Goals:
- To introduce students to the concept of a ray as an infinite figure;
- Learn to show a beam with a pointer;
- Continue the formation of computational skills;
- Improve the ability to solve problems;
- Develop the ability to analyze and generalize.
During the classes
I. Organizing time.
Guys, are you ready for the lesson? ( Yes. )
I hope for you, friends!
You are a good friendly class.
Everything will work out for you!
II. Motivation of educational activity.
I really want the lesson to be interesting, informative, so that together we repeat and consolidate what we already know and try to discover something new for ourselves.
III.Knowledge update.
- Read the numbers and name the "extra" number in each row:
a) 90, 30, 40, 51.60;
b) 88, 64,55,11, 77, 33;
c) 47, 27, 87, 74, 97, 17; - List the numbers in order:
a) from 20 to 30;
b) from 46 to 57;
c) from 75 to 84; - Do you think these texts will be tasks?
Change the question of the second text so that it becomes a challenge.
Change the condition so that the text becomes a task.
Solve the given problems.
IV. Primary assimilation of new knowledge.
Draw such a line.
What is it called?
Draw such a line.
What is it called? How is a segment different from a straight line?
Draw such a line.
Who knows what it's called?
Look at the picture, you see similar lines, what is it?
This line is called a beam. How is it different from a straight line and a line segment?
This is a very interesting figure: it has a beginning and no end.
And they portray it like this. ( Work on the board and in notebooks.) Mark a point, attach a ruler to it and draw a line along the ruler.
No matter how long the ruler is, we still cannot draw the entire beam. In the figure, we have depicted only a part of the beam, which shows the direction of the beam.
A ray can be drawn in any direction:
Draw three different rays in your notebook.
In order to distinguish one ray from another, we will agree to designate a ray with two letters of the Latin alphabet in the same way as we denoted segments with you. You need to write letters in a strictly defined order: the first letter is written that indicates the beginning of the beam, the second is written above or below the beam.
Look at the picture in the textbook. The red beam is indicated by two letters. What letter indicates the beginning of the beam?
Let's read together the entry: "Ray AB"
Now read the following entries: ray BC, ray MK, ray BA, ray OH.
It is important to learn how to correctly show the beam. We will do this with the end of the pointer. ( Show by teacher.)
Now look at the poster. ( Prepared in advance, it has 3 beams.) It shows 3 beams. Read the title of each one. When naming a ray, indicate it with a pointer.
Fizminutka
1, 2, 3, 4, 5
We all know how to count.
We can also take a break.
Put your hands behind your back
Let's raise our heads higher
And let's breathe easy.
One, two - above the head,
Three, four - legs wider,
Five, six - quiet network.
One - get up, stretch.
Two - bend, unbend.
Three - in the hands of three claps,
Three head nods.
Four - arms wider.
Five - wave your hands.
Six - sit quietly at the desk.
v.Initial test of understanding.
1) Work with the textbook.
Is it possible to draw the whole ray?
In what direction can a ray be drawn?
Students name each ray by first reading the letter corresponding to the beginning of the ray.
Students draw a beam in a notebook, designate it with letters.
Put point O in your notebook. Draw a straight line through it. How many rays?
Draw another straight line through this point. How many rays now?
VI. Organization of the assimilation of methods of activity.
1) Work in a notebook on a printed basis.
differentiated task.
1st group - No. 19
2nd group - No. 20
3rd group - No. 21
2) Fizminutka - ophthalmic trainer.
3) Textbook work
Read what addition methods did Znayka come up with?
Find the results of addition in the same way.
What is known about the problem?
What do you need to know?
In short, is it more or less?
How to find out the length of a pencil?
Write down the answer.
VII. Reflection.
What new did you learn in the lesson?
What is a beam?
How to draw a ray
How many rays can pass through one point?
Helped me in class today...
VIII. Homework.
We will look at each of the topics, and at the end there will be tests on the topics.
Point in math
What is a point in mathematics? A mathematical point has no dimensions and is indicated by capital Latin letters: A, B, C, D, F, etc.
In the figure, you can see the image of points A, B, C, D, F, E, M, T, S.
Segment in mathematics
What is a segment in mathematics? In mathematics lessons, you can hear the following explanation: a mathematical segment has a length and ends. A segment in mathematics is a set of all points lying on a straight line between the ends of a segment. The ends of the segment are two boundary points.
In the figure we see the following: segments ,,,, and , as well as two points B and S.
Straight lines in mathematics
What is a straight line in mathematics? Definition of a straight line in mathematics: a straight line has no ends and can continue in both directions to infinity. A straight line in mathematics is denoted by any two points on a straight line. To explain the concept of a straight line to a student, we can say that a straight line is a segment that does not have two ends.
The figure shows two straight lines: CD and EF.
Ray in mathematics
What is a ray? Definition of a ray in mathematics: A ray is a part of a line that has a beginning and no end. The name of the beam contains two letters, for example, DC. Moreover, the first letter always indicates the point of the beginning of the beam, so you cannot swap the letters.
The figure shows the beams: DC, KC, EF, MT, MS. Beams KC and KD - one beam, because they have a common origin.
Number line in mathematics
Definition of a number line in mathematics: A line whose points mark numbers is called a number line.
The figure shows a number line, as well as a ray OD and ED
The ray and the straight line are among the basic geometric elements. Information about them is given already at the first stage of studying the corresponding section of mathematics. How is a ray different from a straight line? Information about this is provided below.
Definition
Ray- this is a half-line, on the one hand emanating from a specific point, on the other - not limited by anything.
Straight- this is a line that is infinite on both sides, passing through any two points and not changing its direction (unlike a curve or a broken line).
Straight Comparison
It can be seen from the definitions that the fundamental difference between a ray and a straight line is whether they are limited in space. So, the beam necessarily has a beginning and continues only on one side. The straight line, in turn, has no limit on either side. In this regard, only a part of it can be drawn, which, by the way, also applies to the beam.
If we take an arbitrary point on a straight line, then an infinite line extending from it will be a ray. In this sense, a ray can be called a part of a straight line. It is also true that the chosen point will serve as the starting point for two oppositely directed rays at once.
Comparing a ray and a straight line, it should be said about the ways of designating them. Each of the geometric objects can be called a small Latin letter: a ray a (c, d, t) or a straight line b (a, h, c). Also, in both cases, the designation is used in two capital letters: a beam NK or a straight line OD.
However, there are differences in the last paragraph. The letters in the name of the line, marking the points through which it is drawn, can be interchanged when reading and writing. Meanwhile, relative to the ray, the first point is strictly its beginning, and then the point located at a certain distance from the original one.
In addition, the beam has its own designation. In this case, after the capital character naming the starting point, the straight line on which the ray is located is indicated with a lowercase letter. Thus, the notation Bo is interpreted as follows: the ray with origin at the point B belongs to the line o.
What is the difference between a ray and a straight line, other than that? The fact that the rays can form an angle. To do this, they must come from the same point. Right angles do not form.
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Books
- A set of tables. Geometry. 7th grade. 14 tables + methodology, . The tables are printed on thick polygraphic cardboard measuring 680 x 980 mm. The kit includes a brochure with methodological recommendations for teachers. Educational album of 14 sheets. Beam and angle...
