Subject. Laws of arithmetic operations: commutative, associative, distributive
Lesson type. Lesson for the initial presentation of new knowledge.
Subject UUD. Learn to write down the laws of mathematical operations using formulas and give a verbal formulation of the law
Metasubject UUD. Communicative: develop the ability to exchange knowledge between classmates to make effective joint decisions.
Regulatory: plan your action in accordance with the task.Cognitive: be able to identify essential information from different types of texts
Personal UUD. Formation of cognitive interest
Lesson plan:
Plan:
1. Organizational moment.
2. Checking previously studied material.
3. Studying new material.
4. Primary test of knowledge acquisition (working with a textbook).
5. Monitoring and self-testing of knowledge (independent work).
6. Homework
7. Reflection.
Lesson script
Lesson stage
Teacher activities
Student activity
1.Organizing moment
Hello guys!
It's time for us to start our lesson.
It's time to calculate.
And to difficult questions
You can give the answer!
Math, friends,
Absolutely everyone needs it.
Work diligently in class
And success is sure to await you!
Getting ready for the lesson
Answer: Mathematics
2.
Checking previously studied material.
S=Vt
Perimeter of a rectangle
P=2(a+b)
Area of a rectangle
S=ab
Distance traveled
- Open your notebooks, sign the number, great job.Pay attention to the screen
1) a=8cm
h=13cm
2)V=70km/h
t=5h
3) a=17m
b=24m
4) S=300 km
t=6 h
5) S=420 km
V=70km/h
S=?
S=?
P=?
V=?
t=?
- We work orally on the next slide.(5 slide).
12 + 5 + 8
25 10
250 – 50
200 – 170
30 + 15
45: 3
15 + 30
45 – 17
28 25 4
Task: find the meaning of expressions.(One student works at the screen.)
– What interesting things did you notice while solving the examples? What examples should you pay special attention to?(Children's answers.)
Problem situation
– What properties of addition and multiplication do you know from elementary school? Can you write them using alphabetic expressions? (Children's answers).
Calculate orally
A formula is an equality that is a recording of the rule for calculating a quantity.
Write down the answers in your notebook. Now turn your attention to the “Test yourself” slide.(4 slide).
Test yourself
104 cm 2
350 km
82 m
50 km/h
6 hours
3.Communication of the topic and purpose of the lesson
– And so, the topic of today’s lesson is “Laws of Arithmetic Operations”(6 slide).
– Write down the topic of the lesson in your notebook.
– What new should we learn in class? (The goals of the lesson are formulated together with the children.)
Application of formulas in solving problems
Formulas for perimeter and area of figures, path
4.
Learning new material.
In class 11D and 12M, how many students are there in total?
How to find out the answer? If by d+m or m+d the result will change?
What conclusion can we draw?
5 pears, 7 bananas and 3 apples were placed in a vase. Can you find out the cost of all fruits?
– We look at the screen.(7 slide) .
Laws of addition
Equality
Example
Traveling
a + b = b + a
7 + 3 = 3 + 7
Conjunctive
(a + b) + c = a + (b + c)
(48 + 3) + 12 = (48 + 12) + 3 = 63
You see the laws of addition written in letter form and examples. (Analysis of examples).
I show on the board 27+148+13=188
124+371+429+346=800+470=1270
Now you try
Well done!
Answer questions
Yes
One student per column
The student works at the blackboard and the rest are in notebooks.
83346+140458+91054 =
107888+32012+213355=
70+90+130+10=
5427+6328+10023+612=
5. Physical training
Close your eyes, relax your body,
Imagine - you are a bird, you suddenly fly!
Now you are swimming in the ocean like a dolphin,
Now you are picking ripe apples in the garden.
Left, right, looked around,
Open your eyes and get back to business!
Followed by the teacher
6. Primary test of knowledge acquisition (working with a textbook)..
№213 consider, verbally 214
At the board we calculate in a convenient way
5*328*12 756*25*4
50*(346*2) 8*(956*125)
7. . Control and self-test of knowledge (independent work).
Option 1.
Option 2.
Complete individually and submit for testing and assessment for the next lesson.
8.Homework
R.t., 212, 214
9. Reflection
From rearranging terms...
From rearranging multipliers...
To multiply the difference by a number, you need...What conclusions did you draw from the lesson?
Thanks everyone for the lesson. Goodbye
Today in class:
A. I found out……
Q. I liked it….
S. I didn’t like it….
D. It was difficult for me….
Match the formulas
S=Vt
Perimeter of a rectangle
P=2(a+b)
Area of a rectangle
S=ab
Distance traveled
2.Fill out the table
1) a=8 cm
V =13 cm
2)V=70 km / h
t=5 h
3) a=17 m
b=24 m
4) S=300 km
t=6 h
5) S=420 km
V=70 km / h
S=?
S=?
P=?
V=?
t=?
Calculate
83346+140458+91054 =
107888+32012+213355=
7893+456342+300758126+319+434+551=
70+90+130+10=
5427+6328+10023+612=
Calculate in a convenient way
5*328*12 756*25*4
50*(346*2) 8*(956*125)
Independent work
A) 25∙4∙86 b) 176+24+8 V) 4∙5∙333
G) (977+23)∙49 d)(202-102)∙87
6. Continue the sentence
From rearranging terms...
If we add a third term to the sum of two terms, then...
From rearranging multipliers...
If the product of two factors is multiplied by a third factor, then...
To multiply a sum by a number, you need...
1. Match the formulas
S=Vt
Perimeter of a rectangle
P=2(a+b)
Area of a rectangle
S=ab
Distance traveled
2.Fill out the table
1) a=8 cm
V =13 cm
2)V=70 km / h
t=5 h
3) a=17 m
b=24 m
4) S=300 km
t=6 h
5) S=420 km
V=70 km / h
S=?
S=?
P=?
V=?
t=?
Calculate
83346+140458+91054 =
107888+32012+213355=
7893+456342+300758126+319+434+551=
70+90+130+10=
5427+6328+10023+612=
Calculate in a convenient way
5*328*12 756*25*4
50*(346*2) 8*(956*125)
Independent work
A) 25∙4∙86 b) 176+24+8 V) 4∙5∙333
G) (977+23)∙49 d)(202-102)∙87
6. Continue the sentence
From rearranging terms...
If we add a third term to the sum of two terms, then...
From rearranging multipliers...
If the product of two factors is multiplied by a third factor, then...
To multiply a sum by a number, you need...
Topic No. 1.
Real numbers. Numerical expressions. Converting Numeric Expressions
I. Theoretical material
Basic Concepts
· Natural numbers
· Decimal notation of number
· Opposite numbers
· Integers
· Common fraction
Rational numbers
· Infinite decimal
· Period of number, periodic fraction
· Irrational numbers
· Real numbers
Arithmetic operations
Numeric expression
· Expression value
· Conversion of a decimal fraction to an ordinary fraction
Converting a fraction to a decimal
Conversion of a periodic fraction into an ordinary fraction
· Laws of arithmetic operations
· Signs of divisibility
Numbers used when counting objects or to indicate the serial number of an object among similar objects are called natural. Any natural number can be written using ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This notation of numbers is called decimal
For example: 24; 3711; 40125.
The set of natural numbers is usually denoted N.
Two numbers that differ from each other only by sign are called opposite numbers.
For example, numbers 7 and – 7.
The natural numbers, their opposites, and the number zero make up the set whole Z.
