Math Level 1
Number Sense and Operations within 10
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Count number to 10 in concrete and pictorial way
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Compare the number sets within 10 using crocodile method and inequality symbols
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Understand the meaning of addition and subtraction
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Add numbers within 10 by counting on
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Subtract numbers within 10 by counting back
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Practicing addition and subtraction within 10
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Make addition and subtraction stories
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Solve one-step addition and subtraction stories and word problems
Number Bonds
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Understand the branches of the number bonds
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Make number bonds
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Complete the number bonds with missing values
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Make number bonds with more than two branches
Ordinal Numbers
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Name the positions
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Express the position with ordinal numbers and words
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Identify the correct position
Shapes and Patterns
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Identify and naming 2-dimensional shapes
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Name sides and corners of basic shapes
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Identify and recognizing shapes in everyday objects
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Group shapes by size, shapes and color
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Complete the shape patterns in sequence with given figures
Number Sense and Operations within 20
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Counting number from 10 to 20 in concrete and pictorial way
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Use tens and ones to show numbers within 20
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Compare the number sets within 20 using crocodile method and inequality symbols
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Arrange the numbers with increasing or decreasing order within 20
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Add numbers within 20 by counting on
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Subtract numbers within 20 by counting back
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Decompose and compose numbers to solve subtraction stories and addition stories
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Observe and complete the number pattern with given sequence
Length
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Compare heights and lengths for two or more objects
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Compare lengths using a start line
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Measure and compare length using common objects
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Measure length in units
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Hand on activities for measuring the length of objects
Mass/Weight
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Understanding how the scales work
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Compare masses and weights for two or more objects
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Measure and compare mass or weight using given unit
Number Sense and Operations within 40
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Count numbers from 20 to 40 in concrete and pictorial way
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Use tens and ones to show numbers from 20 to 40
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Compare the number sets within 40 using crocodile method and inequality symbols
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Arrange the numbers within 20 according to the given order
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Decompose and compose numbers to solve subtraction and addition problems
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Addition and subtraction with regrouping and without regroup for the numbers within 40
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Addition problems involving three numbers
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Solve one-step addition and subtraction word problems
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Observe and complete the number pattern with given sequence
Number Sense and Operations within 100
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Count numbers to 100 in concrete and pictorial way
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Use tens and ones to show numbers within 100
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Compare the number sets within 100 using crocodile method and inequality symbols
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Arrange the numbers within 100 according to the given order
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Decompose and compose numbers to solve subtraction and addition problems
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Addition and subtraction with regrouping and without regroup for the numbers within 100
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Addition problems involving three numbers
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Solve one-step addition and subtraction word problems
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Observe and complete the number pattern with given sequence
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Learn to extend and apply understanding of the number sense to the number over 100
Time
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Understand how the hour hand and minute hand work
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Tell time to hour and half hour using digital and analog clocks
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Tell time in everyday life
Money
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Identify and name the value of dollar bills, quarters, dimes, nickels, and pennies
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Use dollar ($) and cent () symbols appropriately
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Find value of a group of coins and notes
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Exchange coins and notes
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Add and subtraction money in cents or dollars
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Apply the concepts of money in everyday life
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Solve the word problems in money
Extended Content:
Picture Graphs
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Understand and read data from picture graphs
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Understand and interpret data from picture graphs
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Create picture graphs based on the given data
Multiplication
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Understanding the concept of multiplication – repeated addition
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Introduce the multiplication table of 2, 5 and 10 in concrete and pictorial way
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Make multiplication equations and stories
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Solve division word problems
Division
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Understanding the concept of division – equal sharing and equal grouping
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Find the equal number of items in each group
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Find the number of equal groups
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Make division equations and stories
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Solve division word problems
Math Level 2
Number Sense and Operations within 1,000
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Count number to 1,000 in concrete and pictorial way
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Number sense with ones, tens, hundreds, and thousands
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Understand the place value of number within 1,000
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Identify, represent, and write numbers to 1,000 using base ten, standard form, and expanded form
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Form the correct number with the given clues
