4.OA.3 - About the Math, Learning Targets, and Rigor

Grade 4 Number Operations

4.OA.3

About the Math

Full Standard

Solve multi-step 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.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

4th Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of addition and subtraction of whole numbers and fractions.

Report Card Measurement Topic: Demonstrates understanding of patterns, expressions, equations, and algebraic thinking.

  

 

Report Card Measurement Topic: Demonstrates understanding of patterns, expressions, equations, and algebraic thinking.
3rd Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of addition and subtraction.

Report Card Measurement Topic: Solves one-step word problems with any operation.

 

 

Report Card Measurement Topic: Solves one and two-step word problems with any operation.

 

Learning Targets

  • Determine the first step in a two-step problem.
  • Determine the second step in a two-step problem.
  • Represent a two-step word problem with models, pictures, and equations (two equations can be used in place of an equation with two-operations)
  • Write an equation for using a letter for an unknown number.
  • Interpret the remainder when needed.
  • Determine if the solution to a two-step problem is reasonable. 

 

About the Math

This standard is developed and reinforced across the entire year. It begins with one-step problem-solving situations. In the second quarter, students begin to work with two-step problems. In this setting, students should work with 2 related operations before working with all 4 operations in the 3rd and 4th quarter. Students do not have to write a single equation with two operations to represent the problem. This standard (and all other word problem standards) should not focus students on using key words.

  • Determine the first step in a two-step problem.

Students make sense of a problem and determine how they might represent it including pictures or diagrams. Students then determine the first action/step for determining an unknown.

  • Determine the second step in a two-step problem.

Students identify the second step needed to solve the problem. They can identify this step before or after completing the first step. 

  • Represent a two-step word problem with models, pictures, and equations (two equations can be used in place of an equation with two-operations)

Students should represent work problems with models, pictures, and equations. Two equations are recommended for 4th graders who do not know about order of operations.

  • Write an equation for using a letter for an unknown number.

Students should write a letter to represent the unknown in a problem. They can use two different letters in two different equations to represent the two steps in a two-step problem.

  • Interpret the remainder when needed.

Interpreting the remainder is developed over time. Students interpret remainders based on understanding of number and context. They should not be introduced to or held accountable for rules of working with remainders. Students should justify their interpretations.

  • Determine if the solution to a two-step problem is reasonable. 

Determining reasonableness with two-step problems is not as easy as simply estimating a result. Students have to ask themselves different questions. They have to compare the operations and steps taken to the results. Does it make sense to add first? How will this affect the result of my first step? Teacher modeling is important for developing reasonableness with two-step problems.

 

 

 

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Represent a one-step addition or subtraction word problem with multi-digit numbers using models, pictures, and equations.
  • Write an equation for using a letter for an unknown number.
  • Determine if the solution to a one-step problem is reasonable. 
  • Determine the first step in a two-step problem.
  • Determine the second step in a two-step problem.
  • Represent a two-step word problem with addition and/or subtraction using models, pictures, and equations (two equations can be used in place of an equation with two-operations)
  • Determine if the solution to a two-step problem is reasonable.
  • Represent a one-step multiplication or division word problem with multi-digit numbers using models, pictures, and equations. 
  • Write an equation for using a letter for an unknown number.
  • Determine if the solution to a one-step problem is reasonable. 
  • Interpret the remainder when needed.
  • Represent a two-step word problem with models, pictures, and equations (two equations can be used in place of an equation with two-operations)
  • Determine if the solution to a two-step problem is reasonable.
  • Interpret the remainder when needed.
  • Use all four operations .
  • Use two related operations (+/- or x/÷)
  • Represent a two-step word problem with models, pictures, and equations (two equations can be used in place of an equation with two-operations)
  • Determine if the solution to a two-step problem is reasonable.
  • Interpret the remainder when needed.
  • Use all four operations .
  • Use two related operations (+/- or x/÷)

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 3 Grade 7
  • Solve two-step word problems using the four operations.(3.OA.8)
  • Solve real-world and mathematical problems involving the four operations with rational numbers. (7.NS.3)

