Grade 3: Unit 1-Applying Place Value Knowledge to Explore Whole Numbers

Grade 3: Unit 1-Applying Place Value Knowledge to Explore Whole Numbers

3.NBT Number and Operations in Base Ten

3 Use place value understanding and properties of operations to perform multi-digit arithmetic.
3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
Estimation and rounding: Rounding (Third grade - L.1)
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Place values: Value of a digit (Third grade - B.3)
Place values: Identify the digit with a particular place value (Third grade - B.4)
Place values: Convert from expanded form (Third grade - B.7)
Addition: Add two numbers up to three digits (Third grade - C.1)
Addition: Add two numbers up to three digits - word problems (Third grade - C.3)
Addition: Complete the addition sentence - up to three digits (Third grade - C.4)
Addition: Balance addition equations - up to three digits (Third grade - C.5)
Addition: Addition patterns over increasing place values (Third grade - C.8)
Subtraction: Subtract numbers up to three digits (Third grade - D.1)
Subtraction: Subtract numbers up to three digits - word problems (Third grade - D.3)
Subtraction: Complete the subtraction sentence - up to three digits (Third grade - D.4)
Subtraction: Balance subtraction equations - up to three digits (Third grade - D.5)
Subtraction: Subtraction patterns over increasing place values (Third grade - D.6)
Properties: Properties of addition (Third grade - J.3)
Properties: Solve using properties of addition (Third grade - J.4)
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Place values: Value of a digit (Third grade - B.3)
Place values: Identify the digit with a particular place value (Third grade - B.4)
Multiplication: Multiply by a multiple of ten (Third grade - E.8)
Multiplication - skill builders: Multiply by 10 (Third grade - F.11)

Grade 4: Unit 1-A Deeper Look at the Four Operations

4.OA Operations and Algebraic Thinking

4 Use the four operations with whole numbers to solve problems.
4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Multiplication: Missing factors - facts to 12 (Fourth grade - D.2)
Multiplication: Properties of multiplication (Fourth grade - D.7)
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
Multiplication: Estimate products: word problems (Fourth grade - D.9)
Multiplication: Multiply a 2-digit number by a 2-digit number: word problems (Fourth grade - D.12)
Multiplication: Multiply a 2-digit number by a larger number: word problems (Fourth grade - D.16)
Multiplication: Multiply numbers ending in zeroes: word problems (Fourth grade - D.18)
Division: Division facts to 12: word problems (Fourth grade - E.2)
Division: Divide larger numbers, one-digit divisors: word problems (Fourth grade - E.5)
Division: Divide numbers ending in zeroes, multi-digit divisors: word problems (Fourth grade - E.14)
Division: Divide by 2-digit numbers: word problems (Fourth grade - E.17)
Division: Divide larger numbers by 2-digit numbers: word problems (Fourth grade - E.19)
Mixed operations: Addition, subtraction, multiplication, and division word problems (Fourth grade - F.2)
Mixed operations: Estimate sums, differences, products, and quotients: word problems (Fourth grade - F.3)
Money: Price lists with multiplication (Fourth grade - M.7)
Measurement: Compare customary units by multiplying (Fourth grade - N.3)
Measurement: Convert between metric and customary units (Fourth grade - N.6)
4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Number sense: Rounding (Fourth grade - A.6)
Division: Divide by 1-digit numbers: interpret remainders (Fourth grade - E.7)
Mixed operations: Estimate sums, differences, products, and quotients: word problems (Fourth grade - F.3)
Mixed operations: Multi-step word problems (Fourth grade - F.4)
Mixed operations: Word problems with extra or missing information (Fourth grade - F.5)
Mixed operations: Solve word problems using guess-and-check (Fourth grade - F.6)
Mixed operations: Choose numbers with a particular sum, difference, product, or quotient (Fourth grade - F.7)
Algebra: Write variable expressions: word problems (Fourth grade - G.2)
Algebra: Write variable equations to represent word problems (Fourth grade - G.5)
Logical reasoning: Guess two numbers based on sum and difference (Fourth grade - K.1)
Logical reasoning: Guess two numbers based on sum, difference, product, and quotient (Fourth grade - K.2)
4 Gain familiarity with factors and multiples.
4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Number sense: Prime and composite numbers (Fourth grade - A.5)
Multiplication: Choose the multiples of a given number up to 12 (Fourth grade - D.3)
Multiplication: Identify factors (Fourth grade - D.4)
Multiplication: Choose numbers with a particular product (Fourth grade - D.13)
Division: Divisibility rules (Fourth grade - E.11)
4 Generate and analyze patterns.
4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
Functions: Input/output tables with addition, subtraction, multiplication, and division (Fourth grade - H.1)
Functions: Function tables (Fourth grade - H.2)
Patterns and sequences: Geometric growth patterns (Fourth grade - L.1)
Patterns and sequences: Increasing growth patterns (Fourth grade - L.2)
Patterns and sequences: Numeric patterns: word problems (Fourth grade - L.3)
Patterns and sequences: Patterns involving addition and multiplication (Fourth grade - L.4)
Patterns and sequences: Mixed patterns review (Fourth grade - L.5)
Time: Time patterns (Fourth grade - O.8)

