SingaporeMath.com Inc

Whole Numbers

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Understand and use ordinal numbers to describe position.

X

Count, read, and write whole numbers to 20.

X

Compare numbers within 20.

X

X

Use place-value models to represent numbers to 100.

X

Read, write in words and as tens + ones, identify place values of digits for numbers within 100.

X

Count and identify 1 more than, 1 less than, 10 more than, 10 less than a number within 100.

X

Compare numbers to 100.

X

Describe and extend regular number patterns within 100, including counting by 2's and 20's.

X

Use place-value models to represent numbers to 1000.

X

Read, write in words, identify place values of digits, and compare numbers within 1000.

X

Compare numbers within 1000 and use the symbols <, +, >.

X

Describe and extend regular number patterns within 1000.

X

Use place-value models to represent numbers to 10,000.

X

Read, write in words, identify place values of digits, and compare and order numbers within 10,000.

X

Describe and extend regular number patterns within 10,000.

X

Use place-value models to represent numbers to 100,000.

X

Read, write in words, identify place values of digits, and compare and order numbers within 100,000.

X

Complete or extend regular number patterns for numbers within 100,000.

X

Round numbers within 100,000 to the nearest 10 or 100

X

Read, write in words, identify place values of digits, and round numbers in the millions.

X

Round numbers within 100,000 to the nearest 10, 100, or 1000.

X

Addition and Subtraction of Whole Numbers

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Understand number bonds and part-whole concept.

X

Understand the meaning of addition (missing whole, putting together, adding on, simple addition stories).

X

X

Understand the meaning of subtraction (missing part, taking away, counting back, simple subtraction stories).

X

X

Add/Subtract numbers within 20

X

Use inverse relationship between addition and subtraction.

X

X

X

Learn addition and subtraction facts within 20.

X

Compare numbers by using subtraction to find the difference.

X

X

Add/Subtract numbers within 100.

X

Find the sum of 3 1-digit numbers.

X

Add/Subtract numbers within 1000.

X

Add/Subtract numbers within 10,000.

X

X

Use estimation to verify the reasonableness of calculated results in addition and subtraction, check subtraction problems using addition.

X

X

Determine whether an estimate is sufficient for a specific problem situation.

X

Add/subtract numbers in the billions.

Multiplication and Division of Whole Numbers

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Use repeated addition and arrays to solve multiplication problems within 40.

X

X

Use sharing and grouping to divide.

X

X

Relate division to multiplication.

X

X

X

Recognize and extend regular linear patterns.

X

X

X

X

Multiply/divide by 2's and 3's.

X

Learn multiplication/division facts for 2's and 3's.

X

Multiply/divide by 4's, 5's, and 10's.

X

Learn multiplication/division facts for 4's, 5's, and 10's.

X

Understand quotient and remainder.

X

Understand the properties of 0 and 1 in multiplication.

X

Multiply/Divide by 6's, 7's, 8's, and 9's.

X

Learn multiplication/division facts for 6's, 7's, 8's, and 9's.

X

Multiply numbers within 1000 by a 1-digit number.

X

Divide numbers within 1000 by a 1-digit number, including situations where there is a remainder.

X

Multiply numbers within 10,000 by a 1-digit number.

X

Divide numbers within 10,000 by a 1-digit number, including situations where there is a remainder.

X

Multiply numbers within 10,000 by a 2-digit number.

X

X

Divide numbers within 10,000 by a 2-digit number.

X

Multiply/divide numbers within 1,000,000 by tens, hundreds, or thousands.

X

Use estimation to verify the reasonableness of calculated results in multiplication and division problems.

X

X

Find the factors and common factors of whole numbers within 100.

X

X

Find multiples and common multiples of whole numbers within 100.

X

X

Use divisibility rules for 2, 3, 5, 6, 9, and 10.

X

Use order of operations to solve mathematical expressions with or without parentheses.

X

Mental Math Strategies

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Use commutative, distributive, and/or associative properties to perform mental calculations and check results.

X

X

X

X

X

X

Add 1-digit numbers involving renaming (e.g. 7 + 5) by making a ten.

X

Subtract 1-digit numbers involving renaming (e.g. 14 - 8) by subtracting from a ten.

X

Add/Subtract numbers within 100.

X

X

X

X

Add/Subtract 1's, 10's, or 100's to numbers within 1000.

X

X

X

Subtract from 100.

X

Subtract from 1000.

X

Add/Subtract a number close to 100 (e.g. 98).

X

Add and subtract money in compound units (dollars and cents) when the cents are multiples of 5 or close to $1.00.

X

Add/Subtract measurements in compound units.

X

Add/Subtract tenths, hundredths, or thousandths to or from decimal numbers.