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Compare 3-digit numbers using greater than, less than, and equal to with corresponding symbols
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Compare and arrange multiple numbers within 1,000
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Recognize and complete number patterns
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Strategy of performing mental addition and subtraction of 2-digit, 3-digit and 1-digit numbers
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Strategy of performing mental addition and subtraction of 2-digit and 3-digit numbers without regrouping
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Strategy of performing mental addition and subtraction of 2-digit and 3-digit numbers with regrouping ones, tens and hundreds
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Introduce the bar model for solving word problems
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Solve multi-step word problems
Multiplication and Division
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Construct multiplication facts of 2, 3, 4, 5 and 10
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Develop and understand of number sense through skip-counting, repeating addition
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Establish and understand the connection with arrays and multiplication
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Introduce the bar model for solving word problems
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Construct division facts of 2, 3, 4, 5 and 10
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Develop and understand of sharing equally and using equal groups
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Divide numbers using multiplication facts
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Write multiplication and division fact families
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Solve word problems in concrete way and using bar model
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Real-world problems in multiplication and division
Length
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Establish and give a picture of meters and centimeter with daily object
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Estimate and measure length by using meter ruler
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Measure the object in centimeter
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Tell and read the scale on the ruler without aligning 0
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Identify appropriate units of measuring length
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Comparing and ordering multiple length
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Four operations in length
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Solve word problems involve in length with bar model, equation and long operation
Mass
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Understand how to read the mass with different kind of scale
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Measure the object in kilograms and grams
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Identify appropriate units of measuring mass
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Compare and order multiple masses
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Four operations problems in mass
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Solve word problems involve in mass with bar model, equation, and long operation
Fractions
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Introduce fractions and unit fractions
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Understand parts and whole
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Identify and recognize the equal shares of an identical whole
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Compare and order multiple fractions (like fraction and like numerator fraction)
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Add and subtract fractions with common denominators
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Understand how to make a whole
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Solve word problems involve in fractions
Shapes, Solid Figures and Patterns
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Recall – Recognize 2-Dimensional and 3-Dimensional shapes
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Identify shapes and make figures
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Draw the given figure on dot grid and square grid
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Complete and identify the patterns with 2D and 3D shapes
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Make compound shapes or identify the shapes within the compound shapes
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Combine solids to make new figures
Time
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Recall – Telling time to an hour and half an hour
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Telling time to 5 minutes
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Telling time using a.m. and p.m.
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Draw the hour and minute hand on the clock face to show the time
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Read and write the corresponding time from analog and digital clocks
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Find the time after giving the start time and the duration of half or one hour
Money
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Recall – Identify the coins and notes for US dollars and cents
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Count the amount of money mixed with coins and notes
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Convert the value of money in cents and dollars
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Compare and order the amount of money
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Solve word problems related to money with bar model and concrete way
Volume
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Introduce the idea of volume
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Use several real-world examples to guild the students understand volume in a more comprehensive way
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Measure volume in liters
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Compare volumes of liquid with “more than”, “less than” or “same as”
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Compare and order volumes in liters
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Solve word problems related to adding, subtracting, multiplying and dividing volume
Picture Graphs
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Recall – Read the picture graphs
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Understand picture graphs with scales
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Use the corresponding data from picture graphs to answer questions
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Compare the quantities with picture graphs
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Create picture graphs with scales
Extended Content:
Line plots
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Introduce the line plots
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Read and understand line plots
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Use the corresponding data from line plots to answer questions
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Convert the data between bar graphs and line plots
Math Level 3
Number Sense and Operations within 10,000
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Count number to 10,000 in concrete and pictorial way
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Write the given numbers in numerals and words
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Utilize place value and understand to compute values
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Represent, express and write numbers to 10,000 using standard form and expanded form
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Form the correct number with the given clues
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Compare numbers within 10,000 using the corresponding symbols
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Arrange multiple numbers within 10,000 with different order
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Complete the number patterns within 10,000 and create number patterns with own rules
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Perform addition with and without regrouping numbers
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Perform subtraction with and without regrouping numbers
