Teacher: Anna Wasiuta
The topic of the lesson: Scientific notation
The duration of the lesson: 45 min
Curriculum: in accordance with the curriculum approved by MEN (The Ministry of National Education)
After the lesson students will be able to:
– read and write very large and very small numbers in the form of a scientific notation,
– solve simple practical math problems with the use of scientific notation in nature
– read and write numbers in the form of a scientific notation,
– convert units of measurement with the use of scientific notation
– solve more complex practical math problems with the use of scientific notation.
Metoda pracy: Metoda ćwiczeniowa, komunikacyjna, podająca, problemowa.
The method: the practical method, the communicative method, the problem method.
Forms of work: together with the entire class
Teaching aids: a blackboard, an interactive whiteboard, a computer, multimedia, tablets, smartphones, a quiz (QUIZIZZ.com, learningaps.org), computer games.
Coursebook: Helena Lewicka, Marianna Kowalczyk „Matematyka wokół nas. Klasa 8”
|Czynności prowadzącego (Lesson Procedures)
|Przewidywane czynności ucznia Students’ actions
|Uwagi po realizacji lekcji (Remarks after the lesson)
|I start a presentation in Power Point and present the topic of the lesson and display it on an interactive whiteboard. SLIDE 1: SCIENTIFIC NOTATION I tells students that today they will learn how to read and write very large and very small numbers in the form of a scientific notation, We will practice it by solving math problems.
|Students write down the topic of the lesson in their notebooks
|SLIDE 2: I explain to my students that the closest star to the sun is Proxima Centauri. Its distance to Earth is about 40 trillion kilometres – an enormous number. In order to simplify these matters, scientists introduced a unit of distance called parsec. The distance from Proxima Centauri to Earth described in parsecs amounts to 1,29. Much easier, isn’t it? SLIDE 3 I play a short scene from the film „Star Wars” and explain that today we will talk about the space and the science notation. SLIDE 4 I display the first part of today’s topic. SLIDE 5 “Let’s travel into space and talk about stars. The brightest star in the night sky is Sirius The second brightest star is Kanopus, visible amongst millions of other stars. Underneath them you can see their distances from the Earth. Tell me, which of the two stars is closer to our planet? How can we compare these two very large numbers? We can compare the number of digits in each number. – The number on the left side consists of 14 digits. What about the one on the right side? – Which one is bigger? It means that the distance between Kanopus and the Earth is bigger than the distance between Sirius and the Earth so Sirius is closer to our planet. As you see, comparing large in astronomy is problematic. Maybe there is an easier way? SLIDE 6 Actually, there is an easier way. The science notation helps us to write large numbers. In science notation we write numbers in the form of a certain product. The first factor of such multiplication is a number which is not lesser than 1 and not greater than 10, raised to a given power. Let’s see how it is done! At the very beginning, we have to find the first non-zero digit (counting from the left side). It is number 8. Next, we put a comma after this number. We multiply the number on the left side by 10 raised to a given power so that it is equal to the number on the right. Then, we count how many digits are after the comma (or how many digits are to the right side of the first non-zero digit. We can see that there are 13 of them so it’s 10 to the power of 13. Pay attention to the fact that after multiplying this number by 10 to the power of 13 we would move the comma by 13 spaces to the right and in this way we would have the number on the left side. The final step is getting rid of these unnecessary zeros. Finally, the distance between Sirius and the Earth in the science notation is written in the following way: Now let’s write the distance between Kanopus and the Earth in the science notation. Do you remember what we did at first? – What number is it? – What next? After number 2 there are 15 digits, so 10 to the power of 15. The next step is getting rid of these unnecessary zeros. What we get is the distance between Kanopus and the Earth in the science notation. Therefore, in order to compare such numbers it is enough to compare their indexes. 1015 > 1013 Let’s take one more star as an example. It’s called Barnard’s Star. Look, this is its distance from the Earth written in the scientific notation (I show it on the slide). – Is this star closer to the Earth than Sirius? Let’s look at the indexes.” I tell my students that in such cases we compare these two numbers before decimals. “So, which one is lesser 8,117 or 5,6272? Therefore, it’s clear to see that Barnard’s Star is closer to the Earth than Sirius. SLIDE 7 Task 1: „Write the following numbers in the scientific notation.”