If you seem to be having trouble with part 3 of the word problems, here are a few common mistakes of which to be wary.
- Just writing a number: This is being a bit of a stickler, but I definitely take points off for it. Sometimes a student has a great solution going and just needs to be more careful about the presentation of the answer. Take for example the word problem.
- Anna, Lea, and Simon have ages that add up to be 78. If they were all born in consecutive years, how old is each one?
- A student might answer
- Part 1-- x: the youngest child
- Part 2-- x + (x+1) + (x+2) = 78
- Part 3-- 25
- Part 4-- Anna, Lea, and Simon are 25, 26, 27
- This student really knows what they are doing, but got sloppy in part 3. What I'm looking for in part 3 is "x = 25"
- Don't forget to carry down your inequality, also don't forget to check it's direction: Here is a student example of a good looking word problem with a careless mistake.
The problem is that the inequality in part 2 became an equality in part 3. Part 3 should read
- Write all solutions to the equation: This tends to be an issue in Intermediate Algebra after chapter 5.9. Starting in Chapter 5, equations will often have two solutions. Sometimes both solutions will lead to answers in part 4, but often only the positive one will have an interpretation. Regardless, part 3 of the word problem is only asking for the solutions to the equation. It doesn't care wether those solutions can be interpreted or not. That's the difference between the information provided in parts 3 and 4. Part 3 is asking for the solution to the equation. Part 4 is asking for the answer to the word problem. Here is a good example. This student wrote a little more than they had to in parts 1 and 2, but this is a great answer....except for part 3. His/her equation from part 2 is 180=5w(w). He/she needs to provide all w's that solve the equation. The correct answer for part 3 would be w=6,-6. He/she doesn't even need to say L=30.
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