problem solvers: problem
L a u ra B o f f e rd i n g a n d Me l i k e Yi g i t
Jump as far as you can
◗
T h e s t a n d i n g l o n g j u m p was an
Olympic event until 1912. In 1904,
Ray Ewry set the world record for the
longest standing long jump, which was about
11.5 feet, or 138 inches. Although the standing
long jump is no longer an Olympic event, the
Norwegians still include it in their National
Competition, and Arne Tvervaag set a new
world record at about 12 feet, or 144 inches,
on November 11, 1968. This month, we use
the standing long jump as inspiration for our
Problem Solvers activity.
Problem scenario
How far do you think you can jump? Do you
think you could beat the world record? In this
activity, you will jump as far as you can from
a standing position and measure the distance
by using different units, such as cubes, feet,
and inches.
Fi nd t he s t udent ac t i v it y she et on
page 285. A template for the foot and toes
measuring tool is on p. 286. You must enlarge
the template (133 percent) before tracing it
onto cardboard or foam sheets.
CHRIS-MUELLER/THINKSTOCK
Classroom setup
To do a standing long jump, stand with both feet behind a line, and then
jump as far as you can. Access a video of an adult doing a standing long
jump in fast and slow motion at the following link.
http://www.youtube.com/watch?v=6P8qmLl4rZQ
282
This activity is best done as a station activity
with a small group of students. In preparation, use some tape to mark the point where
students will stand before jumping (make
sure they have plenty of room), and keep some
extra tape to mark where students land after
they jump. For younger students, make and
cut out several copies of the foot and inch
illustrations (for an accurate measurement,
you must copy the page at 133 percent). We
found that tracing the foot and inch pictures
on foam sheets makes for sturdy, colorful
measurement tools. Older students could use
rulers. Provide snap cubes or Unifi x ® cubes
for students to use as well, and snap them
together in sticks of ten ahead of time. Finally,
have a copy of the recording sheet (see the
activity sheet on p. 285) for each student. You
may also want to make a larger chart for the
whole class.
December 2013/January 2014 • teaching children mathematics | Vol. 20, No. 5
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Begin the activity by asking your students
if they have ever watched the Olympics, and
encourage them to name a few events that
they have enjoyed watching. They may be
aware that the X XII Winter Olympics will
take place in Sochi, Russia, February 7–23,
2014. Tell your class that over the years, some
events are discontinued, and new events are
added. Acquaint students with the introductory information on the standing long jump.
You may also choose to present the following
video, which shows students jumping: http://
w w w.youtube.com/watch?v=hoirCTr8wi4.
Have students predict how far they can jump
and write their predictions at the top of their
recording sheets. Then, have each student
stand with the front of their shoes behind
the tape line that you put on the floor. Each
student should jump as far as he or she can.
Place a piece of tape where each student’s
heels hit the ground, and mark the tape with
the student’s initials.
When all students have jumped, instruct
them to use the cubes to determine how far they
jumped. Have them record the number on their
charts. (Students on crutches could see how
far they move after one step, and students in
wheelchairs could see how far they move after
one rotation of their wheels.) Some students will
realize that the cubes are already in sticks of ten
and will count by tens; other students will need
to count each cube one by one. Next, have the
group use the foot and inch pictures (or rulers)
to measure. Have students record the numbers
in the second column of their activity sheet.
Finally, have them measure the distance they
jumped using only inches. Encourage older students to convert feet into inches. Have younger
students use just the inch-long “toe” cut-outs (or
have them see how many inch-long representations fit on the foot illustration and count by
that number [twelves]). You could also have students draw their own pictures (see the activity
sheet) to show how they measured with one or
more of the tools.
When students have completed their charts,
ask some additional questions about their
measurements:
• How did your prediction compare to the
length of your actual jump?
• How did you count the blocks?
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Where’s the math?
This problem involves concepts of informal and formal measurement as
well as reasoning about numbers and operations. When students first
learn to measure, they sometimes leave gaps between the units they use
to measure, leading to inaccurate measurements. In this task, students
naturally snap together the cubes. However, they may leave gaps when
using the pictures to measure. Drawing attention to the differences in
how they use the materials can help them understand that the units
should not have gaps between them. As students lay down the cubes or
pictures, they will also visually estimate whether another whole stick of
cubes can fit or whether they must break it apart. With the foot pictures,
this can lead into an exploration of fractions of feet.
Some students will find their total measures by counting the number
of objects they used, regardless of their size (they may even call fifty cubes
five because they perceive the cubes as five sticks). Having students name
their units can draw attention to what they are counting. Further, having
the cubes in groups of ten encourages some students to count by tens
and units instead of just by units. If students then count from the other
end of their cubes, they will end up counting by tens on the off decade
(e.g., 1, 2, 3, 13, 23 instead of 10, 20, 21, 22, 23). Other students might
add groups of tens and units (e.g., 10 + 10 = 20 and 20 + 3 = 23).