For example: – 37; 0; 2541.
Number of the form , where m – integer, n – natural number, called ordinary fraction. Note that any natural number can be represented as a fraction with a denominator of 1.
For example: , .
The union of sets of integers and fractions (positive and negative) constitutes a set rational numbers. It is usually denoted Q.
For example: ; – 17,55; .
Let the given decimal fraction be given. Its value will not change if you add any number of zeros to the right.
For example: 3,47 = 3,470 = 3,4700 = 3,47000… .
Such a decimal is called an infinite decimal.
Any common fraction can be represented as an infinite decimal fraction.
A sequentially repeated group of digits after the decimal point in a number is called period, and an infinite decimal fraction having such a period in its notation is called periodic. For brevity, it is customary to write a period once, enclosing it in parentheses.
For example: 0,2142857142857142857… = 0,2(142857).
2,73000… = 2,73(0).
Infinite decimal non-periodic fractions are called irrational numbers.
The union of the sets of rational and irrational numbers constitutes the set valid numbers. It is usually denoted R.
For example: ; 0,(23); 41,3574…
Number 
is irrational.
For all numbers, the actions of three steps are defined:
· Stage I actions: addition and subtraction;
· Stage II actions: multiplication and division;
· Stage III actions: exponentiation and root extraction.
An expression made up of numbers, arithmetic symbols and parentheses is called numeric.
For example: 
; .
The number obtained as a result of performing actions is called the value of the expression.
Numeric expression doesn't make sense, if it contains division by zero.
When finding the value of the expression, the actions of stage III, stage II and at the end of the action of stage I are performed sequentially. In this case, it is necessary to take into account the placement of brackets in the numerical expression.
Converting a numerical expression consists of sequentially performing arithmetic operations on the numbers included in it using the appropriate rules (the rule for adding ordinary fractions with different denominators, multiplying decimals, etc.). Tasks for converting numerical expressions in textbooks are found in the following formulations: “Find the value of a numerical expression”, “Simplify a numerical expression”, “Calculate”, etc.
When finding the values of some numerical expressions, you have to perform operations with different types of fractions: ordinary, decimal, periodic. In this case, it may be necessary to convert an ordinary fraction to a decimal or perform the opposite action - replace the periodic fraction with an ordinary one.
To convert decimal to common fraction, it is enough to write the number after the decimal point in the numerator of the fraction, and one with zeros in the denominator, and there should be as many zeros as there are digits to the right of the decimal point.
For example: ; .
To convert fraction to decimal, you need to divide its numerator by its denominator according to the rule for dividing a decimal fraction by a whole number.
For example: 
;
;
.
To convert periodic fraction to common fraction, necessary:
1) from the number before the second period, subtract the number before the first period;
2) write this difference as a numerator;
3) write the number 9 in the denominator as many times as there are numbers in the period;
4) add as many zeros to the denominator as there are digits between the decimal point and the first period.
For example: 
; 
.
Laws of arithmetic operations on real numbers
1. Traveling(commutative) law of addition: rearranging the terms does not change the value of the sum:
2. Traveling(commutative) law of multiplication: rearranging the factors does not change the value of the product:
3. Conjunctive(associative) law of addition: the value of the sum will not change if any group of terms is replaced by their sum:
4. Conjunctive(associative) law of multiplication: the value of the product will not change if any group of factors is replaced by their product:
.
5. Distribution(distributive) law of multiplication relative to addition: to multiply a sum by a number, it is enough to multiply each addend by this number and add the resulting products:
Properties 6 – 10 are called absorption laws 0 and 1.
Signs of divisibility
Properties that allow, in some cases, without dividing, to determine whether one number is divisible by another, are called signs of divisibility.
Test for divisibility by 2. A number is divisible by 2 if and only if the number ends in even number. That is, at 0, 2, 4, 6, 8.
For example: 12834; –2538; 39,42.
Test for divisibility by 3. A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
For example: 2742; –17940.
Test for divisibility by 4. A number containing at least three digits is divisible by 4 if and only if the two-digit number formed by the last two digits of the given number is divisible by 4.
For example: 15436; –372516.
Divisibility test by 5. A number is divisible by 5 if and only if its last digit is either 0 or 5.
For example: 754570; –4125.
Divisibility test by 9. A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
For example: 846; –76455.
REFERENCE MATERIAL ON MATHEMATICS FOR GRADES 1-6.
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- a+b=c, where a and b are terms, c is the sum.
- To find the unknown term, you need to subtract the known term from the sum.
- a-b=c, where a is the minuend, b is the subtrahend, c is the difference.
- To find the unknown minuend, you need to add the subtrahend to the difference.
- To find the unknown subtrahend, you need to subtract the difference from the minuend.
- a·b=c, where a and b are factors, c is the product.
- To find an unknown factor, you need to divide the product by the known factor.
- a:b=c, where a is the dividend, b is the divisor, c is the quotient.
- To find the unknown dividend, you need to multiply the divisor by the quotient.
- To find an unknown divisor, you need to divide the dividend by the quotient.
- a+b=b+a(commutative: rearranging the terms does not change the sum).
- (a+b)+c=a+(b+c)(combinative: in order to add a third number to the sum of two terms, you can add the sum of the second and third to the first number).
- 1+9=10; 2+8=10; 3+7=10; 4+6=10; 5+5=10; 6+4=10; 7+3=10; 8+2=10; 9+1=10.
- 1+19=20; 2+18=20; 3+17=20; 4+16=20; 5+15=20; 6+14=20; 7+13=20; 8+12=20; 9+11=20; 10+10=20; 11+9=20; 12+8=20; 13+7=20; 14+6=20; 15+5=20; 16+4=20; 17+3=20; 18+2=20; 19+1=20.
- a·b=b·a(commutative: rearranging the factors does not change the product).
- (a b) c=a (b c)(combinative: to multiply the product of two numbers by a third number, you can multiply the first number by the product of the second and third).
- (a+b)c=ac+bc(distributive law of multiplication relative to addition: in order to multiply the sum of two numbers by a third number, you can multiply each term by this number and add the resulting results).
- (a-b) c=a c-b c(distributive law of multiplication relative to subtraction: in order to multiply the difference of two numbers by a third number, you can multiply the minuend and subtract by this number separately and subtract the second from the first result).
- Divider natural number A name the natural number to which A divided without remainder. (The numbers 1, 2, 3, 4, 6, 8, 12, 24 are divisors of the number 24, since 24 is divisible by each of them without a remainder) 1 is the divisor of any natural number. The greatest divisor of any number is the number itself.
- Multiples natural number b is a natural number that is divisible by b. (The numbers 24, 48, 72,... are multiples of the number 24, since they are divisible by 24 without a remainder). The smallest multiple of any number is the number itself.
Divisibility criteria for natural numbers.
- The numbers used when counting objects (1, 2, 3, 4,...) are called natural numbers. The set of natural numbers is denoted by the letter N.
- Numbers 0, 2, 4, 6, 8 called even in numbers. Numbers that end in even digits are called even numbers.
- Numbers 1, 3, 5, 7, 9 called odd in numbers. Numbers that end in odd digits are called odd numbers.
- Test for divisibility by number 2. All natural numbers ending in an even digit are divisible by 2.
- Test for divisibility by number 5. All natural numbers ending in 0 or 5 are divisible by 5.
- Divisibility test for the number 10. All natural numbers ending in 0 are divisible by 10.