Grade 5 – Unit 1: Understanding the Place Value System

5.NBT Number and Operations in Base Ten

5 Understand the place value system.
5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Place values and number sense: Place values (Fifth grade - A.1)
Place values and number sense: Convert between place values (Fifth grade - A.2)
Decimals: Place values in decimal numbers (Fifth grade - C.3)
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Place values and number sense: Scientific notation (Fifth grade - A.11)
Multiplication: Multiplication patterns over increasing place values (Fifth grade - F.3)
Multiplication: Multiply numbers ending in zeroes (Fifth grade - F.4)
Multiplication: Multiply numbers ending in zeroes: word problems (Fifth grade - F.5)
Multiply decimals: Multiply a decimal by a power of ten (Fifth grade - G.2)
Division: Division patterns over increasing place values (Fifth grade - H.7)
Division with decimals: Divide by powers of ten (Fifth grade - I.1)
Division with decimals: Decimal division patterns over increasing place values (Fifth grade - I.2)
5.NBT.3 Read, write, and compare decimals to thousandths.
5.NBT.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
Decimals: What decimal number is illustrated? (Fifth grade - C.1)
Decimals: Understanding decimals expressed in words (Fifth grade - C.2)
Decimals: Place values in decimal numbers (Fifth grade - C.3)
5.NBT.3.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Decimals: Equivalent decimals (Fifth grade - C.4)
Decimals: Decimal number lines (Fifth grade - C.6)
Decimals: Compare decimal numbers (Fifth grade - C.7)
Decimals: Put decimal numbers in order (Fifth grade - C.8)
Multiply decimals: Inequalities with decimal multiplication (Fifth grade - G.10)
5.NBT.4 Use place value understanding to round decimals to any place.
Decimals: Round decimals (Fifth grade - C.5)
Add and subtract decimals: Estimate sums and differences of decimals (Fifth grade - E.6)
5 Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
Multiplication: Multiply by 2-digit numbers: complete the missing steps (Fifth grade - F.10)
Multiplication: Multiply a 2-digit number by a 2-digit number (Fifth grade - F.11)
Multiplication: Multiply a 2-digit number by a larger number (Fifth grade - F.12)
Multiplication: Multiply by 2-digit numbers: word problems (Fifth grade - F.13)
Multiplication: Multiply three or more numbers up to 2 digits each (Fifth grade - F.14)
Multiplication: Multiply by 3-digit numbers (Fifth grade - F.15)
Multiplication: Multiply three numbers up to 3 digits each (Fifth grade - F.16)
Multiplication: Multiply three or more numbers: word problems (Fifth grade - F.17)
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Multiplication: Properties of multiplication (Fifth grade - F.6)
Division: Division facts to 12 (Fifth grade - H.1)
Division: Division facts to 12: word problems (Fifth grade - H.2)
Division: Divide multi-digit numbers by 1-digit numbers (Fifth grade - H.3)
Division: Divide multi-digit numbers by 1-digit numbers: word problems (Fifth grade - H.4)
Division: Divide numbers ending in zeroes (Fifth grade - H.8)
Division: Divide numbers ending in zeroes: word problems (Fifth grade - H.9)
Division: Divide by 2-digit numbers (Fifth grade - H.10)
Division: Divide by 2-digit numbers: word problems (Fifth grade - H.11)
Division: Choose numbers with a particular quotient (Fifth grade - H.14)
5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Addition and subtraction: Add and subtract money: word problems (Fifth grade - D.4)
Add and subtract decimals: Add and subtract decimal numbers (Fifth grade - E.1)
Add and subtract decimals: Add and subtract decimals: word problems (Fifth grade - E.2)
Add and subtract decimals: Choose decimals with a particular sum or difference (Fifth grade - E.3)
Add and subtract decimals: Complete the addition or subtraction sentence (Fifth grade - E.4)
Add and subtract decimals: Inequalities with decimal addition and subtraction (Fifth grade - E.5)
Multiply decimals: Multiply a decimal by a one-digit whole number (Fifth grade - G.3)
Multiply decimals: Multiply a decimal by a multi-digit whole number (Fifth grade - G.4)
Multiply decimals: Multiply decimals and whole numbers: word problems (Fifth grade - G.5)
Multiply decimals: Multiply money amounts: word problems (Fifth grade - G.6)
Multiply decimals: Multiply three or more numbers, one of which is a decimal (Fifth grade - G.7)
Multiply decimals: Multiply two decimals using grids (Fifth grade - G.8)
Multiply decimals: Multiply two decimals (Fifth grade - G.9)
Division: Divide money amounts: word problems (Fifth grade - H.12)
Division with decimals: Division with decimal quotients (Fifth grade - I.3)
Division with decimals: Division with decimal quotients and rounding (Fifth grade - I.4)
Division with decimals: Division with decimal quotients: word problems (Fifth grade - I.5)
Mixed operations: Add, subtract, multiply, and divide decimals (Fifth grade - P.3)
Mixed operations: Add, subtract, multiply, and divide decimals: word problems (Fifth grade - P.4)
Consumer math: Price lists (Fifth grade - U.1)
Consumer math: Unit prices (Fifth grade - U.2)

