Below is the module of Little Newton that taps both the K-12 curriculum with solving techniques
using the best practices of Singapore Math. Modules cover both mechanicalsums (numbers and
equations) and Problemsums (word problems).
Grade 1
Numbers Up to 10
● Counting in numbers
● Counting in words
● Comparing objects to numbers
● Comparing sets
● Counting to add 1 more
● Counting to subtract 1
● Finding the missing number in the number sequence
● Introduction to number bonds.
Addition within 10
● Number bonds to add two numbers within 10
● Count on to add within 10
● Solve word problems involving addition within 10
Subtraction Within 10
● Subtract by taking away
● Count back to subtract within 10
● Count on to subtract within 10
● Use number bonds to subtract
● Solve word problems involving subtraction by finding the other part
● Solve word problems involving subtraction by taking away
Ordinal Numbers
● Use first, second, up to tenth
● Use symbols 1st, 2nd, 3rd, up to 10th
● Use before, after and between to tell position
● Use left, right and next to
2D Shapes
● Identify 2D shapes
● Identify 2D shapes from real objects and pictures
● Compare shape attributes - sides, corners, sizes and colours
● Complete patterns with 2D shapes
Numbers Up to 20
● Count in numbers
● Count in words
● Comparing objects to numbers
● Comparing sets
● Counting to add 1 more
● Counting to subtract 1
● Finding the missing number in the number sequence
● Introduction to number bonds.
● Use place value charts to show numbers to 20
● Use place value to compare two numbers within 20
● Use place value to compare three numbers within 20
● Find a number more than another number
● Find a number less than another number
● Order numbers within 20 by making number patterns
Addition & Subtraction Within 20
● Add by counting on
● Add two 1-digit numbers by making 10
● Subtract by counting back
● Subtract 1-digit numbers from 2-digit numbers by grouping into 10 and ones using place
value
● Solve one-step word problems involving addition
● Solve one-step word problems involving subtraction
Length
● Measure length using common objects
● Measure length using different objects
● Compare height - tall and short
● Compare length - long and short
● Use the terms tallest, longest, and shortest
Picture Graphs
● Interpret data in picture graphs
● Describe the data presented in a picture graph using 'most', 'least', 'greatest', 'smallest',
'as much as', and 'as many as'
Numbers Up to 40
● Count in numbers
● Count in words
● Comparing objects to numbers
● Count in numbers
● Count in words
● Comparing objects to numbers
● Comparing sets
● Counting to add 1 more
● Counting to subtract 1
● Finding the missing number in the number sequence
● Introduction to number bonds.
● Use place value charts to show numbers to 40
● Use place value to compare two numbers within 40
● Use place value to compare three numbers within 40
● Find a number more than another number
● Find a number less than another number
● Order numbers within 40 by making number patterns
Time
● Tell time from a clock face - using 'o'clock'
● Tell time from a clock face - using 'half past'
● Appropriateness of events at different times of the day
Addition & Subtraction Within 40
● Add two numbers within 40
● Add three 1-digit numbers within 40
● Subtract 1-digit numbers from 2-digit numbers within 40
Numbers Up to 100
● Count in numbers
● Count in words
● Comparing objects to numbers
● Count in numbers
● Count in words
● Comparing objects to numbers
● Comparing sets
● Counting to add 1 more
● Counting to subtract 1
● Finding the missing number in the number sequence
● Introduction to number bonds.
