## Math Level 1 (K-Grade 1)

Operations and Algebraic Thinking :

Understand Numbers within 10

● Counting from 1 to 10

● Reading and writing numbers in numerals and words

● Matching numerals to words

● Comparing numbers

● Making number patterns

Adding and Subtracting Numbers within 10

● Adding and Subtracting using number bonds and counting on

● Subtracting using crossing out and counting back

● Addition and Subtraction equations, stories, and fact families

Understanding, Adding and Subtracting Numbers within 20

● Counting from 10 to 20

● Comparing and Arrange numbers from 10 to 20

● Adding by counting on and making 10

● Subtracting by counting back and from 10

● Solving addition and subtraction word problems

Understanding, Adding and Subtracting Numbers within 40

● Counting from 20 to 40

● Comparing and arranging numbers from 20 to 40

● Adding and subtracting with and without regrouping

● Adding three numbers

● Solving addition and subtraction word problems

Multiplying and Dividing

● Multiplying by adding the same number

● Multiplication equations and stories

● Dividing by finding the equal number of items in each group

● Dividing by finding the number of equal groups

● Solving multiplication and division word problems

Understanding, Adding and Subtracting Numbers within 100

● Counting from 40 to 100

● Comparing and arranging numbers from 40 to 100

● Adding and subtracting numbers within 100 with and without regrouping

Number & Operations in Base Ten :

Understanding, Adding and Subtracting Numbers within 20

● Using tens and ones to show numbers from 10 to 20

Understanding, Adding and Subtracting Numbers within 40

● Using tens and ones to show numbers from 20 to 40

Understanding, Adding and Subtracting Numbers within 100

● Using tens and ones to show numbers from 40 to 100

Ordinal Numbers and Positions

● Understanding ordinal numbers

● Describing numbers with position words like “before”, “after”, “between”, “left”, “right”, “next to”

Measurement and Data :

Length and Height

● Compare heights and lengths of two or more objects

● Measure lengths using common objects and with units

Picture Graphs

● Understand, read and interpret data from picture graphs

● Create picture graphs based on given data

Time

● Read time to the hour/half-hour and in everyday life

Money

● Know money in cents and dollars

● Finding the value of groups of coins and notes

● Adding and subtracting money in dollars and cents

● Solving word problems related to money

Geometry :

Shapes and Patterns

● Identify and recognize squares, circles, triangles and rectangles

● Identify sides and corners of shapes

● Group shapes by size, shape and color

● Identify shapes in everyday objects

## Math Level 2A (Grade 1-2)

Operations and Algebraic Thinking:

Understand Numbers within 1000

● Recognize and write numbers within 1000 in numerals and words

● Identify the place value of number within 1000

● Compare and arrange numbers and complete the number patterns within 1000

Adding and Subtracting Numbers within 1000

● Perform mental addition/subtraction of 2-digit/3-digit number and 1-digit number

● Perform addition/subtraction of 2-digit/3-digit number and 2-digit/3-digit number

● Solve word problems on addition and subtraction using part-whole and comparing sets

Multiplying and Dividing

● Multiple 2-digit number by 2, 3, 4, 5

● Divide 2-digit number by 2, 3, 4, 5

● Solve multiplication/division word problems

Fractions

● Understand fractions and equal parts, parts and whole

● Compare and arrange fractions with same denominator or numerator

● Perform addition/subtraction of fraction with same denominator

Measurement and Data :

● Measure, compare, and order lengths in standard units and relate addition/subtraction/multiplication/division to length

● Measure, compare, and order masses in standard units and relate addition/subtraction/multiplication/division to mass

● Measure and compare volume of liquid, and relate addition/subtraction/multiplication/division to volume

● Recognize, express, and compare money in dollars and cents

● Understand and express the time and duration

● Represent and interpret data from picture graphs

Geometry :

● Recognize two-dimensional figures like squares, rectangles, triangles, circles, semicircles and quarter circles, and combine shapes to make new figures

● Recognize three-dimensional figures like cubes, cuboids, cones, cylinders and spheres, and combine solids to make new figures

