Standard #: MA.3.AR.1.2


This document was generated on CPALMS - www.cpalms.org



Solve one- and two-step real-world problems involving any of four operations with whole numbers.


Examples


A group of students are playing soccer during lunch. How many students are needed to form four teams with eleven players each and to have two referees?

Clarifications


Clarification 1: Instruction includes understanding the context of the problem, as well as the quantities within the problem.

Clarification 2: Multiplication is limited to factors within 12 and related division facts. Refer to Situations Involving Operations with Numbers (Appendix A).



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Algebraic Reasoning
Standard: Solve multiplication and division problems.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Expression 
  • Equation

 

Vertical Alignment

Previous Benchmarks 

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to apply all four operations to solve one- and two-step real-world problems. This benchmark continues the work done in grade 2 solving real-world problems using addition and subtraction (MA.2.AR.1.1). 
  • Instruction should facilitate students’ understanding of contexts and quantities within word problems.
  • The emphasis on teaching problem-solving strategies should focus on the comprehension of problem contexts and what quantities represent in them. Examples of questions that help students comprehend word problems are: 
    • What is happening in the real-world problem? 
    • What do you need to find out? 
    • What do the quantities represent in the problem? 
    • What will the solution represent in the problem? (MTR.1.1, MTR.4.1, MTR.6.1) 
  • Teachers should model answering these questions through rectangular arrays, base-ten blocks, counters and think-alouds. In addition, teachers should help students explore estimation strategies to determine reasonable ranges for solutions (e.g., rounding, finding low and high estimates) and teach problem-solving strategies that build comprehension (e.g., Three Reads) (MTR.4.1, MTR.5.1, MTR.6.1).

 

Common Misconceptions or Errors

  • Students may have difficulty creating effective models (e.g., drawings, equations) that will help them solve real-world problems. To assist students, provide opportunities for them to estimate solutions and try different models before solving. Beginning instruction by showing problems without their quantities is a strategy for helping students determine what steps and operations will be used to solve.
  • Students may also have difficulty identifying when real-world problems require two steps to solve and will complete only one of the steps. Focusing on comprehension of real-world problems helps students determine what step(s) are required to solve.

 

Strategies to Support Tiered Instruction

  • Instruction provides opportunities for students to estimate solutions and try different models before solving. 
  • Instruction includes opportunities to create models (e.g., equations, drawings, manipulatives) to help solve real-world problems. The teacher uses guided questioning to support comprehension, considering levels of reading proficiency for students who may struggle with word problems—some students may need to hear the problems read aloud. The teacher provides opportunities to estimate solutions and try different models before solving, beginning instruction by showing problems without their quantities is a strategy to help students determine what steps and operations will be used to solve.
    • For example, the teacher reads aloud the following problem: Keisha and Diego are selling pies for a fundraiser. Each pie cost five dollars. If Keisha sells 15 pies and Diego sells 5 pies, how much money did they earn for the fundraiser? 
      • The teacher uses questioning to ensure comprehension (e.g., “What do you need to find out?” “What do the quantities represent in the problem?” “What will the solution represent in the problem?”). 
      • The teacher models how to represent this problem using an equation and a drawing: 
(15 + 5) × 5
20 × 5 

a drawing

      • The teacher repeats with additional two-step problems, guiding students to create appropriate models to support problem-solving. 
    • For example, the teacher reads aloud the following problem: Antwan is helping the art teacher get ready for art club. There are a total of 30 paintbrushes. The art teacher asked Antwan to put 6 paintbrushes on each of the 4 tables in the room and then put the rest on the counter. How many paint brushes will he put on the counter? 
      • The teacher uses questioning to ensure comprehension (e.g., “What do you need to find out?” “What do the quantities represent in the problem?” “What will the solution represent in the problem?”). 
      • The teacher models the problem using counters, prompting the students to demonstrate each step of the problem while writing the corresponding equations for each step. 

