Separate Word Problems: Start, Change, and Result Unknown

Solving word problems is difficult for students, but teaching them how to read the word problem and understand the context or situation of the word problem sets a good foundation for future work with complex word problems.  

The Separate Word Problem Type is similar to the Join Word Problem type in structure, but asks students to subtract or separate two things rather than add or join them together. This post will focus on the types of separate word problems, including separate change unknown, separate result unknown, and separate start unknown.

Below is a video that I recorded on Separate Word Problems by Problem Type.  The text below highlights some points from the video, but the video goes deeper with explanations and examples.

One thing I emphasized in this video, more than in the Join Word Problems video, is the use of number lines.  I looked more in-depth at how the number line changes with each unknown in the problem.

Three Types of Math Separate Word Problems

There are three types of separate word problems, including Separate Change Unknown (SCU), Separate Result Unknown (SRU), and Separate Start Unknown (SSU).

The video below and this blog post go in depth on using keywords to solve these types of problems.

Here are three examples of separate word problems.  As you read across these examples, think about the context or the verb in the problem and ask yourself: what is happening in the problem, and what is unknown?

SRU — Separate Result Unknown

In a result unknown problem, students know how many there were at the start and how many left, but they need to find what is left at the end. This is the most intuitive type because the unknown comes at the end of the action.

Example: There were 14 kids on the playground. 6 kids went home. How many kids are left on the playground? (14 – 6 = ?)

On the number line, students start at 14, move left by 6, and find the result. The unknown is at the end of the number line.

SCU — Separate Change Unknown

In a change unknown problem, students know the starting amount and the ending amount, but they need to figure out how many left or were taken away. The unknown is the action in the middle.

Example: There were 14 kids on the playground. Some kids went home. Now there are 8 kids left. How many kids went home? (14 – ? = 8)

On the number line, students see both endpoints (14 and 8) and need to figure out the distance between them. The unknown is the jump, not the landing point.

SSU — Separate Start Unknown

In a start unknown problem, students know how many left and how many are at the end, but they have to work backward to figure out where the situation began. This is the most challenging type for young students because the unknown is at the beginning of the story.

Example: There were some kids on the playground. 6 kids went home. Now there are 8 kids left. How many kids were on the playground at the beginning? (? – 6 = 8)

On the number line, the starting point is open and unknown. Students work from the end (8) and add back the change (6) to find the start. This is where the number line becomes especially useful because students can see that subtraction and addition are inverse operations.

One of the most useful things about teaching by problem type is watching how the number line shifts. In a result unknown problem, the missing piece is at the end. In a change unknown problem, the missing piece is the jump itself. In a start unknown problem, the missing piece is the beginning. Once students see this pattern, they start to think about what is missing in a problem rather than defaulting to keywords or guessing the operation.

How to Teach The Separate Word Problem Type

I go in-depth about teaching word problems in the Join Word Problems Video Post.  I follow a specific routine when I teach Join and Separate word problems to students, which includes using consistent vocabulary, solving for an unknown, labeling the word problem, writing an equation, and giving students the numbers.  You can read more about each component of the routine in the Join Word Problems Video Post.

You can find out more about why I don’t give students the numbers until the very end in this blog post.

Video for Separate Word Problems

This video highlights each of the problem types for Separate Word Problems above and also focuses on how to use a number line when solving two-digit equations.  You can find additional models and strategies that I use with students in this blog post, although a number line is by far my favorite.

Free Word Problems by Problem Type, Including Separate Word Problems

Do you want a free sample of the word problems I use in my classroom?