Math in Science1) Research – Science disciplines

- Definitions and examples- Math in Science

2) Primary Math in Science

Teaching: An effective key to self-learning This project is funded by European Union.

This teacher is thinking about Math in Science.

Míša, Klára, Susan, and Verča are ready for the lesson.

Maths in Physical ScienceMathematics is used in Physical Science very often, for example arithmetic, algebra and advanced mathematics may be used:• to calculate the measurements of objects and their

characteristics• to show the relationship between different functions and

properties. • to establish values • to solve simple equations or formulae• to converse units• in classical or everyday Physics, normal values are used to

solve equations.

Fields of Math used in Science

Mathematics is used in Physical Science for measurements and to show relationships.• Arithmetic consists of simple operations with

numbers and values. • Algebra is used to show relationships before the

measured numbers are used for calculations. • Higher math is used for complex relationships

between properties.

Arithmetic conventions

In using Arithmetic, we can add, subtract, multiply and divide numbers. We also use fractions and decimals.• Addition and subtraction• Multiplication and division• Order of mathematical operations• Use of parentheses• Fractions and decimals

Relationships in AlgebraAlgebra uses letters to denote a relationship between characteristics. Usually, they are just abbreviations for the characteristic. For example, energy is denoted by E and velocity by v.Newton came up with the relationship between force, mass and acceleration. His equation says that force equals the mass of an object times its acceleration. To avoid writing out this sentence, we use the symbols F for force, m for mass and a for acceleration. Thus, the equation can be written: F = ma.This allows us to substitute values for two items and get a value for the third.

Advanced mathematics• Calculus, differential equations and other

advanced mathematics are used in advanced Physical Science calculations and equations.

• One example of where and why advanced mathematics must be used can be seen in the simple gravity equations. F = m*g is the equation for the force of gravity. But that equation is only an approximation for items falling close to Earth. The actual equation is related to the masses of the bodies.

Theory of relativity

E = mc2

Consclusion: Importance of equations, Algebra, Arithmetic, Calculus

You can study the facts of science with little or no math. However, in many areas of science (Physics, Astronomy, and Chemistry) equations are used to make calculations. In such cases, you need some knowledge or Algebra and Arithmetic to work with the equations and make the calculations.Advanced science subjects may require knowledge of advanced math, such as Calculus. Even for students of Psychology is important knowledge of Math as they must take a statistics class. Biopsychology is 100 per cent science.

Math topics used in Science

- Units (Physics, Chemistry)- Stars (Physics – Astronomy)- Temperature (Physics)- Movement (Physics)- Maps (Geography)- Animals and Humans (Biology)- Climate Change (Geography, Ecology)- Density (Chemistry) - Gravity (Physics, Astronomy)- Time (Physics)- Expansion due to Heat (Physics, Chemistry)- Family (Social studies, Budget)

Chemistry – Composition of foodThe majority of the food we eat is composed by nutrients: proteins, fats, mineral salts, and vitamins. During our visit

in Desio in Italy we made an experiment to prove what is in carrot. Math skills: writing data into a table.

Chemistry – Composition of foodFirst we cut and pressed carrot. We measured the liquid. Next we added some substances to prove what nutrients a carrot consists:water, protein, fat, sugar, and fiber.

MeteorologyOur school has a meteorology station. Some pupils measure the temperature and humidity.They observe the sky. Next theywrite down the results in a table and finally they make a graph. Math skills: drawing a graph.

Paedology and geologyWe prepared a map of our school playground. Then we picked places and dug a hole. We collected samples from different depths. We studied those samples, measured pH factor and put the results in a table. We used GPS to put our holes in the map. Math skills: using coordinates and tables.

BotanyBotany is also interested in the growth of plants. We learnt how to measure the width and height of trees. Of course, special electronic gadgets were developed but we used simpler methods which are based on knowledge of PI constant and similarity or triangles.