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Strategy of performing mental addition and subtraction of numbers with and without regrouping
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Strategy of performing critical thinking of addition and subtraction within 10,000
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Solve up to two-step word problems related to addition and subtraction with bar model and concrete way
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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
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Construct multiplication facts of 6, 7, 8, and 9
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Understand the properties of multiplication
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Construct division facts of 6, 7, 8, and 9
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Write multiplication and division fact families
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Word problems involve in multiplication facts and division facts with 6, 7, 8, and 9
Multiplication and Division
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Multiply 2-digit/3-digit number by 1-digit number without regrouping
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Multiply 2-digit/3-digit number by 1-digit number by regrouping ones, tens, hundreds and thousands
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Strategy of performing mental calculation in multiplication
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Make the connection with number bonds and multiplication
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Understand and look for quotient and remainder by dividing
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Divide 2-digit/3-digit number by 1-digit number with long term division
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Solve up to two-step word problems related to multiplication and division
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Using bar models to solve real-world problems in multiplication and division
Money
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Recall – counting money in dollars and cents and converting money
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Understand value of $1,000 by forming notes and cents
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Addition involve money mixed with dollars and cents with/without regrouping
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Subtraction involve money mixed with dollars and cents with/without regrouping
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Solve the word problems related to money with four operations
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Solve the real-world problems related to money
Measurement
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Recall – Estimating and measuring length in meters and centimeters
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Recall – Measuring mass in kilograms or grams
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Measurement and conversion of length in centimeters, meters and kilometers
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Measurement and conversion of mass in grams and kilograms
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Understand the capacity and volume
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Measurement and conversion of volume and capacity in milliliters and liters
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Read and draw the correct volume in measuring beakers
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Express the corresponding measurement in the given scale
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Solve up to two-step word problems related to measurements
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Solve real-world problems and examples related to measurements
Time
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Recall – Telling time to the hour, half hour and 5 minutes
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Recall – Telling time using a.m. and p.m.
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Recall – Time duration of one hour or half hour
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Understand and tell the time to the minute
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Read and write the corresponding time from analog and digital clocks
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Telling time using “past” and “to”
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Draw the hour and minute hand on the clock face to show the time in hours and minutes
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Conversion of hours and minutes
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Measuring time duration in hours and minutes
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Figure out the starting time with given finishing time and time duration
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Figure out the finishing time with given starting time and time duration
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Figure out the time duration with given starting time and finishing time
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Addition and subtraction of time
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Solve word problems and real-world problems related to time
Fractions
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Recall – Naming fractions and equal parts
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Recall - Compare and order multiple like fractions
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Recall – Addition and subtraction of like fractions
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Understand and figure out the equivalent fraction with given fractions
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Read, write and complete the fractions on the number line
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Understand simplifying fractions by dividing same number to numerator and denominator
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Using fraction discs and fraction bars to guild students for understanding how to compare the unlike fractions
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Strategy of comparing fraction with respect to half
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Compare fractions by making equivalent fractions to make the denominators in the same share
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Compare and order multiple unlike fractions in different order
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Addition and subtraction of unlike fractions
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Solve word problems related to fractions
Angles
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Understand the idea of angles
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Understand the right angle and the relationship between the right angles and the daily objects
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Idea of different type of angles (Right angle, Acute angle and Obtuse angle)
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Identify and recognize the type of angles
Perpendicular Lines and Parallel Lines
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Idea of perpendicular lines and parallel lines
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Identify perpendicular and parallel lines
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Naming and drawing perpendicular lines and parallel lines
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Idea of vertical and horizontal lines
Perimeter and Area
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Idea of perimeter and area
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Measure and calculate the perimeter and area using square units
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Compare the area and perimeter of figures and shapes using square units, square centimeters
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Measure the area related to half square unit
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Measure the area by splitting and merging the shapes
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Measure the area related to square centimeters and square meters
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Idea and formula of finding the area of squares and rectangles
Bar graphs
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Recall – Reading and interpreting picture graphs with scales
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Reading and interpreting bar graphs
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Solving problems using data in graphs
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Making vertical and horizontal bar graphs with given data
