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## Math  Level 1

Number Sense and Operations within 10

• Count number to 10 in concrete and pictorial way

• Compare the number sets within 10 using crocodile method and inequality symbols

• Understand the meaning of addition and subtraction

• Add numbers within 10 by counting on

• Subtract numbers within 10 by counting back

• Practicing addition and subtraction within 10

• Make addition and subtraction stories

• Solve one-step addition and subtraction stories and word problems

Number Bonds

• Understand the branches of the number bonds

• Make number bonds

• Complete the number bonds with missing values

• Make number bonds with more than two branches

Ordinal Numbers

• Name the positions

• Express the position with ordinal numbers and words

• Identify the correct position

Shapes and Patterns

• Identify and naming 2-dimensional shapes

• Name sides and corners of basic shapes

• Identify and recognizing shapes in everyday objects

• Group shapes by size, shapes and color

• Complete the shape patterns in sequence with given figures

Number Sense and Operations within 20

• Counting number from 10 to 20 in concrete and pictorial way

• Use tens and ones to show numbers within 20

• Compare the number sets within 20 using crocodile method and inequality symbols

• Arrange the numbers with increasing or decreasing order within 20

• Add numbers within 20 by counting on

• Subtract numbers within 20 by counting back

• Decompose and compose numbers to solve subtraction stories and addition stories

• Observe and complete the number pattern with given sequence

Length

• Compare heights and lengths for two or more objects

• Compare lengths using a start line

• Measure and compare length using common objects

• Measure length in units

• Hand on activities for measuring the length of objects

Mass/Weight

• Understanding how the scales work

• Compare masses and weights for two or more objects

• Measure and compare mass or weight using given unit

Number Sense and Operations within 40

• Count numbers from 20 to 40 in concrete and pictorial way

• Use tens and ones to show numbers from 20 to 40

• Compare the number sets within 40 using crocodile method and inequality symbols

• Arrange the numbers within 20 according to the given order

• Decompose and compose numbers to solve subtraction and addition problems

• Addition and subtraction with regrouping and without regroup for the numbers within 40

• Addition problems involving three numbers

• Solve one-step addition and subtraction word problems

• Observe and complete the number pattern with given sequence

Number Sense and Operations within 100

• Count numbers to 100 in concrete and pictorial way

• Use tens and ones to show numbers within 100

• Compare the number sets within 100 using crocodile method and inequality symbols

• Arrange the numbers within 100 according to the given order

• Decompose and compose numbers to solve subtraction and addition problems

• Addition and subtraction with regrouping and without regroup for the numbers within 100

• Addition problems involving three numbers

• Solve one-step addition and subtraction word problems

• Observe and complete the number pattern with given sequence

• Learn to extend and apply understanding of the number sense to the number over 100

Time

• Understand how the hour hand and minute hand work

• Tell time to hour and half hour using digital and analog clocks

• Tell time in everyday life

Money

• Identify and name the value of dollar bills, quarters, dimes, nickels, and pennies

• Use dollar (\$) and cent () symbols appropriately

• Find value of a group of coins and notes

• Exchange coins and notes

• Add and subtraction money in cents or dollars

• Apply the concepts of money in everyday life

• Solve the word problems in money

Extended Content:

Picture Graphs

• Understand and read data from picture graphs

• Understand and interpret data from picture graphs

• Create picture graphs based on the given data

Multiplication

• Understanding the concept of multiplication – repeated addition

• Introduce the multiplication table of 2, 5 and 10 in concrete and pictorial way

• Make multiplication equations and stories

• Solve division word problems

Division

• Understanding the concept of division – equal sharing and equal grouping

• Find the equal number of items in each group

• Find the number of equal groups

• Make division equations and stories

• Solve division word problems

## Math Level 2

Number Sense and Operations within 1,000

• Count number to 1,000 in concrete and pictorial way

• Number sense with ones, tens, hundreds, and thousands

• Understand the place value of number within 1,000

• Identify, represent, and write numbers to 1,000 using base ten, standard form, and expanded form

• Form the correct number with the given clues

• Compare 3-digit numbers using greater than, less than, and equal to with corresponding symbols