Older students who use rulers to measure will find that they need to use
multiple rulers to measure their distances, so they will need to either add
on from twelve inches or coordinate feet and inches.
The different instruments to measure distance were purposefully
chosen to illuminate how the size of a unit relates to how many units
students need: When they use bigger units of “feet,” they will use fewer
of them than when they measure with the cubes. Using different types
of measuring instruments gives students an opportunity to express larger
units (e.g., feet) in terms of smaller units (e.g., inches) and to describe
how the two measurements relate to each other.
• You measured the same distance each time,
so why are your numbers different? Why
does that happen?
• What if you measured your jumps in
toothpicks? (Show a toothpick.) Would
you expect your jump to be more or fewer
toothpicks than the cubes? Would it be
more or fewer toothpicks than feet? Explain
your reasoning.
If you make a class chart, you could also ask
questions about the data:
• Who jumped the farthest? How do you
know?
• Who got second place?
• How much farther does the person in
second place have to jump to tie with the
farthest jump?
Vol. 20, No. 5 | teaching children mathematics • December 2013/January 2014
283
problem solvers: problem
Extensions
To extend the measurement discussion, have
students compare their jumps
with the world record (about
12 ft., or 144 in.) and calculate
how much farther they would need
to jump to tie the record. You could
also tap into students’ multiplicative
reasoning skills by asking how many times
a student would need to jump to equal or beat
the record.
As an extra challenge, pose the following
question: “If we add all the jumps from your
group together, would you have jumped farther
than the world record? How far over or under
would you be?” Younger students can do this
with inches only, and older students can try it
with feet and inches.
For students in fourth grade and higher,
explore the median and mean jump for their
group. Have each student line up the number
of cubes to represent how far he or she jumped.
Then have the group redistribute the cubes
to make the sticks even. Have them check the
results by calculating the mean, and then discuss how the two processes are related.
284
December 2013/January 2014 • teaching children mathematics | Vol. 20, No. 5
Laura Bofferding, [email protected], teaches an
elementary mathematics course at Purdue University in
West Lafayette, Indiana. She is interested in elementary
students’ mathematical reasoning and their application
of this reasoning in measurement and data analysis.
Melike Yigit, [email protected], assists with the
elementary mathematics methods course at Purdue
University in West Lafayette. She is interested in preservice teachers’ geometric reasoning and students’
and teachers’ learning of angle measurements.
Edited by Signe E. Kastberg, a teacher of prospective
elementary school teachers at Purdue University
in West Lafayette; and Erin Moss, erin.moss@
millersville.edu, an assistant professor in the
mathematics department at Millersville University of
Pennsylvania. Each month, this section of the Problem
Solvers department features a new challenge for
students. Readers are encouraged to submit problems
to be considered for future columns. Receipt of
problems will not be acknowledged; however, those
selected for publication will be credited to the author.
Find detailed submission guidelines for all departments
at www.nctm.org/tcmdepartments.
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PHOTODISC/THINKSTOCK
Try this problem in your classroom. We are
interested in how your students responded to
the problem, what problem-solving strategies
they used, and how they explained or justified their reasoning. Send your thoughts and
reflections—including information about how
you posed the problem, samples of students’
work, and photographs showing your problem
solvers in action—by March 15, 2014, to Problem Solvers department editor Signe Kastberg,
Purdue University, 100 North University St.,
West Lafayette, IN 47907-2098, or e-mail her at
[email protected]. Selected submissions
will be published in a subsequent issue of
Teaching Children Mathematics and acknowledged by name, grade level, and school name
unless you request otherwise.
LAURA BOFFERDING
Students could use
rulers or measuring
sticks made of snap
cubes or foam “feet”
to measure the
distance they jump.
Share your students’ work
➺ problem solvers activity sheet
Name___________________________________
How Far Do You Think You Can Jump?
How far do you think you can jump? Do you think you could beat the world record? In this
activity, you will jump as far as you can from a standing position and measure the distance by
using different instruments and units of measure, such as cubes, feet, and inches.
Your prediction
Name
Cubes
Ruler or foot and inch pictures
1 inch
1 inch
1 inch
1 inch
1 inch
1 inch
1 foot
Draw a picture of how you measured.
From the December 2013/January 2014 issue of
Inches
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Teachers, enlarge the sketches by 133% before tracing them onto cardboard or foam sheets.
How Far Do You Think You Can Jump? Template
➺ problem solvers appendix
December 2013/January 2014 • teaching children mathematics | Vol. 20, No. 5
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