Grade 6-Unit 1: Operating with Positive Rational Numbers

6.NS The Number System

6 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Divide fractions: Divide by fractions - with models (Sixth grade - W.1)
Divide fractions: Reciprocals (Sixth grade - W.2)
Divide fractions: Divide fractions (Sixth grade - W.3)
Divide fractions: Estimate quotients when dividing mixed numbers (Sixth grade - W.4)
Divide fractions: Divide fractions and mixed numbers (Sixth grade - W.5)
Divide fractions: Divide fractions and mixed numbers: word problems (Sixth grade - W.6)
Mixed operations: Add, subtract, multiply, and divide fractions and mixed numbers (Sixth grade - X.6)
Mixed operations: Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Sixth grade - X.7)
6 Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
Division: Divisibility rules (Sixth grade - L.1)
Division: Division patterns with zeroes (Sixth grade - L.2)
Division: Divide numbers ending in zeroes: word problems (Sixth grade - L.3)
Division: Estimate quotients (Sixth grade - L.4)
Division: Divide whole numbers - 2-digit divisors (Sixth grade - L.5)
Division: Divide whole numbers - 3-digit divisors (Sixth grade - L.6)
Mixed operations: Add, subtract, multiply, and divide whole numbers (Sixth grade - X.1)
Mixed operations: Add, subtract, multiply, and divide whole numbers: word problems (Sixth grade - X.2)
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Add and subtract decimals: Add and subtract decimal numbers (Sixth grade - J.1)
Add and subtract decimals: Add and subtract decimals: word problems (Sixth grade - J.2)
Add and subtract decimals: Estimate sums and differences of decimals (Sixth grade - J.3)
Add and subtract decimals: Maps with decimal distances (Sixth grade - J.4)
Multiply and divide decimals: Multiply decimals (Sixth grade - O.1)
Multiply and divide decimals: Estimate products of decimal numbers (Sixth grade - O.2)
Multiply and divide decimals: Inequalities with decimal multiplication (Sixth grade - O.3)
Multiply and divide decimals: Divide decimals by whole numbers (Sixth grade - O.4)
Multiply and divide decimals: Divide decimals by whole numbers: word problems (Sixth grade - O.5)
Multiply and divide decimals: Multiply and divide decimals by powers of ten (Sixth grade - O.6)
Multiply and divide decimals: Division with decimal quotients (Sixth grade - O.7)
Multiply and divide decimals: Inequalities with decimal division (Sixth grade - O.8)
Multiply and divide decimals: Evaluate expressions involving decimals (Sixth grade - O.9)
Mixed operations: Add, subtract, multiply, and divide decimals (Sixth grade - X.4)
Mixed operations: Add, subtract, multiply, and divide decimals: word problems (Sixth grade - X.5)
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Number theory: Identify factors (Sixth grade - N.4)
Number theory: Greatest common factor (Sixth grade - N.7)
Number theory: Least common multiple (Sixth grade - N.8)
Number theory: GCF and LCM: word problems (Sixth grade - N.9)