Binary Numbers

Binary Numbers

Ages 7–10 · 11 minutes · Math

Play a card game and see why binary numbers are as simple as 1, 10, 11

Computers and code run on 1’s and 0’s, but binary numbers have a lot going on beyond these two simple numbers. Students start with a simple card game then see how place value, different bases, and powers of 2 all come together in this fascinating topic.

Part of

Standards alignment

Common Core State Standards

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Alabama

  • MA19.2.6 — Explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
  • MA19.4.6 — Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.
  • MA19.1.9 — Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.

Alaska

  • 4.OA.6 — Extend patterns that use addition, subtraction, multiplication, division or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations.
  • 2.NBT.1 — Model and identify place value positions of three digit numbers. Include:
  • 3.OA.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Arizona

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 * — Apply concepts of place value, multiplication, and division to understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • 4.OA.C.5 — Generate a number pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself and explain the pattern informally (e.g., given the rule “add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers).
  • 3.NBT.A.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.

Arkansas

  • 2.NPV.2 — Identify the value of hundreds, tens, and ones place in a three-digit number.
  • 4-PS4-3 — Generate and compare multiple solutions that use patterns to transfer information.
  • 4.NPV.1 — Recognize that a digit in a given place represents ten times what it represents in the place to its right.
  • 3.CAR.5 — Identify arithmetic patterns including, but not limited to, patterns in an addition or multiplication table, explaining use of properties of operations appropriate to the pattern.

California

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 2.NBT.B.5 — Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Colorado

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Connecticut

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Delaware

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Florida

  • MA.4.NSO.1.1 — Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
  • SC.68.CS-CS.1.1 (Discontinued after 2024-2025) — Examine connections between elements of mathematics and computer science including binary numbers, logic, sets, and functions.
  • MA.1.NSO.2.2 — Add two whole numbers with sums from 0 to 20, and subtract using related facts with procedural reliability.
  • MA.2.NSO.1.2 — Compose and decompose three-digit numbers in multiple ways using hundreds, tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Georgia

  • 2.NR.1.1 — Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.
  • 2.NR.2.1 — Fluently add and subtract within 20 using a variety of mental, part-whole strategies.
  • 2.PAR.4.1 — Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction.
  • 2.MP.7 — Look for and make use of structure.

Hawaii

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • 4.OA.C.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.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Idaho

  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in any place represents ten times as much as it represents in the place to its right
  • 2.MP.7 — Look for and make use of structure.
  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand:
  • MS-PS-4.3 — Students who demonstrate understanding can: Present qualitative scientific and technical information to support the claim that digitized signals (0s and 1s) can be used to encode and transmit information.

Illinois

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 2.NBT.A.3 — Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Indiana

  • 3-5.DI.3 — Demonstrate how a string of bits can be used to represent alphanumeric information and how 1's and 0's represent information.
  • 3.CA.8 — Create, extend, and give an appropriate rule for number patterns within 100 (including patterns in the addition table or multiplication table).
  • 3.CA.2 — Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). (E)

Iowa

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand the following as special cases.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what that same digit represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.5 — Given the rule for a sequence of numbers, identify apparent features of the sequence that were not explicit in the rule itself; explain informally why the numbers will continue to alternate in this way. For example, given the rule "Add 3" and the number sequence 1, 4, 7, 10, 13 observe that the terms appear to alternate between odd and even numbers;
  • 2.NBT.A.3 — Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.

Kansas

  • 2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; (e.g. 706 equals 7 hundreds, 0 tens, and 6 ones.) Understand the following as special cases:
  • 4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 2.NBT.5 — Fluently (efficiently, accurately, and flexibly) add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (e.g. composing/decomposing by like base-10 units, using friendly or benchmark numbers, using related equations, compensation, number line, etc.).

Kentucky

  • KY.2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones. Understand the following as special cases:
  • KY.4.NBT.1 — Recognize in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Louisiana

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 2.NBT.B.5 — Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place represents ten times what it represents in the place to its right. For example, (1) recognize that 700 ÷ 70 = 10; (2) in the number 7,246, the 2 represents 200, but in the number 7,426 the 2 represents 20, recognizing that 200 is ten times as large as 20, by applying concepts of place value and division.