(the answers are displayed in time intervals) “Now, your task is to write the temperature in the centre of the Sun in the scientific notation.” “Remind me, what was the first step?” Now, write the average distance from the Sun in the scientific notation. I ask students to do the remaining part of the task as well. SLIDE 8 Task 2 „Our task is to write numbers in the scientific notation. But they are already written in the form of an index and multiplied by 10 raised to a certain power. REMEMBER: the first number in the scientific notation must be greater than 1 and lesser than 10.” Therefore, we have to correct the mistake. How? We write the number 103 in the scientific notation. E.g. We cannot forget about 102 which is left here. Now, we’ve got the power of the same basis. We add the index and we get 104 . Let’s have a look at the next example: In the third case … We’ve got the comma but we have to put it after a non-zero digit so in this case it is 4. We have to move it by 2 spaces to the left. That’s why we have to multiply this new number by 102 in order to get this number: 435,65. The next example is done by students. Let’s put our results in descending order What attracts your attention? SLIDE 9 (SOLUTION OF THE MATH PROBLEM) SLIDE 10 SUMMARY – a note SLIDE 11 – THE SECOND PART OF THE LESSON Writing small numbers in the form of a scientific notation SLIDE 12 (POLLEN) In the photo you can see pollen in enlargement. With the use of notation we can write very small numbers, too. SLIDE 13 (POWER WITH A NEGATIVE INDEX ) POWER WITH A NEGATIVE INDEX IS THE REVERSE OF THE POWER WITH THE SAME BASE AND AN OPPOSITE INDEX SLIDE 15 Let’s think about the pollen one again. An average diameter of such a pollen can be written in this way: At the beginning we have a certain number, it is not lesser than 1 and lesser than 10 which is multiplied by 10 and raised to a certain power. To what power should we raise 10 ? To -3 What number was written in this notation? Let’s try to read it, we can write 10 to -3 as: So we have to divide 4 by 10 to the third power. 10 to the third power equals 1000 4 divided by 1000 equals 0,004 If we divide a number by the tenth power, we have to move the comma to the left by as many spaces as there are zeros in this number. 1000 has got 3 zeros, so when we start from 4, we have to move the comma by 3 spaces to the left. . SLIDE 16 (THE FLU VIRUS) Do you know what it is? It is a spherical virus A single flu virus can have a diameter of : How can we change the scientific notation into a decimal? The same way as previously. By how many spaces should we move the comma? SLIDE 16 There are 4 numbers in the scientific notation. Now, change them into a decimal. SLIDE 17 I display the solutions to the math problems. SLIDE 18 SLIDE 19 (LET’S SOLVE SOME MATHS PROBLEMS) Students log into the websites shown by the teacher and take part in a quiz. Teacher displays the answers on the board. SLIDE 20 – TASK 1 SLIDE 21 – TASK 2 SLIDE 22 Students watch a film (in English) about the role of the scientific notation in nature. https://www.youtube.com/watch?v=44cv416bKP4
|Students watch a film about Maths in outer space. Students give answers: – the one on the right consists of 16 digits. – The one with the largest number of digits. Students listen to the teacher carefully and observe the slides. Students think about the way greater numbers should be written in the scientific notation. Students answer: – We were looking for the first non-zero digit. – It’s 2. – next, we put a comma after this digit and multiplied this number by 10 to a certain power Students answer: – Here we’ve got 1013 and here also 1013 – the lesser one is 5,6272 Students answer. After some time I display the correct answer on the board. We should look for the first non-zero digit. Here it’s number 1 so we put a comma after it. Next, we count the number of digits after this comma. We’ve got 7 digits so it’s 10 to the power of 7. Then, we get rid of unnecessary zeros and we get the temperature in the centre of the Sun in the scientific notation. Each student solves the problems individually. After some time we write the results on the board. In other examples in this task students write the estimated age of the universe and the mass of the Moon in the scientific notation. Students take notes Students do the task and give their answers Students answer: – on the indexes 109,108,107,105,104 Students answer: When we multiply it by 1,2, we get the following fraction: We will move it by 5 digits, counting from 2. Students log into the websites shown by the teacher and take part in a quiz Students complete slide 20 Students watch a film (in English) about the role of the scientific notation in nature.
|I reward students’ engagement with pluses I give my students some hints I monitor the work of my students Students seem to understand the topic. They didn’t have many problems with answering teacher’s questions.
|I revise the material from today’s classes I set and explain the homework SLIDE 21
|Students answer my questions