Many ways of integrating maths with other subjects

Many ways of integrating maths with other subjects

Ideas in brief:

The method of encouraging more knowledge of the proportions of one’s body is always of interest to students because adolescents are interested in their physical data. If the teacher chooses to implement the first part of the method, he or she can cooperate with the biology or art teachers and integrate the lesson into the art or biology part. The second part of the method is movement-oriented, so it makes sense to integrate with physical culture. The method is designed to work with students in grades 5-8. The workplace can be nature, a library or other space that allows students to move freely. It is recommended to divide the students into pairs. A student research sheet is prepared for the first part of the method. It is attached as well.

Measuring parts of the human body.

It is possible to measure without using any tools. All we need to do to measure certain parts of our body. For example, a meter is from the middle finger of the outstretched hand to the shoulder of the other hand (if you outstretched your left hand, you need to measure the distance from the middle finger of the left hand to the shoulder of the right hand). For a person of average height, it is about one meter. Another method is to measure the distance from the thumb to the forefinger. It is approximately 18 centimetres. To measure one meter, 6 such distances must be taken. The human gold ratio looks like a ratio of 1: 1.618, i.e., the lower part consists of 62% higher. Explanation: If the arm length is 1, then the hand plus forearm should be 1: 1,618. If the foot is 1, the foot plus the foot is 1: 1,618. This and other methods of body measuring lead us to measure without tools. Because students are still growing and of varying heights, we advise you to take the time and allow students to measure different distances on their bodies before conducting experiments and research for use in nature.

1. Measure the width of your hand. Approximately the width of an adult's hand is 10 centimetres.

2. Measure the distance between your thumb to the middle finger. Approximately, the distance is about 20 centimetres.

3. Measure the distance between your thumb to your index finger. The distance is shorter by 2 centimetres than the distance between your thumb to the middle finger.

4. Measure the distance between the two stretched fingers: the middle finger to the index finger. Typically, for adults, this distance is equal to 5 centimetres.

5. It is useful to know the length of your index finger. It is about 9 or 10 centimetres as well.

When conducting these measurements a teacher can give students some hypotheses, which students would like to check the correctness of the hypothesis. This collective work would unite students and show the importance of the contribution of each of them.

  First Hypothesis: The length of a human foot is equal to the distance from the elbow to the wrist.

   Second Hypothesis: Leg length is head height multiplied by 4.5.

  Third Hypothesis: The human height is equal to the distance between the big toe tips of the outstretched arms.

   Forth Hypothesis: The corners of the mouth line up with the pupils of the eyes.

   Fifth Hypothesis: The space between the eyes is approximately the width of an eye.

The sixth Hypothesis is the ancient rule, which says that the average length of an adult is approximately equal to half of the distance between a person’s eyes and heel (ground).

Let students check the correctness of these hypotheses. Even more so, a teacher can ask students to make some new hypotheses about the distances of their bodies. Doing this activity would be the right time to speak about various measurement units and their relations.

Students can be reminded of the proportions of the human body described by Leonardo da Vinci. https://en.wikipedia.org/wiki/Vitruvian_Man .Without a measuring ruler, It is quite convenient to measure long distances by counting your steps. We especially recommend doing that during camping with students. For this reason, we need to know the length of our own steps and count the number of steps. There are plenty of free phone apps which can help you to count the number of steps. Students like measuring their paths by steps. Pedometers work smoothly. The teacher should measure the lengths of steps of their students. Each student has a different length of step. The teacher should take measurements before hiking. Students have to measure the length of the path which they travelled at medium speed. This method requires a measuring tape. The method We measure a section at least 20 meters long. Then each student has to go along that section counting their steps. Take your average speed or the way you plan to go during the hike because your walking speed is changing step length. Discuss what you will do if there is an incomplete step left at the end. You can skip the left section if it is small or add one more step if the section is near the full step, or you can count with the number expressed with the decimal fraction also. Let the students decide for themselves how to deal with this situation, and experiment and justify their opinion. So, we have the length of the step linked with the hiking speed.

One ancient rule speaks about walking speed. A person hikes the same kilometres per hour as a number of steps per 3 seconds. It is needed to mention that the rule is correct only for a certain step length. Even more, it is quite a large step. Let’s count. Let the length of the step be equal to a. The number of steps is equal to n. Then during the 3 seconds, a person will go n x a metres. During an hour n x a x 3600 sec = 1200 m = 1.2 km. Then let’s make an equation: 1.2 x n x a = n; 1.2 x a = 1; a = 0.83 m. We got the length of the step equal to 83 centimetres. Using the first rule about the length of the step and human height, we can say, that the person should be about 175 cm tall. Once you have found human footprints you can measure the distance between the footprints and roughly determine how tall the pedestrian was by using these rules. Wondering, isn't it? During the tour, it is quite interesting to apply such a calculation.

