My thoughts on the Dishes Puzzle
To solve this problem without algebra, I need to phrase this question. An unknown number of guests are handed a number of rice dish, a number of broth dish, a number of meat dish. The total number of dishes handed from rice, broth and meat are 65, and each dish is shared with 2, 3, 4 guests respectively.
In this question, I can begin by trial and error.
Starting with product of 2, 3 and 4 which is 24 guests, we would have 24/2 + 24/3 + 24/4 = 12 + 8 + 6 = 26 dishes. This is too low.
Next I double the number of guests to 48, we would have 48/2 + 48/3 + 48/4 = 24 + 16 + 12 = 52 dishes. It is a little low. But I notice it increase with a linear trend with every 24 guests yielding 26 dishes which can be interpreted that every 1 additional guest contributes to 13/12 additional dishes.
So I compute how many more guests from 48 (which yields 52 dishes) do I need to achieve 65 dishes. Note that, since you can't have fractions with number of guests, we would use a floor value.
48 + (65 - 52)/(13/12) = 48 + 12 = 60 guests exactly
Having a word problem does make algebraic math more interesting. In fact, I would argue most mathematics are more interesting and meaningful when associated with graphical representations. Introducing imagery or other media formats allows students to map the learning of concepts to a tangible form. It has been suggested that seeing Math in the visual lens can provide a richer and deeper understanding too.
With that being said, ELL learners can benefit greatly from understanding context of Math problems in their own culture. It is meaningful to introduce the concepts in a relatable manner and it helps students to be more engaged.
Personally, I enjoy solving word problems, especially ones with pizzazz. This alleviates some of the common headaches I received from working through difficult problems. Having a small mental break to imagine myself in a cultural scenario is nice.
Nice work and reflection, Raymond! Good point about how graphical representations could potentially increase engagement with a math problem. In addition to the 3-act math resource that was introduced in class before, you might find this site interesting: https://www.visualpatterns.org/
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