MATHEMATICS
MATHEMATICS
Review the mathematics content of each grade in Ontario.
Proficiency in knowledge points and improve math scores in the class.
On the basis of in-class mathematics, flexibly grasp basic mathematics knowledge through different teaching methods and example design, and improve the interest and ability to apply mathematics in reality.
Learn the characteristics and ideas of different types of Olympic mathematics topics, and train problem-solving thinking.
Enrich the basic knowledge of Olympic mathematics topics and cultivate logical analysis thinking and divergent thinking.
Proficiency in solving common Olympic math problems, and train more complicated problem-solving methods and techniques.
Further improve the ability of mathematical analysis and flexibly apply the methods and thinking.
Analyze the real questions and train the mathematics knowledge and ideas that are often tested in the competition.
Familiar with the requirements of the competition through a large number of real-question exercises and explanations, and to accumulate the knowledge, problem-solving ideas and skills required for the competition.
SINGAPORE MATHEMATICS
Level 1
Number Sense and Numeration
Representing and ordering numbers to 1 000;
Decomposing and composing three-digit numbers;
Adding and subtracting three-digit numbers;
Relating equal-sized groups to multiplication and relating sharing equally to division;
Counting by 1’s, 2’s, 3’s, 4’s, 5’s, 9’s, 10’s, 25’s, and 100’s;
Solving simple problems involving whole numbers
Patterning and Algebra
Identifying, describing, creating and extending repeating patterns and growing and shrinking patterns;
Developing the concept of equality using the addition and subtraction and the equal sign;
Determining the missing numbers in equations involving addition and subtraction;
Using the commutative property and the property of zero in addition to facilitate computation
Geometry and Spatial Sense
Recognizing line and relationship between two lines;
Identifying, measuring, and comparing angles (acute, right, obtuse, straight angles);
Classifying two-dimensional shapes by geometric properties (number of sides and angles);
Composing and decomposing shapes
Measurement
Measuring length using centimetres and metres;
Telling time;
Developing a sense of perimeter, area, mass, capacity;
Investigating the relationship between the size of a unit and the number of units needed to measure the length of an object
Data Management and Probability
Organizing objects into categories using one attribute;
Collecting and organizing categorical data;
Reading and displaying data using concrete graphs and pictographs;
Describing the likelihood that an event will occur
Level 2
Number Sense and Numeration
Representing and ordering numbers to 1 000 000;
Developing the concept of place value to tenths;
Adding and subtracting four-digit numbers and decimal amounts to tenths;
Multiplying and dividing three-digit whole numbers by two-digit whole numbers;
Applying order of operations in expressions with and without brackets;
Investigating fractions of a set;
Solving simple multi-step problems involving whole numbers
Patterning and Algebra
Generating patterns that involve addition, subtraction, multiplication, and division;
Relating the term and the term number in a numeric sequence;
Representing geometric patterns with a number sequence, a number line, and a bar graph;
Using the associative and distributive properties to facilitate computation;
Investigating the properties of zero and one in multiplication
Geometry and Spatial Sense
Classifying three-dimensional figures by geometric properties (number of faces, edges, and vertices);
Relating different types of triangles;
Relating different types of quadrilaterals;
Describing relative locations and paths of motion
Measurement
Representing money amounts to $100;
Measuring length using millimetres, kilometres, and decimal numbers;
Relating seconds to minutes, minutes to hours, hours to days, days to weeks, weeks to months, and months to years;
Determining elapsed time;
Measuring and comparing perimeter and area using grid paper;
Measuring and comparing mass, capacity, and volume using non-standard units
Data Management and Probability
Organizing objects into categories using two attributes;
Collecting and organizing categorical and discrete data;
Reading and displaying data using line plots and simple bar graphs;
Describing probability, in simple games and experiments, as the likelihood that an event will occur
Level 3
Number Sense and Numeration
Developing the concept of place value to thousandths;
Developing the concept of negative integer;
Adding and subtracting decimal amounts to thousandths;
Multiplying and dividing decimals to tenths by decimals to tenths;
Relating fractions and decimals;
Comparing and ordering fractional amounts with like and unlike denominators;
Adding and subtracting fractions;
Solving multi-step problems involving whole numbers and decimals
Patterning and Algebra
Predicting terms in a pattern;
Representing a pattern using a table of values, ordered pairs and graphs;
Generating patterns that involve multiple additions, subtractions, multiplications, and divisions;
Determining the missing numbers in equations involving multiplication and division;
Solving equations using concrete materials and guess and check
Geometry and Spatial Sense
Recognizing transformations and symmetries;
Relating symmetries to two-dimensional shapes;
Distinguishing among polygons and among prisms;
Naming prisms and pyramids, classifying prisms and pyramids by geometric properties;
Plotting points on number axis;
Describing location using a grid system
Measurement
Measuring time intervals to the nearest minute;
Relating the 12-hour clock to the 24-hour clock;
Relating years to decades and decades to centuries;
Measuring and comparing perimeter, area, mass, capacity, and volume using standard units;
Developing and applying area and perimeter relationships for a square and a rectangle;
Identifying temperature benchmarks, measuring temperature
Data Management and Probability
Organizing objects into categories using more than two attributes;
Collecting and organizing discrete and continuous data;
Reading and displaying data using vertical and horizontal bar graphs, stem-and-leaf plots and double bar graphs;
Understanding mean, mode and median;
Predicting the frequency of an outcome;
Investigating how the number of repetitions of a probability experiment affects the conclusion drawn
Level 4
Number Sense and Numeration
Representing and ordering integers, decimals, and fractions;
Four operations of integers, decimals, and fractions;
Relating fractions, decimals, and percents;
Representing squares and square roots;
Estimating 10%, 25%, 50%, and 75% of a quantity;
Solving multi-step problems involving integers, decimals, fractions, percents and unit rates
Patterning and Algebra
Representing linear growing patterns;
Representing patterns algebraically;
Investigating variables as unknown and changing quantities;
Demonstrating equality using multiplication or division in equations with unknown quantities on both sides
Geometry and Spatial Sense
Recognizing two-dimensional shapes' geometric properties;
Constructing two-dimensional and three-dimensional figures;
Identifying congruent shapes;
Constructing nets of prisms and pyramids;
Representing figures using views and isometric sketches;
Iocating objects using the cardinal directions;
Plotting points in coordinate system
Measurement
Converting between different units of length, area, mass, capacity, and volume;
Developing and applying volume and surface area relationship for a right rectangular prism;
Developing and applying area relationships for a triangle, a parallelogram, and a trapezoid;
Developing and applying volume and surface area relationships for a triangular and a rectangular prism;
Developing and applying the formula for the volume of a prism
Data Management and Probability
Collecting and organizing categorical, discrete, and continuous data;
Displaying data using broken-line and continuous line graphs, relative frequency tables and circle graphs;
Selecting appropriate graphical representations;
Sampling data from a population;
Using continuous line graphs and mean to compare sets of data;
Representing probability using fractions, finding theoretical probabilities;
Predicting the frequency of an outcome based on the theoretical probability