Consecutive Integer Word Problems Worksheet

How to Actually Set Up Consecutive Integer Word Problems for Your Class

The core concept behind a Consecutive Integer Word Problems Worksheet is that students need to translate verbal descriptions into algebraic equations involving integers that follow one another. It sounds simple enough when you first explain it, but the translation step is where most of them stumble. I've been assigning these for years, and the pattern is always the same. They can set up the algebra fine if you tell them what x represents, but the moment they have to figure out how "the sum of three consecutive integers is 54" becomes an equation, they freeze. Here's how I structure the worksheet so it actually teaches the skill instead of just grading it.

Setting Up a Consecutive Integer Word Problems Worksheet

Start with a definition section, but keep it brief. Consecutive integers are whole numbers that follow each other in order with a difference of 1 between each pair. So 4, 5, 6 and 7, 8, 9 both qualify. Consecutive even integers skip by 2: 2, 4, 6, 8. Consecutive odd integers also skip by 2: 1, 3, 5, 7. That's all there is to it. The method students need to learn is straightforward. You define the first integer as x. The next consecutive integer is x + 1. The one after that is x + 2. For consecutive even integers, you still use x for the first one, but the next becomes x + 2 instead of x + 1. Consecutive odd integers work the same way. The variable assignment is what trips people up, not the math itself. When I started giving these worksheets, I noticed something that surprised me. Students who could solve the equations perfectly were completely lost on the word problems. They'd read "the larger integer is 5 less than three times the smaller" and have no idea how to start. The issue isn't algebra. It's that they've never had to practice extracting variables from English sentences before hitting this topic. I rewrote my worksheets to include a translation-only section first, where the problem gives you nothing but the sentence-to-equation mapping and no calculation required. It took ten minutes of class time but cut their error rate on actual problems by about half over the next few weeks.

One thing beginners consistently miss is that x doesn't have to represent the first integer. Sometimes it's more efficient to let x be the middle integer. Take a problem like "the sum of three consecutive integers is 75." If you set the middle one as x, the equation becomes x - 1 + x + x + 1 = 75, which simplifies to 3x = 75 immediately. The negatives and positives cancel out. Setting it as x, x+1, x+2 gives you 3x + 3 = 75, which is fine but requires one extra step. I include at least two problems where the middle-integer approach is noticeably faster, and students who figure it out on their own tend to remember the technique. Another counter-intuitive point: consecutive even and odd integers use the same step size, which causes confusion. Students will sometimes write x + 1 for the second even integer because they're treating "consecutive even" like it just means "numbers that follow each other." I put a side-by-side comparison problem on the worksheet where the same verbal structure is used once with regular consecutive integers and once with consecutive even integers. The different step sizes become obvious when they see both side by side. I should mention a real problem I ran into last semester. I assigned a worksheet problem that said something like "find two consecutive integers whose squares differ by 23." A student solved it correctly and got 5 and 6, but then asked me if negative integers counted. The question didn't specify positive integers. The actual second solution pair is -6 and -5, since (-5)^2 - (-6)^2 also equals 23. I had never explicitly thought about whether my worksheets should constrain the domain. From that point on, every problem on my sheets either specifies "positive integers" or is followed by a note asking students to check whether negative solutions exist. It adds about thirty seconds of work for students but it's the kind of edge case they'll encounter on standardized tests.

Here are a few problems that work well, ordered from easiest to hardest. Find three consecutive integers whose sum is 93. The sum of five consecutive even integers is 130. Find the integers.

The larger of two consecutive integers is 7 less than twice the smaller. Find both integers. Find three consecutive odd integers such that three times the first integer plus twice the second integer equals 47. The product of two consecutive integers is 156. Find both pairs of integers.

For the fifth problem, I explicitly tell students to consider that the answer could involve negative integers. Most of them only find 12 and 13 and stop there. They miss -13 and -12 because they've been trained to assume the answer should be positive. The biggest limitation of this worksheet type is that it doesn't scale well for students who struggle with reading comprehension. The math is usually fine for kids who can parse the sentence structure, but the language barrier is real. If you have students who read at a significant level below grade level, the word problem format becomes a test of reading ability rather than algebra. In those cases, I switch to structured templates where the problem is broken into labeled parts: "First integer = ___", "Second integer = ___", "Equation = ___". It removes the translation step and lets them practice the algebra directly. Another practical issue is that these worksheets tend to produce the same type of problem repeated ten times with different numbers. Students who get the method early on finish in five minutes and then zone out. I've started mixing in a few problems where the answer doesn't come out clean, like "find three consecutive integers whose sum is 100." The answer is not an integer, which forces them to check their work and understand that not all word problems have whole number solutions. It's a small but useful reality check.

If you're building your own Consecutive Integer Word Problems Worksheet, I'd recommend thirty problems total, split into four sections. Ten basic sum problems with regular consecutive integers. Ten with consecutive even and odd integers mixed together. Five translation-only problems where students write the equation but don't solve. Five multi-step problems that require setting up and solving simultaneously. The whole process of creating and grading these worksheets takes me about twenty minutes per set if I'm just shuffling numbers. If I'm writing new problems from scratch, maybe forty-five minutes. Most of that time goes into checking that the numbers actually work out cleanly for the basic sections.