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Three-dimensional printing

1. Key chain with the first letter of the student’s name.

Subjects/area: engineering, ergonomics, design.

Duration: from 1 to 3 academic hours.

The task: to create a model on the tinkercad platform and get it as an stl file. With the teacher's help, send the file for printing. Print the model.

Pupils' abilities: spatial sense, creativity.

Required tools:

• A computer with a connected 3D printer installed software and internet connection;

• Tinkercad environment access for the student.

 Students can create key rings in different shapes. The main parts of the pattern are the letter and the ring for fastening. Both of these parts are found in base forms. It teaches how to align two models with a special tool and combine them into one model. Advanced students can be given a chance of making pendants of more complex shapes. My students created pendants with the letter π that were distributed to the students to celebrate was is called international “π day” at school.

 Students save the prepared file in their tinkercad account and download it to their computers as an stl code. Then use the software of the available 3D printer (MakerBot Desktop Software, 3D Slicer or Creality slicer or others). In the beginning, it is advisable for the teacher to do these preparatory works. When using Ender-type printers, the file must be saved in gcode format. Markerboot replicator printers read stl files. Pay attention to the type of filament selected and the printing temperature, which is stated on the product box.

2. Capacity for pencils or other small items.

Subjects/area: engineering, ergonomics.

Duration: from 3 to 5 academic hours. Working time depends on the individual ability of the students and the complexity of the model created.

 Task: To create stl file in the tinkercad environment. Send the file to the computer and print the model with a 3D printer.

 Students' abilities: sketching skills, a certain spatial sense, creativity.

Required tools:

1. a computer with a connected 3D printer and installed software and the Internet;

2. tinkercad environment access for the student;

3. drawing notebook;

4. scissors, knife, glue.

 At first, students draw sketches on paper. Discuss the shape and size with the teacher. Transfers the models to the tinkercad.com environment and adjusts the dimensions, preparing the media for printing. Students can create containers of various shapes to store pencils and other small items. The simplest model is a roll-shaped pencil case which can be found on the right side of the tinkercad platform.  In the beginning, it is suggested to use the shape of a roll or cube and transform it. Save and download the prepared file to your computer with the stl code. Then use the software of the available 3D printer (MakerBot Desktop Software, 3D Slicer or Creality slicer or others). When using Ender-type printers, the file must be saved in gcode format. Markerboot replicator printers read stl files.

3. Modified cube.

Subjects/area: engineering, ergonomics and math.

Duration from 3 to 5 hours.

Task: Create 3 cubes for a maths game. Two cubes are identical, the numbers 10, 25, 50, 100, 200, and 500 are written on their walls. One cube has arithmetic operations +, +, x, x, -, -. Create stl. file in the tinkercad environment. The working time depends on the student's individual abilities and work skills. In the photo, you can see a set of cubes intended for students who study under to the adapted program.

Students' abilities: sketching skills, creativity and certain spatial skills.

Required tools:

1. a computer with a connected 3D printer and installed software and the Internet;

2. tinkercad environment access for the student;

3. drawing notebook;

4. scissors, knife, glue.

At first, students draw sketches on paper. Discuss the numbers and cubes size with the teacher. Transfers the models to the tinkercad.com environment and adjusts the dimensions and prepares the media for printing. The preparation and printing are straightforward. Students can work independently under the supervision of the teacher.

Description of the game:

The essence of the mathematical game is the training of mental calculation

and the completing understanding of the rules of multiplication by 10, 25, 50, 100 or 200. 4-6 players can play. They have to write down their answers. 3 dice are rolled: two with numbers and one with arithmetic operations. Players take turns rolling the dice performing the unfolded arithmetic operation mentally and writing down the answer. Rolling 10 times in a row. The answers are added up, and whoever rolls the highest sum wins. In the picture, you can see several cubes with one "empty" wall. If a player digs out such a wall, he misses his turn.

Students can make cubes for learning a multiplication table or numbers up to 20, which are suitable for students with special needs. In the photo, you can see coloured cubes for teaching the multiplication table.

 Students can also create a number of cubes for learning a foreign language. In this case, the English teacher recommends several sets of English words, with 6 words in each set. The essence of the game is that after rolling 2 or three cubes, you need to come up with an English sentence with these words. It is most interesting to play when there are many different cubes with different words. Then the player simply chooses the cubes themselves and rolls the words. The game is suitable for use during lessons. In the photo, you can see one of the cubes for making English sentences.