problem solving grade 3 lesson plan

Solving Word Problems (Grades 3-6)

Our Solving Word Problems lesson plan for grades 3-6 provides students with more advanced strategies for solving word problems. Students learn how to use pictures or diagrams to solve word problems and how to solve word problems involving more advanced operations.

Description

Additional information.

Our Solving Word Problems (Grades 3-6) lesson plan strengthens strategies for solving word problems. This interactive lesson plan equips students to identify and define keywords and use pictures or diagrams for math problem solving (all operations). Students are asked to create word problems and use their presentation skills to share their problem-solving steps with the class. Students are also asked to individually complete practice problems in order to demonstrate their understanding of the lesson.

At the end of the lesson, students will be able to identify and define keywords and use pictures or diagrams for math problem solving (all operations).

State Educational Standards: LB.Math.Content.3.OA.D.8, LB.Math.Content.4.OA.A.3

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Examples of Math Problems for 3rd Grade Teachers

Written by Victoria Hegwood

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Solving Word Math Problems

Why students struggle with word math problems, how to help students master math word problems, make 3rd grade math fun with prodigy.

As adults, many of us chuckle when reading elementary math problems because the idea of Charlie having 87 watermelons paints a funny mental picture. 

But for many students, word math problems can be overwhelming. This is largely because word problems require different skills than traditional math problems. 

And not all children have developed the cognitive and communication skills necessary to solve word problems. 

So, if we know that this is a challenging area for our students, what can we do to help them?

This article will look at students' common problems when solving word math problems and what teachers can do to help them. It will also offer you tips on how to effectively deliver word problems based on topics you are likely teaching about in third-grade math class.

By the end of 3rd grade, students are expected to be able to solve word math problems using addition, subtraction, multiplication, and division (four operators). 

Throughout the year, they also learn how to solve two-step problems. This type of problem is one where students will need to solve the first part of the equation and then plug that answer into the second part. 

The other main skill that third graders learn is how to use graphs. Students will be tasked with reading graphs, making their own graphs and using graphs to solve word problems. 

Changing standards and curriculums can make it difficult to keep up with exactly what children should be learning and when. If you want to better understand where your students should be at, check out Komodo Math’s article or Great School’s article on third-grade math skills. 

Let’s go over some examples of these skills to better understand what our students should be learning in the classroom. 

1. Two-Step Problem Example

Let’s start with a division word problem to see an example of a two-step problem. 

Amanda has a jar with 8 chocolate chip cookies and 7 oatmeal cookies. She can only share 3 cookies with each of her friends. How many friends does Amanda have?

Step one is finding out how many cookies Amanda has. To get this answer, 3rd-grade students would need to add together 8 cookies plus 7 cookies. 8+7=15.

Then step two is dividing the number of cookies between her friends. 

15 ÷ 3 = 5. With this equation, the number of people who can be served is determined. Amanda has five friends. 

2. Using three operators: Multiplication, Addition, and Subtraction

Not only do students need to know how to use different types of operators, they also need to be able to decide which operations to use when. Multi-step word problems require this extra layer of thinking. Here is an example.

Sarah bought four bags of oranges at the store. There were 8 oranges in each bag. Sarah ate two oranges after giving three oranges to her friend. How many oranges does Jenny have now?

To find the answer, the word problem must be done in two steps:

Step 1: The number of bags (4) is multiplied by the number of oranges (8) to find the total number of oranges.

4x8 = 32 oranges

Step 2: Subtract the oranges Sarah gave her friend (3) and how many she ate (2) from the total of oranges (32).

32-3-2= 27 oranges.

Sarah has 27 oranges now.

3. Focusing on individual math skills: Time word problems

Understanding time, how it works and how to apply math skills to it, is an essential skill. But it can be one that requires quite a bit of practice to master. Let’s look at an example of a time word problem. 

Eddie started cleaning his room at 8:43 am. If he finally finished at 9:32 am, how long did Eddie spend cleaning his room?

Students first need to understand that there are 60 minutes in 1 hour. Then, they can take 60 minus 43 and add the total to 32 to get the total number of minutes.

60 - 43 = 17

17 + 32 = 49. 

Eddie spent 49 minutes cleaning his room.

