TIMS Laboratory Investigations
Length
|
 |
(ISBN 0-7872-4042-7, primary): This is an introductory length investigation in which the children roll a variety of cars or skates down an incline and measure how far each goes, using plastic links as the unit of measure. The children record their data and make a bar graph of the results. Several new and fundamental concepts are introduced, including length, repeated measurements, and simple averaging. The children solve problems involving addition and subtraction, then interpret information in data tables and bar graphs, and learn the importance of controlling variables in an experiment, such as the height of the ramp and the starting line on the ramp.
Mr. O Left/Right
(ISBN 0-7872-4043-5, primary): Students are introduced to the
concept of locating an object in one dimension relative to an
external reference point. Mr. O, a plastic figure developed by
the SCIS project, is used to specify the reference point (or “origin”).
Distances from Mr. O of objects set up on the children’s desks
are measured using plastic links. In the spirit of Piaget, the
students distinguish the directions left and right not only relative
to themselves but to Mr. O as well. The children learn how to
make scaled one-dimensional maps from their data and, using addition
and subtraction, how to find the distances between the objects
from their maps.
Stepping Out
(ISBN 0-7872-4044-3, primary): Each student uses his or her bare
feet to determine the number of heel-to-toe steps between two
marks on the floor. The children record their results and the
results of their classmates and from this make a frequency distribution
of the data. It becomes evident from the frequency distribution
that everyone did not take the same number of steps to cover the
same distance. We establish a qualitative relationship between
steps and foot size and solve addition and subtraction problems.
Rolling Along with Centimeters
(ISBN 0-7872-4045-1, primary & intermediate): Rolling Along with
Centimeters is a follow-up investigation to Rolling Along with
Links. This is one of several transition investigations where
the children graduate from measurements using nonstandard units
to the accepted standard units of science. In this case, we go
from links to centimeters. The manipulated variable will be the
type of car or skate, the responding variable will be the distance
it rolls, while the type of floor, the release point, and how
the car or skate is released are the controlled variables. The
children will have to use a meterstick and should be counting
up to the hundreds. Using addition and subtraction to two place
values, they will learn who in class had the “best” car or skate,
how much farther one car rolled than another, whether one car
rolled three times farther than another, and will solve a variety
of graphical and word problems.
Mr. O Left/Right or Front/Back
(ISBN 0-7872-4046-X, primary & intermediate): We once again introduce
Mr. O, but now not only do his arms point left/right, his buttons
allow for a second direction, front/back. Even though two axes
are involved, this is still an exercise in one dimension since
all objects are placed on either the left/right axis or the front/back
axis. In either case, the children must still refer to Mr. O and
not to themselves while locating objects. All measurements are
in centimeters. A variety of objects are set up on a table along
each axis, their positions recorded, and a map (our graph) is
made. Both addition and subtraction are used throughout, but in
a way this is quite different from the usual textbook problems.
Moreover, in one of the comprehension questions we show the children
the limits of simple addition. Most importantly, the exercise
is rich in spatial relationships and how they relate to a particular
origin.
Length vs. Number I
(ISBN 0-7872-4047-8, primary & intermediate): This investigation
introduces the children to the basic experimental technique of
using graphical information to make predictions. They continue
to use the nonstandard units of links to measure length. The children
are given a number of identical one-inch tiles to measure. The
number of tiles lined up in a row is the manipulated variable
N; the measured length of these tiles is the responding variable
L. The values of N are 4, 8, and 16 tiles. The resulting pattern
of bars on their graph is used to predict L for other values of
N.
Length vs. Number II
(ISBN 0-7872-4048-6, primary & intermediate): The students measure
the length of 5, 10, and 20 objects. A bar graph and point graph
are constructed on the same axes, providing a transition from
bar graphs to point graphs. Interpolation, extrapolation, and
other graphing techniques are introduced. In the upper grades,
this investigation can be used as part of a discussion of the
slope of a line.
The Bouncing Ball
(ISBN 0-7872-4049-4, intermediate & middle): A ball is dropped
from varying heights, and the bounce height is measured. The manipulated
variable is the drop height, the responding variable is bounce
height, and the type of ball and floor are controlled. This investigation
can serve as an introduction to many of the basic elements of
TIMS including repeated measurements for each value of the manipulated
variable, point graphing, the best-fit line, interpolation, extrapolation,
and simple proportional reasoning. The children learn to pick
the values of the manipulated variable in whole number ratios,
in this case 40 cm, 80 cm, and 120 cm, to facilitate analysis
of the data. Simple proportional reasoning is a major focus of
the investigation, where the children use their data to set up
ratios to solve for either an unknown drop or bounce height. By
repeating the lab with a super ball, the children learn not only
the importance of controlling variables, but also how the results
of one investigation can be generalized to predict the results
of another. This is a big investigation with big ideas in which
the children are asked to reach new heights.
