Sequences and Triangle Numbers: Bonus Challenge

Part of

• Math Problem Solving

Standards alignment

Common Core State Standards

• 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.
• MP7 — Look for and make use of structure.
• 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.
• MP8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Alabama

• MA19.2.5 — Reproduce, extend, create, and describe patterns and sequences using a variety of materials.
• MA19.2.4 — Using concrete and pictorial representations and repeated addition, determine the total number of objects in a rectangular array with up to 5 rows and up to 5 columns.
• MA19.3.9 — Recognize and explain arithmetic patterns using properties of operations.
• MA19.4.5 — Generate and analyze a number or shape pattern that follows a given rule.

Alaska

• 4.OA.5 — Generate a number, shape pattern, table, t-chart, or input/output function that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Be able to express the pattern in algebraic terms. 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.
• 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.
• 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.
• 7. — Look for and make use of structure.

Arizona

• 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.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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Arkansas

• 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.
• 4.CAR.11 — Generate a number or shape pattern that follows a given rule, identifying apparent features of the pattern that are not explicit in the rule itself.
• 2.CAR.5 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

California

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Colorado

• 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.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of 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.

Connecticut

• 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.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• MP7 — Look for and make use of structure.

Delaware

• 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.

Florida

• MA.3.AR.3.3 — Identify, create and extend numerical patterns.
• MA.4.AR.3.2 — Generate, describe and extend a numerical pattern that follows a given rule.
• MA.K12.MTR.5.1 — Use patterns and structure to help understand and connect mathematical concepts. Mathematicians who use patterns and structure to help understand and connect mathematical concepts: • Focus on relevant details within a problem. • Create plans and procedures to logically order events, steps or ideas to solve problems. • Decompose a complex problem into manageable parts. • Relate previously learned concepts to new concepts. • Look for similarities among problems. • Connect solutions of problems to more complicated large-scale situations.

Georgia

• 3.PAR.3.1 — Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.
• 2.PAR.4 — Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.
• 4.PAR.3.1 — Generate both number and shape patterns that follow a provided rule.
• 4.MP.7 — Look for and make use of structure.

Hawaii

• 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
• 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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Idaho

• 4.OA.C.5 — Generate a number or shape pattern that follows a given rule. Identify and explain features of the pattern that were not explicit in the rule itself.
• 3.MP.7 — Look for and make use of structure.
• 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Illinois

• 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.
• MP.7 — Look for and make use of structure.
• MP.8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Indiana

• 3.CA.8 — Create, extend, and give an appropriate rule for number patterns within 100 (including patterns in the addition table or multiplication table).
• 2.CA.4 — Create, extend, and give an appropriate rule for number patterns using addition and subtraction within 1,000.
• PS.8 — Look for and express regularity in repeated reasoning.
• 4.CA.9 — Describe the relationship between two terms and use it to find a second number when a first number is given. Generate a number pattern that follows a given rule.

Iowa

• 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.
• SMP7 — Look for and make use of structure.
• 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;
• SMP8 — Look for and express regularity in repeated reasoning.

Kansas

• 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.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 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.
• MP.7 — Look for and make use of structure.

Kentucky

• KY.4.OA.5 — Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern not explicit in the rule itself.
• KY.3.OA.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.
• MP8 — Look for and express regularity in repeated reasoning.
• KY.2.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Louisiana

• 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.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• MP7 — Look for and make use of structure.

Maine

• 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.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Maryland

• 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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Massachusetts

• 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.
• MP.8 — Look for and express regularity in repeated reasoning.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to five rows and up to five columns; write an equation to express the total as a sum of equal addends.

Michigan

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Minnesota

• 1.2.1.1 — Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. For example: Describe rules that can be used to extend the pattern 2, 4, 6, 8, □, □, □ and complete the pattern 33, 43, □, 63, □, 83 or 20, □, □, 17.
• 2.2.1.1 — Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. For example: Skip count by 5s beginning at 3 to create the pattern 3, 8, 13, 18, … . Another example: Collecting 7 empty milk cartons each day for 5 days will generate the pattern 7, 14, 21, 28, 35, resulting in a total of 35 milk cartons.

Mississippi

• 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.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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.
• 2.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Missouri

• 3.RA.E.11 — Identify arithmetic patterns and explain the patterns using properties of operations.
• 2.RA.B.3 — Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends.
• 4.RA.C.6 — Generate a number pattern that follows a given rule.
• 4.RA.C.7 — Use words or mathematical symbols to express a rule for a given pattern.

Montana

• 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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.

Nebraska

• 2.N.5.c — Use repeated addition to find the total number of objects arranged in an array no larger than five rows and five columns and write an equation to express the total.
• 2.N.5.d — Identify a group of objects from 0 to 20 as even or odd by counting by 2s or by showing even numbers as a sum of two equal parts.

