# Mathematics

MATHEMATICS

###### MATHEMATICS

1 Level 1
2 Level 2
3 Level 3
4 Level 4
5 CEMC Competition Training
1 Level 1

Review the mathematics content of each grade in Ontario.

Proficiency in knowledge points and improve math scores in the class.

2 Level 2

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.

3 Level 3

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.

4 Level 4

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.

5 CEMC Competition Training

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;
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;
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;
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;
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