● Use place value charts to show numbers to 100
● Use place value to compare two numbers within 100
● Use place value to compare three numbers within 100
● Find a number more than another number
● Find a number less than another number
● Order numbers within 100 by making number patterns
Addition & Subtraction Within 100
● Add two numbers within 100
● Add three 1-digit numbers within 100
● Subtract 1-digit numbers from 2-digit numbers within 100
Introduction to Multiplication and Division
● Make equal groups
● Write multiplication sentences
● Multiplication up to 40
● Divide by sharing
● Divide by grouping
● Solve word problems involving multiplication within 40
● Solve word problems involving division within 20
Grade 2
Numbers Up To 1000
● Use base ten blocks to read and write numbers to 1000
● Count on by 1s to 1000
● Count on by 10s to 1000
● Count on by 100s to 1000
● Use place value charts to show numbers to 1000
● Write numbers to 1000 in numerals, words and expanded form
● Compare numbers to 1000
● Order 3-digit numbers
● Find the missing numbers in a pattern
● Identify odd and even numbers
Fractions
● Use fractions to describe equal parts
● Name unit fractions
● Recognize and name a fractional part of a whole
● Recognize the number of unit fractions in one whole
● Compare unit fractions
● Compare and order unit fractions
● Use models to add like fractions
● Use models to subtract like fractions
Addition within 1000
● Add 1-digit numbers to 3-digit numbers without regrouping
● Add 2-digit numbers to 3-digit numbers without regrouping
● Add 3-digit numbers without regrouping
● Add up to 3-digit numbers with regrouping in ones
● Add up to 3-digit numbers with regrouping tens
● Add up to 3-digit numbers with regrouping in tens and ones
Subtraction within 1000
● Subtract ones from 3-digit numbers without regrouping
● Subtract 2-digit numbers from 3-digit numbers without regrouping
● Subtract 3-digit numbers without regrouping
● Subtract 3-digit numbers with regrouping in tens and ones
● Subtract 3-digit numbers with regrouping in hundreds and tens
● Subtract 3-digit numbers with regrouping in hundreds, tens and ones
● Subtract within 1000 across zeros
Multiplication and Division
● Multiply using equal groups
● Divide by sharing
● Divide by grouping
● Write multiplication or division equation
● Multiply by 2 skip-counting
● Multiply by 3 skip-counting
● Multiply by 4 skip-counting
● Multiply by 5 skip-counting
● Multiply by 10 skip-counting
● Find related multiplication facts of 2,3,4,5 and 10
● Divide by sharing using related multiplication facts of 2
● Divide by grouping using related multiplication facts of 2
● Divide by sharing using related multiplication facts of 3
● Divide by grouping using related multiplication facts of 3
● Divide by sharing using related multiplication facts of 4
● Divide by grouping using related multiplication facts of 4
● Divide by sharing using related multiplication facts of 5
● Divide by grouping using related multiplication facts of 10
● Solve 1-step word problems involving multiplication
● Solve 1-step word problems involving division
Word Problems and Models
● Use part-whole models to solve addition problems: putting together
● Use part-whole models to solve subtraction problems: finding one part
● Use part-whole models to solve addition problems: adding on
● Use part-whole models to solve subtraction problems: taking away one part
● Use comparison models to solve addition problems: finding the greater number
● Use comparison models to solve subtraction problems: finding the smaller number
2d Shapes
● Identify lines and curves
● Identify and name 2d shapes
● Combine and separate plane shapes
● Make figures with different shapes
● Complete patterns with 2d shapes
3d Shapes
● Identify three-dimensional shapes
● Count sides, vertices, edges and faces
● Make solid figures with three-dimensional shapes
● Make repeating patterns with solid shapes
● Make patterns with solid shapes involving changes in two attributes
Length
● Use a metre ruler to measure length
● Compare and find differences in heights in metres
● Compare and find differences in length in metres
● Use a centimetre ruler to measure length
● Measure a centimetre tape to measure
● Compare and find differences in lengths of objects in centimetres
● Measure length in centimetres using a different start point
● Solve word problems involving length in metres
● Solve word problems involving length in centimetres
Mass
● Use a balance scale to find mass in kilograms
● Estimate mass in grams
● Compare mass using words
● Addition and subtraction of mass
● Multiplication and division of mass
Money
● Put notes and coins together to find the total amount of money
● Read and write the prices in dollars and cents in decimal notation
● Write amounts of money in different ways