X

Multiply and divide tens, hundreds, and thousands by a 1-digit number.

X

Fractions

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Recognize and name halves and fourths.

X

X

Recognize, write, name, and illustrate fractions of a whole (denominators 1-12).

X

Find the fraction with the same denominator to make a whole with another fraction.

X

Compare and order unit fractions.

X

Compare and order fractions with the same denominator or with the same numerator.

X

Find equivalent fractions and simplest form of a fraction.

X

Compare and order fractions with different denominators.

X

Recognize and name the fraction of a set.

X

Find the fraction of a set.

X

Find fraction of a set for measurements (e.g. 10 minutes as a fraction of one hour).

X

X

Add/Subtract like fractions.

X

Add/Subtract related fractions.

X

Add/Subtract unlike fractions.

X

Understand mixed numbers and improper fractions, convert between them, locate them on a number line.

X

Relate division to fractions.

X

Add/subtract mixed numbers.

X

Multiply a fraction by a whole number.

X

X

Multiply a fraction by a fraction.

X

Divide a fraction by a whole number.

X

X

Divide a whole number or a fraction by a fraction.

X

Apply order of operations with or without parentheses to problems involving fracitons.

X

Money

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Identify and know the value of coins and bills.

X

Use the dollar and cent symbols for money.

X

X

Count combinations of bills or coins.

X

Count combinations of bills and coins to $10.00.

X

Use decimal notation for money.

X

Use decimal notation to add and subtract money within $10.00.

X

Use decimal notation to add and subtract money within $100.00.

X

Multiply and divide money amounts in decimal notation.

X

Decimals

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Understand tenths, hundredths, thousandths, locate decimal numbers on a number line, compare decimal numbers.

X

X

Convert a decimal to a fraction and simplify.

X

X

Convert a fraction to a decimal number (denominators are a factor of 10, 100, or 1000).

X

X

Compare and order decimal numbers of up to 3 decimal places and fractions.

X

X

Round decimal numbers of up to 2 decimal places to the nearest whole number or to 1-decimal place.

X

Round decimal numbers up to 3 decimal places to the nearest whole number, to 1-decimal place, or to 2-decimal places.

X

Add/Subtract decimal numbers of up to 2 decimal places.

X

Add/Subtract decimal numbers of up to 3 decimal places.

X

Multiply/Divide decimal numbers of up to 2 decimal places by a whole number.

X

X

Find the quotient of a division problem correct to 1 decimal place.

X

Find the quotient of a division problem correct to 2-decimal places.

X

Convert fractions to decimals correct to 2-decimal places.

X

Multiply/Divide decimal number by tens, hundreds, or thousands.

X

Multiply/divide a decimal number by a 2-digit whole number.

X

Use estimation to verify the reasonableness of calculated results in problems involving decimal numbers.

X

X

Time

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Tell time to the half-hour (analog clock face).

X

Relate time to events.

X

Tell time to the nearest 5-minute mark (analog clock face).

X

Tell time to the minute (analog clock face).

X

Find the duration of time intervals.

X

X

Find starting or ending times, given a time and the interval.

X

X

Know relationships of time (years, months, days, weeks, hours, seconds).

X

Convert between units of time.

X

X

X

X

Length, Weight, Mass, and Capacity

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Compare and measure length, weight, and capacity using nonstandard units.

X

Measure and estimate length of objects in meters and centimeters, yards, feet, and inches.

X

X

Understand and estimate length in kilometers and miles.

X

Compare metric and U.S. standard measurement units.

X

Measure and estimate weight in kilograms, grams, pounds, and ounces.

X

X

Measure and estimate capacity in liters, cups, pints, quarts, half-gallon, and gallon.

X

X

Measure and estimate capacity in milliliters.

X

Convert units within a measurement system using multiplication.

X

X

X

Add/subtract measurements in compound units.

X

Multiply/divide measurements in compound units.

X

Convert fractional measurements to a measuring system to a different unit or a compound unit, within a measuring system.

X

Convert decimal units within a measuring system.

X

Perimeter, Area, and Volume

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Find the perimeter of polygons.

X

Find the area of shapes by covering them with unit squares or counting squares.

X

X

X

Understand and use units of area, such as square centimeter and square inch.

X

X

Find the area, perimeter, and unknown sides of rectangles.

X

Find the area and perimeter of composite figures made from squares and rectangles.

X

Derive the formula for area of a triangle and find the area of triangles.

X

Count unit cubes in 2-dimensional representations of 3-dimensional solids.

X

Find the volume of solid figures by counting cubic units.

X

Understand and use units of volume, such as cubic centimeter and cubic inch.

X

X

Find the volume of rectangular prisms.

