Grandma wanted to come see her grandson play high school
football but the bleachers were not wheelchair accessible. The students were
asked to build a model wheelchair ramp that was accessible to the top bleacher
while also staying within ADAs (Americans With Disabilities) building code—the slope
must be exactly 1/12 throughout the ramp.
The students were giving the following model conversion
5 yards = 1 inch.
Using this, they modeled a 120 x 50 yards football field into
a 24’’ x 10’’ football field.
Next, using the bleachers my six year old son built for
them, they measured the height at 2’’.
Using the 1/12 slope, they built a 24’’
incline wheelchair ramp.
Then converted these scaled numbers to real life. 5 yards =
1 inch. Meaning a 2’’ height = 10 yards of actual height and 24’’ ramp = 120
What would it
mean if students could jump proportionally as far grasshoppers? To find out, I
brought in some grasshoppers.
measured the length of two grasshoppers to be approximately 1 inch. Next, we
measured the distance of three jumps (in inches) from two grasshoppers I found
in my backyard and took the average of all three jumps for an average of 43
measured the height of two students in inches and took the average for a result
of 62 inches.
formed the proportion
1/43 = 62/x
x = 2,666
inches which is roughly 74 yards.
In essence, if students could jump proportional to grasshoppers we could nearly jump 3/4 of a football field.
Take your class outside and designate a single starting
point. From that point throw 5 or 6 objects at various distances. Next, ask
your students to estimate how many feet each object is from the starting point.
After they have estimated each object have them measure the length to the
nearest foot and record their data in a table such as that below.
Next, have each student calculate their error rate using the
formula (actual) – (estimate) / (actual) and change their decimal to a percent.
Finally, have the students plot the points on a coordinate
(x,y) plane and form a scatter plot. It’s best to have them graph the equation
y = x so that they can see their error rates.
Scatter plots move in two dimensions which allow students to see changes in
slope as well as the relationship of the two data sets. The study of scatter
plots lends to a lot of fun experiments and can also serve as a great segue to
discussions on proportionality or the coordinate system.
Ramp Height & Distance Traveled.
We decided to build ramps and plot the height verses distance traveled. We
increased the ramp in (approximately) one inch blocks and rolled a golf ball
off the ramp to measure the distance traveled. See Below. To get better results we took the average of three rolls. Lots of FUN!
A good icebreaker to use when introducing Measures of
Central Tendency (Mean, Median, Mode, etc) is to grab a handful of pennies from
your vehicle and lay them out on a table and have your students work in groups to place them in order
of date from least to greatest (if you have a large class you may need multiple handfuls of pennies).
Next, start collecting data.
Mode can easily be seen by the largest stack.
Median, Range, Q1, Q3, IQR can also easily be found
Mean is slightly tougher unless you allow your students access to a calculator
Next, have your students create a dot plot of the data
Finally, have your students pick 5 pennies for their homework. Tape the pennies to their worksheet so that they can read the date (see pic below).