● Exchange cents for dollars
● Exchange dollars for cents
● Compare two or three amounts of money
● Solve word problems involving money in dollars only
● Solve word problems involving money in cents only
Time
● Read time to the nearest 5 minutes
● Tell time in hours and minutes
● Use a.m. and p.m. to show morning, afternoon or night
● Use visual cues to tell time
● Find how much time has passed
Volume
● Compare the volume of liquid in containers of the same size
● Estimate volume in litres
● Measure volume in litres
● Solve word problems involving volume
Picture Graphs
● Make and interpret picture graphs
● Interpret picture graphs in both vertical and horizontal forms
● Solve 1-step word problems using data from picture graphs
Grade 3
Numbers to 10 000
● Express the numbers to 10 000 in words and numerals
● Count to 10 000
● Use a place value to show numbers to 10 000
● Show numbers greater than 1000
● Compare numbers with different digits in the thousands place
● Compare numbers with the same digits in the thousands place and hundreds place
● Order numbers using a place value chart
● Look for patterns on a number line
● Identify odd and even numbers
Fractions
● Understand numerators and denominators
● Write the equivalent fraction of a given fraction
● Use multiplication to find equivalent fractions
● Use division to find equivalent fractions
● Express a fraction in its simplest form
● Compare unlike fractions using multiplication
● Compare unlike fractions using division
● Oder like fractions
● Compare fractions with the same numerator
● Compare and order unlike fractions
● Add fractions
● Subtract fractions
Multiplication and Division
● Build up the multiplication table of 6
● Build up the multiplication table of 7
● Build up the multiplication table of 8
● Build up the multiplication table of 9
● Divide to find the number of items in each group using related multiplication facts of 6,7,8
and 9
● Divide to make equal groups using related multiplication facts of 6,7,8, and 9
● Multiply a 2-digit number by a 1-digit number without regrouping
● Multiply a 3-digit number by a 1-digit number without regrouping
● Multiply a 2-digit number by a 1-digit number with regrouping in ones and tens
● Multiply a 3-digit number by a 1-digit number with regrouping in ones, tens and hundres
● Divide a 1-digit number by a 1-digit number without a remainder
● Divide a 2-digit number by a 1-digit number with a remainder
● Divide a 2-digit number by a 1-digit number without regrouping and remainder
● Divide a 2-digit number by a 1-digit number with regrouping without a remainder
● Use part-whole models to solve multiplication problems
● Use comparison models to solve multiplication problems
● Use comparison models to solve two-step multiplication problems
● Use part-whole models to solve division problems
● Use comparison models to solve division problems
● Use models to solve two-step problems involving whole numbers
Addition and Subtraction of Numbers within 10 000
● Add 4-digit numbers without regrouping
● Add 4-digit numbers with regrouping in hundreds
● Add 4-digit numbers with regourping in ones, tens and hundreds
● Subtract 4-digit numbers without regrouping
● Subtract 4-digit numbers with regrouping in thousand and hundreds
● Subtract 4-digit numbers with regrouping in ones, tens, hundreds and thousands
● Subtract 4-digit numbers across zeroes
● Solve two-step addition and subtraction problems
Angles
● Find angles in shapes and objects around you
● Count the number of sides and angles of shapes
● Compare angles to right angles
● Find right angles in shapes
Perpendicular and Parallel Lines
● Identify perpendicular lines
● Identify parallel lines
● Identify horizontal and vertical lines
Length
● Convert metres and centimetres to centimetres
● Convert centimetres to metres and centimetres
● Convert kilometres and metres to metres
● Convert metres to kilometres and meters
● Solve one-step word problems involving length
● Solve two-step word problems involving length
Mass
● Read scales in grams
● Read scales in kilograms and grams
● Convert kilograms and grams to grams
● Convert grams to kilograms and grams
● Solve one-step word problems involving mass
● Solve two-step word problems involving mass
Area and Perimeter
● Count square tiles to find area
● Use square units and half-square units to measure area
● Find the area of plane figures in square centimetres
● Find the area of plane surfaces in square metres
● Find the area of a figure
● Find the perimeter of a figure
● Solve word problems involving the area of squares and rectangles
● Solve word problems involving the perimeter of square and rectangles
Volume
● Use litres and millilitres to measure capacity
● Use measuring cups to measure volume
● Use measuring cups to measure in litres and millilitres
● Convert litres and millilitres to millilitres
