Understanding Word Problem Types in Elementary Math

Word problems can be challenging for young learners. Did you know that by the end of 2nd grade, those students are exposed to 11 different word problem types? In this blog post, we’ll explore the various types of word problems students encounter with addition and subtraction, why these problem types matter, and how we can support our students in mastering them.

Teaching problem-solving can be tricky. One reason is that it involves guiding students through a combination of critical skills. Unfortunately, solving word problems isn’t as simple as solving an addition problem. Word problems require reading, drawing from prior knowledge, and using higher-order thinking. Helping students develop these skills takes time. 

If you are more of a visual learner like myself, you can watch the YouTube video for Understanding Word Problem Types. If you would rather read, keep on scrolling!

What Are Word Problem Types?

Word problem types refer to the different structures or formats in which mathematical scenarios are presented to students. According to the research of Thomas Carpenter and his colleagues in Cognitively Guided Instruction (1999), elementary students encounter four main types of word problems when learning addition and subtraction: join, separate, part-part-whole, and compare problems.

Research shows that students perform better when explicitly taught to recognize and solve different types of word problems rather than relying on keywords or rote memorization. Understanding the structure of word problems helps students develop more sophisticated problem-solving strategies than simply looking for keywords.

Why are Word Problem Types Important?

Teaching students about problem-solving types or structures helps them develop strong problem-solving skills. Instead of relying on tricks like looking for keywords (e.g., “in all” means addition, “takeaway” means subtraction), students learn to analyze the situation and apply logical reasoning.

I shared in different posts why I stopped explicitly teaching key words in word problems. 

Recognizing different types of word problems can help bridge learning gaps. When you can understand the difference in each problem-solving type, you can help determine what your students need to do to solve the problem. 

Word Problem Vocabulary 

Often, when referring to problem-solving types, it can be easy to get lost in the academic language used. Our students can feel this way, too. Let me explain some of the academic vocabulary you will see throughout this post: 

• Set – A set is the numbers given within a problem.
• Strategy – A strategy is how you mess with the numbers and use relationships and connections between numbers to solve a problem. There are a handful of essential strategies for each operation. 
• Model – A model is what they do to solve the problem directly. They do exactly what the problem says to do. Typically, they’ll use physical objects to move and solve the problem or draw it out on paper.

Types of Word Problems

There are four basic types of word problems for addition and subtraction. 

• Join
• Separate
• Part part whole
• Compare

Each type contains subcategories that help students understand the problem’s unknown value.

The numbers, theme, and context within the problem can vary, but the basic structure and action of the problem remain the same.

Join Problems

Join problems are often the first type of word problems kids are exposed to. In join problems, something is added to a given set. 

Join problems involve a direct or implied action in which the set or number increases. 

These problems have three variations: 

• Result unknown – the sum of the problem is not known.
• Change unknown – the second addend within the problem is missing.
• Start Unknown – the starting or first addend within the problem is missing. 

Each type of join problem has a different action; therefore, the strategy to solve them is different. 

Separate Problems

In separate problems, something is removed from a given set. These problems are similar to join problems, but the action involves a set decreasing rather than increasing.

These problems have three variations: 

• Result unknown – the difference in the problem is not known.
• Change unknown – we do not know what set or number is changed within the problem.
• Start Unknown – we do not know what the starting set or number within the problem is.

Each separate problem has a different action; therefore, the strategy to solve them is different. 

Part Part Whole Problems

These problems differ from join and separate problems because no action is involved. Instead, they describe a relationship between parts and wholes. 

These problems have two variations: 

• Whole unknown
• Part unknown

Part-part-whole problems are different because they do not involve a change over time. There is no direct or implied action. Since one number is not joined to the other, both sets have the same role within a problem. These problems either give two parts and ask the solver to find the whole, or they provide only one part and the whole and ask the solver to find the other part. 

Take a look at the image below. You’ll notice nothing is being added about these types of problems. 

In the unknown example, the blue and red crayons have the same thing within the problem. Nothing is being added to them. There weren’t 3 blue crayons, and 5 more got added to them. There is no direct or implied action related to this problem. 

For part unknown, there is no implied action. One of the parts is missing. 

Compare Problems

Compare problems involve comparing two sets to find their difference or one set when the difference and the other set are known.

Compare problems, like part-part-whole, involve relationships between quantities rather than joining or separating an action. These types of problems include comparing two disjoint sets. 

These problems have three variations and subcategories within each type: 

• Unknown difference – how many more or how many fewer
• Bigger unknown – with more or fewer
• Smaller unknown – with more or fewer

Bigger unknown and smaller unknown problems are challenging because they can be asking for more or fewer in various ways within the problem.

How Can We Support Our Students With These Types of Word Problems?

Understanding word problem structures is just the first step. Here are some strategies to help students become confident problem solvers:

1. Introduce Problem Types Gradually

Start with the easier types (join and separate with result unknown) before moving to more challenging ones (comparing). 

2. Use Visual Representations

To start, follow a CPA (concrete, pictorial, abstract) approach. Use a variety of manipulatives, such as ten frames or unfix cubes, to solve. Then, move on to bar models, number lines, and whole mats. 

3. Focus on Understanding and Not Key Words

Rather than teaching students to look for specific words, help them understand the situation described. Ask questions like:

• “Is something being joined together or separated?”
• “Are we comparing two numbers?”
• “Do we know the beginning, change, or end amount?”

4. Encourage Multiple Solution Strategies 

 What works best for one student might not work for the other. Acknowledge that problems can be solved in different ways. 

5. Practice with Real World Contexts

Make word problems relatable by using real-life examples from students’ everyday experiences. If you live in a rural area, students will not relate to a word problem about parking garages or skyscrapers. The same goes for urban areas. Students who live in a big city will not relate to a word problem about cows in a pasture. 

6. Scaffold Instruction 

Use a gradual release approach to teach word problem types:

• Model problem-solving by thinking aloud
• Solve problems collaboratively as a class
• Have students work in pairs or small groups
• Eventually,  move to independent practice

Resources for Word Problem Types

Looking for resources to help students master word problem types? I’ve got you covered with everything you need to successfully teach word problem structures.

I used a daily word problem that is glued into their journal each day for continuous practice. These include pre-made word problems and numberless word problems that allow you to differentiate your numbers.

All of my guided math units include word problems to go along with each day.

I have resources aligned explicitly to each word problem types. Each unit includes anchor charts, interactive notebooks, numberless word problems, task cards, crafts, and more!

By explicitly teaching word problem structures and providing students with the tools they need, we can help them build strong problem-solving skills that will serve them throughout their math journey!

You could get instant access to this and ALL my other math resources inside the Inner Circle Math Membership! It’s your one-stop shop for all things math including guided math units, math centers, exit tickets, math crafts, seasonal surprises and more!

Save these ideas for teaching word problem types for later by pinning any image from this post to your favorite math Pinterest board.