Botany facts: Trees grow more or less evenly. Most trees increase their circumference by 2.5 cm per year. This means that a tree with circumference 2.5 m is about 100 years old if it has enough space. The circumference of a tree is measured in the height of 1.30 m. This method can not be used for trees which are very young nor very old, so it is only approximate. This method can not be applied to poplars as they grow far faster than other trees nor trees growing in the high mountains.

Measuring procedure - age of a tree

1) Measure the circumference of a tree2) You can measure the diameter and

calculate it (c = PI * diameter)3) Find out the age of the tree (c : 2.5)

Measuring procedure 1) Place 4 m long stick next to tree2) Make a special paper ruler 3) Hold the ruler in straighten arm4) Find a spot where you will see

the top and bottom of the tree in the corners of the ruler

5) Read the number which you see at the end of the stick

A special paper ruler stick from two parts. Each part is 15 cm long.

Math explanation – ratio, similarity

1 m long stick

pict. 1

A

B

C

C´

B´

Triangle ABB´ is similar to triangle ACC´ because the angles ABB´and ACC´ are right (90°) and the angle BAB´ is the same as the angle CAC´.

AB : AC = BB´ : CC´AB : BB´ = AC : CC´

RATIO OF SIDES

1) Lay on ground2) Ask your friend to place the stick as in the picture3) Measure distances AB and AC4) Calculate the hightCC´ = k * ACk = tangens of BAB´

Math explanation – ratio, similarity

Pict. 2

1) Triangle eye – foot and top of the tree is right angled. 2) Place a pencil in the vertical position as in the picture.3) Turn the pencil in the horizontal position as in the picture, do not change its distance from your eye.4) Ask your friend to stand in the line where you can see the end of your pencil and his feet.5) Compare the distance between the eye and the tree foot to the distance between your eye and your friends feet.

Opposite legtg = Adjacent leg

Math explanation – trigonometry (tg)

1) Measure the angle with a special protractor

2) Measure distance between you and the foot of the tree

3) Calculate the distancex = tg * distance to the tree

a straw

Angle 90 °Angle 0 °

string with weight

Law of the lever: M1a = M2b Levers are used to lift heavy weights with the least amount of effort. In the photos the weight on the left hand side is been lifted by the person because of the lever. The longer the 'rod' the easier it is to lift the weight. Under normal circumstances the person would not be able to lift the weight at all. The fulcrum is the place where the rod pivots (or rotates).

In this case, the power into the lever equals the power out, and the ratio of output to input force is given by

the ratio of the distances from the fulcrum to the points of application of these forces.

A microscope – lenses, focal lengthA microscope is an instrument that uses a lens or a series of lenses to magnify small objects. When you look through a simple microscope, you are looking through a biconvex lens made of glass. Light from the object passes through the lens and is bent (refracted) towards your eye, so it seems as though it comes from a much bigger object.

There are more ways how to place lenses to construct a microscope. To calculate the distances you need to know fractions.

FractalsA fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. It is also known as expanding symmetry or evolving symmetry. On the left, frost crystals occurring naturally on cold glass form fractal patterns. On the right, we constructed a fractal triangle.

Computers and robotsThere is no doubt that advanced math is needed to construct computers and robots and to write programs which help normal people to communicate with them.

Sources• https://en.wikipedia.org/wiki/Branches_of_science• http://www.school-for-champions.com/science/math.ht

m#.Vrh9aBjhDcs• https://www.shodor.org/unchem/math/• http://science.howstuffworks.com/math-concepts/

fractals.htm• http://www.ncpublicschools.org/docs/accountability/

common-exams/released-forms/highschool/science/physics/formula-sheet.pdf

• https://en.wikipedia.org/wiki/Fractal#/media/File:Frost_patterns_2.jpg

• https://en.wikipedia.org/wiki/Focal_length• https://en.wikipedia.org/wiki/Theory_of_relativity• Other pictures and drawings are from our teacher Mrs.

Buroňová