4. Word problems with tricky wording: Subtraction vs. Addition

With some word problems, the math skill itself isn’t the tricky part. The difficult part is figuring out what the words in the word problem are trying to tell you. Here’s an example.

There were 353 people attending a baseball game after 31 people left. How many people were at the game before the people left?

In this problem, students need to understand that the math skill this problem is looking to test is addition - not subtraction. Students can add 31 + 353 to get the total number of attendees.

353 + 31 = 384 attendees.

5. Testing different operations: Multiplication Word Problems

Sometimes there are multiple ways to solve math problems, but one way is much easier. 

Susie is making cookies for her third-grade class at school. There are 24 students in her class and she made 3 cookies for each person. How many cookies did Susie make in total?

Students need to understand that multiplication is the easiest solution in order to solve this problem. Multiplying 24 x 3 will provide the correct answer.

24 x 3 = 72 cookies total.

While 3rd grade math word problems can be challenging, many students make similar mistakes. Understanding where students often stumble will allow you to help your students succeed.

Difficulty Reading and Understanding the Problem

In order to solve word problems, students don’t just need math skills. They also need reading comprehension skills. 

If students struggle with reading or can’t understand what the words in the problem mean, they won’t even get to the stage where they can apply what they learned in their math lesson. 

Sometimes students can read the problem step-by-step, but the way that it’s worded can seem tricky and confuse students. They may have difficulty mapping out and visualizing the word math problem. We saw this earlier in problem 4 about the baseball game. 

Seeing Only the Numbers

Another common issue is students only looking at the digit numbers and don’t fully read the word math problem. 

Reading and fully understanding the word problem is essential to knowing what operation to use with the numbers. Students also need to be able to understand what order to do the operations in. These skills are important ones to touch on in your lesson plan. 

Problem 6 in this article gives another example of how students need to be able to use the words in a word problem to decide on steps and operators to use. 

Mastering this skill helps students translate word problems into real-world scenarios as they can take numbers and know how to use them to find a solution.

Lacking Math Vocabulary

A lack of math vocabulary can make it difficult for students to understand what the word math problem is asking. It’s so important to lay a foundation of math vocabulary at the beginning of your lesson plan. 

If students don’t know which math operation to use, they will arrive at the wrong answer on math word problem worksheets.

Lacking Numerical Language Skills

Students can also face extra challenges if they have a math-related learning disability . These common challenges include: 

• Mistakes such as adding or omitting numbers that aren’t originally included in the problems
• Difficulty with abstract concepts like time and direction
• Getting inconsistent results when performing addition, subtraction, multiplication and division skills
• Inability to visualize math problems
• Difficulty remembering math facts, concepts, rules, formulas, rules and procedures
• Inability to memorize math facts
• Difficulty with understanding left and right
• Confusing operations signs or performing them in wrong order

For further reading on how to help students struggling with math skills, check out this article or this article .

So now that you understand what students may be struggling with, let’s dive into some practical ways to help your students conquer word problems. 

The first step is evaluating where your students are at. This can be easy to do with a formative assessment or third grade math worksheets . Then, you can work through the following steps. 

Formalize Your Approach

You should have a well-defined strategy when it comes to helping students understand how to solve word math problems. Try creating a system that simplifies word math problems. 

Prodigy Math Journey can be an effective tool for you to help students solve word math problems. This game has lots of useful features like the ability to monitor your students’ progress. You can also look at specific skills, like the ability to solve two-step word problems. 

It can be very effective at helping students understand how to use various math operations together, like using addition and subtraction or multiplication division.

Make Sure to Read the Entire Word Problem

A simple step that makes a big difference is emphasizing that students should read the entire word problem before attempting to solve it. 

Sometimes students have a lack of flexibility in how they think about math word problems. This makes them think that every problem can be solved exactly the same way with the same procedures. However, they need to approach each problem as a new challenge. 

Teaching students to read the entire math word problem will give students a better understanding of the problem . And this will give them a better chance of solving it on their own.

Identify and Highlight the Relevant Information

It can also be helpful for you to break the problem down for students. Show them how to focus on the most important parts. 

Make sure that your students can recognize the most important numbers and phrases in math problems so they can concentrate on what matters.

Give Them an Equation Without Numbers

Word math problems can be complex for 3rd graders to understand. Sometimes if you can  present the word math problem without the numbers, your students may be better able to extract the correct information. 

