The induction of mathematics knowledge points in the sixth grade
First, the learning objectives:
1. Let the students use numbers to determine the position on the grid paper;
2. Make students understand the meaning of fractional multiplication, master the calculation rules of fractional multiplication, and be skilled in calculation;
3. Make students understand the meaning of reciprocal and master the method of finding reciprocal;
4. Understand and master the calculation method of fractional division and carry out fractional division calculation;
5. Understand the meaning of ratio, know the relationship between ratio and fraction and division, and deduce the basic properties of ratio. Can correctly simplify the ratio and find the ratio;
6. Let students know the circle and master its characteristics; Understand the relationship between diameter and radius; Understand the meaning of pi and master the approximate value of pi.
7. Make students understand and master the formula for calculating the circumference and area of a circle, and can correctly calculate the circumference and area of a circle.
Second, learning difficulties:
1. You can use pairs to represent the position of objects and correctly distinguish the order of columns and rows;
2. Make students understand the meaning of fractional multiplication by integer and master the calculation method of fractional multiplication by integer;
3. Master the method of finding the reciprocal;
4. The meaning of the circumference and pi of a circle, and the derivation process of the circumference formula;
5. The meaning of percentage, find the application problem that one number is a few percent of another number;
6. Understand pi; Derivation of formula for calculating circle area and drawing a circle with fixed radius or diameter;
7. Understand the meaning of comparison.
Summary of important knowledge points in the first volume of mathematics in the sixth grade of primary school
Unit 1: Location
1. Determine the position of a point with a number pair, as shown in (3,5): (third column, fifth row).
How many columns and rows?
↓↓
Vertical columns are called rows and rows.
(looking from left to right) (looking from front to back)
2. Translation is expressed by "up", "down", "before", "after", "left" and "right".
3. The left and right translation of the figure: the line is unchanged; The graph is translated up and down: the columns are unchanged.
Unit 2 Fractional Multiplication
I. Fractional multiplication
(A) the significance of fractional multiplication:
1, fractional multiplication by integer has the same meaning as integer multiplication. Is a simple operation to find the sum of several identical addends.
For example, what is the sum of five when x 5 means?
2. the score multiplied by the score is to find the score of a number.
For example, × indicates what the solution is.
(2), the calculation rules of fractional multiplication:
1, Fraction multiplied by integer: the product of numerator multiplied by integer is numerator, and the denominator remains unchanged. (Integer and denominator divisor)
2. Fraction and fractional multiplication: use the product of molecular multiplication as the numerator and the product of denominator multiplication as the denominator.
3. In order to simplify the calculation, the points that can be reduced are reduced first and then calculated.
Note: When multiplying with a fraction, the fraction should be converted into a false fraction before calculation.
(3) Law: (When the multiplication is relatively large)
A number (except 0) is multiplied by a number greater than 1, and the product is greater than this number.
A number (except 0) multiplied by a number (except 0) is less than 1, and the product is less than this number.
A number (except 0) is multiplied by 1, and the product is equal to this number.
(4) The operation order of fractional mixed operation is the same as that of integer.
(5) The commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.
Multiplicative commutative law: a×b=b×a
Law of multiplicative association: (a×b)×c=a×(b×c)
Multiplication and distribution law: (a+b)×c=ac+bc.
Second, solve the problem of fractional multiplication.
(Know the quantity (multiplication) of the unit "1" and what is the fraction of the unit "1")
1, draw a line chart:
(1) The relationship between two quantities: draw two line segments; (2) The relationship between the part and the whole: draw a line segment.
2. Find the company "1": before the rate in the rate sentence; Or "occupy", "be" and "compare"
3. Find several times a number: a number × several times; Find the fraction of a number: a number ×.
4, write quantitative relationship skills:
(1) "De" is equivalent to "X", "Zhan", "Yes" and "Bi" is equivalent to "="
(2) "De" before the score: the quantity of unit "1" × score = the quantity corresponding to the score.
(3) Before the score, it means "more or less": the quantity of unit "1" ×( 1 fraction) = the quantity corresponding to the score.
Third, the countdown.
The meaning of 1 and reciprocal: two numbers whose product is 1 are reciprocal.
Emphasis: reciprocal, that is, reciprocal is the relationship between two numbers. They are interdependent and reciprocity cannot exist alone.
Make it clear who is the reciprocal of who.
2. Reciprocal method:
(1), find the reciprocal of the fraction: exchange the position of the denominator of the numerator.
(2) Find the reciprocal of an integer: treat an integer as a fraction with a denominator of 1, and then exchange the positions of the denominator of the numerator.
(3) Find the reciprocal of the band score: turn the band score into a false score, and then find the reciprocal.
(4) Find the reciprocal of decimals: Turn decimals into fractions, and then find the reciprocal.
3. The reciprocal of1is1; 0 has no reciprocal. Because/kloc-0 /×1=1; Multiply 0 by any number to get 0 (denominator cannot be 0).
4. For any number, its reciprocal is; The reciprocal of a nonzero integer is; The reciprocal of the score is;
5. The reciprocal of the true score is greater than1; The reciprocal of the false score is less than or equal to1; The reciprocal of the score is less than 1.
Summary of basic knowledge points in the first volume of sixth grade mathematics
I. Fractional multiplication
(A) the significance and calculation rules of decimal multiplication
The meaning of 1, the fraction multiplied by the integer.
2/ 1 1×3 means: What is the number of three 2/1? What is the 3 times of 2/ 1 1?
2. Calculation method of integer and decimal multiplication
Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged. If you can cut the point, cut the point first and then multiply. )
3. Multiplying a number by a fraction means finding a fraction of this number. 3/5× 1/4 means: what is 3/5 of 1/4?
4. Calculation Method of Fraction Multiplying Fraction
Fraction times fraction, numerator times numerator, denominator times denominator. If you can cut the point, cut the point first and then multiply. )
(2) What is the score of a number?
1, the method of finding the unit "1"
Whoever is a score of (1) is regarded as the unit "1".
(2) Generally, the quantity after "Bi", "Yes", "Zhan" and "Equivalent" is regarded as the unit "1".
Note: Look for the unit "1" in fractional sentences. Sentences with fractional rates are called fractional sentences.
Fractions have no units, but specific quantities have units.
2. Find multiples and fractions of a number and calculate by multiplication.
What is three fifths of 15? 15×3/5=9
3. The known unit "1" is calculated by multiplication.
Unit "1"× fraction = corresponding number of fractions.
Note: (1) multiplied by what score equals what amount.
(2) whose share is multiplied is equal to whose number.
(3) Multiply a score of who it is by a score of who it is.
4. Given that A is more (or less) than B, find the solution of A..
5. The relationship between products and elements
The product of numbers greater than 1 is greater than a.
A (except 0) times
The product of numbers less than 1 is less than a.