# Teaching Material Here You´ll find all teaching material for direct use in the classroom, in English.

The material is developed and evaluated in European classrooms (EU-project ScienceMath). All the developed teaching modules of the ScienceMath-project are available in English.

Please chose a theme. Chosing „material“ you´ll see the concrete teaching proposal including materials like working sheets etc.

arclengthbackground and material and table

(arc length; 18 to 20 years old students; the lesson is a kind of a »proof«. However it is more the use of mathematical formula and an approximation from physics)

arithmetic meanbackground and material and further information

(Arithmetic mean, Car differential. Applicable for 13 years old students and older. It is an independent lesson, which (of the formal knowledge)requeires only basic arithmetic skills of addition and division. Comprehension of the arithmetic mean (i.e. (a+b)/2) is welcome but not necessary. The lessons can be used as a rich intuitive insight into the meaning of the simple formula of the arithmetic mean. Even if no special background is required, the ideas presented, can lead students and teachers ever deeper into intuitive comprehension of sophisticated mathematical ideas. Teachers are advised to thoroughly study through the topic, as some of the ideas are very practical and the use of abstract concepts might seem unusual)

bicycle: background and material and further information

(Bicycle gears, bicycle shifting, ratios. For 13 years old students and older. It is an independent lesson, which (of the formal knowledge) requires only basic understanding of equations, line slope and ratio of two natural numbers. The lesson can be adopted to avoid mentioning equations at all.  The lesson is oriented and based on practical experience that students have with bike gear shifting and riding. Teachers are advised to thoroughly study the topic, as some of the ideas are very practical so the use of abstract concepts might seem unusual. Furthermore, we advise teachers to adopt the numbers to their own bicycles or even better, to bicycles that are brought to the lesson. In advance, students might be given the practical tasks of counting the teeth on the chainrings of their bicycles and measuring the sizes of their bikes in order to make the lesson as ‚real life‘ as possible)

BoyleMariotte: background and material and further information

(concept of variable, modelling, functional relationship, antiproportional relationship, Boyle’s law. 12-16 year old students. Lesson can be used to introduce the concept of variable and/or the concept and functional relationships or as an independent lesson to deepen the concept of variable and functional relationships. Teacher should be familiar with experiment, if needed, trying out experiment in advance; Since measuring errors appear, an introduction about handling with measuring errors is useful)

bouyancy: background and material and further information

centermass: background and material

decay: background and background

((stunted) growth, decay, experiments, analysing measuring values, regression of measuring values, modelling. 15-16 year old students. Suitable after covering functions representing growth in mathematics lesson and/or enhancing concept of half-life in physics lesson. Lesson can be separated into two parts, if needed. Mathematical performance level can be lowered by using modelling software (e.g. coach))

fermat-pythagoras: background and material and further information

fermats principle: background and material

functional relation 1: background and material and further information

(12 to 17 years old students. The lesson can be used independent during the school year or integrated into a course about functions/ functional relations. The suggested experiments lead to linear, quadratic, cubic and inverse proportional relations. The aim is to support the learning of the concept of function: The aspects like correspondence and especially the aspect of covariation should be experienced by experimental activities which should also lead to a vivid talk about it. It is recommended to arrange the experiments in stations. Time-frame should be 3 double-lessons (4,5 hours, minimum 3,5 hours). Depending on the time each group (2 to 4 students) should work at minimum 3 experiments. The sequence should be closed by a common discussion in the classroom, where every group presents the results of one experiment. The experiments are simple interdisciplinary experiments which does not need complex equipment and can be easily arranged in the normal classroom)

functional relation 2: background and material and further information

functional relation 3: background and material and further information

gps: material

growth: material

horizontal launch: background and material and further information

(Parabola; 15 to 16 years old students. The lesson demands very correlated teaching of the two subject: physics and mathematics. It is not designed to introduce parabola at math lessones but to show its aplicability. All details how should the math teacher use the material (measuring results) prepared by physics teacher is described)

lego: background and material  and further information

(Lego, Robot, Mindstorms, NXT, Coordinate system. For 10-18 years old students (and even older). It is an independent lesson, which can be adopted to different levels. It can be an intuitive and hands-on fun experience to introduce the notion of coordinate system. Older students, who are already familiar with coordinates can be challenged with more sophisticated tasks of ’sending the robot to the right position‘. The lesson is a demanding task for a teacher, as it is necessary to get familiar with the Lego Mindstorms NXT  robot. We strongly discourage a shallow presentations only based on attached (with Lego Mindstorms NXT sets) demo programs. For any learning to take place it is necessary that teachers and students do and program their own (possibly very simple) moves)

logarithm: background and material and further information

massvolume: background and material

minussquare: background and material and worksheet

(Square root function in divisor. 16 years old. The students should find the relationship between variables describing a natural phenomenon. The solution is square root function in divisor which use is very rarely presented in real world situation)