- Test for divisibility by number 3. If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3.
- Divisibility test for the number 9. If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
- Test for divisibility by number 4. If a number made up of the last two digits of a given number is divisible by 4, then the given number itself is divisible by 4.
- Divisibility test for the number 11. If the difference between the sum of the digits in odd places and the sum of the digits in even places is divisible by 11, then the number itself is divisible by 11.
- A prime number is a number that has only two divisors: one and the number itself.
- A number that has more than two divisors is called composite.
- The number 1 is neither a prime number nor a composite number.
- Writing a composite number as a product of only prime numbers is called factoring a composite number into prime factors. Any composite number can be uniquely represented as a product of prime factors.
- The greatest common divisor of given natural numbers is the largest natural number by which each of these numbers is divided.
- The greatest common divisor of these numbers is equal to the product of the common prime factors in the expansions of these numbers. Example. GCD(24, 42)=2·3=6, since 24=2·2·2·3, 42=2·3·7, their common prime factors are 2 and 3.
- If natural numbers have only one common divisor - one, then these numbers are called relatively prime.
- The least common multiple of given natural numbers is the smallest natural number that is a multiple of each of the given numbers. Example. LCM(24, 42)=168. This is the smallest number that is divisible by both 24 and 42.
- To find the LCM of several given natural numbers, you need to: 1) decompose each of the given numbers into prime factors; 2) write out the decomposition of the larger number and multiply it by the missing factors from the decomposition of other numbers.
- The least multiple of two relatively prime numbers is equal to the product of these numbers.
b- the denominator of the fraction shows how many equal parts it is divided into;
a-the numerator of the fraction shows how many such parts were taken. The fraction bar means the division sign.
Sometimes instead of a horizontal fractional line they put an oblique line, and an ordinary fraction is written like this: a/b.
- U proper fraction the numerator is less than the denominator.
- U improper fraction the numerator is greater than the denominator or equal to the denominator.
If the numerator and denominator of a fraction are multiplied or divided by the same natural number, you get an equal fraction.
Dividing both the numerator and denominator of a fraction by their common divisor other than one is called reducing the fraction.
- A number consisting of an integer part and a fractional part is called a mixed number.
- To represent an improper fraction as a mixed number, you need to divide the numerator of the fraction by the denominator, then the incomplete quotient will be the integer part of the mixed number, the remainder will be the numerator of the fractional part, and the denominator will remain the same.
- To represent a mixed number as an improper fraction, you need to multiply the integer part of the mixed number by the denominator, add the numerator of the fractional part to the resulting result and write it in the numerator of the improper fraction, leaving the denominator the same.
- Beam Oh with the starting point at the point ABOUT, on which are indicated single cut to and direction, called coordinate beam.
- The number corresponding to the point of the coordinate ray is called coordinate this point. For example , A(3). Read: point A with coordinate 3.
- Lowest common denominator ( NCD) of these irreducible fractions is the least common multiple ( NOC) denominators of these fractions.
- To reduce fractions to the lowest common denominator, you need to: 1) find the least common multiple of the denominators of the given fractions, it will be the lowest common denominator. 2) find an additional factor for each fraction by dividing the new denominator by the denominator of each fraction. 3) multiply the numerator and denominator of each fraction by its additional factor.
- Of two fractions with the same denominator, the one with the larger numerator is greater, and the one with the smaller numerator is smaller.
- Of two fractions with the same numerators, the one with the smaller denominator is greater, and the one with the larger denominator is smaller.
- To compare fractions with different numerators and different denominators, you must reduce the fractions to their lowest common denominator and then compare fractions with the same denominators.
- To add fractions with the same denominators, you need to add their numerators and leave the denominator the same.
- If you need to add fractions with different denominators, first reduce the fractions to the lowest common denominator, and then add the fractions with the same denominators.
- To subtract fractions with like denominators, subtract the numerator of the second fraction from the numerator of the first fraction, leaving the denominator the same.
- If you need to subtract fractions with different denominators, then they are first brought to a common denominator, and then fractions with the same denominators are subtracted.
- When performing addition or subtraction operations on mixed numbers, these operations are performed separately for the whole parts and for the fractional parts, and then the result is written as a mixed number.
- The product of two ordinary fractions is equal to a fraction whose numerator is equal to the product of the numerators, and the denominator is equal to the product of the denominators of these fractions.
- To multiply a common fraction by a natural number, you need to multiply the numerator of the fraction by this number, but leave the denominator the same.
- Two numbers whose product is equal to one are called reciprocal numbers.
- When multiplying mixed numbers, they are first converted to improper fractions.
- To find a fraction of a number, you need to multiply the number by that fraction.
- To divide a common fraction by a common fraction, you need to multiply the dividend by the reciprocal of the divisor.
- When dividing mixed numbers, they are first converted into improper fractions.
- To divide a common fraction by a natural number, you need to multiply the denominator of the fraction by this natural number, and leave the numerator the same. ((2/7):5=2/(7·5)=2/35).
- To find a number by its fraction, you need to divide the number corresponding to it by this fraction.
- A decimal fraction is a number written in the decimal system and having digits less than one. (3.25; 0.1457, etc.)
- The places after the decimal point in a decimal fraction are called decimal places.
- The decimal will not change if you add or remove zeros at the end of the decimal.
To add decimal fractions, you need to: 1) equalize the number of decimal places in these fractions; 2) write them down one after the other so that the comma is written under the comma; 3) perform the addition, not paying attention to the comma, and put a comma in the sum under the commas in the added fractions.
To subtract decimal fractions, you need to: 1) equalize the number of decimal places in the minuend and the subtrahend; 2) sign the subtrahend under the minuend so that the comma is under the comma; 3) perform the subtraction without paying attention to the comma, and in the resulting result place a comma under the commas of the minuend and the subtrahend.
- To multiply a decimal fraction by a natural number, you need to multiply it by this number, ignoring the comma, and in the resulting product, separate as many digits to the right with a comma as there were after the decimal point in this fraction.
- To multiply one decimal fraction by another, you need to perform the multiplication, not paying attention to the commas, and in the resulting result, separate as many digits on the right with a comma as there were after the decimal points in both factors together.
- To multiply a decimal fraction by 10, 100, 1000, etc., you need to move the decimal point to the right by 1, 2, 3, etc. digits.
- To multiply a decimal by 0.1; 0.01; 0.001, etc. you need to move the decimal point to the left by 1, 2, 3, etc. digits.
- To divide a decimal fraction by a natural number, you need to divide the fraction by this number, as natural numbers are divided, and put a comma in the quotient when the division of the whole part is completed.
- To divide a decimal fraction by 10, 100, 1000, etc., you need to move the decimal point to the left by 1, 2, 3, etc. digits.
- To divide a number by a decimal fraction, you need to move the decimal places in the dividend and divisor as many digits to the right as there are after the decimal point in the divisor, and then divide by the natural number.
- To divide a decimal by 0.1; 0.01; 0.001, etc., you need to move the decimal point to the right by 1, 2, 3, etc. digits. (Dividing a decimal by 0.1, 0.01, 0.001, etc. is the same as multiplying that decimal by 10, 100, 1000, etc.)
To round a number to any digit, we underline the digit of this digit, and then we replace all the digits after the underlined one with zeros, and if they are after the decimal point, we discard them. If the first digit replaced by a zero or discarded is 0, 1, 2, 3 or 4, then the underlined digit is left unchanged. If the first digit replaced by a zero or discarded is 5, 6, 7, 8 or 9, then the underlined digit is increased by 1.
