Math Kangaroo 袋鼠数学竞赛精品课

Math Kangaroo 袋鼠数学竞赛 1-2 年级教学大纲

• Counting to 20 and ordering small numbers for 3 and 4 point problems; for 5 point problems can be up to 30
• Comparing sizes (more, less, equal) of small numbers and geometrical regions
• Ordinal numbers
• Place value (ones, tens, and up to hundreds for 5 point problems)
• Simple addition and subtraction should be just for 2 single-digit numbers
• Number line just in simple applications
• Fractions (1/2, 1/3, 1/4), only using the words half, third, quarter
• Ordering objects by applying one specific characteristic; Sorting and classifying objects
• Measurement – length, capacity, weight, temperature, time only with small integers
• Patterns— numerical and geometrical, no sequences to be continued somehow
• Perimeter; comparing length of broken lines
• Relative positions in a figure or in space (behind, in front of, next to, left, right, over, under, middle, in, out)
• Descriptive properties of geometrical figures
• Puzzles with mazes or shapes
• Simple spatial visualization of cubes and cuboids
• More likely, less likely, certain, impossible
• Barsand graphs (pictographs)
• Venn diagrams (easy situations)
• Calendar (week, month, year)
• Money with small numbers
• Clock faces (full and half hours), but no minutes for 3 and 4 point problems
• Simple axial symmetry; rotated shapes
• Pre-algebra ideas like balances with concepts like equal, more, less, …

Math Kangaroo 袋鼠数学竞赛 3-4 年级教学大纲

1. Geometry

• Measurement: simple area and perimeter, for instance comparing lengths, counting in boxes on squared paper
• Symmetry

2. Numbers

• Basic operations with positive integers (+, -, x, / ) with numbers under 1000
• Comparing sizes of numbers; ordering numbers
• Multiples and divisors
• Simple fractions representing parts of figures, like quarter, half and third
• Number of the year problem can be an exception to the under 1000 rule for problems about the digits or similar ideas
• Averages (arithmetic mean)

3. Logic

• Strategies for simple games
• Classification of objects
• Puzzles

Math Kangaroo 袋鼠数学竞赛 5-6 年级教学大纲

1a. Geometry — plane geometry

• Points, lines, segments, circles, (special) triangles and (special) quadrilaterals
• Symmetry
• Perimeter and area of squares, rectangles and right triangles

1b. Geometry — solid geometry

• Only problems in solid geometry that allow an intuitive approach

2. Numbers and algebra

• Calculations with natural numbers
• Recognizing multiples of 2, 3, 5, 9 and 10
• Very easy calculations with positive rational numbers (fractions or decimals)
• Algebraic thinking without the use of formal algebraic notation
• Counting problems that do not involve any formulas
• Problems about decimal number system
• Easy problems with order between numbers (integers, decimal, fractions) and links with their representations (on graduate line, surfaces, …)
• Very easy problems with percentages
• Metric system (length, weight, area, volume, temperature, time)
• Problems using time, distance and/or velocity

3. Logic

• Logical problems that can be solved in a limited number of steps or by analyzing a limited number of cases or hypotheses

Math Kangaroo 袋鼠数学竞赛 7-8 年级教学大纲

1a. Geometry — plane geometry

• Point, line, segment, angle, acute angle, right angle, obtuse angle, circle, radius, diameter, triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle, parallelogram, rhombus, trapezium, diagonal, regular polygon
• Symmetry, translation and rotation in the plane
• Sum of the angles of a triangle, sum of the angles of a square, angles formed by two parallel lines intersected by a third line
• Elementary propositions about angles, sides and diagonals in special triangles and quadrilaterals
• Perimeter and area of a square, rectangle, parallelogram, rhombus, trapezium, triangle
• Coordinates of a point in the plane

1b. Geometry — solid geometry

• Cube, regular parallelepiped, prism, pyramid, cone, cylinder, sphere
• Area and volume of a cube and a regular parallelepiped
• 3-d movement of one- and two-dimensional objects (such as knots and folding)
• Intuitive 2-d representation of a 3-d object

2. Numbers

• Calculations with integers and rational numbers (fractions or decimals)
• Prime numbers
• gcd and lcm
• Recognizing multiples of 2, 3, 4, 5, 6, 9 and 10
• Intuitive knowledge about the divisibility of a sum and a difference
• Powers with exponent 2
• Square root of a perfect square, cubic root of a perfect cube
• Combinatorial problems that do not involve any formulas
  Percentage
• Metric system (length, weight, area, volume, temperature …)
• Problems using time, distance and velocity that do not involve algebraic calculation.
• Problems that involve only an intuitive knowledge of probability

3. Algebra

• Linear algebraic calculations (adding and subtracting monomials of degree 1, multiplying a rational number and a monomial of degree 1)
• Problems that can be reduced to a linear equation or inequality in one variable.