• Compare and arrange multiple numbers within 1,000

• Recognize and complete number patterns

• Strategy of performing mental addition and subtraction of 2-digit, 3-digit and 1-digit numbers

• Strategy of performing mental addition and subtraction of 2-digit and 3-digit numbers without regrouping

• Strategy of performing mental addition and subtraction of 2-digit and 3-digit numbers with regrouping ones, tens and hundreds

• Introduce the bar model for solving word problems

• Solve multi-step word problems

Multiplication and Division

• Construct multiplication facts of 2, 3, 4, 5 and 10

• Develop and understand of number sense through skip-counting, repeating addition

• Establish and understand the connection with arrays and multiplication

• Introduce the bar model for solving word problems

• Construct division facts of 2, 3, 4, 5 and 10

• Develop and understand of sharing equally and using equal groups

• Divide numbers using multiplication facts

• Write multiplication and division fact families

• Solve word problems in concrete way and using bar model

• Real-world problems in multiplication and division

Length

• Establish and give a picture of meters and centimeter with daily object

• Estimate and measure length by using meter ruler

• Measure the object in centimeter

• Tell and read the scale on the ruler without aligning 0

• Identify appropriate units of measuring length

• Comparing and ordering multiple length

• Four operations in length

• Solve word problems involve in length with bar model, equation and long operation

Mass

• Understand how to read the mass with different kind of scale

• Measure the object in kilograms and grams

• Identify appropriate units of measuring mass

• Compare and order multiple masses

• Four operations problems in mass

• Solve word problems involve in mass with bar model, equation, and long operation

Fractions

• Introduce fractions and unit fractions

• Understand parts and whole

• Identify and recognize the equal shares of an identical whole

• Compare and order multiple fractions (like fraction and like numerator fraction)

• Add and subtract fractions with common denominators

• Understand how to make a whole

• Solve word problems involve in fractions

Shapes, Solid Figures and Patterns

• Recall – Recognize 2-Dimensional and 3-Dimensional shapes

• Identify shapes and make figures

• Draw the given figure on dot grid and square grid

• Complete and identify the patterns with 2D and 3D shapes

• Make compound shapes or identify the shapes within the compound shapes

• Combine solids to make new figures

Time

• Recall – Telling time to an hour and half an hour

• Telling time to 5 minutes

• Telling time using a.m. and p.m.

• Draw the hour and minute hand on the clock face to show the time

• Read and write the corresponding time from analog and digital clocks

• Find the time after giving the start time and the duration of half or one hour

Money

• Recall – Identify the coins and notes for US dollars and cents

• Count the amount of money mixed with coins and notes

• Convert the value of money in cents and dollars

• Compare and order the amount of money

• Solve word problems related to money with bar model and concrete way

Volume

• Introduce the idea of volume

• Use several real-world examples to guild the students understand volume in a more comprehensive way

• Measure volume in liters

• Compare volumes of liquid with “more than”, “less than” or “same as”

• Compare and order volumes in liters

• Solve word problems related to adding, subtracting, multiplying and dividing volume

Picture Graphs

• Recall – Read the picture graphs

• Understand picture graphs with scales

• Use the corresponding data from picture graphs to answer questions

• Compare the quantities with picture graphs

• Create picture graphs with scales

Extended Content:

Line plots

• Introduce the line plots

• Read and understand line plots

• Use the corresponding data from line plots to answer questions

• Convert the data between bar graphs and line plots

## Math Level 3

Number Sense and Operations within 10,000

• Count number to 10,000 in concrete and pictorial way

• Write the given numbers in numerals and words

• Utilize place value and understand to compute values

• Represent, express and write numbers to 10,000 using standard form and expanded form

• Form the correct number with the given clues

• Compare numbers within 10,000 using the corresponding symbols

• Arrange multiple numbers within 10,000 with different order

• Complete the number patterns within 10,000 and create number patterns with own rules

• Perform addition with and without regrouping numbers

• Perform subtraction with and without regrouping numbers

• Strategy of performing mental addition and subtraction of numbers with and without regrouping

• Strategy of performing critical thinking of addition and subtraction within 10,000

