Grades

lesson 1

• 1. Writing natural numbers
• 2. Understanding classes of natural numbers
• 3. Writing natural numbers in words
• 4. Writing natural numbers in digits
• 5. Roman numerals

lesson 2

• 1. Units of length measurement
• 2. Units of weight measurement
• 3. Units of time measurement
• 4. Problems related to measurement units

lesson 3

• 1. Addition and subtraction within thousands
• 2. Problems involving addition and subtraction of sums and differences
• 3. Addition and subtraction within billions
• 4. Commutative property of addition
• 5. Associative property of addition
• 6. Properties of zero in addition and subtraction

lesson 4

• 1. Scales and number systems
• 2. Comparing natural numbers
• 3. Rounding natural numbers

lesson 5

• 1. Multiplying numbers ending in zero
• 2. Converting a sum to a product
• 3. Multiplying by a one-digit number
• 4. Multiplying by a two-digit number
• 5. Multiplying by a three-digit number
• 6. Associative property of multiplication
• 7. Multiplying using convenient methods
• 8. Filling in missing parts in multiplication
• 9. Multiplication problems

lesson 6

• 1. Dividing numbers ending in zero
• 2. Dividing by a one-digit number
• 3. Dividing by a two-digit number
• 4. Dividing by a three-digit number
• 5. Division with remainders
• 6. Checking division with remainders
• 7. Division: Problems

lesson 7

• 1. Checking division results by multiplication
• 2. Checking multiplication results by division
• 3. Adding, subtracting, multiplying, and dividing natural numbers
• 4. Adding, subtracting, multiplying, and dividing natural numbers: Problems
• 5. Distributive property of multiplication over addition
• 6. Distributive property of multiplication over subtraction

lesson 8

• 1. Algebraic expressions
• 2. Problems related to numerical and algebraic expressions
• 3. Rules for expanding parentheses
• 4. Rule for factoring out the greatest common factor
• 5. Finding the value of expressions

lesson 9

• 1. Finding an unknown addend
• 2. Finding an unknown subtrahend
• 3. Dividing by a three-digit number
• 4. Finding an unknown multiplier
• 5. Finding an unknown divisor
• 6. Finding an unknown divisor in division
• 7. Problems related to formulating equations

lesson 10

• 1. Order of operations for addition and subtraction
• 2. Order of operations for multiplication and division
• 3. Order of operations for four operations
• 4. Order of operations involving parentheses

lesson 11

• 1. Exponentiation of numbers
• 2. Square of a number
• 3. Cube of a number
• 4. Expressions involving exponents

lesson 12

• 1. Word problems: more by and less by
• 2. Word problems: times more and times less
• 3. Finding speed, time, and distance
• 4. Relative movement of two objects
• 5. Approaching and separating of two objects
• 6. One object overtaking another
• 7. Economic problems

lesson 13

• 1. Expressing in fractions
• 2. Reading and writing simple fractions
• 3. Finding a fraction of a number
• 4. Problems involving fractions
• 5. Proper and improper fractions
• 6. Expressing fractions with measurement units

lesson 14

• 1. Comparing fractions on a number line
• 2. Comparing simple fractions
• 3. Ordering fractions

lesson 15

• 1. Adding fractions with the same denominator
• 2. Subtracting fractions with the same denominator
• 3. Simple fractions: Word problems
• 4. Adding three or more fractions
• 5. Subtracting three or more fractions
• 6. Adding and subtracting three or more fractions
• 7. Adding and subtracting three or more fractions: Word problems
• 8. Fractions: Algebraic expressions
• 9. Fractions: Equations

lesson 16

• 1. Representing a quotient as a simple fraction
• 2. Representing a fraction as a quotient
• 3. Dividing a sum by a number
• 4. Division and fractions: Word problems

lesson 17

• 1. Reading and writing mixed numbers
• 2. Converting improper fractions to mixed numbers
• 3. Converting mixed numbers to improper fractions
• 4. Mixed numbers: Word problems

lesson 18

• 1. Finding the sum: Mixed numbers and natural numbers
• 2. Adding mixed numbers
• 3. Finding the difference: Mixed numbers and natural numbers
• 4. Subtracting mixed numbers
• 5. Adding and subtracting mixed numbers
• 6. Adding and subtracting mixed numbers: Word problems

lesson 19

• 1. Reading and writing decimal fractions
• 2. Representing a quotient as a decimal fraction
• 3. Converting decimal fractions to simple fractions
• 4. Converting decimal fractions to mixed numbers
• 5. Expressing decimal fractions with the same denominator

lesson 20

• 1. Equivalent decimal fractions
• 2. Comparing decimal fractions on a number line
• 3. Comparing decimal fractions
• 4. Ordering decimal fractions
• 5. Rounding decimal fractions

lesson 21

• 1. Adding decimal fractions
• 2. Subtracting decimal fractions
• 3. Adding and subtracting decimal fractions
• 4. Adding and subtracting decimal fractions: Word problems

lesson 22

• 1. Types of angles
• 2. Identifying angle types
• 3. Using a compass to determine cardinal directions
• 4. Parallel and perpendicular lines
• 5. Adjacent angles formed by the intersection of two lines
• 6. Vertical angles formed by the intersection of two lines
• 7. Length of a broken line
• 8. Circle and disk

lesson 23

• 1. Perimeter of a rectangle
• 2. Perimeter of a square
• 3. Perimeter of a polygon
• 4. Perimeter of a composite shape

lesson 24

• 1. Area of a rectangle
• 2. Area of a square
• 3. Area of a composite shape
• 4. Units of area measurement

lesson 25

• 1. Polyhedra
• 2. Surface area of a rectangular parallelepiped
• 3. Surface area of a cube
• 4. Volume of a rectangular parallelepiped
• 5. Volume of a cube
• 6. Units of volume measurement
• 7. Calculating the volume of complex spatial shapes

lesson 26

• 1. Creating tables
• 2. Constructing diagrams
• 3. Finding the mean of a data set
• 4. Mean of a data set: Word problems
• 5. Finding the range of a data set
• 6. Finding the mode of a data set
• 7. Finding the median of a data set