Maine

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Maryland

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Massachusetts

  • 4-PS4-3 — Develop and compare multiple ways to transfer information through encoding, sending, receiving, and decoding a pattern.*
  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Michigan

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 1.OA.C.6 — Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Minnesota

  • 2.1.1.2 — Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. For example: Writing 853 is a shorter way of writing 8 hundreds + 5 tens + 3 ones.
  • 2.1.1.1 — Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.
  • 2.1.2.5 — Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits.

Mississippi

  • 2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Missouri

  • 2.NBT.A.1 — Understand three-digit numbers are composed of hundreds, tens and ones.
  • 3.RA.E.11 — Identify arithmetic patterns and explain the patterns using properties of operations.
  • 4.NBT.A.4 — Understand that in a multi-digit whole number, a digit represents 10 times what it would represent in the place to its right.
  • 1.RA.A.2 — Solve problems that call for addition of three whole numbers whose sum is within 20.

Montana

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • using mathematics and computational thinking

Nebraska

  • 4.N.1.c — Recognize a digit in one place represents ten times what it represents in the place to its right.
  • 3.N.1 — Numeric Relationships: Students will demonstrate and represent multi-digit numbers using place value understanding.
  • 4.N.1 — Numeric Relationships: Students will demonstrate and represent multi-digit numbers using relationships with the base-ten number system.
  • 1.N.5.e — Solve problems that call for addition of three whole numbers whose sum is less than or equal to 20 using flexible strategies with objects, drawings, and/or equations.

Nevada

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • K.OA.A.3 — Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

New Hampshire

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

New Jersey

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way

New Mexico

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

New York

  • NY-2.NBT.1 — Understand that the digits of a three-digit number represent amounts of hundreds, tens, and ones.
  • NY-3.OA.9 — Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).
  • NY-4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

North Carolina

  • NC.1.OA.6 — Add and subtract, within 20, using strategies such as: • Counting on • Making ten • Decomposing a number leading to a ten • Using the relationship between addition and subtraction • Using a number line • Creating equivalent but simpler or known sums
  • NC.2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. • Unitize by making a hundred from a collection of ten tens. • Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds, with 0 tens and 0 ones. • Compose and decompose numbers using various groupings of hundreds, tens, and ones.
  • NC.4.NBT.1 — Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000.
  • MP.8 — Look for and express regularity in repeated reasoning.

North Dakota

  • 2.NO.NBT.1 — Understand that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones.
  • 3.AR.OA.6 — Identify arithmetic patterns and explain them using the properties of operations.
  • 4.NO.NBT.1 — Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • 1.AR.OA.4 — Solve authentic word problems with addition, including three numbers and unknowns, within 20.
  • 4-PS4-3 — Construct a code to convey information by researching past and present methods of transmitting information.

Ohio

  • 2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 2.NBT.3 — Read and write numbers to 1,000 using base-ten numerals, number names, expanded form, and equivalent representations, e.g., 716 is 700 + 10 + 6, or 6 + 700 + 10, or 6 ones and 71 tens, etc.
  • 4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right by applying concepts of place value, multiplication, or division.
  • 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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Oklahoma

  • 2.N.1.3 — Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens, and ones, including written, standard, and expanded forms. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens.
  • 2.N.1.1 — Read, write, discuss, and represent whole numbers up to 1,000. Representations should include, but are not limited to, numerals, words, pictures, tally marks, number lines, and manipulatives.

Oregon

  • 2.NBT.A.1 — Understand 100 as a bundle of ten tens and that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • 4.OA.C.5 — Analyze a number, visual, or contextual pattern that follows a given rule.
  • 1.OA.A.2 — Solve problems that call for addition of three whole numbers whose sum is less than or equal to 20 using objects, drawings or equations.

