3.OA.8 - About the Math, Learning Targets, and Rigor

Grade 3 Whole Numbers

3.OA.D.8

About the Math

Full 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.

 

Measurement Topic

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

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

 

Report Card Measurement Topic: Solves one and two-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 word problem (quarter 4).
  • Determine the second step in a two-step word problem (quarter 4).
  • 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 using a letter for the unknown number.
  • Determine if a solution to a two-step problem is reasonable.

 

About the Math

To solve problems, we must understand the problem, select a strategy, and assess if our solution is reasonable. It is critical for students to develop these skills through practice and conversation. As teachers, we must be careful not to highlight or modify a singular approach to solving any one problem. We should monitor as students solve problems and pause the process for the group to highlight questions students have or strategies they are using.

Key Words:

Key words are not a viable strategy for solving word problems. Instead, we want students to make sense of problems and make use of their understanding to solve the problems. Moreover, research tells us that the use of key words as a strategy for solving problems adds to our students' inability to solve problems. 

Problem Solving Situations:

Students have worked with problems representing all problem types in previous grades. The types of problem-solving situations are shown to the right. Students in grade 3 must also have access to and work with all of these problem structures.

  • Determine the first step in a two-step word problem (quarter 3 and 4).
  • Determine the second step in a two-step word problem (quarter 3 and 4)

One must determine what to do first in a two-step problem. The results of the first step are then used in the second step to solve a problem. Work with two-step word problems should feature making sense of the problem and representing the problem rather than a formulaic, procedural approach. Tools and representations used for single step word problems are appropriate for two-step problems as well. Because two-step problems are naturally more challenging, it is critical that students have opportunities to explore and discuss strategies and solution paths with others.

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

There are many ways that students can represent problems to solve them. We should be sure to encourage diverse representations. We also should be sure to connect representations. For example, it is important to connect drawings and equations or physical models and equations. Bar diagrams are highly useful representations that help students develop an understanding of the relationships within a problem. Thinking Blocks Links to an external site. (pictured to the right) is an online resource that helps students develop an understanding of different problem-solving situations by modeling them with bar diagrams.

It's reasonable to begin with two-step word problems that feature one operation or two related operations (e.g. addition and subtraction) before transitioning to two-step problems that feature multiplication and division. As students show developing proficiency with two-step problems, we can begin to use any of the four operations.

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

Third-grade students do not need to write a single equation for two-step problems. Instead, students can write 2 different equations to express what is happening in the problem.

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

Estimating First:

We can help students develop a sense of reasonableness of their answers. One way to do this it to estimate the approximate solution of the problem before finding the exact solution. 

Looking Back:

Estimating an answer for a two-step problem can be problematic. Though it can be done, one can also put the solution into the context to see if it makes sense. For example, if Susan has 9 apples, eats 2, and gives 4 away the solution can't be anything more than the 9 she started with. 

 

Progression of Standard within Grade 3

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 word problem (all operations) with models, pictures, and equations.
  • Write an equation using a letter for the unknown number.

 
  • Determine the first step in a two-step word problem.
  • Determine the second step in a two-step word 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 using a letter for the unknown number.
  • Determine if a solution to a two-step problem is reasonable.
  • Reinforce through problem solving with area, perimeter, time, volume, and mass.

 

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 2 Grade 4
U se +/- to solve one- and two-step word problems (2.OA.A.1) Solve multi-step word problems using the four operations (4.OA.3)

 

 

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Instructional Tasks

Tasks

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

  • Module 8 one-step problems: Pose one-step word problems and through conversation help students make meaning of the problem and what operation is needed to solve the problem. Students should use a letter to represent the unknown when writing their equations. 3rd grade is the first year where students use letters to represent the unknown. Create story problems that involve your students' interests and cultures. Problems can involve multi-digit numbers if using addition and subtraction. When the problems involve multiplication or division, problems should stay with the basic facts or multiples of 10 times a single digit. Two examples: Larae has $264 in the bank and Donte has $120 more than Larae. How much money does Donte have? Juan's mother made 3 batches of pupusas and each batch had 8, how many total pupusas will Juan get to eat?
  • Module 14 two-step problems: Repeat from the first bullet above, remembering to create story problems that are unique to your students' interests and cultures. Two examples: In the morning, the bakery baked 5 pies and each pie is cut into 6 pieces, throughout the day the bakery sold 23 pieces of pie. How many pieces do they have left at the end of the day? Leah earned 231 points on her video game yesterday. Today she earned 59 more points. If she uses 36 points to stay in the game longer, how many points will Leah have left?
  • About how many days have you been in school? Tell how you estimated and what mathematical operations you used.
  • Ben has two cats. Each cat eats one can of wet cat food per day. Cat food is sold with 24 cans in a case. Ben wants to buy enough cat food for two weeks. If he buys one case is this enough cat food? Explain your answer.
  • The answer is 42. What is the question?
  • There are 61 third-grade students in Amy’s school. 19 of the them are in the library. How many are left in their classrooms? If each classroom holds about 20 students, how many classrooms are likely being used?
  • Andrea had some markers. When she puts them in groups of 3, there was 1 left over. When she put them in groups of 4, there were 3 left over. If she had fewer than 20 markers, how many could she have had?
  • A farm has a fenced area that can hold 28 animals.  There are 16 chickens and 11 pigs.  Will all of the animals fit in the fenced area.  Explain how you know.
  • Joseph has 34 cupcakes and is putting them into boxes that each hold 10 cupcakes.  He has 3 boxes.  Does he have enough boxes?  Will any cupcakes be left over?  Show your understanding of x10 to explain how you know.

 

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 8 • One-Step Word Problems with Any Operation and Basic Facts (1s and 0s)

Solve One-Step Word Problems with Any Operation, Letter for the Unknown:

Module 14 • Two-Step Word Problems and Basic Facts (8s)

Solve Two-Step Word Problems with Addition and/or Subtraction:

Solve Two-Step Word Problems with 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
  Nimble With Numbers 3-4

82-86

100-104
  Fundamentals
 3-4

16 (On Target)

24 (Total Two)

  Groundworks Reasoning with Number 3 80-87 (Shape Numbers)

56-63, (House Numbers)
 

Hands On Standards

 		 3-4
 		 116-117 (Multiplication and Division)
  Developing Mathematics with Base Ten  

13-15, 25-28, 29-30

56-57, 58-59, 59-61
 

Math Intervention: Building Number Power

 3-5 59-63
   

Brain-Compatible Activities for Mathematics

 2-3 127-129
  Problem-Driven Math

3

55 - 57 (Florida Freeway)

73 - 75 (Shell Seeking)
  Developing Number Concepts Book 3    99-131
  Navigating Through Algebra  3-5 37-57
  Roads to Reasoning 2

78-79 (Candle Sales), 40 (Double Dessert)

50-51 (String Along), 24 (Tooth Fairy)

65 (What is Missy Missing?)

Math In Practice

Teaching Third-Grade Math

 3

Module 4

 

More Ideas

 

 

 

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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.

 

 

 

 

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Assessment

Learning Targets

  • Determine the first step in a two-step word problem.
  • Determine the second step in a two-step word 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 using a letter for the unknown number.
  • Determine if a solution to a two-step problem is reasonable.

 

Learning targets identify what students should be able to do. The 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.