Engaging word problem activities are simple to put together, you have to look no further than a word problem type that is often overlooked. You likely won’t find it on a standardized test because the answers aren’t cut and dry. I consider this word problem to be *cousins *of numberless word problems— not the same but sharing many benefits.

In these word problems, both “parts” are unknown.

## Addition and Subtraction Word Problem Types

As early as kindergarten on up through second grade, students are focused on word problems involving addition and subtraction. These word problem types include problems that put together, take apart and compare with unknowns in all positions. As you can see in the Common Core State Standards glossary, however, put together and take apart problems where BOTH addends are unknown are a specific type of problem in and of itself!

These problems might sound like:

This problem type is open ended! Much like numberless word problems prevent “number pluckers” this word problem type does the same- your students are forced to focus on the action and what is happening in the problem in order to solve.

## Multiplication and Division Word Problem Types

Multiplication and division problem types in the CCLS do not specifically call out word problems where multiple parts of the problem are unknown, however, you can still engage in open ended word problems with your students.

An open ended multilplication/division problem might sound like:

These problem types make for engaging word problem activities because they aren’t quick and simple to solve. Your students may be able to find a single solution quickly but they will need to examine patterns in their work to find additional solutions and to determine if they have found *all* of the possible solutions.

## Creating and Differentiating Engaging Word Problem Activities

Creating these engaging word problem activities is simple.

**Think of a typical word problem that matches the content you are currently teaching.**For example, if you are a kindergarten teacher working on fluency with partners of ten, start with a word problem related to this content. Ex:*Shea has 2 cheddar cheese squares and 8 mozzerella squares in his lunch box. How many cheese cubes does Shea have in all?*- T
**urn the problem around**so you are presenting your students with the TOTAL rather than the parts. Ex:*Shea has 10 cheese cubes in his lunch box. Some of the cheese cubes are cheddar and the rest are mozzerella. What might be the number of mozzerella and cheese cubes in Shea’s lunch?* **Scaffold**the activity by asking your students to find one combination, multiple combinations or all of the combinations that might satisfy the problem.**Scaffold further**by choosing the materials or models that each student (or set of partners!) will use to solve. Consider tools like linking cubes, base ten blocks, place value disks, counting bears, etc.

As your students are working you can engage in discussions about your students’ work. Ask questions such as:

- What was the first answer you found? How did did you find it?
- Describe to me how you are going about this problem.
- Do you think you have found all of the solutions? How do you know?
- Could you prove your thinking using another math tool?
- Is there an equation that matches your work?
- How could you organize the different solutions you are finding on your paper?

Lastly, consider the format you are asking your students to work in as they explore an open-ended word problem. Your students might work independently but this activity is best suited for a partner or small group. Part of creating engaging word problem activities is ensuring that your students have the opportunity to talk and use math language as they are working! By working with a partner they will need to justify and explain their thinking as they work together which will create deeper understanding as well.

## Getting a Quick Start with Open-Ended Word Problems

A very quick way to create open-ended word problems is to begin with a numberless word problem but, rather than working through the entire sequence, show your students the initial problem with NO numbers and present them with the solution so that they will need to work backwards towards multiple solutions.

Given this numberless word problem starting slide, you could ask your students simply “*If the garden has 18 flowers, what might be the number of purple and green flowers?*”

Given this equal groups scenario you might ask “*If there are 30 fish in the pond, how many different types of fish might there be?” *

These open-ended tasks end up being motivating and engaging word problem activities that your students will enjoy and that will stretch their thinking and skills as mathematicians!