The arithmetic mean of several numbers.
The arithmetic mean of several numbers is the quotient of dividing the sum of these numbers by the number of terms.
The difference between the largest and smallest values of a data series is called the range of the series of numbers.
The number that occurs with the highest frequency among the given numbers in a series is called the mode of the number series.
- One hundredth part is called a percentage. Purchase a book that teaches “How to Solve Percentage Problems.”
- To express percentages as a fraction or a natural number, you need to divide the percentage by 100%. (4%=0.04; 32%=0.32).
- To express a number as a percentage, you need to multiply it by 100%. (0.65=0.65·100%=65%; 1.5=1.5·100%=150%).
- To find the percentage of a number, you need to express the percentage as a common or decimal fraction and multiply the resulting fraction by the given number.
- To find a number by its percentage, you need to express the percentage as an ordinary or decimal fraction and divide the given number by this fraction.
- To find what percentage the first number is from the second, you need to divide the first number by the second and multiply the result by 100%.
- The quotient of two numbers is called the ratio of these numbers. a:b or a/b– the ratio of numbers a and b, and a is the previous term, b is the next term.
- If the members of a given relation are rearranged, the resulting relation is called the inverse of the given relation. The relationships b/a and a/b are mutually inverse.
- The ratio will not change if both terms of the ratio are multiplied or divided by the same number other than zero.
- The equality of two ratios is called proportion.
- a:b=c:d. This is a proportion. Read: A this applies to b, How c refers to d. The numbers a and d are called the extreme terms of the proportion, and the numbers b and c are called the middle terms of the proportion.
- The product of the extreme terms of a proportion is equal to the product of its middle terms. For proportion a:b=c:d or a/b=c/d the main property is written like this: a·d=b·c.
- To find the unknown extreme term of a proportion, you need to divide the product of the middle terms of the proportion by the known extreme term.
- To find the unknown middle term of a proportion, you need to divide the product of the extreme terms of the proportion by the known middle term. Proportion problems.
Let the value y depends on the size X. If when increasing X several times the size at increases by the same amount, then such values X And at are called directly proportional.
If two quantities are directly proportional, then the ratio of two arbitrarily taken values of the first quantity is equal to the ratio of two corresponding values of the second quantity.
The ratio of the length of a segment on a map to the length of the corresponding distance on the ground is called the map scale.
Let the value at depends on the size X. If when increasing X several times the size at decreases by the same amount, then such values X And at are called inversely proportional.
If two quantities are inversely proportional, then the ratio of two arbitrarily taken values of one quantity is equal to the inverse ratio of the corresponding values of the other quantity.
- A set is a collection of some objects or numbers, composed according to some general properties or laws (many letters on a page, many proper fractions with a denominator of 5, many stars in the sky, etc.).
- Sets consist of elements and can be finite or infinite. A set that does not contain a single element is called the empty set and is denoted by O.
- Many IN called a subset of a set A, if all elements of the set IN are elements of the set A.
- Intersection of sets A And IN is a set whose elements belong to the set A and many IN.
- Union of sets A And IN is a set whose elements belong to at least one of these sets A And IN.
- N– set of natural numbers: 1, 2, 3, 4,…
- Z– a set of integers: …, -4, -3, -2, -1, 0, 1, 2, 3, 4,…
- Q– a set of rational numbers representable as a fraction m/n, Where m– whole, n– natural (-2; 3/5; v9; v25, etc.)
- A coordinate line is a straight line on which a positive direction, a reference point (point O) and a unit segment are given.
- Each point on the coordinate line corresponds to a certain number, which is called the coordinate of this point. For example, A(5). They read: point A with coordinate five. B(-3). They read: point B with coordinate minus three.
- Modulus of the number a (write |a|) call the distance from the origin to the point corresponding to a given number A. The modulus of any number is non-negative. |3|=3; |-3|=3, because the distance from the origin to the number -3 and to the number 3 is equal to three unit segments. |0|=0 .
- By definition of the modulus of a number: |a|=a, If a?0 And |a|=-a, If a b.
- If, when comparing numbers a and b, the difference a-b is a negative number, then a , then they are called strict inequalities.
- If inequalities are written by signs? or?, then they are called non-strict inequalities.
a) Double inequality of the form a 0, the branches of the hyperbola are located in I and III, and for k
Linear equation in two variables and its graph.
- Linear equationwith two variables called an equation of the form ax+by=c, Where x And y- variables, numbers a And b- coefficients, number With- free member.
- A pair of values of variables for which a linear equation with two variables becomes a true numerical equality is called a solution to this equation. The solution to the equation is written in parentheses. For example, (2; -1) is a solution to the equation 3x+2y=4, since 3·2+2·(-1)=4.
- Equations with two variables that have the same solutions are called equivalent.
- The set of points on the coordinate plane whose coordinates are a solution to the equation is called scheduleequations.
- Graph of a linear equation in two variablesax+by=c, in which at least one of the coefficients of the variables is not equal to zero is straight.
Systems of linear equations with two variables.
- A pair of variable values, converting each equation of a system of linear equations with two variables into true equality is called solving a system of equations.
- Solving a system of equations means finding all its solutions or proving that there are no solutions.
- To solve a system of linear equations with two variables, use graphical method, substitution method and addition method.
- The method is plotting each equation, included in this system, in one coordinate plane and finding the intersection points of these graphs V. Coordinates of this point (x; y) and will appear decision of this system of equations.
- If straight intersect, then the system of equations has the only thingsolution.
- If straight, which are graphs of the system equations, parallel, then the system of equations has no solutions.
- If straight, which are graphs of the system equations, match, then the system of equations has infinitemany solutions.
- In one of the equations one variable is expressed in terms of another, for example, expressed y through X.
- Substitute the resulting expression instead y into the second equation - an equation with one variable is obtained X.
- From the resulting equation, find the value of this variable X.
- Substitute value X into the expression obtained in 1) point and find the value of the variable y.
- Pair (x; y) is a solution to this system of equations.
- Multiply the left and right sides of one or both equations by such a number that odds with one of the variables in the equations turned out to be opposite numbers.
- Added up piece by piece the resulting equations remain an equation with one variable, from which the value of this variable is found.
- Substitute the found value of the variable into any of these equations and find the value of the second variable.
- The resulting pair of variable values serves as a solution to this system of equations.
Solving systems of linear inequalities with one variable.
- The value of the variable at which each inequality in the system turns into a true numerical inequality is called a solution to the system of inequalities with one variable.
- Algorithm for solving systems of inequalities with one variable.
- Find the set of solutions to each inequality of the system.
- Draw on one coordinate line the set of solutions to each of the inequalities.
- The intersection of intervals - sets of solutions to these inequalities - is the solution to this system.
- The solution to a system of inequalities can be written as an inequality or as a numerical interval
Absolute and relative errors.
- Absolute error(denoted by?x) - the module of the difference between the given and approximate values of a given number. ?x= |x-x 0 |, where x is a given number, x 0 is its approximate value.
- Relative error(denote?) - the modulus of the ratio of the absolute error to the approximate value of the number. ?=|?x/x 0 |, where?x is the absolute error of the number x, x0 is its approximate value.
www.mathematics-repetition.com
Increasingly, a computer, a multimedia projector and an interactive whiteboard appear in primary school lessons in order to keep students active in the lesson, arouse their interest in learning new material and explain complex concepts in an accessible way. Mathematics lessons in grade 2 using presentations are more intense; they stimulate each student’s interest in learning the subject, develop attention and curiosity.
