LEARNING TO MEASURE THE WORLD

Hello everyone! Along this Blog you will find a series of entries with information and resources about Mathematical Measures. First of all, it will be given some important information and concepts about measurement,  digital resources will be also described, teaching methodologies or techniques, interesting websites and videos, manipulative materials...  All this content could be used for whoever wants, children, students, parents, mathematics lovers and, specially, for teachers, who can use all the material, resources and ideas when teaching measurement in Primary Education classes. I hope it is useful for you and you like it!

From its origins, man needed to compare objects or events (number of animals to trade, seasons, temperature, etc.). His first result was the creation of the concept of number . After this conceptualization, in the act of comparison, man was able to distinguish differences between the properties of objects. For example: if what you want to compare is the length of two threads, you can say "this is longer or shorter than this other". But these expressions do not allow us to specify too much. A more precise expression is "the first corresponds to twice the second". An important act in history was when man realized that to compare two objects he could do it indirectly through a third object used as a standard measure or unit of measure . This would solve the fact of being able to compare things that are not in the same place, for example, as long as we can take the unit of measurement with one. As we know, when talking about length, the first units of measurem...

Comparison is the basis of measurement. If you want to measure a length, you need to compare the object to be measured with a suitable unit of measurement. Before the implementation in Spain of the International System to measure: lengths, surfaces, capacity, weight..., each region had its own measures. Since that is no longer possible, they have fallen into disuse.  Some old units of measurement will be shown below: In length , the legua real  was very common, which is equivalent to 6,687 Km., but there was also the legua marina , a little smaller. These long distances were taken from what a horse could cover in about an hour. Other minor distances were measured in braza, step, vara, elbow, foot, hand, inch , names that have their origin in the physical distance to which they were equivalent measured on a person or an object. In mass , the ton  already existed, which was less than what we now call by that name, 920.16 kg. It was equivalent to 80 arrobas , ap...

Why do people measure? To communicate to another distant person in space or time how many things we have or problems are its dimensions. Due to the impossibility of transferring the object in question, due to its size or constitution. Due to the search for a relationship between two or more magnitudes. If we want to measure the length of an object we must handle a unit of length. We compare this with the object to be measured, the result of the comparison is the measurement, that is, the number of times that the unit is contained in the object to be measured. Historically, humanity has accompanied the need to quantify the continuum through stable units of measurement according to the problems they face. A new problem arises. How to build measuring instruments that were modified, above all, taking into account the increasingly small objects offered by current technology. Mathematics supported these constructions by endowing technology with numbers that allow us to measure: rational...

The most appropriate way to start measuring with students is, above all, creating them the necessity to measure. When people realize that something truly serves the reality of their day-to-day life, it is when they begin to be truly interested in learning it. In this way, if children realize that measurement is something that will work for their lives, it will be more interesting and meaningful learning for them. The objective of working with measurement is: To discover the necessity of measurement. To understand that to measure is to compare. To discover that we use units to measure. To discover that the measurement depends on the chosen unit and not on the quantity to be measured. How does a child learn to measure?  The process proceeds sequentially from perception to comparison. Measurement begins with the perception of what should be measured. Undoubtedly, some attributes can be perceived more simply than others. A child's height makes sense of length, weigh...

Since measuring is a difficult and complex act, which requires the student to practice and fluency in the classification and serialisation processes, it seems interesting that children have the opportunity very early on to find opportunities in their environment that put them in contact with the magnitudes physical, although initially this contact is carried out in an intuitive way, exploring with the senses. Consequently, the student must find in the classroom environment appropriate materials, structured or not, whose observation and manipulation provide him with data, such as their attributes. Thus, the student is able to establish a relationship between objects and actions, to observe similarities and differences, so that, ultimately, he can build logical-mathematical knowledge. Some didactic materials that can be used in the classroom: Length: Tape measure, ruler, meter, calipers ... Mass: weight perception game, scales, weights ... Capacity: sets of capacity me...

Concept games An example of an exercise could be: a box containing various objects will be taken, and children will be asked to choose a pencil "shorter" than the one they are taught, or a "bigger" object, etc. Children themselves can be used as a comparison object to establish the "greater than" or "smaller than". Objects in the classroom or yard can be used in terms of distance concepts, and children can also be asked to place certain objects so that they satisfy various conditions of distance or proximity. Ordering sizes It could be an extension of the previous games. Various objects are compared, making the children align them according to size, distance, etc., but always based only on perception, without the intervention of the measurement. Distance evaluation The teacher might start with questions from the classroom, such as: "if we left the large closet in the corner, do you think I could fit my table and the small c...

