Lesson on Divisibility Rules for 10, 5, and 2

MBOU "Secondary General Education School No. 19
with in-depth study of individual subjects"

Signs of divisibility by 10,
5, and 2

Grade 6

Simakova I.N.
Mathematics teacher
MBOU "Secondary School No. 19 with In-depth Study of Individual Subjects"

City of Stary Oskol
Lesson Topic: "Signs of divisibility by 10, by 5, and by 2."
Lesson Objective: To study and initially understand the new learning material, to comprehend the relationships and connections within the objects of study, and to create conditions for conscious and confident use of the divisibility rules for 10, 5, and 2 when solving exercises and problems.

Educational tasks of the lesson:

• To derive the divisibility rules for 10, 5, and 2;

• To apply the divisibility rules in solving exercises and problems;

• To develop skills in mathematical modeling;

Developmental tasks of the lesson:

• To develop the creative aspect of students' thinking;

• To foster the ability to generalize, classify, draw conclusions, and make inferences;

• To enhance the students' communicative competence;

• To create conditions for the manifestation of students' cognitive activity;

Educational tasks of the lesson:

• To cultivate intellectual work culture;

• To foster collective work culture;

• To promote information culture.

Type of lesson:
– Lesson on new material study and initial application of the acquired knowledge.

Lesson Plan:
Organizational moment
Activation of prior knowledge
Slide 1: Which of the concepts written on the board are you familiar with, and can you explain their meanings?

• Divisibility of a product

• Divisibility of a sum

• Divisibility of a difference

• Divisibility rules

It turns out that, in some cases, we can determine if a number is divisible by another without performing calculations, just by looking at the number’s notation.
Would you like to learn more about these cases?
Then, write down the topic of our lesson: "Signs of divisibility by 10, by 5, and by 2."
Formulate the lesson goal.
To get familiar with the divisibility rules for 10, 5, and 2, and learn how to apply them in exercises.

Slide 2
Which of the following numbers do you think are divisible by 10?
34560 42650
65403 53064
65540 30346

Slide 3
Can you prove, without division, that:
34560
42650
65540
are divisible by 10?
Could each of these numbers be written as a product of two factors, and thus we can use the property of divisibility of products?

Slide 4
Thus, by just looking at the number, we can determine whether it is divisible by 10 or not.

Slide 5
Why are numbers like 53064, 30346, 65403 not divisible by 10?
Because the ones place of these numbers does not contain the digit 0, but rather 4, 6, and 3.

Formulate the divisibility rule for 10. (Textbook, p. 9)

Group Work
Group 1 (Slide 7)
Group 2 (Slide 9)

Which numbers are divisible by 5?
Which numbers are divisible by 2?
48732
54270
30876
84785
36781

Prove your statement and formulate the divisibility rule for 5.
Prove your statement and formulate the divisibility rule for 2.
You can ask for a hint.

Slide 11: Self-check
Consolidation
We have studied the divisibility rules for 10, 5, and 2. But why are we learning them?

Slide 12: Independent Work
Variant 1

1. Choose from the numbers 4, 5, 10, 25, 50, 75, 105, 120:
   a) numbers divisible by 2;
   b) odd numbers;
   c) numbers divisible by 5;
   d) numbers divisible by 10.

2. Write all two-digit numbers containing only the digits 2, 4, 5, and:
   a) divisible by 2;
   b) divisible by 5;
   c) divisible by 10.

Variant 2

1. Choose from the numbers 3, 5, 15, 20, 93, 115, 200, 286:
   a) even numbers;
   b) numbers not divisible by 2;
   c) numbers divisible by 5;
   d) numbers divisible by 10.

2. Write all two-digit numbers containing only the digits 3, 5, and 8, which:
   a) are divisible by 2;
   b) are divisible by 5;
   c) are divisible by 10.

Lesson Conclusion
Let’s recall the goal we set at the beginning of the lesson. Did we achieve the goal, and why?
Homework: P. 2, pp. 9-10, pp. 12-13. Nos. 57, 58, additionally: No. 49.