● Convert millilitres to litres and millilitres
● Solve one-step word problems involving volume
● Solve two-step word problems involving volume
Money
● Add the dollars only
● Add the cents only
● Add the dollars and cents using number bonds
● Add dollars and cents by first adding cents to make one dollar
● Add dollars and cents by first making dollars
● Add money by adding dollar and subtracting the extra cents
● Add money by first changing dollars and cents to cents
● Subtract the dollars only
● Subtract the cents only
● Subtract the dollars and cents using number bonds
● Subtract money by subtracting one dollar and adding the extra cents
● Subtract money by subtracting whole dollars and adding the extra cents
● Subtract money by first changing dollars and cents to cents
● Solve two-step word problems involving money
Time
● Tell and write time to 1 minute
● Tell time and use the terms “past” and “to”
● Convert hours to minutes
● Convert hours and minutes to minutes
● Convert minutes to hours and minutes
● Add time without regrouping
● Add time with regrouping
● Subtract time without regrouping
● Subtract time with regrouping
● Solve word problems involving addition and subtraction of time
● Find duration
● Find duration un hours and minutes
● Find the end time given the start time and duration
● Find the start time give the duration and end time
Bar Graphs
● Make bar graphs from picture graphs
● Read and interpret vertical bar graphs
● Read and interpret horizontal bar graphs
Grade 4
Number up to 100 000
● Count to 10 000
● Write numbers in numerals and words
● Count on to one hundred thousand
● Find the value of each digit of a 5-digit number using a place value chart
● Find the expanded form of a 5-digit number
● Compare numbers within 100 000 using greater than and less than
● Order numbers within 100 000
● Round a 2-digit number up or down to the nearest ten
● Round off a 3-digit number to the nearest ten
● Round off a 3-digit number to the nearest hundred
● Round off a 4-digit number to the nearest ten/hundre/thousand
● Estimate and checking sums by rounding off
● Estimate and checking differences by rounding off
● Round off to check the reasonableness of products
Fractions
● Add a whole number and a fraction to get a mixed number
● Express mixed numbers in simplest form
● Express improper fractions in simplest form
● Express mixed numbers as improper fractions in simplest form
● Express improper fractions as mixed numbers in simplest form
● Add two fractions to get mixed numbers
● Add three fractions to get mixed numbers
● Subtract fractions from whole numbers
● Multiply a proper or improper fraction by a whole number
● Solve word problems involving multiplications of fractions
● Find the fraction of a part of subjects
● Find the fractional part of a set
● Find the fractional part of a number
● Use part-whole models to solve addition word problems involving fractions
● Use part-whole models to solve word problems involving fractions
● Use part-whole models to solve word problems involving fraction of a set or part of a set
Four Operations of Whole Numbers
● Multiply with regrouping in thousands, hundreds, tens and ones using a place value
chart
● Multiply by a 1-digit number without a place value chart
● Multiply a 2-digit number by tens
● Multiply a 2-digit number by a 2-digit number
● Multiply a 3-digit number by a 2-digit number
● Divide a 4-digit number by a 1-digit number without a remainder
● Divide a 4-digit number by a 1-digit number with a remainder
● Use models to solve multi-step word problems
Time
● Measurement of time in seconds
● 24-hour clock
● Solve word problems involving time in 24-hour clock
Factors and Multiples
● Determine if a 1-digit number is a factor of a given number
● Find common factors of two whole numbers
● Find multiples of a number
● Determine if a number is a multiple of another number
● Find the first twelve multiples of a number
● Find common multiples of two whole numbers
Decimals
● Express fractions in tenths as decimals
● Find equivalent ones and tenths
● Write mixed numbers in decimal notation
● Write improper fractions in decimal notation
● Write decimals to tenths in expanded form
● Express fractions in hundredths as decimals
● Find equivalent tenths and hundredths
● Express tenths and hundredths as decimals
● Express fractions as two-place decimals
● Express ones, tenths and hundredths as decimals
● Express mixed numbers as two-place decimals
● Express improper fractions of two-place decimals
● Write decimals to hundredths in expanded form
● Represent thousandths
● Find equivalent hundredths and thousandths
● Write hundredths and thousandths in decimal notation
● Express fractions as three-place decimals
● Write decimals to thousandths in expanded form
● Find 0.1 more than or 0.1 less than