Mr. O—One Quadrant
(ISBN 0-7872-4050-8, intermediate): Both axes of Mr. O are now
used to define and locate objects in the first quadrant. The values
of x and y are both positive. The children have to measure x and
y of an object (in cm) and record its location. They will also
find objects using x- and y-coordinate information. Moving to
the playground, the children learn how to use a scale factor to
compress data. In both the classroom and the playground, the children
learn how to locate the distance between objects using their first-quadrant
map.
Walking Around Shapes
(ISBN 0-7872-4051-6, intermediate): Children explore the relationship
between the length of one side (S) and the perimeter (P) of four
different-sized equilateral triangles, four different-sized squares,
and four different-sized regular hexagons. Patterns in the data
are discovered by children as we deal with simple proportions.
Arm Span vs. Height
(ISBN 0-7872-4052-4, intermediate & middle): Arm span and height
are measured for each student in the class. These variables are
weakly correlated so the data points for a class do not fall on
a line: instead they tend to cluster. The collection of data is
then extended to other grades and to adults. The result is a distribution
of data points that approximates a line that passes through (0,0).
This correlation forms the basis for discussing quantitative biology
investigations.
Length vs. Number III
(ISBN 0-7872-4053-2, intermediate): We once again take advantage
of the inherent regularity in identical objects to make predictions.
In the past we used whole number data. The new idea in this investigation
is to make measurements out to one decimal place and to use decimals
to make graphical and proportional reasoning predictions. As before,
the manipulated variable will be the number of objects (N), and
the responding variable will be the length (L) of N objects. Unlike
the previous Length vs. Number labs, the children will choose
from several different types of objects (new chalk, paper clips,
links, unsharpened pencils, etc.) which ones they will measure.
The comprehension questions extend the lab to a wide range of
applications using identical objects of decimal length.
Them Bones
(ISBN 0-7872-4054-0, intermediate): In this open-ended lab, the
students are asked if the length (L) of any of the 4 bones in
their arms or legs is correlated with their height (H). The children
pick one of the four bones to study and collect data from their
classmates. On their own each student draws a picture, sets up
a data table, collects the data, and makes the appropriate graph.
To find a true correlation in this weakly correlated data set,
the children should realize that their measurements should also
include upper graders and/or adults. The children compare the
results on the four different types of bones to see which has
the best correlation with height.
Downhill Racer
(ISBN 0-7872-4055-9, intermediate): This is a more advanced companion
piece to the Rolling Along investigations. In those investigations,
the type of car is the manipulated variable, the distance it rolls
(D) is the responding variable, and the height of the incline
(H) is controlled. In Downhill Racer, H is the manipulated variable,
D is still the responding variable, and the type of car is controlled.
Data of H vs. D are plotted and analyzed as a point graph. From
picking the values of H, to carrying out multiple trials, to averaging
results, and then making and checking predictions, the children
are truly carrying out scientific investigation. Predictions are
made using interpolation, extrapolation, and proportional reasoning
and checked to see if they fall within 10 percent of the new data.
To complete the scientific investigation, the children are asked
to find out what happens when the release point is changed and
when mass is added to the cart.
Mr. O—4 Quadrants
(ISBN 0-7872-4056-7, intermediate & middle): In this exercise,
Mr. O’s Left/Right is turned into +/– x and his front/back into
+/– y. We have finally arrived at a full four-quadrant location
of objects using the 15th-century invention of a signed number,
which combines distance and direction into one number and so allows
us to locate objects anywhere in a plane. Direction, a new idea
for the children, is bound up in the (+) and (–) sign, and will
be used over and over again as we discuss the concepts of velocity,
acceleration, and force. By placing objects on a table or around
the classroom and using centimeters and meters, the children measure
each object’s x/y coordinates and then convert these distances
into four quadrant maps. Besides learning to make maps using +
and - signs, the children are asked to read maps, to find distances
between objects not on either axis, to use scale factors to plot
playground data, and in several challenge questions to use their
map-making skill to find out the distance between objects starting
with just coordinate information.
Rolling Spheres
(ISBN 0-7872-4057-5, intermediate & middle): The children roll
a 1-inch steel sphere down a short ramp a distance (L1) and measure how far it rolls up a long ramp (L2). The manipulated variable is L1, the responding variable is L2, and the mass of the sphere and the height of each ramp are controlled.
Using several trials, averaging results, and plotting the data,
the children determine the relationship between L1 and L2 both graphically and analytically. The children then make predictions
on what L1 would be given L2 and vice versa, check out their predictions, and determine the
percentage difference between the measured and predicted values.
What turns out to be particularly exciting is to predict the values
of L1 so that the sphere just makes it to the edge of the long incline.
