This diagram shows four small squares and one rectangle composed of 10 small. (A) Andre says that the diagram can represent 140. Do you agree with Andre? Explain why or not

(B) Diego says that this diagram can represent 410. Do you agree with Diego? Explain why or why not.

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  (A) yes; each small square could represent 10 units

  (B) no; there are a total of 14 small squares. No reasonable relationship maps this to 410

Step-by-step explanation:

(A) The total number of small squares is 14, so we expect any number represented by the diagram to be a multiple of 14. If each small square represents 10 units, then the 4 small squares represent 40 units, and the rectangle represents 100 units, for a total of 140 units being represented in the diagram. Andre is correct.

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(B) The above argument suggests that 410 will not be reasonably represented by the diagram. To represent 410, we expect 4 tokens that each represent 10 of a smaller token. The rectangle of 10 squares would be such a token, but the diagram has only one of those, not 4 of them. Similarly, we expect 1 of a smaller token, but the diagram has 4 of them. In any event, 410 is not a multiple of 14, so there is no (integer) value that can be assigned to a small square that lets the diagram represent 410.

I do not agree with Diego.