● Make patterns with shapes or solids

## Math Level 2B (Grade 2)

Term 1

Lesson 1-2

● Count and write numbers within 10000 in numerals and words

● Understand the place value of numbers within 10000

● Compare and arrange numbers within 10000

● Recognize and complete number patterns

Lesson 3-4

● Find sum of numbers within 10000 by number models

● Perform addition of 3-digit/4-digit number and 3-digit/4-digit number by regrouping ones, tens and hundreds

● Perform mental addition of 2-digit number and 2-digit number

Lesson 5 Review

Lesson 6-7

● Find difference of numbers within 10000 by number models

● Perform subtraction of 3-digit/4-digit number and 3-digit/4-digit number by regrouping ones, tens and hundreds

● Perform mental subtraction of 2-digit number and 2-digit number

Lesson 8-9

● Solve for two-step word problems related to addition and subtraction

● Brainstorming and Problem-Solving Practice

Lesson 10 Review

Lesson 11-12

● Multiple numbers by 6, 7, 8, 9

● Divide numbers using multiplication facts

● Solve two-step word problems related to multiplication and division

Lesson 13-14

● Multiply 2-digit/3-digit number by 1-digit number without regrouping

● Multiply 2-digit/3-digit number by 1-digit number by regrouping ones, tens, hundreds and thousands

Lesson 15 Review

Lesson 16-17

● Look for quotient and remainder by dividing

● Divide 2-digit/3-digit number by 1-digit number without regrouping

● Multiply 2-digit/3-digit number by 1-digit number by regrouping ones, tens, and hundreds

Lesson 18-19

● Solve 1-step word problems related to multiplication and division

● Solve two-step word problems on the four operations

Lesson 20-21 Review & Test

Term 2

Lesson 22-23

● Add money in dollars and cents

● Subtract money in dollars and cents

● Solve related money word problems

Lesson 24-25

● Express length in kilometers, meters, or centimeters

● Read correct mass on scale, and express mass in kilograms and grams

● Read correct volume in measuring beakers, and express volume in liters and milliliters

● Solve word problems related to length, mass and volume

Lesson 26 Review

Lesson 27-28

● Read and interpret data from bar graphs

● Solve word problems using data from bar graphs

Lesson 29-30

● Recognize and understand equivalent fractions

● Express a fraction in its simplest form

● Perform addition/subtraction of fraction with different denominators

Lesson 31 Review

Lesson 32-33

● Express time in minutes or hours and minutes

● Look for duration given two different times

● Look for starting time or ending time

● Solve word problems related to time

Lesson 34-35

● Identify angles and right angles

● Identify and draw perpendicular lines in grids and figures

● Identify and draw parallel lines in grids and figures

Lesson 36 Review

Lesson 37-38

● Understand perimeter and area of figures in squares units

● Look for perimeters and area of rectangles and squares using formula

Lesson 39-40

● Solve word problems related to perimeter and area of rectangles or squares

● Brainstorming and Problem-Solving Practice

Lesson 41-42 Review & Test

## Math Level 3A (Grade 3)

Operations and Algebraic Thinking :

Understand Numbers within 100,000

● Recognize and write numbers within 100,000 in numerals and words

● Identify the place value of numbers within 100,000

● Compare, order and complete number patterns within 100,000

● Round off numbers to the nearest ten, hundred and thousand, and estimate sums and difference

Operations of multi-digit whole numbers

● List factors, common factors, multiples and common multiples of whole numbers within 100

● Perform multiplication and division by 1-digit/2-digit numbers

● Solve word problems related to whole numbers

Fractions

● Recognize mixed numbers and improper fractions, convert mixed numbers to improper fractions and convert improper fractions to mixed numbers

● Compare and order fractions with different numerators and different denominators

● Perform addition and subtraction fractions (mixed numbers and improper fractions) with different numerators and denominators

Decimals

● Recognize decimal place - tenths, hundredths and thousands

● Compare and order decimals, and round off decimals to the nearest whole number, 1 decimal place or 2 decimal places

● Perform four operations (addition, subtraction, multiplication, division) decimals and estimate the value of decimals

● Express a fraction (with denominator as 10 or 100) as a decimal, and vice versa, and solve word problems related to decimals