This method can help students understand if the problem is an additional word problem, subtraction word problem, a time word problem or something else. Once the student understands what the problem is asking for, add the numbers back in.

This strategy may be more difficult for first-grade or second-grade students, but third-grade math students are at the appropriate level to grasp word problems without numbers.

Help Them Visualize the Problem

Visuals can be used as an interactive tool that can help students see and understand the problem more fully. Visuals often help students see the real world representation of numbers. 

You can use physical objects, drawings and labels to help students visualize the problem and solve the equation. It’s easier to do this with smaller numbers and may be more difficult if students are doing more advanced operations instead of just basic multiplication or division. 

Identify and Compare Similar Word Problems

You can also use word problems with similar equations to help students analyze and solve word math problems.

Similarities between problems help students gain confidence . With repetition, learners won’t feel repeated frustration as they keep working on new skills. 

Once they feel confident with one type of problem, they will be more excited to tackle new challenges and skills in daily math activities.

Teaching word math problems may feel as daunting to you as it does to you as learning how to do them feels to your students. While there are many challenges, there are also approaches and strategies that can make it easier and more fun for everyone. 

If you’re looking for a great program to make the whole process more fun and less stressful, Prodigy is here to help! Prodigy is a game-based learning tool that can help deliver these word problems through gameplay that puts fun at the heart of learning. 

In addition to being a fun activity that your students will be excited to do, Prodigy has also been shown to reduce students’ math anxiety and build math confidence. It also aligns with US state standards for 1st-8th grades and automatically adapts to each student. 

Ready to get started today? Make a free teacher account here!

Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 3

Lesson 3 of 24

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations—Fractions

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Foundational Standards

The foundational standards covered in this lesson

2.G.A.3 — Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Understand non-unit fractions are built from unit fractions.
• Understand the  denominator of a fraction to be the fractional unit and the numerator of a fraction to be the number of units.
• Identify a non-unit fraction of a whole and write it using fraction notation.
• Partition and shade a pictorial area or length model to represent a non-unit fraction (MP.5).
• Explain whether or not a pictorial area or length model represents a particular non-unit fraction (MP.3).
• Determine the non-unit fraction represented by an abstract description of a situation (MP.2).

Suggestions for teachers to help them teach this lesson

• This is a dense lesson so you may decide to split it over two days. It covers a variety of non-unit fractions, including those equivalent to and greater than 1. As the Progressions state, “there is no need to introduce ‘proper fractions’ and ‘improper fractions’ initially;  $$\frac{5}{3}$$ is what you get by combining 5 parts when a whole is partitioned into 3 equal parts”, so addressing them in the same lesson helps students see that all fractions are built from unit fractions. However, if you’d like to split this lesson over two days, you could use Anchor Tasks 1 and 2 on the first day, and save Anchor Task 3 which involves fractions greater than 1 for the second day. The Problem Set and Extra Practice Problems can be split similarly, since all problems involving fractions greater than 1 are at the end of each resource. 
• While there is no need to introduce “proper fractions” and “improper fractions” as mentioned above, it of course might come up in discussion. If it does, it’s a good idea to avoid using the term “improper fraction”, since it implies that there’s something wrong with this way of writing a number, when in fact sometimes it’s the preferred way to write it. Instead, use the term “fraction greater than one” with students, which after this task, makes sense to them.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Each shape below represents one whole. What fraction of each whole is shaded?

a.    

b.    

c.    

d.    

Guiding Questions

Make a model in which the shaded part represents the corresponding fraction.

a.   Each shape below represents 1 whole. What fraction is represented by the shaded parts? Be prepared to explain your reasoning.

b.   Draw a model to represent the fraction  $$\frac{5}{2}$$ .

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• How would you change each of the incorrect statements in #2 to make them true statements?
• What were the two reasons why Gregory was incorrect in #5? How would you change Gregory’s claim and/or the model to make him correct?
• How did you determine how Nadia needed to finish the math problem in #7? How was this problem different from some of the others on the Problem Set?
• How did you determine the correct answer in #8 without an image?
• Did students eat  $$\frac{10}{8}$$  or  $$\frac{10}{16}$$  of a pan in #12? How do you know? What does  $$\frac{10}{16}$$  represent?