There will be lots of oohs, aahs, and applause as physics meets
reality. Finally, the children predict what would happen when
the height of the incline is changed and the mass of the sphere
is changed. Measurements are made and percent differences calculated.
This is an investigation that is rich in proportional reasoning
and will go a long way in sharpening the children’s analytical
skills.
Plant Growth
(ISBN 0-7872-4058-3, intermediate): Since plants grow rather leisurely,
this is a two- or three-week investigation. The children plant
four seeds and follow the growth of one. The investigation raises
the issue of how to distinguish calendar time, i.e., the date,
from “scientific time” which starts from t = 0, the moment the
plant first pushes out of the soil. The children record the plant
height, h, vs. t. The amount of water, light, soil, and the number
of seeds are the controlled variables. Since the relationship
between h and t is nonlinear, the children get a chance to make
nontrivial real time predictions and then, waiting a day or two,
to check them out. The children collect class data on the mean
height of the plants, determine the probability one seed will
germinate, and then carry out a series of class investigations
in which the volume of dirt, the amount of light, the number of
seeds, and the temperature are varied. By carrying out Plant Growth,
we are sure the children will grow scientifically.
Through Thick and Thin
(ISBN 0-7872-4059-1, intermediate & middle): In this open-ended
lab, the children have to find the page thickness (t) of a single
book, then gather data from lots of different books, make a frequency
distribution data table, and plot their results. There are no
explicit instructions, only some leading statements. The children
are essentially on their own. Decimal numbers on the order of
0.005 to 0.010 are involved. The children have to solve proportional
reasoning problems involving decimal fractions. The students are
challenged to see if there is a relationship between t and the
number of pages in a book.
Leaf It to Me
(ISBN 0-7872-4060-5, intermediate): Each child brings in 30 to
40 leaves from a single tree or bush and measures the length of
each leaf (L) and its width (W) at L/2. The data is analyzed to
see if there is a relationship between the two variables. Data
from different trees and bushes are compared. In spite of the
chaos of size, shape, color, and edge types, one finds a simple
straight line relationship between W and L—not the same straight
line for all species but a weakly correlated straight line nonetheless.
This underlying simplification illustrates how integrating math
and science brings order out of a complex physical system.
View Tube
(ISBN 0-7872-4061-3, intermediate & middle): The students look
at a meterstick taped to the wall through a toilet paper roll.
They determine how much of the meterstick they can see vs. the
distance from the ruler. The length and diameter of the tube are
controlled variables. The experiment contains all the TIMS quantitative
elements: interpolation, extrapolation, proportional reasoning,
controlling variables, and inductive logic. The investigation
has marvelous applications, from learning how the Egyptians built
their pyramids to measuring the size of a giraffe at the zoo.
The children use their view tubes as range finders, determining
the distance to objects knowing their height, or as height finders,
determining the height of objects (the school is one) knowing
the distance. The children are challenged to a View Tube Playground
Olympics. All of this for one toilet paper roll and a meterstick.
This is what elementary school science should be all about.
Circumference vs. Diameter
(ISBN 0-7872-4062-1, intermediate & middle): The children roll
cylindrical objects, like tin cans, of various sizes to determine
their circumference. After averaging several trials, the children
plot circumference vs. diameter. The resulting straight line through
(0,0) means that the children can not only use interpolation,
extrapolation, and proportional reasoning to make their predictions,
but they can determine π from the slope of the best-fit straight line to the data. The
children then set up the equation C = πD and solve a wide variety of problems from determining the diameter
of giant Sequoia trees to finding the circumference of tires on
the family car.
Getting the Range of It
(ISBN 0-7872-4063-X, intermediate & middle): A follow-up of the
View Tube experiment, the children try to find out how far they
are from a set of given objects placed both inside and outside
the classroom by using just the length of their arm and the width
of the thumb, finger, fist, or coin. The investigation requires
estimation and proportional reasoning. Percent differences are
calculated in order to compare predictions with actual measurements.
The children make a class frequency distribution of their percentage
difference data in order to learn how accurate this technique
really is. Using a dime, on a clear night, the children are challenged
to learn something about the distance to the moon. Powers to ten
will come into play. This lab has an open-ended quality, which
allows the children to look at a wide variety of circumstances.
Getting the Range of It carries us from the playground to the
moon. You can’t go farther than that.
One Back—Two Forward
(ISBN 0-7872-4064-8, intermediate & middle): This is an open-ended
investigation in which the children use a spring-loaded car that
shoots forward after it is rolled backward. The initial statement
on the work sheet is “Design and carry out an experiment to find
the relationship between the distance one pushes the car back,
B, and the distance it rolls forward, F, from where you released
it.” That is all that is given. The rest is up to the students.
The children pick the values of B, note the controlled variables,
draw their picture, set up the data tables, take the data, make
the graph, and answer a few questions. Since the relationship
between F and B is linear, the children have an opportunity to
show what they know about interpolation, extrapolation, and proportional
reasoning. Class data is compared to see if different cars produce
different results.