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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
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Count number to 100,000 in concrete and pictorial way
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Write number up to 100,000 in numerals and words
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Understand the place value of numbers within 100,000
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Represent, express and write numbers to 100,000 using standard form and expanded form
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Form the correct number with the given clues
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Compare numbers within 100,00 using the corresponding symbols
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Arrange multiple numbers within 100,000 with different order
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Identify and complete the number patterns up to 100,000
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Create and make the number patterns with own rules
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Round off to the nearest tens, hundreds and thousands
Factors and Multiples
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Understand the idea of factors and multiples
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Understand the common factor and common multiple
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Use the cake/ladder method to figure out the greatest common factor and least common multiple
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Properties of the greatest common factor and least common multiple
Four operations of Whole Numbers
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Recall – Multiply up to a 3-digit number by a 1-digit number
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Recall – Division up to 3-digit number by a 1-digit number with/without remainder
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Multiply 3-digit number by a 2-digit number
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Strategy of multiplying tens, hundreds and thousands
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Division up to 4-digit number by a 1-digit number with/without remainder
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Word problems related to four operations of whole numbers
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Solve up to three-step word problems related to four operations of whole numbers
Mixed Number
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Understanding the idea of mixed numbers
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Recognize mixed numbers and improper fractions
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Conversion between mixed numbers and improper fractions
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Compare and order improper fractions, proper fractions and mixed numbers
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Addition and Subtraction related to proper fractions, improper fractions and mixed numbers
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Understanding and applying the idea of fraction of a set
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Word problems related in fractions and mixed numbers
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Solve word problems by using bar models
Angles
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Recall – The types of angles (acute angles, obtuse angles and right angles)
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Understanding how to name the angles
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Learn about the protractor (center, base line, outer scale and inner scale)
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Understand how to measure the given angles with the protractor in degrees
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Learn about how to draw the angles with a protractor
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Idea of quarter, half, three-quarter and complete turns
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Identify clockwise and anticlockwise turns
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Learning 8-point compass
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Telling the direction from the reference point with the 8-point compass
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Understand and find the turns and degrees on 8-point compass
Squares and Rectangles
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Recall – The shapes of squares and rectangles
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Recognize properties of squares and rectangles
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Find unknow length in squares and rectangles
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Find unknown angles in squares and rectangles
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Draw squares and rectangles on square grid
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Decimals
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Understand and identify tenths, hundreds and thousandths in concrete and pictorial way
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Understand the place value of tenths, hundreds and thousandths
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Represent, express and write the decimals using standard form and expanded form
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Compare and order decimals
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Round off decimals to the nearest whole number, 1st decimal place or 2nd decimals places
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Express a fraction with denominator as 10 or 100 as a decimal
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Convert the fractions to decimals or decimals to fractions
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Add and subtract decimals with 1st decimal place or 2nd decimal places
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Multiply and divide decimals with 1st decimal place or 2nd decimal places
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Estimate the values of decimals to whole number
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Solve word problems related to the decimals (1st decimal place and 2nd decimal places decimals)
Symmetry
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Understand symmetric figures and lines of symmetry
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Identify lines of symmetry of given figures and shapes
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Complete the symmetric figures on square grids
Area and Perimeter
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Recall – Idea of perimeter and area
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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
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Solve the word problems related to the area or perimeter of squares and rectangles
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Understand the fundamental idea of composite figures of squares and rectangles
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Find the perimeter and area of the composite figures with splitting method
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Solve the word problems related to the area or perimeter of composite figures
Tables and Line Graphs
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Recognize and understand the data in different table
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Understand the pros and cons from different tables
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Draw and make an appropriate table with given data
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Complete tables using given data
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Solve problems using given data in tables and line graphs
Time
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Recall – Time in hours and minutes
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Measuring time in seconds
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Understand the 24-hour clock
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Convert the time with 12-hour and 24-hour clock
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Find the starting time with given finishing time and time duration up to seconds
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Find the finishing time with given starting time and time duration up to seconds
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Find the time duration with given starting time and finishing time up to seconds
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Solve word problems related to time in seconds and hours