I have a word problem: The price of a pen was $5, The price of a pencil was $2. Miss Lee bought a number of pens and pencils for $26. How many pens and pencils did she buy?

The day before yesterday I taught my pupils this: I made a list for the pens : 1 x $5 = $5 , 2 x $5 = $10 and so on. And also a list for the pencils : 1 x $2 = $2 and so on. Miss Lee bought 4 pens and 3 pencils because (4 x $5) + (3 x $2) = $26. However, I realize that this method cannot be used in big numbers.

Merry

*The method you used is called make a list. It is a common problem-solving heuristic. Please continue to use it with your younger students. I wonder if Miss Lee could also buy 2 pens and some pencils. I know 5 pens is not possible because the money left is an odd number $1 and the price of a pencil is $2. Similarly, 1 pen or 3 pens are not possible. Students learn reasoning.*

*If students know algebra, they can set up equation 5x + 2y =26 where x is the number of pens and y is the number of pencils. As there is only one condition, you still need to use guess-and-check to solve this equation. Unless the problem says something about x + y.*

*If the value is not 26 but larger then the equation is 5x + 2y = k where k is the large number. A graph can be plotted and possible solutions seen on the graph. (With larger k the number of solutions increases).*

*For the young students, the method you use is probably the best. When they are older, they will learn to solve the same problem with larger k values.*

In my opinion, it is much easier for kids to visualise the mathematical patterns and relationships when the numbers are in the table form such as the guess-and-check method, which I use when coaching kids esp. when they deal with large numbers, when they are in the pre-algebra stage. (:

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