Nevada

• 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.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.

New Hampshire

• 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.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning.

New Jersey

• 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.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 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.
• 7 — Look for and make use of structure.

New Mexico

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 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.
• MP8 — Look for and express regularity in repeated reasoning.

New York

• NY-3.OA.9 — Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).
• NY-4.OA.5 — Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself.
• MP.7 — Look for and make use of structure.
• MP.8 — Look for and express regularity in repeated reasoning.
• NY-2.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as a sum of equal addends.

North Carolina

• MP.8 — Look for and express regularity in repeated reasoning.
• NC.4.OA.5 — Generate and analyze a number or shape pattern that follows a given rule.
• NC.2.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

North Dakota

• 1.AR.OA.7 — Identify, create, complete, and extend patterns that are repeating, increasing, and decreasing in a variety of contexts.
• 4.AR.OA.6 — Generate a number or shape pattern that follows a given rule while identifying apparent features of the pattern that were not explicit in the rule itself.
• 3.AR.OA.6 — Identify arithmetic patterns and explain them using the properties of operations.
• 2.AR.OA.5 — Use repeated addition to find the total number of objects arranged in a rectangular array.

Ohio

• 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.
• MP.7 — Look for and make use of structure.
• 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.
• MP.8 — Look for and express regularity in repeated reasoning.

Oklahoma

• 3.A.1.3 — Explore and develop visual representations of increasing and decreasing geometric patterns and construct the next steps.
• 2.A.1.1 — Represent, create, describe, complete, and extend increasing and decreasing patterns with quantity and numbers in a variety of contexts.
• 3.A.1 — Describe and create representations of numerical and geometric patterns.
• 3.A.1.1 — Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.

Oregon

• 3.OA.D.9 — Identify and explain arithmetic patterns using properties of operations, including patterns in the addition table or multiplication table.
• 4.OA.C.5 — Analyze a number, visual, or contextual pattern that follows a given rule.
• MP7 — Look for and make use of structure.
• MP8 — Look for and express regularity in repeated reasoning
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Pennsylvania

• CC.2.2.4.A.4 — Generate and analyze patterns using one rule.
• Look for and express regularity in repeated reasoning.
• CC.2.2.3.A.4 — Solve problems involving the four operations, and identify and explain patterns in arithmetic.
• CC.2.2.2.A.3 — Work with equal groups of objects to gain foundations for multiplication.

Rhode Island

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to five rows and up to five columns; write an equation to express the total as a sum of equal addends.
• 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.
• MP8 — Look for and express regularity in repeated reasoning.

South Carolina

• 1.ATO.9b — Create, extend and explain using pictures and words for growing patterns (between 2 and 4 terms/figures).
• 3.ATO.9 — Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table).
• 3.PS.7b — Recognize mathematical repetition in order to make generalizations.
• 4.ATO.5 — Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence.

South Dakota

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Tennessee

• 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.OA.C.4 — Use repeated addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. For example, a 3 by 4 array can be expressed as 3 + 3 + 3 + 3 = 12 or 4 + 4 + 4 = 12.

Texas

• 3.4D — determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10;
• 3.4E — represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting;
• 1.5B — skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set;

Utah

• 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.OA.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 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.
• 4.MP.8 — Look for and express regularity in repeated reasoning.

Vermont

• 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.
• MP7 — Look for and make use of structure.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• MP8 — Look for and express regularity in repeated reasoning.

Virginia

• 3.PFA.1a — Identify and describe increasing and decreasing patterns using various representations (e.g., objects, pictures, numbers, number lines).
• 3.PFA.1b — Analyze an increasing or decreasing pattern and generalize the change to extend the pattern or identify missing terms using various representations.
• 2.PFA.1b — Analyze a repeating or increasing pattern and generalize the change to extend the pattern using objects, pictures, and numbers.
• 3.PFA.1e — Investigate and explain the connection between two different representations of the same increasing or decreasing pattern.
• 6.NS.3b — Recognize and represent patterns of perfect squares not to exceed 20^2 , by using concrete and pictorial models.

Washington

• 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.

Washington, D.C.

• 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.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 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.
• MP7 — Look for and make use of structure.

West Virginia

• 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).
• MHM7 — Look for and make use of structure.
• M.2.5 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns to describe the arrays; write expressions to describe the array and equations to express the total as a sum of equal addends.
• M.4.5 — Generate a number pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself (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; explain informally why the numbers will continue to alternate in this way).

Wisconsin

• 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.
• M.2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• M.3.OA.D.8 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Wyoming

• 4.OA.C.5 — Given a pattern, explain a rule that the pattern follows and extend the pattern. 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.
• 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• 3.OA.D.9 — Identify arithmetic patterns and explain the relationships using properties of operations.
• MP8 — Look for and express regularity in repeated reasoning.