Mathematics in primary school is a special, specific subject. Not every student can master it with ease. Interesting, well-written presentation on mathematics in 2nd grade helps keep children interested throughout the 45-minute lesson.
A computer presentation for a mathematics lesson in 2nd grade is the most advanced technology that is being implemented in all schools today, regardless of what program it is used for, what teaching materials are the basis for teaching children. It can be used throughout the lesson or at certain stages. Thanks to the use of a presentation in a mathematics lesson, the most difficult topic in 2nd grade will seem accessible and understandable.
Practicing teachers noted that an open lesson in mathematics with a presentation for grade 2, both according to Peterson and Moreau, will arouse interest not only among children, but also among colleagues who attend such events. In such open lessons, students can achieve greater productivity. Even passive children strive to be active when the lesson is interesting.
2nd grade students look forward to mathematics lessons if they know that their teacher will not only give new knowledge at the next lesson, but will also be able to surprise them with the form of presentation. It is difficult for a teacher to prepare for 2nd grade mathematics according to the 2100 program or PNS presentations every day. This will take a lot of time even if you have mastered the Power Point program well. Our portal was created for those who work creatively. We offer download free ready-made presentations of a mathematics lesson for grade 2 on all topics, which comply with the Federal State Educational Standard. All developments were compiled by the best teachers working in primary schools in large cities and small towns. These teachers shared their ideas on the Internet, and we collected them on one portal and organized them by grade and subject.
It is impossible to turn a mathematics lesson in 2nd grade according to the Federal State Educational Standard into a continuous display of presentations. When planning its stages, you should think about the health of students. Make your lesson bright, rich, intellectually rich, but do not oversaturate it with useless pictures and unnecessary animation. Some presentations for a 2nd grade math lesson contain only 6-7 slides, but they are enough to use computer support at a certain stage of the lesson and focus students' attention on a specific problem.
Downloading a presentation for a 2nd grade math lesson does not mean freeing yourself completely from preparing for classes. This material should be reviewed in advance and adapted to your class. Only in this case will it be possible to maintain children’s interest in this subject and involve them in the work process, developing the desire to independently search for answers to available questions.
Students will be able to learn how to solve the most complex examples correctly only when they master the order of performing actions. The first acquaintance with this material takes place in 2nd grade. The 2nd grade presentation "Routine of Operations" draws attention to the importance of each operation and the distinctive features of multiplication and division when they occur alongside addition and.
The presentation on 13 slides provides rich material for explaining the topic “The specific meaning of division” in grade 2 using the Moro textbook according to the School of Russia program. The first slides contain tasks for mental calculation and repetition of previous material. Next comes an introduction to the meaning of division using dynamic pictures as an example: 9 tulips must be divided into.
The presentation introduces cases of tabular division by the number 2. At the beginning of the lesson, there is preliminary preparation for studying this material. Together with Smesharik, children count orally, repeat the meaning of division and its connection with multiplication. Using a specific example, we get acquainted with division by 2. When we get acquainted with division into 2 parts, presentation.
Having mastered two basic operations (addition and subtraction) in the first grade, students gradually expand the range of their mathematical knowledge and in the 2nd grade receive information about new operations. A presentation on the topic of multiplication involves familiarizing yourself in a mathematics lesson with the meaning of this arithmetic operation. The development is made on 16 slides in the form of a mathematical journey, which.
The topic “Multiplication by 2” begins the compilation of a multiplication table, which very soon every second-grader will have to learn by heart. Presentation slides for the lesson on the topic “Multiplication tables by 2 and numbers 2” are the beginning of a lot of work on studying the topic, which will be carried out over several more lessons. The development was completed in the form.
Not every child can learn all cases of table multiplication right away. A presentation on the topic “Multiplication tables in verse” is a fascinating accompaniment to not just one, but a whole series of mathematics lessons in grade 2 devoted to the study of this material. Each example of a multiplication table, starting with 2, is advertised on the presentation slides in the form of small quatrain tips.
A presentation of 24 slides forms in 2nd grade students the concept that the specific meaning of multiplication is nothing more than the sum of identical terms. The lesson is held at the very beginning of acquaintance with multiplication. Using specific examples, 2nd grade students understand from the presentation what the meaning of multiplication is: 10+10+10+10=10 4. Notation using.
A presentation made for a mathematics lesson will help you get acquainted with the new arithmetic operation of division, which involves primary perception of the material and mastering the notation of the action in writing. To conduct the lesson and cover all its stages, 13 slides were created. In these presentations, material is presented for oral calculation, introducing a new concept, consolidating the material, and summarizing.
Moving on to special cases of multiplication and division, second-graders will learn an interesting way to multiply by 1. The best assistant in explaining the material will be a presentation on mathematics, which is made on 15 slides and clearly introduces how you can divide by 1 or multiply by 1. Having done conclusion, 2nd grade students receive.
Second-graders are happy to accept material that does not require memorization. An unusual discovery will be for them a lesson in which, looking through presentation slides, they will discover the technique of multiplying and dividing numbers by 10, although one of the teachers, seeing the children’s preparation, immediately shows multiplication and division by 100 using the example of presentation slides. Multiplication techniques .
There are a variety of ways to introduce students to multiplication and division by 3 tables. We offer to download a presentation for a 2nd grade mathematics lesson according to the Federal State Educational Standard, which is filled with interesting material that motivates second-graders to quickly memorize the table. The presentation is impeccably designed and beautifully animated. At the stage of familiarization with tabular cases of multiplication it is interesting to use.
Together with Dunno, looking through the presentation slides, 2nd grade students learn the multiplication table and division by 4 in their favorite non-boring mathematics lesson. You'll really get bored, because our hero doesn't just appear on the slides. He carries his own tasks, the purpose of which is to facilitate the rapid assimilation of tabular cases of multiplication with the number 4. First.
Mathematics is a country of new discoveries and constant journeys for knowledge. This is once again made possible by the lesson in which a new topic will be studied: the multiplication table and division by 5 in 2nd grade. Presentation for a mathematics lesson, which introduces multiplication and division of numbers by 5 and definition.
A presentation for introducing 2nd grade students to the multiplication and division tables by 6 offers a journey to the land of magic, Hogwarts. This is a real habitat for wizards, and every second grader can become one if they complete a number of tasks in math class. Students need to: Find the magic number Compose a multiplication and division table without errors.
The presentation was made for a mathematics lesson (Federal State Educational Standard, School 2100) in 2nd grade, where the multiplication table and division by 7 will be studied, as well as an introduction to the seventh fraction of a number. Using presentation slides, it is easy to organize oral calculations, study of new material and its initial consolidation. Any teacher will find it easy to teach a lesson using this one.
To become proficient in mathematics, students must learn to count verbally. Mental arithmetic is a mandatory stage of a mathematics lesson in 2nd grade. The presentation offers a number of interesting tasks that sharpen the skill of mental calculations within 100: Examples for addition within 20 and 100 Examples for subtraction within 20 and 100 Task.
Mathematics can be studied not only in the classroom, but also during the class period during the school week of mathematical sciences. If you want such a class hour to be interesting and not tire the children, download the presentation called “Entertaining Mathematics.” Her tasks require not only knowledge of calculation techniques, but also intelligence. Provide children with fun tasks to do.
