Which grade students in Vietnam start to study space geometry?
Which grade students in Vietnam start to study space geometry?
Based on sub-item 2 of Section 5 in the High School Mathematics Curriculum issued together with Circular 32/2018/TT-BGDĐT, students in grades 11 and 12 are allowed to study space geometry. The specific distribution of content strands across the grades is as follows:
|
Space geometry |
Grade 11 |
Grade 12 |
|
Straight lines and planes in space |
x |
|
|
Parallel relationships in space. Parallel projection |
x |
|
|
Perpendicular relationships in space. Perpendicular projection |
x |
|
|
Vectors in space |
|
x |
|
Coordinate method in space |
|
x |
>> See the High School Mathematics Curriculum issued together with Circular 32/2018/TT-BGDĐT:
Which grade students in Vietnam start to study space geometry? (Internet image)
What are the required learning outcomes for 11th grade students in Vietnam studying space geometry?
Based on sub-item 3 of Section 5 in the High School Mathematics Curriculum issued together with Circular 32/2018/TT-BGDĐT, the required outcomes for 11th grade students studying space geometry include the following:
(1) Requirements regarding lines and planes in space:
Including content about lines and planes in space; How to determine a plane; Pyramids and tetrahedrons.
- Identify basic affiliated relationships between points, lines, and planes in space.
- Describe three ways to determine a plane (through three non-collinear points; through a line and a point not on that line; through two intersecting lines).
- Determine the intersection line of two planes; the intersection point of a line and a plane.
- Apply properties of the intersection line of two planes; the intersection point of a line and a plane to solve exercises.
- Recognize pyramids and tetrahedrons.
- Apply knowledge of lines and planes in space to describe some images in practice.
(2) Requirements regarding parallel relationships in space. Parallel projection:- Two parallel lines:
+ Identify relative positions of two lines in space: two overlapping lines, parallel lines, intersecting lines, skew lines in space.
+ Explain the basic property of two parallel lines in space.
+ Apply knowledge of two parallel lines to describe some images in practice.
- Line parallel to plane:
+ Recognize a line parallel to a plane.
+ Explain the condition for a line to be parallel to a plane.
+ Explain the basic property of a line parallel to a plane.
+ Apply knowledge of lines parallel to planes to describe some images in practice.
- Two parallel planes. Thales theorem in space. Prism and box shapes:
+ Recognize two parallel planes in space.
+ Explain the condition for two planes to be parallel.
+ Explain the basic property of two parallel planes.
+ Explain Thales' theorem in space.
+ Explain the basic properties of prismatic and box shapes.
+ Apply knowledge of parallel relationships to describe some images in practice.
- Parallel projection. The representation of a shape in space:
+ Recognize the concept and basic properties of parallel projection.
+ Determine the image of a point, a segment, a triangle, a circle through a parallel projection.
+ Draw representative figures of some simple solid shapes.
+ Apply knowledge of parallel projection to describe some images in practice.
(3) Requirements regarding perpendicular relationships in space. Perpendicular projection:
- The angle between two lines. Two perpendicular lines:
+ Recognize the concept of the angle between two lines in space.
+ Recognize two perpendicular lines in space.
+ Prove two perpendicular lines in space in some simple cases.
+ Use knowledge of two perpendicular lines to describe some images in practice.
- Line perpendicular to plane. The three-perpendicular theorem. Perpendicular projection:
+ Recognize a line perpendicular to a plane.
+ Determine the condition for a line to be perpendicular to a plane.
+ Explain the three-perpendicular theorem.
+ Explain the relationship between parallelism and perpendicularity of lines and planes.
+ Recognize the concept of perpendicular projection.
+ Determine the perpendicular projection of a point, a line, a triangle.
+ Recognize the formula for the volume of pyramids, prisms, and boxes.
+ Calculate the volume of pyramids, prisms, and boxes in simple cases (e.g., recognize the height and base area of a pyramid).
+ Apply knowledge of lines perpendicular to planes to describe some images in practice.
- Two perpendicular planes. Prismatic shapes, square prism shapes, rectangular box shapes, cube shapes, regular pyramids:
+ Recognize two perpendicular planes in space.
+ Determine the condition for two planes to be perpendicular.
+ Explain the basic property of two perpendicular planes.
+ Explain the basic properties of prismatic shapes, square prisms, rectangular boxes, cubes, regular pyramids.
+ Apply knowledge of two perpendicular planes to describe some images in practice.
- Distance in space:+ Determine the distance from a point to a line; the distance from a point to a plane; the distance between two parallel lines; the distance between a line and a parallel plane; the distance between two parallel planes in simple cases.
+ Recognize the common perpendicular of two skew lines; calculate the distance between two skew lines in simple cases (e.g., one line perpendicular to the plane containing the other line).
+ Use knowledge of distance in space to describe some images in practice.
- The angle between a line and a plane. Dihedral angle and plane angle of a dihedral angle:
+ Recognize the concept of the angle between a line and a plane.
+ Determine and calculate the angle between a line and a plane in simple cases (e.g., know the perpendicular projection of the line onto the plane).
+ Recognize the concept of dihedral angle, plane angle of a dihedral angle.
+ Determine and calculate the measure of the dihedral angle, plane angle of a dihedral angle in simple cases (e.g., recognize the plane perpendicular to the edge of the dihedral angle).
+ Use knowledge of the angle between a line and a plane, dihedral angles to describe some images in practice.
- Truncated regular pyramids and volume:+ Recognize the concept of truncated regular pyramids.
+ Calculate the volume of truncated regular pyramids.
+ Apply knowledge of truncated regular pyramids to describe some images in practice.
What are the required learning outcomes for 12th grade students in Vietnam studying space geometry?
Based on sub-item 3 of Section 5 in the High School Mathematics Curriculum issued together with Circular 32/2018/TT-BGDĐT, the specified required outcomes for 12th grade students studying space geometry are as follows:
Requirements regarding the coordinate method in space:
(1) The coordinates of a vector with respect to a coordinate system. Coordinate expressions of vector operations:
- Recognize vectors and vector operations in space (addition and subtraction of two vectors, scalar multiplication of a vector, dot product of two vectors).
- Recognize the coordinates of a vector with respect to a coordinate system.
- Determine the length of a vector given the coordinates of its endpoints and the coordinate expressions of vector operations.
- Determine the coordinate expressions of vector operations.
- Apply vector coordinates to solve some real-life related problems.
(2) Plane equations:
- Recognize the general equation of a plane.
- Formulate the general equation of a plane in the Oxyz coordinate system in one of three basic ways: through a point and knowing the normal vector; through a point and knowing a pair of direction vectors (derive the normal vector by finding a vector perpendicular to the pair of direction vectors); through three non-collinear points.
- Formulate the conditions for two planes to be parallel, perpendicular to each other.
- Calculate the distance from a point to a plane using the coordinate method.
- Apply knowledge of plane equations to solve some real-life related problems.
(3) Line equations in space:
- Recognize canonical equations, parametric equations, and direction vectors of a line in space.
- Formulate the equation of a line in the coordinate system by one of two basic ways: through a point and knowing a direction vector, through two points.
- Determine the conditions for two lines to be skew, intersect, parallel, or perpendicular to each other.
- Formulate the formula to calculate angles between two lines, between a line and a plane, between two planes.
- Apply knowledge of line equations in space to solve some real-life related problems.
(4) Sphere equations:
- Recognize the equation of a sphere.
- Determine the center and radius of the sphere given its equation.
- Formulate the equation of the sphere given its center and radius.
- Apply knowledge of sphere equations to solve some real-life related problems.
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