How many pizzas should Jeremy order in #13? How do you know? How can you tell just by looking at the numbers involved that it will be more than one pizza?

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Which figure is  $$\frac{2}{3}$$ shaded?

Draw a visual fraction model that represents each fraction below. Be sure to indicate what represents 1 whole.

a.    $$\frac{6}{6}$$

b.    $$\frac{5}{4}$$

Student Response

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Partition a whole into equal parts using area models, identifying fractional units.

3.G.A.2 3.NF.A.1

Partition a whole into equal parts using tape diagrams (i.e., fraction strips), identifying and writing unit fractions in fraction notation.

Identify fractions of a whole that is not partitioned into equal parts.

Draw the whole when given the unit fraction.

Identify a shaded fractional part in different ways, depending on the designation of the whole.

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Topic B: Fractions on a Number Line

Partition a number line from 0 to 1 into fractional units.

Place any fraction on a number line with endpoints 0 and 1.

Place any fraction on a number line with endpoints 0 and another whole number greater than 1.

Place any fraction on a number line with endpoints greater than 0.

3.NF.A.2 3.NF.A.3.C

Place various fractions on a number line where the given interval is not a whole.

3.NF.A.2 3.NF.A.3.D

Topic C: Equivalent Fractions

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

3.NF.A.3.A 3.NF.A.3.B

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Explain equivalence by manipulating units and reasoning about their size.

3.NF.A.3.A 3.NF.A.3.B 3.NF.A.3.C

Topic D: Comparing Fractions

Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

Compare fractions with the same denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.

Compare and order fractions using various methods.

Understand fractions as numbers.

Topic E: Line Plots

Measure lengths to the nearest half inch.

Measure lengths to the nearest quarter inch. 

Generate measurement data and represent it in a line plot.

Create line plots (dot plots). 

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3rd Grade Math Lesson Plans

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Problem-Based Tasks in Math

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Providing students with opportunities to grapple with math has led to amazing things happening in my class. Students are totally excited and are driven to figure out not just how to solve a problem but why it works.

– Jessica Proffitt, Fifth-Grade Teacher at Two Rivers

Watch two rivers’s teachers and students at work on problem-based tasks in math.

Problem-Based Tasks Require Students to Apply Their Knowledge in New Contexts

Problem-based tasks are math lessons built around a single, compelling problem. The problems are truly “problematic” for students — that is, they do not offer an immediate solution.

The problems provide an opportunity for students to build conceptual understanding. Problem-based tasks require students to apply their current understanding and skills to new contexts that highlight core math concepts. For example, when students solve a problem that could be solved with multiplication before they have formally been taught what multiplication is and how it works, they build an understanding that multiplication is repeated addition.

Well-designed problem-based tasks provide multiple entry points for students to engage in problem solving, ensuring that all students have access to the same concepts. When students solve the problems in different ways—including drawing pictures, acting out the problem, writing algorithms, and using manipulatives—they make connections between the variety of models that all accurately illustrate the underlying mathematics.

Problem-Based Tasks in Math Resources

Grade 3 Multiplication Lesson Plan: Illustrating Multiplication

• Patricia Gable
• Categories : Lesson plans & worksheets for grades 3 to 5
• Tags : Teaching grades pre k to 5

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. MA3-OA-A-1

Materials and Preparation

“Amanda Bean’s Amazing Dream” by Cindy Neuschwander

White 12” x 18” construction paper, one piece per student

Variety of stickers, beans, buttons, etc.

Slips of paper, each with a different single digit multiplication problem (one for each student)

Show students the book “Amanda Bean’s Amazing Dream” and say, “Poor Amanda! She loves to count, but she is having trouble counting larger groups of things in a fast way. Maybe she will be convinced that there is an easier way!”

Read and discuss the book and then provide supplies for students to show four ways to solve a multiplication problem.

Ask students to create a poster illustrating an array, repeated addition, fact family and groups as a way to find the product of the problem.

• Give each student a slip of paper with a multiplication problem on it.
• Provide white paper, glue, markers, crayons and a variety of objects such as stickers, beans, buttons, etc.
• Show students how to fold the 12”x18” piece of paper to make four equal sections.
• Label each section: “Repeated Addition,” “An Array,” “Fact Family” and “Groups.”
• If necessary, do an example together.
• Encourage students to make their projects neat, colorful and accurate!
• Neuschwander, Cindy. Amanda Bean’s Amazing Dream. Scholastic Press, 1998.