The ancient Japanese art of origami can help in the study of mathematics in grade 2, as it is very closely related to this science. The presentation presents a project that proves this hypothesis. First, a short excursion into the early days of origami in Japan is given, then the main methods of folding paper are shown. It’s already clear here in the presentation.
Math Bazaar is a new and interesting math quiz for 2nd grade students, presented in a 17-slide presentation. The narrative begins with the story of Pythagoras. This start of the event was not without reason, since this great scientist considered the number 1 to be the main number in mathematics. It is to the first task that second-graders are invited to move on. In development.
The topic of adding and subtracting numbers in the 2nd grade is given no less importance than in the first. A presentation on mathematics for grade 2 was created for lesson 1.4, where we will explain how addition and subtraction of quantities occur. The development is carried out on 12 slides, which contain material not only to explain the new material, but also.
On the eve of Cosmonautics Day, you can conduct a lesson on a trip to space in mathematics (Moro) with 2nd grade students using the prepared presentation provided. To have fun traveling from Earth to the Nebula planet, you will have to take a whole lesson in counting, solving, comparing and guessing. A cheerful mood, a cheerful pace and a number of exciting tasks will make a mathematical journey into space in no time.
The main focus in 2nd grade mathematics lessons is on learning the numbering of numbers within 100. Only by learning this topic can you master computational skills with two-digit numbers. The presentation introduces numbers up to 100, their names, location in a series, composition, and neighbors. The development allows you to study the topic “Oral numbering of numbers within 100.”
Introducing the concepts of “price, quantity, cost” in a mathematics presentation for grade 2 takes place in a fun way - a trip to the Sunshine store. The situation is quite common. Each toy or item has its own price. The children are met by an attentive seller, with whom they will have to pay. You can prepare “virtual” money for the lesson. Making up problems in class p.
The basic arithmetic operations with numbers that second grade students work with are addition and subtraction. Everyone will have to master it, but so that the process of studying the topic does not seem difficult, we suggest using a presentation on mathematics for an open or working lesson in the 2nd grade according to the Federal State Educational Standard for the educational complex “School 2100” on the topic “Arithmetic.
27 presentation slides are excellent material for learning units of time in 2nd grade. After an oral count, the teacher invites the second-graders to guess a riddle (slide 10) and only after that formulates the goals that the children face in the lesson: to learn how to tell time by a clock, using new units: hour, minute. To attract attention.
Is it possible to see time and what is this quantity? Students receive the answer in a mathematics lesson in 2nd grade. The length of a segment can be measured, the weight of an object is determined by weighing, but how can one determine a person’s age or the duration of a vacation? Children will learn to determine for themselves whether the New Year will be soon and how many days later grandma will arrive.
The presentation gives the teacher the opportunity to introduce visually for 2nd grade students in a mathematics lesson (School 2100) the new concept of the area of a rectangle, using knowledge about length and width. First, the method of finding the perimeter is repeated using the example of solving the problem. Then, for the same task, it is necessary to find the area of the site in order to determine how many buckets of water will be needed.
The presentation resembles a little fairy tale that will introduce 2nd grade students to a rectangle and its properties. The story begins with the fact that the square went to look for his relatives, since he was very bored living in the geometric kingdom. Walking towards him was a figure somewhat reminiscent of a square: the angles were just as right, and there were also some of them.
The presentation for a mathematics lesson in 2nd grade was compiled taking into account the children’s knowledge about the square, which they received in the first grade. When studying a new topic in class, schoolchildren should see and remember the properties of a square, its difference from a rectangle and its similarity to this figure. The math lesson begins by reviewing knowledge about a rectangle. According to the presentation.
The presentation was compiled by a mathematics teacher for a lesson in 2nd grade on the topic “Perimeter of a rectangle.” In grade 1, students already found the perimeter of various figures: triangle, square, rectangle, polygon, but used only the action of addition to do this. At this stage, new opportunities open up for finding the perimeter of a rectangle, as children know multiplication. Multimedia.
A presentation on the topic “Broken Line” gives 2nd grade students a general idea of this figure and teaches how to measure its length. Showing slides will help explain the topic to each student in an accessible way, despite the different levels of preparation of children in the class. Learning new material begins by looking at a picture on one of the presentation slides, where everyone.
A presentation with logical problems is a treasure trove of material for developing the mental abilities of 2nd grade students. The development can be used not only in mathematics lessons. Its use will be appropriate when preparing children for school Olympiads, competitions, during extracurricular activities, and organizing thematic subject weeks. The presentation slides contain logical problems.
A presentation with the game “Field of Miracles” in mathematics can be used during extracurricular activities on the subject in any grade of elementary school (grades 1, 2, 3, 4). Like the television game “Field of Miracles”, which appears on our TV screens every Friday, this electronic game will arouse great interest among children. Her questions.
A presentation for a mathematics lesson on the topic “How many times more, how many times less” was compiled for work in 2nd grade at the educational complex “School 2100” (Demidova). The interactive manual is made taking into account program requirements and the Federal State Educational Standard, so it can be used to conduct an open lesson in mathematics in grade 2. For an open event.
The maths presentation contains a number of simple multiplication and division problems for grade 2. The multimedia development is made in the form of a test, so it can be used in the classroom to test students’ ability to solve simple problems of the types they have learned. Each task is written in poetic form. An interesting plot does not at all distract students from the condition.
A computer presentation was made for a mathematics lesson in grade 2 to familiarize schoolchildren with the names of the components and the results of division. Students will learn to divide numbers into a certain number of equal parts. To do this, they are offered a number of practical tasks that are performed based on clarity: mental calculation, operations with two-digit numbers, division of numbers.
KVN with a presentation can be carried out both in a mathematics lesson in grades 2-3, and when organizing extracurricular activities during a subject week, in a camp. All teachers working in primary schools can download the manual with a summary of the mathematical competition. Students should do a little prep work before the event.
The presentation, on the pages of which schoolchildren will travel on an amazing ship with white sails, offers an introduction to numerical expressions. This is not a simple math lesson where computational skills will be honed. This is a small journey according to its own special scenario, where there is a place for solving problems, for getting to know the heroes of Daniel Defoe’s books, for...
The presentation will be a wonderful multimedia tool for the teacher for a 2nd grade math lesson on the topic “Components of Multiplication.” It is filled with high-quality and quite interesting material, which makes it possible to systematize new knowledge and organize practical work on studying a new topic. Here the theoretical concepts that you have to remember are presented in a simple and clear manner on the slides. Students are offered.
The presentation is filled with stunningly beautiful material for schoolchildren to learn about a new category of multi-digit numbers. In a math lesson in 2nd or 3rd grade, you will count by hundreds, which will culminate in learning about a thousand. Children go on a trip. They have treasure chests. All wealth must be counted. This is how memorization goes.
The presentation will help organize work in a mathematics lesson with 2nd grade students on the topic “Solving Equations.” The manual can be downloaded to work with the Peterson textbook (PNSh) or on another OS. The electronic manual is quite high quality. It will interest students and attract their attention to studying the topic. Students not only get acquainted with equalities, but...
The presentation was made for primary school teachers. Using it, you can conduct a mathematics lesson in 2nd grade using the Peterson textbook (UMK “Perspective”, “Learning to Learn” and others) on the topic “Circle and Circle.” By looking through the manual and working with its material, it will be easy for students to remember new terms on the topic and learn to draw a circle and a circle.