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • Addition - Use the prompts from the Crossing the Bridge Links to an external site. to engage students in a task that focuses on estimating in order to select reasonable answers. While finding accurate answers is important, there are several opportunities in this task for students to select options that complete the prompt without calculating the exact answer.
  • Division - Provide students with unifix cubes or colored tiles. Pose the prompt and allow students to use the manipulatives to represent their thinking and interpret the remainder. Prompt: A baker has 85 cookies that need to be packaged into bags so they can be sold. Each bag holds 7 cookies. How many bags are needed to hold the cookies? Are all the bags full? If they are not full, how many more cookies can fit in the bag? Ask students to justify their thinking using the manipulatives. It is important for students to identify what the manipulatives represent throughout this task. Continue this process with similar prompts.
  • There are 583 students in Suzy’s school. 99 third grade students left the school on a field trip. There are about 20 students in each class. How many classrooms are being used today? Explain your answer.
  • The school bought apples to give to students. They have 30 boxes with 8 apples in each box and they have 20 boxes with 10 apples in each box. Each student needs 3 apples for the week. How many students can the school feed?
  • Why is it important to consider the remainder when answering a problem? Give a real-life example of when it is important to drop the remainder? Give a real-life example of when you need to round the remainder.
  • Zoe is having a wedding. She has 178 guests attending. The party location can set up tables with 10 at each table OR tables with 8 at each table. How many tables will Zoe need under each situation?
  • Write a division problem that has 15 R2 as the quotient.
  • Barry’s family donated 11 cases of tomato soup to the local food kitchen. Each case has 12 cans of soup. The shelter already has 16 cans of tomato soup. How many cans of tomato soup does the food kitchen have now? The food kitchen uses 20 cans of tomato soup each week. How many weeks will go by before the food kitchen needs more tomato soup?

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 3 • Addition and Subtraction (Decomposition and Standard Algorithm) and Review Basic Facts (9s)

Represent and solve word problems that add/subtract multi-digit numbers:

Module 4 • Addition and Subtraction (Adjusting and Standard Algorithm) and Review Basic Facts (4s)

Multi-step word problems with addition/subtraction:

Module 6 • Multiplication & Division (2-Digit by 1-Digit) and Connect Basic Facts Review (8s) to Factors and Multiples

Solve one-step multiplication/division problems (2-digit by 1-digit) with remainders; interpret remainders:

Module 7 • Multiplication & Division (3- and 4-Digit by 1-Digit)

Solve one-step multiplication/division problems (3-digit or 4-digit by 1-digit) with remainders; interpret remainders:

Module 12 • Multiplication (2-Digit by 2-Digit) & Division and Solve Multiplication and Division Problems

Solve Multi-Step Problems Involving Multiplication and/or Division:

Module 15 • Measurement and Problem Solving

Solve Multi-Step Problems Involving Any of the Four Operations:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 3-5

 


 

Developing Mathematics with Base Ten

 2-6

3-15, 16-17, 25-28, 29-20, 30-31,

49-50, 56-57, 58-59, 59-61,

62-63 and 64-66
  Brain-Compatible Activities for Mathematics 4-5 32-35
  Problem Driven Math Grade 3 31-35

Math In Practice

Teaching Fourth-Grade Math

 4 Module 15

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

Represent and solve word problems that add/subtract multi-digit numbers:

Solve one-step multiplication/division problems with remainders; interpret remainders:

 

Multi-step word problems with addition/subtraction:

Multi-step word problems with all four operations and interpret remainders:

 

 

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Assessment

Learning Targets

rubric

  • Determine the first step in a two-step problem.
  • Determine the second step in a two-step problem.
  • Represent a two-step word problem with models, pictures, and equations (two equations can be used in place of an equation with two-operations)
  • Write an equation for using a letter for an unknown number.
  • Interpret the remainder when needed.
  • Determine if the solution to a two-step problem is reasonable.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.