Activity Sheet
Counting M&Ms
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NAME ___________________________
DATE ___________________________
Pour a half-pound bag of M&Ms onto a paper plate so that the candies are one layer thick.
You will need to spread the M&Ms to the edges of the plate.
Remove all the M&Ms that have the M showing on the top side (look closely at the yellow
ones because the M is hard to see). Count and record the number of M&Ms remaining and
pour them into a container.
Shake the container and pour these M&Ms back onto the plate. Again remove all the M&Ms
with the M showing, record the number remaining, and pour them back into the container.
Keep repeating this process until all the M&Ms are removed. Use the following chart to
record your information. Add additional trial numbers as the experiment progresses.
TRIAL
NUMBER
1
2
3
M&MS ON PLATE
Let x be the trial number and let y be the number of pieces remaining. Plot all points (x, y) and
analyze the data.
1. What category of function can be used to
approximate the data?
2. Find the equation for a function that
approximates the data. Graph the function
over your scatter plot.
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Activity Sheet
Balloons and Breaths
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NAME ___________________________
DATE ___________________________
Select one person to inflate the balloon, one breath at a time.
A second person measures the circumference at the widest point of the balloon, in
centimeters, after each breath.
A third person records the data in the table below.
Each breath should contain about the same volume of air. In addition, a breath should not be so
large that the balloon reaches its capacity in just two or three breaths. You may want to practice
before gathering the data.
OF BREATHS
NUMBER
(IN CM)
1
2
3
CIRCUMFERENCE
Let x be the breath number and let y be the circumference. Plot all points (x,y) and analyze the data.
1. What category of function can be used to
approximate the data?
2. Find the equation for a function that
approximates the data. Graph the function
over your scatter plot.
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Activity Sheet
Stacking Cups
NAME ___________________________
DATE ___________________________
We want to know the height of a stack of cups. Measure the height of one cup. Stack a second cup
on the first and measure the new height of cups. Measure the height of stacks of cups made with
different numbers of cups.
NUMBER OF CUPS
HEIGHT(IN CM)
Let x be the number of cups, and let y be the height of the stack. Plot all points (x,y) and analyze the
data.
1. What category of function can be used to
approximate the data?
2. Find the equation for a function that
approximates the data. Graph the function
over your scatter plot.
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Activity Sheet
Volume of a Box
NAME ___________________________
DATE ___________________________
Take a piece of grid paper that is 20 cm by 20 cm and cut congruent squares from each corner.
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Fold up the sides to form a rectangular-shaped box with no lid.
Determine the volume of the box and complete the following chart. Repeat this process on
other pieces of grid paper for several different-sized cut squares. You may sketch or
visualize the boxes if you can find the volume without constructing each box.
HEIGHT
(IN CM)
LENGTH
(IN CM)
WIDTH
(IN CM)
VOLUME
(IN CUBIC CM)
Let x be the height of the box and let y be the volume of the box. Plot the ordered pairs (x,y) and
analyze the data.
1. What category of function can be used to
approximate the data?
2. Find the equation for a function that
approximates the data. Graph the function
over your scatter plot.
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Activity Sheet
Weather Patterns
NAME ___________________________
DATE ___________________________
Most years have 365 days. The first day of the calendar year is 1 January, 15 January is the 15th day
of the calendar year, 1 February is the 32nd day of the calendar year, and so on. Determine whether
a relationship exists between the number of the day of the year and the normal high temperature for
that day for the first and fifteenth days of each month. Use weather data from your local area.
DATE
Jan 1
Jan 15
Feb 1
Feb 15
Mar 1
Mar 15
April 1
April 15
May 1
May 15
June 1
June 15
July 1
July 15
Aug 1
Aug 15
Sept 1
Sept 15
Oct 1
Oct 15
Nov 1
Nov 15
Dec 1
Dec 15
DAYS SINCE NEW
YEARS
HIGH TEMP
(FAHRENHEIT)
0
15
32
46
60
74
91
105
121
135
152
166
182
196
213
227
244
258
274
288
305
319
335
349
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Let x be the number of the day of the year and y be the normal high temperature on that day. Plot
all ordered pairs (x, y) and analyze the data.
1. What category of function can be used to
approximate the data?
2. Find the equation for a function that
approximates the data. Graph the function
over your scatter plot.
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org