4. Logic

• Logic problems that can be solved in a limited number of steps or by analyzing a limited number of cases or hypotheses

Math Kangaroo 袋鼠数学竞赛 9-10 年级教学大纲

1a. Geometry — plane geometry

• symmetry
• Pythagorean theorem
• similarity
• areaof simple plane figures
• angle calculations (parallel and normal angles, angles in a circle, angles in triangles and simple polygons)
• circles
• parabola
• rotation, translation, scaling
• point coordinates without computations
• simple regular polygons

1b. Geometry — solid geometry

• spatial relationships
• cubes, prisms, pyramids
• spheres, cones, cylinders
• Platonic solids
• volume
• 3-d movement of one- and two-dimensional objects, ¡.e. knots, folding, etc.

2. Number Theory

• number puzzles
• simple usage of powers of numbers
• prime numbers
• use of prime factorisation (low level)
• using digits
• number patterns
• simple Diophantine equations
• very simple modulo calculations, no modulo calculus

3a. Functions, Sequences

• interpreting simple graphs
• simple arithmetic and geometric sequences
• simple functional equations
• simple finite recursions

3b. Algebra

• addition, subtraction and multiplication of polynomials
• powers and roots
• equations, simple quadratic equations
• simple systems of linear equations
• simple inequalities; solutions with sets written as intervals

4a. Combinatorics and Probability

• simple combinatorics as for instance countable permutations
• simple probability without theoretical knowledge
• inclusion/exclusion principle

4b. Logic / Puzzles

Math Kangaroo 袋鼠数学竞赛 11-12 年级教学大纲

1a. Geometry — plane geometry

• lines, segments, polygons
• congruence and similarity
• symmetry
• Pythagorean theorem
• areaofsimple plane figures (including those that can be solved by breaking a shape into smaller self-similar shapes)
• angle calculations (parallel and normal angles, angles in a circle, angles in triangles and polygons)
• circles and parabolas
• concurrency, collinearity and concyclicity
• rotation, reflection, translation, homothety (i.e. isometries and similarities)
• regular polygons

1b. Geometry — plane analytic geometry

• point coordinates, equations of the line, the circle and the parabola
• calculating points and lines in the plane
• triangle calculations with trigonometric methods

1c. Geometry — solid geometry

• spatial relationships (chirality/spatial orientation, nets of solids)
• cubes, prisms, pyramids
• spheres, cones, cylinders
• Platonic solids
• point coordinates
• volume
• projections
• 3-d movement of one- and two-dimensional objects, ¡.e. knots, folding, etc.

2. Number Theory

• number puzzles
• powers of numbers
• prime numbers
• prime factorisation
• triangular numbers
• Diophantine equations
• divisibility and simple modulo calculations, parity considerations

3a. Functions, Sequences

• interpreting graphs
• simple arithmetic and geometric sequences, other well-defined sequences (e.g. by recursion)
• simple functional equations

3b. Algebra

• absolute value
• powers and roots
• logarithms (only elementary properties, no change of base)
• systems of equations; replacement or change of variables
• simple inequalities; solutions with sets written as intervals
• factorising simple polynomials
• quadratic equations / polynomial equations
• solving worded or situational questions by applying algebraic methods

4a. Combinatorics and Probability

• n! (permutations)
• binomial coefficients; number of subsets
• inclusion/exclusion principle
• systematic counting (by analysing cases)
• calculating with probability trees

4b. Logic / Puzzles

• interpretation of a problem: the possibility of reduction of the problem to another problem in any other subject
• semantics and syntax: inference of facts from partial information in a network of logically connected statements
• models: puzzles created from a specific set of axioms and/or rules
• language structure
• Boolean problems (e.g. truth-tellers and liars)

上课规则

在上课前，请您确保和孩子做好以下的准备，以免耽误上课。

• 家长们协助孩子安装上课软件 Zoom，协助孩子调试设备，方便进行线上学习。
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• 让孩子熟悉使用 Zoom 的静音，Chat，和举手的功能。
• 为保证课程顺利进行，工作人员将参与上课，进行协助和监督。
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退费规则

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