• Solve up to two-step word problems related to addition and subtraction with bar model and concrete way

• Using bar models to solve real-world problems in addition and subtraction within 10,000

Multiplication facts and Division facts with 6, 7, 8 and 9

• Construct multiplication facts of 6, 7, 8, and 9

• Understand the properties of multiplication

• Construct division facts of 6, 7, 8, and 9

• Write multiplication and division fact families

• Word problems involve in multiplication facts and division facts with 6, 7, 8, and 9

Multiplication and Division

• 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

• Strategy of performing mental calculation in multiplication

• Make the connection with number bonds and multiplication

• Understand and look for quotient and remainder by dividing

• Divide 2-digit/3-digit number by 1-digit number with long term division

• Solve up to two-step word problems related to multiplication and division

• Using bar models to solve real-world problems in multiplication and division

Money

• Recall – counting money in dollars and cents and converting money

• Understand value of \$1,000 by forming notes and cents

• Addition involve money mixed with dollars and cents with/without regrouping

• Subtraction involve money mixed with dollars and cents with/without regrouping

• Solve the word problems related to money with four operations

• Solve the real-world problems related to money

Measurement

• Recall – Estimating and measuring length in meters and centimeters

• Recall – Measuring mass in kilograms or grams

• Measurement and conversion of length in centimeters, meters and kilometers

• Measurement and conversion of mass in grams and kilograms

• Understand the capacity and volume

• Measurement and conversion of volume and capacity in milliliters and liters

• Read and draw the correct volume in measuring beakers

• Express the corresponding measurement in the given scale

• Solve up to two-step word problems related to measurements

• Solve real-world problems and examples related to measurements

Time

• Recall – Telling time to the hour, half hour and 5 minutes

• Recall – Telling time using a.m. and p.m.

• Recall – Time duration of one hour or half hour

• Understand and tell the time to the minute

• Read and write the corresponding time from analog and digital clocks

• Telling time using “past” and “to”

• Draw the hour and minute hand on the clock face to show the time in hours and minutes

• Conversion of hours and minutes

• Measuring time duration in hours and minutes

• Figure out the starting time with given finishing time and time duration

• Figure out the finishing time with given starting time and time duration

• Figure out the time duration with given starting time and finishing time

• Addition and subtraction of time

• Solve word problems and real-world problems related to time

Fractions

• Recall – Naming fractions and equal parts

• Recall - Compare and order multiple like fractions

• Recall – Addition and subtraction of like fractions

• Understand and figure out the equivalent fraction with given fractions

• Read, write and complete the fractions on the number line

• Understand simplifying fractions by dividing same number to numerator and denominator

• Using fraction discs and fraction bars to guild students for understanding how to compare the unlike fractions

• Strategy of comparing fraction with respect to half

• Compare fractions by making equivalent fractions to make the denominators in the same share

• Compare and order multiple unlike fractions in different order

• Addition and subtraction of unlike fractions

• Solve word problems related to fractions

Angles

• Understand the idea of angles

• Understand the right angle and the relationship between the right angles and the daily objects

• Idea of different type of angles (Right angle, Acute angle and Obtuse angle)

• Identify and recognize the type of angles

Perpendicular Lines and Parallel Lines

• Idea of perpendicular lines and parallel lines

• Identify perpendicular and parallel lines

• Naming and drawing perpendicular lines and parallel lines

• Idea of vertical and horizontal lines

Perimeter and Area

• Idea of perimeter and area

• Measure and calculate the perimeter and area using square units

• Compare the area and perimeter of figures and shapes using square units, square centimeters

• Measure the area related to half square unit

• Measure the area by splitting and merging the shapes

• Measure the area related to square centimeters and square meters

• Idea and formula of finding the area of squares and rectangles

Bar graphs

• Recall – Reading and interpreting picture graphs with scales

• Reading and interpreting bar graphs

• Solving problems using data in graphs

• Making vertical and horizontal bar graphs with given data

• Mixed practice with tally marks, picture graphs with scale, line plots and bar graphs with/without scale