6 × 4 = 24
30 − 24 = 6 
      • The teacher repeats with additional two-step problems, guiding students to create appropriate models using manipulatives to support problem- solving. Some students may benefit from “ acting out” the story in the problem to support the problem-solving process. 
  • Instruction includes guided practice identifying and completing two steps in a real-world problem. The teacher uses guided questioning to support comprehension considering levels of reading proficiency for students who may struggle with word problems—some students may need to hear the problems read aloud. The teacher uses explicit prompts for each step. 
    • For example, the teacher reads aloud the following problem: Suni is taking piano lessons. Her piano teacher told her to practice for 90 minutes this week. On Monday, she practiced for 15 minutes. She practiced 20 minutes on Tuesday and 25 minutes on Wednesday. How much more time does she still need to practice this week? 
      • The teacher uses guided questioning and prompts to help students identify the steps (e.g., “ What do you already know?” “ What do you need to find out?” “ What do we need to do before we can find out the remaining time she has left to practice?”). Through questioning, the teacher guides students to identify the first step: adding the amount of time Suni has already practiced. 
      • The teacher uses a model to represent the problem and an equation to represent the first step.
        15 + 20 + 25 = 60 
      • After students complete the first step, the teacher uses questioning to prompt the next step (e.g., “ What does the sum we just found show us?” “ What do you need to find out to solve this problem?” “ What should we do next?”). The problem may need to be reread aloud. 
15 + 20 + 25 = 60 
60+ ___=90 
90−60= 30 minutes 

      • The teacher repeats with additional two-step problems, guiding students to identify and solve each step. 
    • For example, the teacher reads aloud the following problem: Rahim is learning about instruments in music class. He learns that guitars have six strings and mandolins have four strings. If there are three guitars and four mandolins in the classroom, how many strings are there altogether on the guitars and mandolins? 
      • The teacher uses guided questioning and prompts to help students to identify the steps (e.g., “ What do you already know?” “ What do you need to find out?” “ What do we need to do before we can find out the remaining time she has left to practice?”). Through questioning, the teacher guides students to identify the first step: Multiplying the number of strings by the number of each instrument. 
      • The teacher guides the students to create a model (using manipulatives such as counters) with corresponding equations. 

counters

      • After students complete the first step, the teacher uses questioning to prompt next step (e.g., “ What have we learned about the numbers of strings?” “ What do you need to find out to solve this problem?” “ What should we do next?”). The problem may need to be reread aloud. 18 + 16 = 34 total strings 
      • The teacher repeats with additional two-step problems, guiding students to identify and solve each step using manipulatives. Some students may benefit from “ acting out” the story in the problem to support the problem-solving process.

 

Instructional Tasks

Instructional Task 1 

Solve the problem. Oak Hill Elementary third-grade students are taking a field trip to the zoo. There are 71 students who paid to attend the field trip. Of those that paid, 8 students cannot go on the day of the trip. There needs to be 7 groups at the zoo and each group must have an equal number of students. How many students will be in each group on the field trip?

 

Instructional Items

Instructional Item 1 

For a school food drive, three students bring in cases of canned goods to donate. Uriel brings 4 cases, Paola brings 6 cases, and Mika brings 5 cases. Each case contains 8 canned goods. How many canned goods in all does the school collect? 

 

Instructional Item 2 

A bookstore has 8 boxes of books. Each box contains 10 books. On Monday, the bookstore sold 16 books. How many books remain to be sold? 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.3.AR.1.AP.2a Solve one- and two-step addition and subtraction real-world problems within 100.
MA.3.AR.1.AP.2b Solve one-step multiplication and division real-world problems. Multiplication may not exceed two single-digit whole numbers and their related division facts.


Related Resources

Formative Assessments

Name Description
Writing a Problem With a Quotient

Students are asked to solve a division equation and then interpret the quotient by writing a word problem that can be modeled by the equation.

Finding the Number of Groups

Students are asked to model an equal groups and an array problem in which the number of groups is unknown with multiplication or division equations and then solve each problem.

Finding an Unknown Product

Students are asked to model an equal groups and an array problem in which the product is unknown with multiplication or division equations and then solve each problem.

Finding the Group Size

Students are asked to model an equal groups and an array problem in which the group size is unknown with multiplication or division equations and then solve each problem.

Zoo Field Trip

Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.

Party Beverages

Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.

Bake Sale

Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.

Books at the Book Fair

Students solve a two-step word problem involving multiplication and subtraction and then write an equation to represent the problem.

Lesson Plans

Name Description
U.S. Symbols Construction

Students will interpret and make comparisons of construction start and end dates and heights of U.S. symbols. Students will solve one- and two-step word problems based on the data. 

How Many Years?

Students will discuss what they know about individuals who represent the U.S. or Florida and interpret data including important dates in the lives of these individuals. Students will use the data to solve one and two-step word problems in this integrated lesson.  

