Working With the Even More Fun With Equations Worksheet Set
I spent a lot of time going through these sheets with students last year, and there are a few things that aren't obvious from just looking at the answer key. The worksheet covers one-step and two-step equations, plus some introduction to multi-step problems with variables on both sides. It is not particularly difficult material, but students mess it up in predictable ways. The answer key is typically found in the back of the teacher's edition if you are using a published curriculum like McGraw-Hill or Pearson. Some districts host the PDF on their shared drives. You can also find legitimate copies on sites like Lesson Planet or Teachers Pay Teachers. Avoid the sketchy download sites that bundle malware — I learned that the hard way when my computer started flashing suspicious pop-ups after a late-night search. When you do get the answers, here is what you need to know about how to actually use them.
The first section is straightforward. For example, a problem like 3x + 7 = 22 gives x = 5. Students who just memorize "subtract then divide" will get it right here. The problems that trip people up start around problem 14 or so, where the coefficient is a fraction and the constant is negative. Something like (2/3)x - 4 = -10. The answer is x = -9, but a lot of students will divide by 2/3 incorrectly and get x = -27 or something equally wrong because they multiply by 3/2 without flipping the sign correctly. I ran into this exact issue with a student who kept getting the same fraction problems wrong across three different worksheet sets. The workaround was to make him write out the reciprocal step separately before computing. He had to literally write "flip to 3/2 and multiply" on his paper before doing any arithmetic. It took longer but eliminated the error pattern entirely. That is the kind of thing the answer key alone won't tell you. The second half of the worksheet introduces equations with variables on both sides. A problem like 5x + 3 = 2x - 9 has x = -4. The pitfall here is students moving the variable term to the wrong side and ending up with a negative coefficient they do not know how to handle. The key insight is that it does not matter which side you move the smaller coefficient to. Moving 2x to the left gives 3x + 3 = -9, which is cleaner. Moving 5x to the right gives 3 = -3x - 9, which works fine too but looks uglier. Both are valid. I have seen teachers insist on one method over the other, but either approach is mathematically sound. Just pick one and be consistent.
One counter-intuitive thing about this worksheet: the later problems look harder but are often simpler in structure. Problems 25 through 30 have larger numbers but follow the exact same two-step pattern as the first section. Students panic at the big coefficients and second-guess themselves. They do not need to. The process is identical regardless of whether the numbers are small or large. If you are grading these sheets, mark any answer that is numerically correct but uses an unconventional method as right. I used to lose points for students who solved things differently than I taught, and that caused more frustration than it was worth. The answer is the answer. How they got there matters less at this level. Some things this worksheet does not cover that you might expect it to. It does not go into absolute value equations. It does not cover equations that result in infinitely many solutions or no solution. If your students need that, you will have to supplement with another resource. I found the Glencoe Math Textbook supplementary worksheets to be a decent follow-up for that material.
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There is also a section where the answers involve decimals rather than clean integers. Students who are uncomfortable with decimal arithmetic will stall out even though the algebra itself is correct. Double check those calculations if a student gets stuck — the issue is often arithmetic, not understanding of the equation concept.
Common Mistakes to Watch For
The most frequent error I see is sign errors when distributing a negative. A problem like -(3x - 5) = 10. Students often write -3x - 5 instead of -3x + 5. This is by far the most common single mistake on this worksheet. It shows up in roughly a third of the submissions. Mark it clearly and make the student redo those problems. It is a habit issue, not an intelligence issue, and it gets fixed with repetition. Another thing is leaving the variable on the wrong side at the end. Some students solve correctly and arrive at -4 = x but then circle x = 4 because they think the answer should look positive. Make sure they understand that x = -4 and -4 = x are the same statement. If you are a student looking at the answers to check your work, do not just compare the final number. Look at each step. The answer key gives you x = 7, but if you got x = 7 through a flawed process, you still do not actually know how to solve the problem. That is a real risk when people use answer keys without doing the work first.
The worksheet itself is fine for practice. It is not innovative. It is not especially engaging. But it covers the material adequately and the answer key is accurate. I have used it for years and it does its job. Just be aware of where students tend to stumble and plan around those spots instead of assuming the worksheet will teach everything on its own.
