학습 센터 (PKG12)
과외 · 방과후
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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 onestep 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 2dimensional 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 onestep 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 onestep 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 3digit 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 2digit, 3digit and 1digit numbers

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

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

Introduce the bar model for solving word problems

Solve multistep word problems
Multiplication and Division

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

Develop and understand of number sense through skipcounting, 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

Realworld 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 2Dimensional and 3Dimensional 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 realworld 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 twostep word problems related to addition and subtraction with bar model and concrete way

Using bar models to solve realworld 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 2digit/3digit number by 1digit number without regrouping

Multiply 2digit/3digit number by 1digit 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 2digit/3digit number by 1digit number with long term division

Solve up to twostep word problems related to multiplication and division

Using bar models to solve realworld 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 realworld 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 twostep word problems related to measurements

Solve realworld 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 realworld 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 3digit number by a 1digit number

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

Multiply 3digit number by a 2digit number

Strategy of multiplying tens, hundreds and thousands

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

Word problems related to four operations of whole numbers

Solve up to threestep 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, threequarter and complete turns

Identify clockwise and anticlockwise turns

Learning 8point compass

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

Understand and find the turns and degrees on 8point 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 24hour clock

Convert the time with 12hour and 24hour 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