1, the definition of axial symmetry: a graph is folded in half along a straight line. If it can overlap with another figure, it is said that the two figures form an axis symmetry, and this straight line is the axis symmetry. 2. Draw the symmetry axis of the graph. 3. Axisymmetric drawing: (1) Find the key points of a given figure (2) Count or measure the distance between the key points of the figure and the axis of symmetry (3) Find the corresponding points of the key points on the other side of the axis of symmetry (4) Connect the points in the order of the given figure. 4. Definition of rotation: The phenomenon that an object moves around a certain point or axis is called rotation.

5. Characteristics of rotation: After the rotation, the shape and size of the figure have not changed, but the position has changed. 6. Drawing method of rotating the figure by 90: (1) Find several key points of the original figure, and use a triangle as the perpendicular of the line segment where the key points and rotation points are located. (2) Starting from the rotation point, measure the length equal to the original line segment on the vertical line. (3) Connect the corresponding points drawn in sequence.

7. Translation: In a plane, a graphic moves a certain distance in a certain direction, and such graphic movement is called translation. 8. Draw a translation diagram (1) to find the key point (turning point) (2) Determine the translation direction (up, down, left and right) (3) Determine the translation distance (several squares) (4) Connect the lines.

9. Learn to judge whether various phenomena are translational, rotational or axisymmetric.

I. Factors and multiples

1, meaning of factor and multiple: if a× b = c (a, b and c are all integers other than 0), then a and b are factors of c, and c is a multiple of a and b ... if A ÷ B = C (A, b and c are all integers not equal to 0), then b and c are a. ..

2. Relationship between factor and multiple: factor and multiple are two different concepts, but they are a pair of interdependent concepts and cannot exist separately. 3. The method of finding the factor of a number: (1) column multiplication formula (2) column division formula.

4. How to find the multiple of a number: To find the multiple of a number is to multiply this number by a non-zero natural number in turn, and the product obtained is the multiple of this number. Characteristics of multiples of two, two, three and five

Multiplication characteristics of 1 2: Numbers with 0, 2, 4, 6 and 8 are all multiples of 2.

2. Meaning of odd and even numbers: In natural numbers, numbers that are multiples of 2 are called even numbers. Numbers that are not multiples of 2 are called odd numbers.

3. Method for judging odd and even numbers: 0, 2, 4, 6 and 8 are even numbers, and 1, 3, 5, 7 and 9 are odd numbers. 4. Operational properties of odd and even numbers: odd number = even number, even number = even number, odd number = even number (greatly reduced), odd number × odd number = odd number, odd number × even number = even number, even number × even number = even number.

Multiplication characteristics of 5 and 5: Numbers with 0 or 5 are multiples of 5.

Multiplication characteristics of 6 and 3: the sum of the numbers on each digit of a number is a multiple of 3, and this number is a multiple of 3.