● Find 0.01 more than or 0.01 less than
● Find the missing numbers in a pattern
● Compare decimals to hundredths
● Order decimals to hundredths
● Round off decimals to the nearest whole number
● Round off decimals to the nearest tenth
● Express fractions as decimals
● Express improper fractions as decimals
● Express mixed numbers as decimals
● Express decimals as fractions
● Express decimals as mixed numbers
● Estimate sums by rounding off to the nearest whole number
● Estimate differences by rounding off to the nearest whole number
● Estimate products by rounding off to the nearest whole number
● Estimate quotients by rounding off to a whole number
● Estimate by round off to the nearest tenth
● Use models to solve word problems involving decimals
Four Operations of Decimal
● Add decimals with one decimal place without regrouping
● Add decimals with one decimal place with regrouping in tenths
● Add decimals with one decimal place with regrouping in ones and tenths
● Add decimals with two decimal places without regrouping
● Add decimals with two decimal places with regrouping in hundredths
● Add decimals with two decimal places with regrouping in tenths and hundredths
● Subtract decimals with one decimal place without regrouping
● Subtract decimals with one decimal place with regrouping in ones and tenths
● Subtract decimals with one decimal place from whole numbers
● Subtract decimals with two decimal places with regrouping in tenths and hundredths
● Subtract decimals with placeholder zeroes
● Multiply one-place decimals by whole numbers
● Multiply hundredths by whole numbers
● Multiply two-place decimals by whole numbers
● Divide tenths by whole numbers without regrouping
● Divide hundredths by whole numbers without regrouping
● Divide one-place decimals by whole numbers with regrouping
● Find quotients correct to 1 decimal place
● Find quotients correct to 2 decimal places
Angles
● Use a protractor to measure angles in degrees
● Angles of 90, 180, 270 and 360 degrees
● Show directions using 8-point compass
● Describe movement using ‘clockwise’ and ‘anticlockwise’
Area & Perimeter
● Find the perimeter of a rectangle using a formula
● Find one side of a rectangle given its perimeter and the other side
● Find one side of a square given its perimeter
● Find one side of a rectangle given its area and the other side
● Find one side and the perimeter of a square given its area
● Find the perimeter of a composite figure by adding the lengths of its sides
● Find the area of composite figure by adding the area of its parts
● Use subtraction to find the area of a composite figure
● Find the area of a path around a rectangle
● Find the area and perimeter of parts of a figure
Symmetry
● Identify symmetric figures
● Identify lines of symmetry of a figure
Squares & Rectangles
● Identify squares and their properties
● Identify rectangles and their properties
● Use properties of squares and rectangles to find unknown angles
● Use properties of squares and rectangles to find the side lengths of figures
Tables and Line Graphs
● Compete a table from given data
● Read and interpret tables
● Read and interpret line graphs
Grade 5
Whole Numbers
● Count by ten thousands
● Count by hundred thousands
● Count by millions to 10 000 000
● Write numbers to 10 000 000 in numerals and words
● Find the value of each digit using a place value chart
● Find the expanded form of a 6-digit number
● Identify the place value and value of any digit
● Write numbers to 10 million in expanded form
● Compare numbers to 1 000 000 using greater than and less than
● Compare numbers up to 10 000 000
● Complete number patterns involving numbers to 10 000 000
● Round numbers to the nearest hundred or thousand
Fractions
● Add unlike fractions
● Subtract unlike fractions
● Express division as fractions
● Express division as mixed numbers
● Express fractions as decimals
● Express division as decimals
● Express mixed numbers as decimals
Decimals
● Convert one-and two-place decimals to fractions and mixed numbers
● Convert three-place decimals to fractions and mixed numbers
Four Operations of Decimals
● Multiply decimals by tens
● Multiply decimals by hundreds or thousands
● Divide decimals by tens
● Divide decimals by hundreds or thousands
Four Operations of Fractions
● Add mixed numbers without regrouping
● Add mixed numbers with regrouping
● Subtract mixed numbers without regrouping
● Subtract mixed numbers with regrouping
● Express division as fractions and mixed numbers
● Multiply proper fractions
● Multiply improper fractions by proper fractions
● Multiply an improper fraction by an improper fraction
● Multiply mixed numbers by whole numbers
● Express the product of a mixed number and a whole number as a decimal
● Solve word problems involving multiplying with proper fractions
● Solve two-step problems involving multiplying with mixed numbers
