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DESCRIPTIONcross curricular guide (maths applied on different fields of science)
Cross-curricular Approach of Mathematics
QED Quality in Europe's Diversity
Comenius Multilateral Partnership 2011 - 2013
I. Applications of Mathematics in Science ..page 3
QED team of Borgarholtsskli from Reykjavik, Iceland
II, Maths in cultural and social life ..page 12
QED team of Geniko Likeio from Kissamos, Greece
III. Mathematics &Economy ..page 24
QED team of Ahmet Eren Anadolu Lisesi from Kayseri Turkey
IV. ICT applications in math teaching ..page 28
QED teams of Goetheshule Wetzlar, Germany, and CETCP Botosani,
I. Applications of Mathematics in Science
The QED team from Borgarholtsskli, Iceland
Natural sciences are important for daily life. It is important that students choose to study
natural sciences, health sciences and engineering. In Iceland today there is a lack of students
who study these subjects. Students seem to choose something else.
Mathematics is closely related to science. Natural sciences can not be without
mathematics. For students, natural sciences and mathematics, tend to be difficult and they are
intimidated by them. For those who like to study these subjects it is often difficult to transfer the
knowledge of them to other subjects.
The exercises in this pamphlet are based on to link together mathematics and physics
through assignments which are done manually! The goal by combining mathematics and
physics is to integrate natural sciences with mathematics. By using practical and manual
exercises the students should increase their understanding and also they might be more positive
towards natural sciences. In addition these exercises are important for physics.
The exercises have been used in the first and second level in physics in
Borgarholtsskli, Iceland. The uniqueness of the school is that the background of the students is
very different and that means that the teaching is very individually based.
The exercises can easily be changed, that is, their focus can be changed, they can be
made more difficult, they can be less time consuming or more time consuming.
Exercise 1: Errors in measurements
When doing measurements in science there is never a 100% certainty in the numbers we
measure. There is always some minimum resolution we can get, determined by the
instruments we use or by the users doing the measurements. In this exercise student will
practice measuring objects using simple tools, determining the uncertainty or error in the
measurements and then use errors in simple calculations. As a prerequisite, students need
to know how to determine errors in measurements and to do calculations using errors.
Ruler or caliper
A few pencils or sticks
Part 1: Sticks, length, addition
Groups get one stick/pencil for each member of the group
a) Find an empty page in your workbook. Write down the name of the exercise, the date
and the names of the students in your group
b) Give each stick a name or make sure to be able to distinguish between them.
c) Each student measures the length of one stick and determines the uncertainty/error in
the measurements. Write all the results down, including the name of the person doing
d) Calculate the total length of the sticks and determine the total error in that
e) Calculate the average length of all the sticks and the error in that value using the
MIN/MAX method of determining total errors. Make sure to document everything in
Part 2: Box, volume, multiplication, % error
Each group of students gets one small box
a) Write down a name for the box, draw a picture and mark each edge so its certain
what side is what
b) Measure the length of the edges and determine the error in the measurements.
c) Calculate the volume of the box and determine the errors in that using the
d) Calculate percentage error which is the error divided by volume
Part 3: Measuring time, % error, instrument error, user error
Each group of students gets a stopwatch
a) Each student tries 5 times to start a stopwatch and stop at exactly 10:00 sec. Each
student writes down his numbers
b) Each student calculates the average time and determines the error. Also the % error
which is error divided by average time
There are 2 main ways to determine the errors in this step
i) Standard deviation: Use a spreadsheet or a calculator to calculate average time and
standard deviation. The error is then the standard deviation
ii) Min/max variation:
Exercise 2: Graphs and lines
The purpose of this exercise is for students to practice matching curves or lines to specific
equations. Once that is done, its possible to match the curves and values from the curves
to certain physical laws or rules.
Graphing paper and a ruler
Part 1: Calculating a trend line
Draw the points/coordinates in table 2 on a graph. The v
[m/s ] is on the y-axis and t [s] on the x-axis and make sure
to mark clearly the axis t or v. Draw a straight line (using a
ruler) that intersects all the points on the graph and calculate
the equation for the line. The equation is on the form y = kx
Part 2: Graph matching
Draw the data in table 2 on a graph and try to determine
which type of a line/curve fits the data. Then determine the
equation for the line. I.e. calculate a value for k or a, b and
t [s] v [m/s]
Suggestions to try out:
x. The force constant (k) of each spring, determines how hard it is to stretch or compress it. A
stiff spring has a large k but a loose spring has a low k. The purpose of this experiment is to
determine the force constant in a spring by drawing a graph and calculating the trend line. An
experiment was done where force was applied to the spring and the stretching of the spring was
Graphing paper and a ruler
Table 1 contains data from a physics experiment. Force was applied to a spring and the length
that the spring stretched was measured.
1. Draw a graph and each point on the graph. Mark the axis
clearly as y-axis Force, F, [N] and x-axis as
expansion/stretch of the spring, x, [m]. Make sure to keep
the scale on the graph such that its is detailed. Try to use
whole page in your book.
2. Draw the error bars on each point. The errors in F will
be shown as small lines extending up and down from each
point. The error in x will be shown from left to right. When
all is done, the graph should look like it has six small
3. Use a ruler and try to find out what you feel is the best straight line that intersects the group
of points the best. Do not connect the dots, the end results should be a graph showing small
crosses and one straight line intersecting most of them.
4. Determine the equation for the line you have drawn. Make sure to pick points that are
actually on the line, to do the calculations. The equation should be on the form y=kx+c, (F=kx)
where c is 0.
5. Compare the equation and Hookes law. What is the value of the springs force constant (k)?
X [m] +/-
F [N] +/-
6. Use the equation to forecast how much you would expect the spring to stretch if a force of 23
N was applied to the spring.
Exercise 4: Graph matching
Scientist often do experiments to test hypothesis. A large number of data points are then
measured and then the scientist tries to make sense of it all and to find the mathematical
correlation between variables. In this exercise data from physics experiments is collected in
tables. The data must be entered into graphing software, the relevant graph plotted and matched
to mathematical functions. When the equations are determined the software shows the relevant
constants that can then be matched to the variables that are unknown in each physics equation.
Graphic calculator or graphing software
Input the data in tables 1-4 in to a graphics calculator or graphing software one at a time. Then
match each curve to the correct physics equations. I.e. find the equation that matches each table.
Use the equations for the curves to c