We will begin by explaining the hours to the students, using an analog alarm clock as an instrument.  Firstly, we explain the hours on the dot, then the averages, and then the quarters and the quarter quarter. To make the learning of the hours meaningful, we associate a sound, that of the alarm clock. That is, when we indicate one o'clock the alarm clock will sound and the same will happen with the other hours. We will also use a digital watch to observe the differences. Once the hours have been explained on the analog clock, they will make a clock, but since time has forbidden us by limiting our activities, it will be carried out by the educators who will present themselves to the students to check if the explanation has been efficient.  We can develop the following activities: To draw needles on clocks. To write the hours that the clocks mark. To find and paste each clock in its place. Once these activities have been completed, you can move on to learning...

Arbitrary units of capacity By playing to fill or empty a large container with the help of one or more small containers, it is how the child gains his first experience of volume or capacity. The best way to do this at school could be using dry sand instead of liquids, taking a cup as a small container, and a basin or bowl as a large container. For starters, there is no need to count or record how many cups have been filled. When the cup is full, it empties and starts again.  Then the game can be varied by taking the same large container, but changing the cup for a smaller or larger one. When children have become accustomed to these games and are able to count, they can be encouraged to pre-appreciate the amount needed to fill the large container, and then the number of cups they need. Arbitrary unit series It is necessary to have a series of containers of different capacities, but in the same way, in order to facilitate understanding. It would be desirable, initially, t...

Concept games Before children begin to measure weights, they need to know what heavy, light, heavier than, less heavy than, as heavy as, etc. means, and their experiences need to be developed in such a way that they cannot confuse the size with weight. You could use stones of various sizes, small packages, books, pieces of wood, metal, etc. Each child must be given numerous occasions to have an object in each hand, to evaluate which is the heaviest or the lightest. Objects can also be made to sort into two heaps, the "light" heap and the "heavy" object heap. Later, they will be made to decide between two objects of similar weight, chosen so that children cannot easily find the difference. As students become aware of the difficulty in deciding which object is heavier among objects of similar weights, they will be led to think that the use of an element is necessary for the weight of these objects. Using the balance The teacher can present an ordinary sca...

Measurement of surfaces with arbitrary units To bring the class to this purpose, the teacher can start by showing the tabletop and the seat of a chair, at the same time asking: "Which piece of wood is larger, this one or that one? Next, the children will be asked children to compare the teacher's tabletop with that of a child's table. In this way different surfaces will be compared, deciding in all cases by simple visual appreciation. Then children can be asked to compare a long surface and narrow with another shorter and wider surface. To help them, the teacher can propose any arbitrary unit, for example rectangular tiles or cardboard. She will then pose the question in other terms, asking: "How many pieces of cardboard do we need to cover this table, or that one? With the help of the teacher, the children put the pieces of cardboard or the tiles until the entire surface is covered (or is, approximately) and they are counted how many have been used in each case. ...

Nowadays' children are borned in the digital era, so they are used to use Internet in their day to day. When teachers use digital tools in their lessons, students usually pay more attention and enjoy the classes more. For the explanation, educators can make use of some videos that motivate the students to learn, for example: Also, there are a lot of interactive resources on the Internet that we can use with children in order to practice and understand measurement concepts. They will participate interactively while they learn both mathematics and using ITC.  Some digital useful resources can be:  - A world tailored for you A world tailored for you “from the Internet in the Classroom series” from Spanish Ministry of Education introduces students of first Cycle of Primary Education (first and second courses) to the world of measurement in a very simple and appropriate way. It can be used for individual practice of the student or ...

When learning to measure in mathematics classes, it is important that students have the real manipulative material that serves to measure in the real life. With this kind of tools they can play, experiment, investigate and find out a lot of facts, like needing an instrument if they want to measure some magnitude, the necessity of a unit of measurement...  There are a lot of manipulative materials that teachers can bring to the classes, depending on what magnitude students are learning: Length :  Ruler Meter Capacity Recipients of different sizes Time Analog clock Digital clock Calendar  Money Fake coins and notes Weight Balance Weight meter