Standard

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.

Student language:

• "I can use what I know about addition, subtraction, multiplication and division to solve multi-step word problems involving whole numbers."
• "I can represent word problems by using equations with a letter standing for the unknown number."
• "I can determine how reasonable my answers to word problems are by using estimation, mental math and rounding."

Explanation

About the Math, Learning Targets, and Rigor

The focus in this standard is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Students need many opportunities solving multistep story problems using all four operations.

This standard references interpreting remainders. Remainders should be put into context for interpretation. Ways to address remainders:

1. Remain as a left over
2. Partitioned into fractions or decimals
3. Discarded leaving only the whole number answer
4. Increase the whole number answer up one
5. Round to the nearest whole number for an approximate result

Example:

Write different word problems involving 44 ÷ 6 =? where the answers are best represented as:

1. Problem A: 7
2. Problem B: 7 r. 2
3. Problem C: 8
4. Problem D: 7 or 8
5. Problem E: 7 2/6

Problem A

Mary had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches did she fill?

44 ÷ 6 = p; p = 7 r. 2. Mary can fill 7 pouches completely.

Problem B

Mary had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches could she fill and how many pencils would she have left?

44 ÷ 6 = p; p = 7 r. 2; Mary can fill 7 pouches and have 2 left over.

Problem C

Mary had 44 pencils. Six pencils fit into each of her pencil pouches. What would the fewest number of pouches she would need in order to hold all of her pencils?

44 ÷ 6 = p; p = 7 r. 2; Mary can needs 8 pouches to hold all of the pencils.

Problem D

Mary had 44 pencils. She divided them equally among her friends before giving one of the leftovers to each of her friends. How many pencils could her friends have received?

44 ÷ 6 = p; p = 7 r. 2; Some of her friends received 7 pencils. Two friends received 8 pencils.

Problem E

Mary had 44 pencils and put six pencils in each pouch. What fraction represents the number of pouches that Mary filled?

44 ÷ 6 = p; p = 7 2/6

Resources

Videos

• Khan Academy
  • scroll to 4.OA.3, click on skill, find videos on left side in each skill
• Learn Zillion
• Virtual Nerd

EngageNY Lessons

• Module 1, Topic D, Lesson 12: Solve multi-step word problems using the standard addition algorithm modeled with tape diagrams and assess the reasonableness of answers using rounding.
• Module 1, Topic E, Lesson 16: Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using rounding.
• Module 1, Topic F, Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding.
• Module 3, Topic D, Lesson 13: Use multiplication, addition, or subtraction to solve multi-step word problems.
• Module 3, Topic E, Lesson 19: Explain remainders by using place value understanding and models.
• Module 3, Topic G, Lesson 31: Interpret division word problems as either number of groups unknown or group size unknown.
• Module 7, Topic B, Lesson 10: Solve multi-step measurement word problems.
• Module 7, Topic B, Lesson 11: Solve multi-step measurement word problems.
• Module 7, Topic C, Lesson 14: Solve multi-step word problems involving converting mixed number measurements to a single unit.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.OA.3
• Common Core Sheets
• Teachers Cafe
• Math Worksheet Land

Released Assessment Questions

PARCC

Common Core State Standards

4.OA.3-1

Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations.

• Assessing reasonableness of answer is not assessed here.
• Tasks do not involve interpreting remainders.

4.OA.3-2

Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, in which remainders must be interpreted.

• Assessing reasonableness of answer is not assessed here.
• Tasks involve interpreting remainders.
• See p. 30 of the OA Progression document.
• Multi-step problems must have at least 3 steps.

Performance Indicators: 4.OA.3-1, 4.OA.3-2

Level 5: Exceeds Expectations

• Solves multi-step word problems using the four operations with whole numbers: in multiplying a three-or four-digit by a one-digit number or two two-digit numbers.
• Finds whole number quotients and remainders with up to four-digit dividends and one-digit divisors and interprets remainders as appropriate.
• Chooses from a variety of strategies to solve these problems and selects an appropriate context for the task.

Level 4: Meets Expectations

• Solves two-step word and other problems using the four operations with whole numbers: in multiplying a three-digit by a one-digit number or two two-digit numbers
• Finds whole number quotients and remainders with up to three-digit dividends and one-digit divisors and interprets remainders as appropriate.
• Chooses from a variety of strategies to solve these problems.

Integrated Standards

4.INT.5

Solve multi-step word problems posed with whole numbers and involving computations best performed by applying conceptual understanding of place value, perhaps involving rounding.

• Multi-step problems must have at least 3 steps.
• Tasks must be aligned to the first standard and 1 or more of the subsequent standards listed in the content scope. (4.OA.3, 4.NBT)

Critiquing & Reasoning Standards

4.C.5-1

Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed ‘student’ reasoning is presented and the task is to correct and improve it.)

(Content Scope: Knowledge and skills articulated in 4.OA.3)

• Reasoning in these tasks centers on interpretation of remainders.

4.C.6-1

Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions.

(Content Scope: Knowledge and skills articulated in 4.OA.3)

• Tasks may involve interpreting remainders.
• Multi-step problems must have at least 3 steps.

Performance Indicators: 4.C.5-1

"Distinguish correct explanation/reasoning from that which is flawed"

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• presenting and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• evaluating explanation/reasoning; if there is a flaw in the argument
• presenting and defending corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning, and providing a counterexample where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• presenting and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• distinguishing correct explanation/reasoning from that which is flawed
• identifying and describing the flaw in reasoning or describing errors in solutions to multi-step problems
• presenting corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.

Performance Indicators: 4.C.6-1

"Distinguish correct explanation/reasoning from that which is flawed"

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• presenting and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• evaluating explanation/reasoning; if there is a flaw in the argument
• presenting and defending corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning, and providing a counterexample where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• presenting and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• distinguishing correct explanation/reasoning from that which is flawed
• identifying and describing the flaw in reasoning or describing errors in solutions to multi-step problems
• presenting corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.

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