One of my students is having difficulty turning abstract problems (using sentences instead of concrete numbers) into a mathematical equation. I have not yet found any information that assists me to teach this skill effectively.
The main challenge in questions like this is translating words into maths. Often the resulting equation is very simple but getting to it is the main problem for most students. Typically students are overwhelmed by the words and don’t know how to get started. Ultimately, the process of translation is just a problem solving process and the Self Questioning process should be used but tutoring a student to do this is challenging. Here are some tips.
The translation needs to be done in steps. A student can’t translate words into an equation if they don’t know what the question is about or what the question wants from them, what area of math it could relate to? First the student should read the question completely, not start trying to solve it after they have read half a sentence. Then, guess what? Get them to read it again and get a feel for the whole question! Understanding the problem is always the first step in any problem solving endeavour. You can even ask the student to explain what they think the question is about.
Next they should define the variables of a problem in a structured and organised manner. They should figure out what they need but don’t have and then label it, give it a name like and write down what it stands for. Pick a variable to stand for each of the unknowns. While doing this the student should be mindful of the purpose of the question. It is also important to stress correct format skills in this process. It may sound silly to your student but neatness and leaving lots of working space will go a long way in allowing clarity in their thinking process. This allows thinking without being constantly interrupted by having to decipher your own scribbles and messy writing.
“A problem well stated is a problem half-solved”, Charles F. Kettering
It is also useful to write down any known values next to the unknown and to label them also. Basically, what you’re doing is breaking the question up into components of information and rewriting that information in a list or other form conducive to mathematics rather than whole sentences.
Get the student to look for keywords regarding the basic operations:
- Increased by, added to, more than, combined, together, total of
- Decrease, less than, minus, difference between, fewer than
- Times, multiplied by, of, increased/decreased by a factor of, product
- Per, out of, percent, quotient of, ratio
- Is, were, was, are, yield, gives, sold for, will be
Next is to construct the equation, keeping the objective in mind the whole time. Based on the data items and key words used to connect them in the question, the student should be able to put together a basic equation.
Does practice with easier questions first so they can get used to the process, then try harder ones. Examples like this are quite easy to come up with. Practice this kind of maths language translation with your student:
- The sum of 4 and BECOMES 4+X
- The difference of 9 and BECOMES 9-X
- 7 less than some number and 6 BECOMES (X+6)-7
- The length of a basketball court is 10metres more than its width BECOMES L= 10+W
- 15 litres of water are poured into 2 containers – one big and one little, express how much water is in the little container BECOMES L=15-B
This kind of practice should help!