What is a set? What is an element of a set? What are contents of Lession 1 about "Set" of grade 6 Maths in Vietnam?

What is a set? What is an element of a set? What are contents of Lession 1 about "Set" of grade 6 Maths in Vietnam?

The concept of a set is commonly encountered in mathematics as well as in life. A set includes elements that share one or a few common properties.

Example: “The set of natural numbers divisible by 3 and less than 20”: This is the set of natural numbers that satisfy two properties: being divisible by 3 and being less than 20.

Set notation: A set is denoted by a capital letter. The elements are recorded within two curly braces { }, separated by commas, or semicolons.

Example: a is an element of set X denoted as a ∈ X.

An element of a set is any one of the distinct objects that make up that set. A set can have one element, many elements, an infinite number of elements, or it can have no elements.

A set with no elements is called a null set. The null set is denoted ∅

Ways to describe a set: There are 2 ways to describe a set:

Method 1: Listing the elements of the set

Example: B = {0; 2; 4; 6; 8}

Method 2: Indicating the characteristic properties of the elements of the set

Example: B = {x | x is an even natural number, x < 10}

Types of exercises related to sets

Type 1: Writing a set

Example: Write set A of natural numbers greater than 5 and less than 15 in two ways.

Answer:

Method 1: Listing the elements of the set

The set A of natural numbers greater than 5 and less than 10 is: A = {6; 7; 8; 9; 10; 11; 12; 13; 14}

Method 2: Indicating the characteristic properties of the elements of the set.

The set A of natural numbers greater than 5 and less than 10 is: A = {x "belongs to" N | 5 < x < 15}

Type 2: Determining the number of elements in a set

Example: Calculate the number of elements in set A consisting of consecutive even natural numbers from 1990 to 3000.

Answer: The consecutive even natural numbers from 1990 to 3000 differ by 2 units. Therefore, the number of elements in set A is: (3000 - 1990) / 2 + 1 = 506 elements.

Type 3: Subset

Example 1: Given set A = {Grapes; Plums; Persimmons; Peaches}. Write all the subsets of A with 3 elements.

Answer: The subsets with 3 elements of A are: {Grapes; Plums; Persimmons}, {Grapes; Plums; Peaches}, {Plums; Persimmons; Peaches}, {Grapes; Persimmons; Peaches}.

What is a set? What is an element of a set? What are contents of Lession 1 about "Set" of grade 6 Maths in Vietnam? (Image from the Internet)

What are required achievements in natural number content for Math 6 in Vietnam?

Based on the General Education Program in Mathematics issued with Circular 32/2018/TT-BGDDT, the required achievements in the natural number content for Math 6 are as follows:

Content of natural numbers and the set of natural numbers. Order in the set of natural numbers

- Be able to use the terms set, element belonging (not belonging) to a set; be able to use the ways to describe a set.

- Recognize the set of natural numbers.

- Represent natural numbers in the decimal system.

- Represent natural numbers from 1 to 30 using Roman numerals.

- Recognize (relations) order in the set of natural numbers; compare two given natural numbers.

Content of operations with natural numbers. Exponentiation with natural exponents:

- Carry out operations: addition, subtraction, multiplication, and division within the set of natural numbers.

- Apply commutative, associative, and distributive properties of multiplication over addition in calculations.

- Perform exponentiation with natural exponents; perform multiplication and division of two powers with the same base raised to natural exponents.

- Recognize the order of operations.

- Apply properties of operations (including exponentiation with natural exponents) to mental calculation and quick calculation in a reasonable way.

- Solve practical problems associated with operations (for example: calculate shopping expenses, determine the amount of goods that can be purchased with available money,...)

Content of divisibility in the set of natural numbers. Prime numbers. Greatest common divisor and least common multiple

- Recognize the relationship of divisibility, the concept of divisor and multiple.

- Apply divisibility rules for 2, 5, 9, 3 to determine if a given number is divisible by 2, 5, 9, 3.

- Recognize the concept of prime numbers, composite numbers.

- Perform factorization of a natural number greater than 1 into a product of prime factors in simple cases.

- Determine the greatest common divisor, least common multiple; recognize simplest fractions; perform addition and subtraction of fractions using greatest common divisor and least common multiple.

- Recognize division with remainder, theorem on division with remainder.

- Apply arithmetic knowledge to solve practical problems (for example: calculate money or amount of goods when shopping, determine the necessary items to arrange them according to given rules,...).

How to calculate the average score for Math 6 in Vietnam?

According to Article 9 of Circular 22/2021/TT-BGDDT, the method to calculate the average score for Math 6 is as follows:

- The semester average score for Math 6 (hereinafter referred to as SA) for each subject is calculated as follows:

Total continuous assessment points: Sum of continuous assessment points.

- The full year average score for Math 6 is calculated as follows:

SA1: Semester 1 average score.

SA2: Semester 2 average score.