School Food Drive- Word Problems

Students will solve one- and two-step word problems using a given set of data of collected food items from a school food drive. Students will use the word problems to identify roles volunteers have in a food drive in this integrated lesson plan.

This lesson is Part 2 of 3 math lesson integrating the importance of volunteering in a food drive.

Sightseeing the U.S. Symbols

Students will review the details of various trips to landmark destinations in the U.S. and rank the trips from most to least preferred, in this model eliciting activity.

Feeding the Community

Students analyze various proposed sites to determine which site would be best for a group of volunteers to construct and maintain a community garden in this model eliciting activity.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.  Click here to learn more about MEAs and how they can transform your classroom.

Astounding Addition

Students will solve real-world addition problems within 1,000 using strategies and an algorithm and justify their solutions.

From Array to Van De Walle 100-Dot Matrix

This lesson builds upon student knowledge of arrays to using the Van de Walle 100-Dot Matrix model to solve multiplication problems involving rows and columns.

Bridging Multiplication with Word Problems

This introductory lesson uses word problems to help students make connections between arrays and multiplication with single and two-digit factors within 100.

The Array Frame, your best friend

In this lesson, students will learn to use the structure of array frames to build familiarity and fluency with the array as a tool. Students will explore multiplication by solving several multiplication word problems involving rows and columns situations using the array as a representation.

Circles and Stars

This is an introductory lesson to prepare students to move from using repeated addition to using multiplication to represent equal groups situations.

Chess Wish List

The 3rd grade chess club members will make two wish lists on how to spend $75 on chess related materials. Then they have to make two new wish lists on how to spend $750 on chess related materials.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Best Vegetable Garden

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Science Space Camp

This MEA asks the students to compare information provided on various Science Space Camps to be attended by a student during the summer. They will take into account past attendee's reviews of the camps which should create interesting student discussions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Water Park Fun Day

This third grade MEA asks students to work as a team to figure out which activities they would like to do at the water park with a given amount of tickets and time. Students will make informed decisions about which activities and food and beverage items on which to spend their allotted tickets.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Same Perimeter, Different Area

In this lesson, students are presented with a problem that requires them to create rectangles with the same perimeter but different areas.  Students also search for relationships among the perimeters and areas of different rectangles and find which characteristics produce a rectangle with the greatest area.

Make Your Way With Arrays

Students will solve multiplication and division word problems by drawing arrays and writing the related equation.

What Does Your Garden Grow?

In this model eliciting activity students use data about the temperature and water requirements of plants to figure out when the plants should be planted. They also use data such as space requirements and time until harvest to make judgments about which plants would best suit the needs of students planning a school garden in Florida.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Kites for Education MEA

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Hungry Zero

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.   

Great Estimations!

In this lesson, students will deepen their knowledge of using equal groups in multiplication and their ability to visualize the quantity of an item in a given object. They will use problem-solving skills and see the value in using benchmarks.

Subtraction Attraction

In this lesson, students will demonstrate fluency in using a standard algorithm to complete story problems involving subtraction with regrouping using multi-digit whole numbers.

Pet Store Partitive Division

In this lesson students will model partitive division through the real-world activity of a pet store owner.

Chip Chip Array!

Students work together to create arrays to represent given numbers.

Tasty Algebra: Using toasted O cereal to find the missing factor in a multiplication equation.

In this lesson students will use Cheerios to solve multiplication equations relating 3 whole numbers from word problems that include missing factors ranging from one through ten. Students will also argue the validity of multiplication equations that include missing factors and products with corresponding word problems.

Apples, Oranges, and Bananas of Math?

In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.

How Many Seeds in a Pumpkin?

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Way Too Much!

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

Original Student Tutorial

Name Description
Protect the Turtles: Solve Two-Step Word Problems

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.  

Perspectives Video: Teaching Idea

Name Description
Representing Remainders as Fractions

Unlock an effective teaching strategy for representing remainders as fractions in this Teacher Perspectives video for educators.

Problem-Solving Tasks

Name Description
The Stamp Collection

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Classroom Supplies

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.

Student Resources

Original Student Tutorial

Name Description
Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.  

Problem-Solving Tasks

Name Description
The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Classroom Supplies:

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.



Parent Resources

Problem-Solving Tasks

Name Description
The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Classroom Supplies:

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.



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