Pennsylvania

  • CC.2.1.4.B.1 — Apply place-value concepts to show an understanding of multi-digit whole numbers.
  • Look for and express regularity in repeated reasoning.
  • 3.2.4.G — Generate and compare multiple solutions that use patterns to transfer information.
  • CC.2.2.2.A.2 — Use mental strategies to add and subtract within 20.
  • CC.2.2.3.A.4 — Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Rhode Island

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

South Carolina

  • 2.NSBT.1b — Understand place value through 999 by demonstrating that the hundreds digit in a three-digit number represents the number of hundreds, the tens digit represents the number of tens, and the ones digit represents the number of ones.
  • 4.NSBT.1 — Understand that, in a multi-digit whole number, a digit represents ten times what the same digit represents in the place to its right.
  • 1.ATO.2 — Solve real-world/story problems that include three whole number addends whose sum is less than or equal to 20.
  • 1.ATO.9b — Create, extend and explain using pictures and words for growing patterns (between 2 and 4 terms/figures).

South Dakota

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that the 7 in 700 is 10 times greater than the 7 in 70 because 700 ÷ 70 =10 and 70 x 10=700.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Tennessee

  • 2.NBT.A.1 — Know that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 can be represented in multiple ways as 7 hundreds, 0 tens, and 6 ones; 706 ones; or 70 tens and 6 ones).
  • 1.OA.C.5 — Add and subtract within 20 using strategies such as counting on, counting back, making 10, related known facts, and composing/decomposing numbers with an emphasis on making ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9 or adding 6 + 7 by creating the known equivalent 6 + 4 + 3 = 10 + 3 = 13 OR 6 + 6 + 1 = 12 + 1).
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the place to its right. For example, recognize that 7 in 700 is 10 times bigger than the 7 in 70 because 700 ÷ 70 = 10 and 70 x 10 = 700.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Texas

  • 3.2B — describe the mathematical relationships found in the base-10 place value system through the hundred thousands place;
  • 3.2A — compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate;
  • 4.2A — interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left;

Utah

  • 2.NBT.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; for example, 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 3.MP.7 — Look for and make use of structure.
  • 4.NBT.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 3.OA.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that four times a number is always even, and explain why four times a number can be decomposed into two equal addends.

Vermont

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 2.NBT.A.3 — Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Virginia

  • 2.NS.2c — Apply patterns within the base 10 system to determine and communicate, orally and in written form, the place (ones, tens, hundreds) and value of each digit in a three-digit whole number (e.g., in 352, the 5 represents 5 tens and its value is 50).
  • 2.NS.2d — Investigate and explain the ten-to-one relationships among ones, tens, and hundreds, using models.
  • 2.NS.2e — Compose and decompose whole numbers up to 200 by making connections between a variety of models (e.g., base 10 blocks, place value cards, presented orally, in expanded or standard form) and counting strategies (e.g., 156 can be 1 hundred, 5 tens, 6 ones; 1 hundred, 4 tens, 16 ones; 15 tens, 6 ones).

Washington

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 2.NBT.B.5 — Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Washington, D.C.

  • 2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
  • 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • 4.OA.C.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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

West Virginia

  • M.2.6 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens - called a "hundred." b. Numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight or nine hundreds, and 0 tens and 0 ones.
  • M.3.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends).
  • M.4.6 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 + 70 = 10 by applying concepts of place value and division).
  • M.2.10 — Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction.

Wisconsin

  • M.2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens -- called a "hundred". b. The numbers 100,200,300,400,500,600,700,800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
  • M.2.OA.B.2 — Flexibly and efficiently add and subtract within 20 using multiple mental strategies which may include counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
  • M.4.OA.C.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.
  • Waves can be used to transmit digital information. Digitized information is comprised of a pattern of 1s and 0s.
  • M.4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Wyoming

  • 2.NBT.D.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; and demonstrate that:
  • 4.NBT.D.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • 2.NBT.E.5 — Add and subtract within 100 using strategies based on place value, properties of addition, and/or the relationship between addition and subtraction.