Chinese Word Problem: The Turtle, the Cat and the Table

 In Aspire Math Academy

Originally posted in English by China Focus on Twitter, this challenging math problem appeared on elementary school curriculum in China in 2018, and this image was adapted by Presh Talwalkar for 

The problem looks simple enough at first glance—however, without knowing the heights of each animal, most students aren’t sure where to begin. Because this problem relies on one’s ability to understand spatial realities and manipulate them mathematically, it has stumped both young learners and adults alike. Here are a couple ways to approach it: 

Method 1: Algebraically 

For those students who have begun working with algebra, we can begin by assigning abstract variables to each object and constructing equations for each diagram: 

Table + Cat − Turtle = 170 cm 

Table + Turtle − Cat = 130 cm 

If we then add both equations together, we’ll get something like this: 

Table + Table + Cat − Cat + Turtle − Turtle = 300 cm 

Because both cats and both turtles will cancel each other out, we can then simplify to obtain the following: 

Table + Table (+ Cat − Cat) (+ Turtle − Turtle) = 300 cm 

Table + Table + Cat − Cat + Turtle − Turtle = 300 cm 

Table + Table = 300 cm 

At this point, we can conclude that if two tables would be 300 cm high, then one table would be 150 cm high! 

Method 2: Visually 

This method may be more accessible for students who have not begun algebra, or for whom visual methods come more easily than computational ones. Presh Talwalkar has designed a helpful image for this method, in which we stack both images atop each other: 

In this method, we can easily see that the height from the top of the head of one cat to the next cat is 300 cm. From here, we can subtract the cat from the equation and slide the measurement downwards by the height of one cat, effectively removing all the animals from the equation (similar to how we achieved this algebraically): 

At this point, we can conclude that the height of two tables is 300 cm, and therefore one table would be 150 cm! 

Many students (rightfully) approach math and word problems by looking for numbers to manipulate, deducing which operation(s) should be used, and finally crunching the numbers to achieve the final solution. However, many of the most challenging math problems contain few numbers to manipulate, and rely upon logic and higher reasoning to fill in the missing pieces and solve successfully. By equipping students with multiple methods of approaching and solving problems, as well as moving away from specific numbers and looking at problems more abstractly and strategically, good tutors and teachers can ensure young learners are prepared for anything their textbooks (or the world at large) will toss their way! 

This article was written by one of Aspire Learning Academy’s very own instructor, Daniel Marcotte.

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