Measurement and Data :

● Measure time in seconds, express time in 12-hour clock and 24-hour clock, and understand the starting or ending time given the duration (in hours and minutes), and solve word problems related to time

● Interpret data in a table, complete table using given data, and solve problems related to given data

Geometry :

● Understand angles, turns, 8-point compass and measure angles

● Recognize properties of squares and rectangles, and find unknown lengths and angles in squares and rectangles

● Calculate perimeter and area of rectangles, squares and composite figures, look for missing length or width of rectangle/square given perimeter or area, and solve related word problems

● Understand the concept of symmetry, recognize symmetric figures and the lines of symmetry in figures, and complete symmetric figures and patterns

## Math Level 3B (Grade 3-4)

Operations and Algebraic Thinking :

Understand Numbers within 10 million

● Recognize and write numbers within 10 million in numerals and words

● Identify the place value of number within 10 million

Operations of multi-digit whole numbers

● Perform multiplication of tens, hundreds, thousands and their multiples

● Perform division of tens, hundreds, thousands and their multiples

● Perform order of operations for whole numbers

● Solve word problems related to whole numbers

Fractions

● Use equivalent fractions as a strategy to add and subtract fractions, and mixed numbers

● Perform multiplication of whole numbers, fractions (proper and improper fractions) and mixed numbers

● Solve word problems related to fractions

Decimals

● Perform conversion from fractions (proper and improper fractions) to decimals

● Multiply and divide decimals to thousands by tens, hundreds, thousands and their multiples

Measurement and Data :

● Recognize volume as an attribute of solid figure, understand concepts of volume measurement

● Measure volumes by counting unit cubes, using cubic cm, l, and ml, and apply formula to calculate volume of cubes and cuboids

● Understand the concept of percentage, relate percent to decimals and fractions, and calculate percentage based on quantities and vice versa

● Understand the concept of average, calculate the average or total number, and solve real-world word problems related to average

● Understand the concept of ratio, look for ratio and equivalent ratio of two or three given quantities, and solve word problems related to ratio

● Understand the rate between different currency, and solve real-world word problems related to rate

Geometry :

● Recognize and understand angles on a straight line, angles at a point and vertically opposite angles, and look for unknown angles using angle properties

● Recognize and classify triangles, look for unknown angles in right-angled, isosceles and equilateral triangles, and apply formula to calculate the area of triangles

● Recognize and classify quadrilaterals, look for unknown angles in a parallelogram, rhombus and trapezium

## Math Level 4 (Grade 4)

Operations and Algebraic Thinking :

● Apply and extend previous understanding of arithmetic to algebraic expression

✧ Write and evaluate numerical expressions involving whole-number exponents

✧ Write, read, and evaluate expressions in which letters stands for numbers

✧ Apply the properties of operations to generate equivalent expressions

● Apply and extend previous understanding of multiplication and division to divide fractions by fractions

● Fluently divide multi-digit numbers using the standard algorithm

● Fluently perform addition and subtraction of multi-digit decimals

● Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12, and use distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers without common factor

Measurement and Data :

● Understand ratio, rate, and proportion concept and use ratio and rate reasoning to solve real-world mathematical problems

● Understand percentage, discount, GST, percentage increase and percentage decrease, and solve real-world mathematical problems

● Read and interpret pie charts and use data from pie chart to solve word problems

● Understand distance and speed, look for average speed and solve word problems related to speed

● Use angle properties to find unknown angles in geometric figures like square, rectangle, parallelogram, rhombus, trapezium, and different types of triangles

Geometry :

● Recognize center, radius, diameter and circumference of a circle as well as semicircle and quarter circle, calculate circumference and area of a circle using formula, and solve word problems related to circles and composite figures

● Calculate the volume of a right rectangular prism, look for one dimension of a cuboid given its volume and other dimensions, or the edge of a cube given its volume, find surface area and volume of solids and liquids and solve related word problems

● Represent three-dimensional figures such as cube, cuboid, prism and pyramid using nets made up of rectangles and triangles, and use the nets to find the number of surfaces and surface area of these figures