Mr. O’s Neighborhood
(ISBN 0-7872-4065-6, intermediate & middle): The children learn
how to make a scaled-down map of the streets in the neighborhood
around their school and then locate on this map a variety of commercial
and residential establishments. From the distribution of these
establishments they learn about the “archeology” of where they
live, i.e., about the location of grocery stores, restaurants,
movies, and places of residence, and how all of these may be related
to each other. Parallels are made between their map and the maps
archeologists make to understand ancient civilizations. Using
their maps, students estimate the areas of their neighborhood
devoted to parks, malls, public buildings (like schools and hospitals),
and residences. The children estimate the total population of
their neighborhood. They pick a type of commercial establishment
and see if it clusters together, how many people on the average
might use it, and if it is profitable. We draw an analogy between
these studies and recent archeological work on the Giza Plateau
in Egypt.
Know All the Angles
(ISBN 0-7872-4066-4, middle): Everyone thinks the proper units
of angles are degrees. How wrong they are. In Know All the Angles,
the children learn that an angle is the ratio of an arc length
to a radius, and that the proper units of an angle are the dimensionless
quantities called radians. For a given angle, the children have
to construct arcs and measure their lengths for different radii.
The graph of arc length vs. radius is a straight line, the slope
of which is the true measure of an angle. Since angle is a ratio
and since converting from radians to degrees requires using a
ratio, the experiment is filled with proportional reasoning problems.
For us that’s great, although the children may disagree. Regardless,
as we show in the Teacher Lab Discussion, degrees, radians, and
the concept of an angle put us in touch with our ancient past
where the rivers of the Middle East angle toward the sea.
Mr. O in Polar Coordinates
(ISBN 0-7872-4067-2, middle): We start by giving the children
a little review for measuring angles, and then we set out to explore
the world of polar coordinates. First, we show how to locate a
new kind of origin which, instead of a simple point, will be a
baseline for locating R = 0 and q = 0 deg. We see that Mr. O is of great help in finding the baseline.
Then we show the children how to set up a polar grid, how to read
a polar map, how to locate objects in the room in polar coordinates,
and how to find objects if given their polar coordinates. The
children use scale factors to plot their data, and an example
is drawn from the use of polar coordinates in radar.
Bull’s-Eye I: Projectile Motion
(ISBN 0-7872-4068-0, middle): In this investigation we first introduce
the children to the important concept of projectile motion qualitatively,
and then use projectile motion to do an experiment. In the investigation,
the students find the relationship between the release point of
a steel sphere on an incline, h, to the distance the sphere lands
from the edge of a desk or table, d. The children use their results
to make predictions about the landing distance and then draw a
bull’s-eye to see if their predictions check out. They find that
the relationship between h and d is not proportional and so have
another opportunity to straighten out a curve and see how that
leads to more accurate predictions. The children will have to
use square roots to find answers. We also extend the investigation
in an open-ended fashion to determine how changing the values
of some of the initially controlled variables changes the results.
The Shadows Know
(ISBN 0-7872-4069-9, middle): Using a flashlight, the children
project the shadow of a disk onto a piece of paper. By sliding
the disk back and forth along a meterstick, the students vary
the distance, L, between the light and disk, and the size of the
shadow, D. The children determine that L and D are inversely proportional.
We explore this relationship by making analytical predictions
which are then compared to the experimental data. The students
also determine what happens to the shadow when the diameter of
the disk is varied and L remains fixed. The children explore the
shadow in detail, with and without a mask over the flashlight,
as the disk slides along the meterstick. They are asked to speculate
on why the shadow has light and dark regions which vary as L varies.
The Teacher Lab Discussion discusses ray tracing which then becomes
an option for a further lesson on making shadows.
Out on a Limb
(ISBN 0-7872-4070-2, middle): This is a multivariable investigation
involving four primary variables, one mass and three length, and
which incorporates simple proportional reasoning, straightening
out the curve, and an inverse relationship between the variables.
Organizing four variables into three distinct investigations and
dealing with multistep logic problems are integrated into the
exercise. The central idea is to find what variables affect the
displacement (d) of the tip of the force gauge blade from equilibrium,
and then to determine the quantitative relationships between these
variables in separate experiments. The responding variable is
d; the manipulated variables are m, the mass attached to the blade;
L, the length of the blade; and t, the thickness of the blade.
The comprehension questions link the three investigations as the
children explore how d changes when m, L, and t are changed singly,
in pairs, and all three at once.
Back to TIMS Laboratory Investigations Home Page
Copyright © 1997 by Kendall/Hunt Publishing Company
Copyright © 1999 Institute for Mathematics and Science Education.
All rights reserved.
UIC—University of Illinois at Chicago