X

X

Find the side of a rectangular prism given the volume and two sides or area of one side.

X

Understand the relationship between cubic centimeters, milliliters, and liters

X

X

Solve problems involving the change in height of liquids and volume of liquids in rectangular tanks, including rate problems.

X

Find the volume of solids by displacement.

X

Solve multistep problems involving the volume of liquids and solids.

 X

Identify the radius and diameter of a circle, find one given the other.

X

Derive the formula for circumference of a circle and find circumference when given the radius or diameter.

X

Derive the formula for area of a circle and find area when given the radius or diameter.

X

Find the perimeter and area of compound figures involving squares, rectangles, triangles, and half-circles or quarter circles.

X

Geometry

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Identify, describe, and categorize common 2-dimensional shapes, including the faces of 3-dimensional objects.

X

X

Identify common 2-domensional shapes within compound shapes, combine shapes to form common shapes.

X

X

Describe and classify common 3-dimensional shapes according to number and shape of faces and edges.

X

X

Describe and classify common 3-dimensional shapes according to number and shape of faces, edges, and vertices.

Describe and extend repeating patterns involving color and shapes.

X

X

Describe and extend repeating patterns involving combination of shapes (compound shapes).

X

Identify right angles and compare angles to right angles, find right angles in polygons.

X

Identify acute, obtuse, and right angles and relate 90^o, 180^o, 270^o, and 360^owith quarter, half, three-quarter, and whole turn.

X

Measure and construct angles.

X

X

Identify perpendicular and parallel lines.

X

Name and identify different types of triangles and quadrilaterals based on angle and side properties

X

X

Know and use angle properties of intersecting lines to solve problems involving finding find unknown angles.

X

X

Know and use angle properties of triangles, parallelograms, rhombuses, and trapezoids to solve problems involving finding find unknown angles.

X

X

Construct triangles, parallelograms, and rhombuses with specified angles.

X

Identify nets of solids, or solids of nets.

X

Create tessellations with congruent figures.

X

Identify figures that have line symmetry.

X

Visualize, describe, and draw geometric solids.

X

Data Analysis and Probability

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Sort objects and data by common attributes.

X

X

Represent and compare data using picture graphs.

X

X

Represent and compare data using bar graphs.

X

X

Collect, organize, and analyze data using tables and bar graphs.

X

Ask and solve questions related to data representation, including finding the range and mode.

X

X

X

X

Collect, organize, and analyze data using line graphs.

X

Analyze data using pie charts.

X

Percentage

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Understand and use percent.

X

Find decimal and fraction equivalents for percentages.

X

Write fractions as percentages.

X

Solve problems involving percentage of a quantity.

X

X

Solve problems involving part of a whole as a percentage.

X

Solve problems involving one quantity as a percentage of another.

X

Solve percentage problems using a unitary method.

X

Ratio/Average/Rate/Speed

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Understand and use ratios to solve problems.

X

Find equivalent ratios.

X

Relate ratios to fractions.

X

Relate ratios to proportions.

X

Solve problems involving changing ratios.

X

Find the average of a set of data.

X

Find a data value given the average and the other values.

X

Understand rates and solve problems involving rates.

X

Understand and use speed and average speed to solve problems.

X

Word Problems

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Make addition/subtraction stories from problem situations.

X

Write equations and solve simple addition/subtraction stories.

X

X

Solve simple multiplication/division problems using objects and pictures.

X

Write equations and solve one-step word problems involving addition/subtraction.

X

X

X

Write equations and solve one-step word problems involving multiplication/division.

X

X

Solve simple word problems involving fraction of a set.

X

Solve 2-step word problems which involve the four operations on whole numbers.

X

X

Solve 2-step word problems which involve fraction of a set.

X

Solve 2-steip word problems which involve decimals and fractions.

X

Solve multi-step word problems involving all four operations on whole numbers, fractions, decimals, percentage, and ratios.

X

X

X

X

Solve multi-step word problems involving average, rate, and percentage.

X

X

X

Solve multi-step word problems involving speed and average speed.

X

X

Solve challenging word problems

X

Algebra

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Solve problems involving numeric equations or inequalities.

X

X

X

X

Select appropriate operational symbol to make an expression true.

X

X

X

X

Use boxes and other symbols to stand for unknown numbers in expressions and equations.

X

X

X

X

X

X

X

Represent unknown quantities with bar diagrams and solve word problems using bar diagrams.

X

X

X

Use bar diagrams to solve complex word problems involving while numbers and fractions.

X

X

X

X

X

X

Use bar diagrams to solve complex word problems.

X

X

X

X

X

Write and evaluate simple algebraic expressions in one variable using substitution.

X

Simplify algebraic expressions in one variable.

X