![]() But that's good for a student! Thinking hard is good. So the answer is 112 cm^2.ĭoes that make sense? Do you think that's more like what he's been learning? This is actually a little harder than the algebra in a sense, because you have to do more special thinking and less routine. What is 28, 1/4 of? The whole must be 4 times 28, which is 112. ![]() But the difference of 5/8 and 3/8 is 2/8, or 1/4 of the whole. The difference between A and B is supposed to be 28. If the larger one is 5/8 of the whole, then the smaller one must be 3/8, right? Here's how I'd do this with a younger student:ĭraw a rectangle, and divide it into two unequal parts. This can be done easily enough without algebra, if he's not doing much of that yet. That way, we could try to stick to methods he's used to. It would be very helpful to see what sort of problems your son has been doing, and what methods were used. We could also help you create a model for this exercise, by cutting paper sheets into pairs of labeled pieces. If your son has specific questions, let us know. The basic strategy was to start with the relationship R=A+B, followed by using given information to substitute expressions for symbols A and B, to obtain an equation that contains only the symbol whose value we're trying to find (R). It's good form to answer word problems with a sentence, including units. We substitute that expression for symbol B: We have another expression for the area of piece B (the exercise provided it, and it's written above in red). We've discovered that the rectangle's area is twice the area of piece B plus 28 more. It doesn't matter in what order we add numbers, so we can rewrite the new expression for R: Let's make that replacement in our equation for the total area: Therefore, we're now free to replace symbol A with the expression B+28 anywhere we choose. Symbol A and the expression B+28 both represent the same number (they're equal). As Jomo explained, that means we can write: We're also told that A is 28 more than B. With these three symbol definitions, I expect your son understands why we can write: We can remove "clutter" from some equations, by leaving out defining words and units. If your son is currently studying pre-algebra topics, then this is a good opportunity to become familiar with using letters as symbols that represent numbers and using substitution methods to rewrite relationships (equations). I'm glad you're there to offer encouragement because symbolic reasoning skills are very important. Beginning students need exposure and practice, to understand symbolic math.
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