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;

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