computationally —
that his speed (or rate of change) is the same between any two points
on the graph. This may be confusing or unexpected for some students.
The Winning Goal Activity Sheet & Answer Key
If time allows, allow students to work on The Winning Goal Activity Sheet. The activity allows students to compare two different
forms of data for two players on a field hockey team. Kaitlin’s data
are presented in a table, and Brea’s data are presented in a graph.
Students analyze these data, create the slope-intercept equations, and
make a recommendation to the field hockey coach regarding which player
to substitute based on a mathematical analysis of each player's speed.
This helps reinforce the concepts learned earlier in the lesson.
Questions for Students
1. How can you tell by looking at a graph which student is fastest?
[The steepest line corresponds to the fastest student.
Students with steeper slopes traveled a greater distance during the
time interval. This is an ideal time to bring up the visual
representation of rise/run, where rise is the distance and run is the time.]
2. What happens to a line if run is changed in the formula m = rise/run?
[If run is increased, the fraction becomes smaller. This
would correspond to a traveling the same distance in a great time
resulting in a slower speed in this scenario. If rise decreases, the
3. Why is y = mx + b called the slope-intercept form of a linear equation?
[The value of m represents slope and b represents the y-intercept. In other words, without doing any calculations, you can see the slope and y-intercept of a line just by looking at the equation.]
4. What is a real-world example that demonstrates the meaning of slope?
[In this lesson, slope represents speed in yards per
second. Other examples of slope include miles per gallon, dollars per
hour, or cost per minute. In general, slope refers to the rate of
change in a linear equation.]
5. What is a real-world example that demonstrates the meaning of y-intercept?
[In this lesson, the y-intercept is position 0 on
the football field, i.e., the goal line of the opposing team. Another
common example is a cell phone plan—often, the monthly charge includes
a fixed cost plus some cost per minute. The y-intercept is the fixed cost.]
6. What did you notice about the slope between any 2 points on the line representing Coleman’s position? Why did this happen?
[The slopes are all the same in the activity. This is
because the slope between any two points on any given line is the same.
This relates to the constant motion result in Lesson 1.]
7. If a player were at position 0 and position 100 simultaneously at time 0, what would the slope of that player's line be?
[There would be no slope. On a graph, this would be
represented by a vertical line. The situation is impossible because a
person cannot physically at 2 places at the same time. You may wish to
ask students to compare this scenario with the one experienced by the
student who stayed in one place in the How Did I Move? activity.]
3rd to 5th
6th to 8th
How Should I Move?
Grade: 6th to 8th, High School
Grade: High School