The presentation was made to accompany Peterson’s 2nd grade math lesson on the topic “Divisors and Multiples.” On the development pages, students will find all the definitions they need to remember. By referring to them several times during the lesson, you can be sure that this material will remain in memory. In addition, the visualization for it was well chosen.
Based on this presentation, you can conduct a test mathematical dictation in a mathematics lesson in grade 2. Schoolchildren just need to read the assignments, complete them orally and write down answers to questions asked in notebooks, solve problems, and self-test the work completed. After completing all the tasks, each student will be able to give himself a grade by doing the math.
The presentation will allow you to learn the laws of multiplying a sum by a number and make a trip to India at the same time as 2nd grade students in a mathematics lesson. This activity will be extremely interesting for children. They will like the tasks that the teacher offers. They will enjoy working in class as they prepare to multiply two-digit numbers by one-digit numbers. On.
The presentation will be used in a mathematics lesson in grade 2 (Harmony educational complex), when the multiplication and division tables with the number 8 will be reinforced. Table cases have already been discussed in the previous lesson, however, improving and consolidating computational skills is no less important in the teaching system, than getting to know new material. That's why this lesson.
The presentation was created for those who like to play in mathematics lessons. In grades 2–4, any mathematical topic can be taught in a playful way, but most of all, schoolchildren like games that require children to correctly answer difficult questions, where they need to solve logical problems, remember history, and show ingenuity. It is this joy.
The presentation offers material for conducting an extracurricular event in mathematics in elementary school (grades 2–4) on the topic “Math Tournament.” On 29 slides of the manual, schoolchildren are offered tasks that are logical in nature, which will arouse interest in the subject and will help expand knowledge on various topics, including the history of mathematics. The guys need it.
The presentation was made by a talented teacher who has been teaching children in one of the Moscow schools for many years now. Anna Vasilievna Tatuzova simply loves mathematics, which is why her personal website has so many guides that will help teach an interesting lesson in grades 1-2. Some of its benefits are offered only upon placing an order, some are.
The presentation offers material for a mathematics lesson in grade 2, in which the multiplication table and division by 6 will be reinforced. The indicated table cases were introduced in the previous lesson, and this one will be used to practice computational skills, so a simulator for memorizing the table will be of great interest . Masha and Vitya.
The presentation is designed to study the topic “Commutative property of multiplication.” The teacher conducted a mathematics lesson in grade 2 with hearing-impaired children, but this does not at all impose any restrictions on the use of the proposed material. It can be downloaded to familiarize yourself with or reinforce the commutative law and for other programs (“Harmony”, “PNSh”, “School 2100” and others). Using.
This presentation on “Multiplication and Division by 1 and 0” will help you understand special cases of calculations that are easy to remember if you know the formulas. The material can be used in 2nd or 3rd grade. You can download it along with a synopsis and annotation for the work, which describes in detail the techniques for multiplying numbers by zero.
The presentation presents a simulator for fixing the multiplication and division tables with the number 9. It can be used to work with any educational computer. It will be interesting to show it both in mathematics lessons and at home for children who are studying mathematics in 2nd grade in the teaching and learning complex “School of Russia”, “Harmony”, “School 2100”. After working it several times.
The presentation offers useful and interesting material that can be used to organize an elective in mathematics or a lesson in 2nd grade. These are Olympiad tasks that children often meet in competitions and math Olympiads at school. The tasks will contribute to the development of logical thinking. They will arouse interest in the subject and develop the ability to find a solution.
The presentation offers tasks that can be used for 2nd grade students to complete a test in mathematics. The material was selected by a teacher who has worked in elementary school for many years. All test tasks satisfy the requirements of the program. The work can be written at the end of the 3rd quarter according to the educational complex “School 2100”. All tasks are presented on.
The presentation will introduce 2nd grade children to multiplying and dividing numbers. Reinforcing the topic in a mathematics lesson takes place through the pages of a Russian fairy tale. The geese-swans stole her beloved brother from the girl. Urgent help is needed, but this time you will have to complete mathematical tasks in order to move forward. And for this you need to multiply and divide, solve.
The presentation will help consolidate tabular cases of multiplying and dividing numbers by 5, 6, 7, 8, 9. Cinderella comes to visit the 2nd grade students for this math lesson. Her appearance will bring joy to younger schoolchildren. Their attention will be activated, and their interest in solving the tasks offered on 17 slides will increase. The development can also be downloaded for.
The presentation offers schoolchildren a journey through the land of geometry, where they will get acquainted with angles and study their types, learn to build, find from among the proposed figures, and draw in their own notebooks. The topic is studied in a mathematics lesson in 2nd grade. Its material is not tied to a specific textbook, so you can use the manual for work.
The presentation will help 2nd grade students studying under the “21st Century School” program to remember the names of numbers in the arithmetic operations of addition, subtraction, division and multiplication. The development includes diagrams that contain all the necessary terms. All main titles are highlighted in red. Each diagram has an example demonstrating the action and the names of the numbers are labeled.
It is recommended to download the presentation to find out in a mathematics lesson (2nd – 3rd grade) the connection between the operations of division and multiplication. The material was prepared by students of advanced training courses. The development can be used by those who work with the School 2100 educational complex. The lesson manual contains 10 slides. These are the rules that students need to know. Theoretical material.
The presentation contains basic rules for some cases of multiplication and division that are not tabular. They need to be remembered, but this is best done through studying the corresponding formulas. The manual will help teach a lesson using the textbook by Zankov or Arginskaya, since it was compiled taking into account the requirements of the Federal State Educational Standard. There are a number of 9 development slides.
The presentation introduces schoolchildren to what fractions and fractions are, how they are obtained and how they are written, and how the fraction of a number is found. The manual will arouse genuine interest in a mathematics lesson in grades 2–3. It is made in a clear and interesting way and can be used for any teaching and learning complexes (PNSh, School of the 21st century.
The presentation is made in the form of an electronic simulator for testing addition and subtraction within 20 in a mathematics lesson in 2nd grade. Electronic development can be used not only in the classroom. It will be interesting for schoolchildren to work with it at home, so anyone who wants to automate their knowledge of tabular cases can download the simulator.
The presentation offers interesting didactic material that can be used in 2nd grade mathematics lessons when working with Rudnitskaya’s textbook. All exercises are selected in accordance with the program. They will be of interest to schoolchildren. Completing them will not take much time, but will significantly defuse the situation in the lesson, help change the children’s activities, and challenge them.
The presentation was created to help teachers who teach students in 2nd grade mathematics lessons to solve simple equations. In this lesson, students will learn how to find an unknown subtrahend or minuend. They will repeat how those equations are solved where it is necessary to find one of their terms, designated by X. There is a lot of interesting material in development, including the words of Einstein.
The presentation was made for a mathematics lesson in grade 2 using Cheklin’s textbook (PNSh) to learn how to find an unknown term. The lesson is proposed to be conducted in an interesting way. Schoolchildren not only learn to solve equations, they go on a space journey and complete certain tasks. This kind of work for 45 minutes will give wonderful results. Not.
The presentation will introduce schoolchildren to the liter, the basic unit of measurement of capacity. This development was made to accompany a mathematics lesson in grades 2–3 (Peterson). By viewing 21 slides of the electronic manual, schoolchildren will study a new topic and consolidate what they have learned. To do this, the work contains enough information about measuring capacity (volume) using a new unit.
