Standard

Solve two-step word problems using the four operations. 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.

Note: This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in conventional order when there are no parentheses to specify a particular order (Order of Operations).

Student language:

• "I can use addition, subtraction, multiplication and division to solve multi-step word problems and then use mental math to decide if my answers are reasonable. "

Explanation

About the Math, Learning Targets, and Rigor

This standard refers to multi-step word problems using the four operations.

• The size of the numbers should be limited to related 3rd grade standards (e.g., 3.OA.7 and 3.NBT.2).
• Adding and subtracting numbers should include numbers within 1,000.
• Multiplying and dividing numbers should include single-digit factors and products less than 100.

This standard calls for students to represent problems using equations with a letter to represent unknown quantities (variable).

This standard refers to estimation strategies or rounding. The focus in this standard is to have students use and discuss various strategies. Students should estimate during problem solving, and then revisit their estimate to check for reasonableness.

The above diagram helps the student write the equation, w + w + 13 = 63. Using the diagram, a student might think, “I know that the two wristbands cost $50 ($63-$13) so one wristband costs $25.”

Students gain a full understanding of which operation to use in any given situation through contextual problems. Number skills and concepts are developed as students solve problems. Problems should be presented on a regular basis as students work with numbers and computations.

Researchers and mathematics educators advise against providing “key words” for students to look for in problem situations because they can be misleading. Students should use various strategies to solve problems. Encourage students to represent the problem situation with a drawing or model.

Resources

Videos

• Khan Academy
  • scroll to 3.OA.8, click on a skill, watch videos on left side in each skill
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.OA.8
• Common Core Sheets

Released Assessment Questions

PARCC

3.OA.8

Solve two-step word problems using the four operations. 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.

• Tasks do not require a student to write a single equation with a letter standing for the unknown quantity in a two-step problem, and then solve that equation.
• Tasks may require students to write an equation as part of their work to find a solution, but students are not required to use a letter for the unknown.
• Addition, subtraction, multiplication and division situations in these problems may involve any of the basic situation types with unknowns in various positions (see CCSSM, Table 1,Common addition and subtraction situations, p. 88; CCSSM, Table 2, Common multiplication and division situations, p. 89; and the document for the OA Progression ).

Performance Indicators: 3.OA.8

Level 5: Exceeds Expectations

Solves two-step unscaffolded word problems using the four operations, including rounding where appropriate, in which the unknown is in a variety of positions. Both values for each operation performed is substantial (towards the upper limits as defined by the standard assessed).

Level 4: Meets Expectations

Solves two-step scaffolded word problems using the four operations in which the unknown is in a variety of positions. One of the values for each operation performed is substantial (towards the upper limits as defined by the standard assessed).

Critiquing Standards

3.C.4-3

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 3.OA.8)

• Tasks do not require a student to write a single equation with a letter standing for the unknown quantity in a two-step problem, and then solve that equation.
• Tasks may require students to write an equation as part of their work to find a solution, but students are not required to use a letter for the unknown.
• Addition, subtraction, multiplication and division situations in these problems may involve any of the basic situation types with unknowns in various positions (see CCSSM, Table 1,Common addition and subtraction situations, p. 88; CCSSM, Table 2, Common multiplication and division situations, p. 89; and the Progression document for the OA Progression).

3.C.5-1

Present solutions to two-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 two-step problems and present corrected solutions.

(Content Scope: Knowledge and skills articulated in 3.OA.8)

• Tasks do not require a student to write a single equation with a letter standing for the unknown quantity in a two-step problem, and then solve that equation.
• Tasks may require students to write an equation as part of their work to find a solution, but students are not required to use a letter for the unknown.
• Addition, subtraction, multiplication and division situations in these problems may involve any of the basic situation types with unknowns in various positions (see CCSSM, Table 1,Common addition and subtraction situations, p. 88; CCSSM, Table 2, Common multiplication and division situations, p. 89; and the Progression document for the OA Progression).

Performance Indicators: 3.C.4-3

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 counter-example 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
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.

Performance Indicators: 3.C.5-1

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 counter-example 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
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.