nutrition: background and material and further information

parabola: background and material and further information

(Parabola, Car lights. For 15 years old students and older. For good understanding of the lesson students should be familiar with the notion of parabola. Ideas can also be used to build up the geometric understanding of parabola. Such an ancient, non-standard but intuitive and applicable approach might in fact be a good introduction to the more abstract algebraic notion of parabola. The ideas of the lesson can, depending on the audience, be successfully joined with a rather informal discussion about the technology, and in particular about the technology of car lights, where one can start very practically with car lights bulbs. The idea explains how high-beam and low-beam car lights function and how satellite dish works. Teachers are advised to thoroughly study the geometric properties of the parabola, as some of the main ideas are simple geometric ideas which offer far easier approach to understanding of some aspects of parabola than ‚modern algebraic and analytical approach‘)

paralax: background and material and further information

parallel: background and material and further information

paramecia: material

pot functions: background and material and further information and Example_x^0.5

proportionalfactor 1: background and material and further information

(Proportionality, proportional factor, concept of function, functional relation, linear function. 12- to 15years old. The lesson can be integrated into a course about functions/ functional relation. Aim is a networked learning with an insight into the possible, not only formal meanings of the proportional factor in a proportional function. It is recommended to arrange the experiments in stations. Time-frame should be 1 or (better) 2 double-lessons. Depending on the time every group (2 to 4 students) should work at about 3 experiments. The sequence should be closed by a plenary discussion in the class-room, where every group presents the results of one experiment including the extra-mathematical meaning of the proportional factor in that special relation. The experiments are simple interdisciplinary experiments for the use in mathematical lessons)

proportionalfactor 2: background and material and further information

(Proportionality, proportional factor, concept of function, functional relation, linear function. 12- to 15years old. The lesson can be integrated into a course about functions/ functional relation. Aim is a networked learning with an insight into the possible, not only formal meanings of the proportional factor in a proportional function. It is advised to arrange the experiments in stations. Time-frame should be 1 or (better) 2 double-lessons. Depending on the time every group (2 to 4 students) should work at about 3 experiments. The sequence should be closed by a plenary discussion in the class-room, where every group presents the results of one experiment including the extra-mathematical meaning of the proportional factor in that special relation. The experiments are simple physics experiments, which can be realised in the classroom. To some of the experiments the physics background should be discussed)

proportions: background andmaterial and further information

refraction: background and material and further information

(concept of variable, modelling, functional relationship, proportional relationship, refraction. 12-16 year old students. Lesson can be used to introduce the concept of variable and/or the concept and functional relationships or as an independent lesson to deepen the concept of variable and functional relationships). Teacher should be familiar with experiment, if needed, trying out experiment in advance. Since measuring errors appear, an introduction about handling with measuring errors is useful)

small car: background and material and further information

(Velocity, speed, safety in traffic situations. 10- to 16 years old, also for elementary school teacher students. The purpose of teaching material is to teach the concepts of velocity and acceleration and their relations, and to use toys as a teaching material to decrease anxiety towards physics and mathematics especially for girls)

solarsystem: background and material and further information

(Solar system, distances, star, planet, large numbers. Age 12 – 17, elementary teacher students. In this teaching sequence role play is used as a teaching method, when teaching the order of the objects in solar system)

sound: background and material and further information

(Function, Digital, Sound, Resolution. … 15 years old students and older. For good understanding of the lesson students should be familiar with functions. Ideas can also be used to build up the notion and understanding of functions by non-standard but intuitive and applicable means. Ideas introduced by the lesson can also be used selectively in the development of students understanding of the notion of decimal, rational, irational,… numbers. The ideas of the lession can, depending on the audience group, be successefuly joined with a rather informal discussion about the sophistication of modern IT technology, which based on the ideas presented in the lecture, provides modern MP3, MP4, … and a whole new array of mobile devices with incredible memory and processor capabilities. Teachers are advised to thoroughly study through the topic, as some of the ideas might – regardless of their simplicity – be unusual)

temperature: background and material

(Variable, change, rate of change, controlling variables, controlled variable, dependent variable, fair test. 12 to 15 years old students. The students get a possibility to do authentic hands-on activities. The emphasis of science concepts may vary depending on the age group and the level of openness of the task that the teacher chooses. Anyhow this sequence deals with energy removed from a system, which is called heat. The sequence is divided into three subsequences that are about identifying variables related to a given experimental setting, interpreting/drawing a graph, understanding the concept of a fair test, controlling one variable at a time and recognizing cause-effect relations)

thermal expansion: background and material and further information

(concept of variable, modelling, functional relationship, thermal expansion of liquid. 12-16 year old students. Lesson can be used to introduce the concept of variable and/or the concept and functional relationships or as an independent lesson to deepen the concept of variable and functional relationships.Teacher should be familiar with experiment, if needed, trying out experiment in advance; Since measuring errors appear, an introduction about handling with measuring errors is useful)

traffic modelling: material and further information

trigonometric function: material and applets

(Trigonometric functions, circulation, oscillation. 16 to 17 years old students. Introduction of trigonometric function not purely mathematically but in combinations with physics. Students can find themselves some objects from every day life which oscillate and some objects which circulate and then derive relationship between these two movements. Math teacher introduces the concept of function sinx and its graph. Students carry out the properties of trigonometric functions by observing real oscillating and circulating objects)