● Divide unit fractions by whole numbers
● Divide fractions by whole numbers
Ratio
● Express a ratio in its simplest form
● Find the missing term in a pair of equivalent ratios
● Find the equivalent raiot of two or three given quantities
● Find one quantity given the other quantity and their ratio
● Solve up to 2-step word problems involving ratio
Percentage
● Express a part of a whole as a percentage
● Express fractions and decimals as percentages
● Express percentages as fractions and decimals
● Solve problems involving discount
● Solve problems involving GST
● Solve problems involving annual interest
Rate
● Finding rates involving time
● Finding rates involving money
● Finding total amount involving time
● Finding total amount involving money
● Finding number of units
Average
● Calculate average value of a set
● Find the total amount given the average and the number of items
● Solve up to 3-step word problems involving average
Four Operations of Whole Numbers
● Round to estimate sums
● Round to estimate differences
● Round to estimate products
● Estimate quotients using compatible numbers
● Multiply by tens
● Multiply by hundreds
● Multiply by thousands
● Divide by tens
● Divide by hundreds
● Divide by thousands
● Use rounding to estimate quotients
● Calculate, involving only addition and subtraction
● Calculate, involving only multiplication and division
● Calculate, involving addition, subtraction, multiplication and division
● Calculate, involving brackets
● Calculate and apply the order of operations
● Solve multi-step problems involving whole problems
● Solve word problems using systematic lists
Area of Triangle
● Identify the base and corresponding height of a triangle
● Calculate the area of a triangle given a base and corresponding height
Volume of cube and cuboid
● Measure volume in cubic units
● Measure volume in cubic centimetres and cubic metres
● Convert between ℓ, ml and cm³
● Find the volume of cuboid by computing the product of its length, breadth and height
● Find one dimension of a cuboid knowing its volume and other dimensions
● Find volume of liquid in a rectangular tank
● Solve up to 3-step word problems involving volume of cuboids
Angles
● Estimate given angles in degrees
● Determine and unknown angle by using angles on a straight line, angle at a point or by
using vertically opposite angles
4-sided Figures
● Identify and name parallelogram, rhombus and trapezium
● Find unknown angles using properties of parallelogram, rhombus and trapezium
Properties of Triangle
● Identify isosceles, equilateral and right-angled triangle
● Find unknown angles using properties of triangles
Grade 6
Algebra
● Represent an unknown number using a letter
● Substitute the letter with a given number
● Write simple algebraic expressions
● Simplify algebraic expressions
● Solve word problems involving algebraic expressions
Fractions
● Divide a whole number by a proper fraction
● Divide a proper fraction by a proper fraction
● Solve word problems involving fractions
Ratio
● Express one quantity as a fraction of another, given their ratio
● Find ratio of one quantity to another, given their fraction
● Compare ratios
● Solve word problems involving 2 pairs of ratios
Percentage
● Find the whole given a part and the percentage
● Find the percentage increase or decrease
● Solve word problems involving percentage
Pie Charts
● Read and interpret pie charts
● Solve 1-step word problems using information presented in pie charts
Speed
● Calculate distance and time given and other two quantities
● Write speed in different units such as km/h, m/min, m/s and cm/s
● Solve up to 3-step word problems involving speed and average speed
Angles in Geometric Figures
● Find unknown angles in geometrical figures involving square, rectangle and triangle
● Find unknown angles in geometrical figures involving parallelogram, rhombus and
trapezium
Solid Figures and Nets
● Identify cube, cuboid, cone, cylinder, prism and pyramid
● Identify nets of cube, cuboid, prism and pyramid
● Identify the solid which can be formed by a given net
Area and Circumference of Circle
● Calculate the area and circumference of a circle
● Find the area and perimeter of semicircle and quarter circle
● Solve word problems involving area and perimeter
Volume of Cube and Cuboid
● Find one dimension of a cuboid given its volume and the other dimensions
● Find the length of one edge of a cube given its volume
● Find the height and area of a face of a cuboid
● Solve word problems involving volume of a cube and cuboid
Area and Perimeter of Composite Figure
● Find area and perimeter of a figure made up of square, rectangle and triangle
● Find area and perimeter of a figure made up of square, rectangle, triangle, semicircle
and quarter circle
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