TOPIC: Using the laws and properties of arithmetic operations
for rational calculations
Target: Consider the possibilities of applying the laws and properties of arithmetic operations for rational calculations.
Planned results:
They know : laws and properties of arithmetic operations (verbal formulation and symbolic notation)
They know how : competently, correctly express your thoughts, use mathematical symbols, apply the laws and properties of arithmetic operations to simplify calculations.
Developmental tasks:
Develop logical thinking, mental work skills, strong-willed habits, mathematical speech, memory, attention, interest in mathematics, practicality;
Educational tasks:
Cultivate respect for each other, a sense of camaraderie, and trust.
Name of general competenceOK 1.
Understand the essence and social significance of your future profession, show a strong interest in her.
OK 2.
Organize your own activities, determine methods for solving professional problems, evaluate their effectiveness and quality.
OK 4.
Search, analyze and evaluate information necessary for setting and solving professional problems, professional and personal development.
OK 6.
Work in a team and team, interact with management, colleagues and social partners.
Setting lesson goals and objectives
Good afternoon I want to start today's lesson with a few statements...
Counting and calculations are the basis of order in the head. (Johann Pestalozzi - Swiss teacher)
In mathematics there are no symbols for unclear thoughts. (Henri Poincaré - French mathematician)
It is mathematics that gives the most reliable rules: whoever follows them is not in danger of deceiving the senses. (L. Euler - Russian mathematician)
Read these statements to yourself again and say - who guessed what we will talk about today? What will we repeat in class today? What are we going to do?
You are right, the topic of our lesson is...Using the laws and properties of arithmetic operations for rational calculations
We'll start the lesson with a math warm-up.
Updating knowledge
1. Complete the sentence. What is this rule?
From rearranging terms...
To subtract an amount from a number...
To multiply the product of two factors by a third factor, you can...
To multiply a sum by a number, you can...
To divide a number by a product, you can...
2. This was a verbal formulation of the rules, and now let's remember how these rules can be written using symbols of mathematical language. On your desks you have white sheets of paper on which the rules of identical transformations are written in symbolic, letter form. You need to complete these equalities, determine what these rules are and remember the wording of these rules. (We work in pairs)
3. The slide contains examples of identical transformations of numerical expressions; on the basis of what rules can they be performed?
Swap multipliers
Restore and omit parentheses
Put the common factor out of brackets
Reinforcing previously learned
What do you think - what are these rules for? There are many of them and they are all studied in primary school. (the meaning of the word rational is reasonable, logical, expedient)
1. Find the meaning of the expressions in a rational way (in writing):
a) 156 + 79 + 21 + 44(y)
b) 2 5 126 4 25(y)
c) (120+36+186):6 (U)
d)56 387 - (6 307+82) (U)
d) 62 16 + 38 16(U)
d) 240 710 + 7100 76
e) 45 40 – 40 25
e) 4 63 + 4 79 + 142 6
g) 107*93 -109*91
2. Without performing calculations, compare the meanings of the expressions (orally):
a) 258 (764 + 548) and 258 764 + 258 545
c) 496 (862 – 715) and 496 860+ 496 715
d) 6720: (7*4) and 6720:7:4
e) 732*(12*2) and 732*20+732*6
3. In the elementary grades, oral computational techniques are based on the laws and rules discussed. You have pink sheets of paper on your tables with examples written on them. You need to offer your own version of the calculations and explain which rule elementary school students can use. (We work in pairs)
Example: 60-7=(50+10)-7=50+(10-7)=53 The rule is subtracting a number from the sum.
Let's check if Olya is right? ... (video)
36-20
350-70
26+7
124*3
6 28
840:7
25*12
560:28
4. Logic tasks:
Find the error in reasoning:
35+10-45=42+12-54
5*(7+2-9)= 6*(7+2-9)
5=6
What number does it end with?
A) the product of all natural numbers from 7 to 81 inclusive
B) sum 26*27*28 + 51*52*53
C) difference 43*45*47- 39*41*42
D) the sum of all three-digit numbers?
D/z: come up with numerical expressions yourself to apply the rules .
Lesson summary: Continue the phrases
During class I remembered...
repeated...
Understood…..
It was difficult for me...
I liked it...
Purpose: to check the development of skills to perform calculations using formulas; introduce children to the commutative, associative and distributive laws of arithmetic operations.
- introduce the alphabetic notation of the laws of addition and multiplication; teach to apply the laws of arithmetic operations to simplify calculations and letter expressions;
- develop logical thinking, mental work skills, strong-willed habits, mathematical speech, memory, attention, interest in mathematics, practicality;
- cultivate respect for each other, a sense of camaraderie, and trust.
Lesson type: combined.
- testing previously acquired knowledge;
- preparing students to learn new material
- presentation of new material;
- students’ perception and awareness of new material;
- primary consolidation of the studied material;
- summing up the lesson and setting homework.
Equipment: computer, projector, presentation.
Plan:
1. Organizational moment.
2. Checking previously studied material.
3. Studying new material.
4. Primary test of knowledge acquisition (working with a textbook).
5. Monitoring and self-testing of knowledge (independent work).
6. Summing up the lesson.
7. Reflection.
Lesson progress
1. Organizational moment
Teacher: Good afternoon, children! We begin our lesson with a parting poem. Pay attention to the screen. (1 slide). Appendix 2 .
Math, friends,
Absolutely everyone needs it.
Work diligently in class
And success is sure to await you!
2. Repetition of material
Let's review the material we covered. I invite the student to the screen. Task: use a pointer to connect the written formula with its name and answer the question what else can be found using this formula. (2 slide).
Open your notebooks, sign the number, great job. Pay attention to the screen. (3 slide).
We work orally on the next slide. (5 slide).
12 + 5 + 8 25 10 250 – 50 200 – 170 30 + 15 45: 3 15 + 30 45 – 17 28 25 4
Task: find the meaning of expressions. (One student works at the screen.)
– What interesting things did you notice while solving the examples? What examples should you pay special attention to? (Children's answers.)
Problem situation
– What properties of addition and multiplication do you know from elementary school? Can you write them using alphabetic expressions? (Children's answers).
3. Learning new material
– And so, the topic of today’s lesson is “Laws of Arithmetic Operations” (6 slide).
– Write down the topic of the lesson in your notebook.
– What new should we learn in class? (The goals of the lesson are formulated together with the children.)
- We look at the screen. (7 slide).
You see the laws of addition written in letter form and examples. (Analysis of examples).
– Next slide (8 slide).
Let's look at the laws of multiplication.
– Now let’s get acquainted with a very important distribution law (9 slide).
- Let's sum it up. (10 slide).
– Why is it necessary to know the laws of arithmetic operations? Will they be useful in further studies, when studying what subjects? (Children's answers.)
- Write the laws in your notebook.
4. Fixing the material
– Open the textbook and find No. 212 (a, b, d) orally.
No. 212 (c, d, g, h) in writing on the board and in notebooks. (Examination).
– We are working on No. 214 orally.
– We carry out task No. 215. What law is used to solve this number? (Children's answers).
5. Independent work
– Write down the answer on the card and compare your results with your neighbor at your desk. Now turn your attention to the screen. (11 slide).(Checking independent work).
6. Lesson summary
– Attention to the screen. (12 slide). Complete the sentence.
Lesson grades.
7. Homework
§13, no. 227, 229.
8. Reflection