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Problem solving lesson plan

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Problem Solving: Lesson plan

Problem solving: Presentation slides

Demonstrating your skills quick fire activity

Problem solving in practice: Interactive worksheet

Our problem solving content focuses on one of these skills and develops understanding of the six stages of problem solving, as well as identifying different types of situations in which young people might already be using these skills. Furthermore, it encourages them to use an adaptive approach, explaining that different types of problems can be approached in different ways.

The activities on this page support your teaching of these skills through an independent activity, quick activities or a full length, curriculum-linked lesson plan. 

Teaching resources:

• Problem solving: Lesson plan and presentation slides – full lesson plan including icebreaker for use with a group of students in the classroom
• Demonstrating your skills: Quick-fire activity  – 10 minute activity for a group of students in the classroom, can be used as an icebreaker for the lesson plan
• Problem solving in practice: Interactive worksheet – activity for independent learning whether remote or in class

Lesson plan

(60 -75 minutes)

This lesson is designed to equip young people with an adaptable approach to solving problems, large or small. It includes a short film and scenarios that encourage development of practical problem solving skills which can be useful for learning, day to day life, and when in employment.

By the end of the lesson, students will be able to:

• Identify problems of different scales and what is needed to solve them
• Illustrate the use of an adaptable approach to solving problems
• Understand that problem solving is a core transferable skill and identify its usefulness in a work setting
• Work on a problem solving activity in a team

The lesson aims to reinforce students’ understanding of the potential future applications of this skill as they move into the world of work, particularly in an activity differentiated for an older or more able group on creating new opportunities.

Quick-fire activity

(5 - 10 minutes)

The demonstrating your skills quick-fire activity focuses on helping young people understand the key skills that are needed in the workplace, including the importance of problem solving.

Students will be asked to name the skills being demonstrated in a variety of scenarios, and identify ways they’re already using those skills in this short activity.

You might find it useful as a starter or icebreaker activity to begin a lesson, or at the end to allow students to put what they have just learnt in the Problem solving lesson into practice.

Interactive worksheet

(20 - 25 minutes)

Please note that students below the age of 14 cannot sign up for their own LifeSkills account. Any independent tasks must be printed or downloaded and provided digitally for them to complete as they are currently hosted on educator pages.

The Problem solving in practice interactive worksheet introduces some of the themes from the full lesson plan and gives students some practical strategies for problem solving, including introducing the six stages of problem solving. The worksheet can be printed or completed digitally, so can be used flexibly to give students practise putting their problem solving skills into action. You might choose to assign it:

• As homework following the Problem solving lesson
• For independent study
• For remote learning

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Other lessons that may prove useful for students to build on these activities include the  Adaptability  and  Innovation and idea generation  lessons. Alternatively, consider encouraging them to apply their skills through  Steps to starting a business  or the  Social action toolkit .

Why not build problem solving in as a focus in your students’ wider curriculum? Refer to our  Content guide to find out how this resources can be used as part of your teaching.

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Subtraction Lesson Plans for 3rd Graders

CONTENT TYPE

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• Number Sense (3)
• Place Value (3)
• Addition (4)
• Subtraction (4)
• Multiplication (14)
• Times Tables (6)
• Division (6)
• Fractions (7)
• Geometry (1)
• Word Problems (8)
• Reading (22)
• Reading Skills (22)
• Grammar (25)
• Adverbs and Adjectives (3)
• Nouns and Pronouns (5)
• Prepositions and Conjunctions (3)
• Punctuation (5)
• Sentences (3)
• Verbs and Tenses (7)
• Vocabulary (1)
• Making Connections in Reading (1)

Dive into Math: Mastering Sum & Difference up to 100 Lesson Plan

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Your one stop solution for all grade learning needs.

• STEAM Grade 3 – Lesson 3
• Grade 3 | K12 Curriculum

Lesson Overview

During this STEAM lesson for Grade 3, students will gain understanding of the concept of friction and the difference between helpful and unhelpful friction. Students will integrate and exhibit learning by creating a ‘car’ and testing it on different surfaces to investigate how friction affects movement.

Google Classrooms

What's included.

• Lesson Plan
• Step by Step