## Math Level 4

Number Sense and Operations within 100,000

• Count number to 100,000 in concrete and pictorial way

• Write number up to 100,000 in numerals and words

• Understand the place value of numbers within 100,000

• Represent, express and write numbers to 100,000 using standard form and expanded form

• Form the correct number with the given clues

• Compare numbers within 100,00 using the corresponding symbols

• Arrange multiple numbers within 100,000 with different order

• Identify and complete the number patterns up to 100,000

• Create and make the number patterns with own rules

• Round off to the nearest tens, hundreds and thousands

Factors and Multiples

• Understand the idea of factors and multiples

• Understand the common factor and common multiple

• Use the cake/ladder method to figure out the greatest common factor and least common multiple

• Properties of the greatest common factor and least common multiple

Four operations of Whole Numbers

• Recall – Multiply up to a 3-digit number by a 1-digit number

• Recall – Division up to 3-digit number by a 1-digit number with/without remainder

• Multiply 3-digit number by a 2-digit number

• Strategy of multiplying tens, hundreds and thousands

• Division up to 4-digit number by a 1-digit number with/without remainder

• Word problems related to four operations of whole numbers

• Solve up to three-step word problems related to four operations of whole numbers

Mixed Number

• Understanding the idea of mixed numbers

• Recognize mixed numbers and improper fractions

• Conversion between mixed numbers and improper fractions

• Compare and order improper fractions, proper fractions and mixed numbers

• Addition and Subtraction related to proper fractions, improper fractions and mixed numbers

• Understanding and applying the idea of fraction of a set

• Word problems related in fractions and mixed numbers

• Solve word problems by using bar models

Angles

• Recall – The types of angles (acute angles, obtuse angles and right angles)

• Understanding how to name the angles

• Learn about the protractor (center, base line, outer scale and inner scale)

• Understand how to measure the given angles with the protractor in degrees

• Learn about how to draw the angles with a protractor

• Idea of quarter, half, three-quarter and complete turns

• Identify clockwise and anticlockwise turns

• Learning 8-point compass

• Telling the direction from the reference point with the 8-point compass

• Understand and find the turns and degrees on 8-point compass

Squares and Rectangles

• Recall – The shapes of squares and rectangles

• Recognize properties of squares and rectangles

• Find unknow length in squares and rectangles

• Find unknown angles in squares and rectangles

• Draw squares and rectangles on square grid

•

Decimals

• Understand and identify tenths, hundreds and thousandths in concrete and pictorial way

• Understand the place value of tenths, hundreds and thousandths

• Represent, express and write the decimals using standard form and expanded form

• Compare and order decimals

• Round off decimals to the nearest whole number, 1st decimal place or 2nd decimals places

• Express a fraction with denominator as 10 or 100 as a decimal

• Convert the fractions to decimals or decimals to fractions

• Add and subtract decimals with 1st decimal place or 2nd decimal places

• Multiply and divide decimals with 1st decimal place or 2nd decimal places

• Estimate the values of decimals to whole number

• Solve word problems related to the decimals (1st decimal place and 2nd decimal places decimals)

Symmetry

• Understand symmetric figures and lines of symmetry

• Identify lines of symmetry of given figures and shapes

• Complete the symmetric figures on square grids

Area and Perimeter

• Recall – Idea of perimeter and area

• Find unknown sides of rectangles and squares by using the properties of squares and rectangles, perimeter of the given squares and rectangles and area of the given squares and rectangles

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

• Understand the fundamental idea of composite figures of squares and rectangles

• Find the perimeter and area of the composite figures with splitting method

• Solve the word problems related to the area or perimeter of composite figures

Tables and Line Graphs

• Recognize and understand the data in different table

• Understand the pros and cons from different tables

• Draw and make an appropriate table with given data

• Complete tables using given data

• Solve problems using given data in tables and line graphs

Time

• Recall – Time in hours and minutes

• Measuring time in seconds

• Understand the 24-hour clock

• Convert the time with 12-hour and 24-hour clock

• Find the starting time with given finishing time and time duration up to seconds

• Find the finishing time with given starting time and time duration up to seconds

• Find the time duration with given starting time and finishing time up to seconds

• Solve word problems related to time in seconds and hours

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