I'm reading a certain set of kindergarten/lower primary maths textbooks that is written by North American authors for a European company.

Whenever students are asked to identify the number of rectangles in a given picture, the answer booklet gives the number of oblongs instead of the number of rectangles.

While the topic may be too advanced for kindergarten students, the maths textbooks indeed explicitly say at the bottom of the first page of a textbook at the very first level to tell students that squares are special types of rectangles, where levels 1-4 are for kindergarten students.

Additionally, the accompany guide for teachers devotes a whole page of discussion as to how to teach that squares are special types of rectangles. There's even a paragraph about teaching to kindergarten students. The authors/some of the co-authors of the teacher guides are also authors/co-authors of the textbooks. They have also said that if students are taught that squares are not rectangles, then they will have misconceptions later.

Perhaps, the ones who wrote the answer booklets were not fluent in English while the ones who wrote the textbooks were.

For example

[picture with 4 circles, 2 triangles, 3 square rectangles, 2 oblong rectangles for a total of 5 rectangles]

Circle ___

Triangle ___

Square ___

Rectangle ___

The answer key would give only the numbers:





So, the last line is wrong since it should be 5.

Could this happen in Portugese? Or a Portugese dialect? I mean, is there something specific about the translations of any of the following words 'rectangle, square, oblong, quadrilateral, quadrangle, parallelogram, trapezoid/trapezium, rhombus' that would cause such confusion? I guess the translator/s thought that when English speakers say 'rectangle', it means 'oblong in their language/dialect, but I don't see that as specifically a problem for this particular language.

By the way, are squares considered rectangles in Portugal? Apparently, these things can vary by state, curricula, culture, time, etc. Please provide a document from the education department of your government or something.

P.S. I'm a monolinguist.


Are kindergartners supposed to be steered from squares being rectangles?

In what curricula are “rectangles” defined so as to exclude squares?

Why do we have circles for ellipses, squares for rectangles but nothing for triangles?

What are/should kids (be) taught about the colour of the sun?

  • 1
    You're only interested in pt-PT, i.e., European Portuguese?
    – stafusa
    Mar 23, 2018 at 12:22
  • @stafusa As many Portuguese dialects as possible please.
    – BCLC
    Mar 23, 2018 at 12:25
  • 1
    Your question is very confusing. What, for instance, is an "oblong"? A rectangle is oblong in shape. Oblong is an adjective. Also, do you mean that a square is a special case of rectangle?? Also, why are you talking about translation INTO Portuguese, when you are clearly not a native speaker of English? I'm afraid I just do not get it. Geometry is universal. How could it be "different" in Portuguese? And if you are monolingual, why is your English non-native?? It sounds to me like you are expressing ideas in English from another language. Therefore, you are hardly monolingual, right?
    – Lambie
    Mar 23, 2018 at 17:31
  • 1
    @Lambie As I perfectly understood the question, and as both it and stafusa's answer are perfectly intercoherent, I can convincedly affirm that there is no problem in the question. Thereby and that it should be noted, your commentary itself starts confusing and then transforms into pure ad hominem.
    – user2786
    Mar 25, 2018 at 12:06
  • @Lambie geometry is universal yet my employers insist that where I am, squares are not rectangles. :( Also, how is my English non-native please? Perhaps I did not speak so volubly due to fear of unemployment.
    – BCLC
    Mar 25, 2018 at 14:42

1 Answer 1


From the mathematical point of view, there's no doubt: squares (quadrados) are a special case of rectangles (retângulos), and any teaching material saying otherwise is in error. That's not dependent on the dialect.

That said, in informal or any other less precise speech (which should not be used when teaching or discussing mathematics), one may mean "typical rectangle" when saying "rectangle", excluding therefore special cases such as the square, as well as degenerate cases, such as a segment of a line (i.e., a rectangle with a side of length zero).

A similar situation arises when discussing ellipses and circles, as the latter is a particular case of the former; and humans and animals, where the latter might implicitly not include the former, even though biologically it does.

Português / Portuguese translation

Do ponto de vista da matemática, não há dúvida: quadrados são um caso especial de retângulos, e qualquer material didático afirmando o oposto está equivocado. Isto não é dependente do dialeto.

Dito isto, em discurso informal/pouco preciso (que não deveria ser usado para o ensino ou discussão de matemática), "retângulo" pode implicitamente significar "retângulo típico", excluindo portanto casos especiais como o quadrado, e também degenerados, como o segmento de reta (i.e., um retângulo com um lado de comprimento nulo).

Uma situação similar surge na discussão de elipses e círculos, dado que o último é um caso particular do primeiro; e de humanos e animais, em que o último pode implicitamente não incluir o primeiro, embora biologicamente ele inclua.

  • But stafusa what specifically about the portugese language is or isn't relevant here? Is this a geometric issue rather than a portugese language issue? why/why not?
    – BCLC
    Mar 23, 2018 at 15:08
  • 1
    @BCLC Exactly, that's what I meant with "From the mathematical point of view, there's no doubt". Portuguese doesn't play any role here, at least in the sense of existing any relevant difference to English. What you have is sloppy people not being careful enough when talking about things that have precise definitions.
    – stafusa
    Mar 23, 2018 at 16:23

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