Paradox

1. Two of the statements in this box are wrong.

2. There are 604800 seconds in a week.

3. The sum of the first 10 square numbers is 385.

4. A square is also a rectangle.

5. Multiplying a value by a whole number makes it bigger.

6. The numbers from 1 to 20 add up to 210.

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Topics: Starter | Logic | Mixed | Multiple Intelligences | Puzzles

  • Wikipedia,
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  • A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition.
  • Natalie, London
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  • I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable.
  • Rhonda, Arizona
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  • The answer states that multiplying by a negative whole number makes the answer negative. However, whole numbers cannot be negative by the definition of what whole numbers are. So that answer is true.
  • Wiliam, Lincoln
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  • Number 5 is wrong since multiplying a value by 1 which is a whole number gives an answer the same value as before neither smaller or bigger.
  • Meilyr Wyn, Ysgol Syr Thomas Jones
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  • Excellent Starter - Thank you very much
    There has been some debate amongst the department about whether a square is a rectangle. A square is not a rectangle if the definition of a rectangle includes "top and bottom same length as each other, right and left same length as each other but different length to top".
  • The Best Maths Class Ever (7cd/m2), King Alfred's Oxfordshire
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  • It was a silly starter but it made us all think! Students: We thought that it was not very logical because the statement was true and false at the same time. We found that when it was false it became true.
  • Tony Graham, Stevenage, Hertfordshire
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  • Sorry, Rhonda, it is possible to have a negative integer.
  • Nick Ball, Enoree, South Carolina
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  • The definition we use in the USA for whole numbers are numbers 0 and greater. So you can't have a negative whole number. But the value you start with could be negative or a fraction...and one of our social studies teachers says that zero is a concept, not a number. So this was a dumb question.
  • Simon, Hampshire
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  • Whole number means an integer (from the Latin 'integer'), so whole numbers can be negative. Natural numbers can only be positive - as to whether zero is a natural numbers depends on your view as a mathematician.
    A rectangle is defined as a quadrilateral with two pairs of parallel sides at right angles, so a square is a rectangle. Equally, a rectangle and a square are both parallelograms.
  • Chas, New York
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  • The person who said that there is no such thing as a negative integer is dead wrong!
    The answer key's reasoning for statement 5 is wrong, because there is no such thing as a negative whole number.
    Statement 5 IS false though, because 0 is a whole number.
  • Grace Harrison, West Kirby Grammar
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  • I loved this starter it really made me think and involved some good classroom discussions.
    Thanks.
  • Kiwi, New Zealand
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  • Here whole numbers cannot be negative, so multiplying by a negative integer would not be allowed. You are allowed to multiply by one, though, giving an equal but not larger answer so the statement is incorrect.
  • RB, UK
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  • Multiplying by 1 would also be a counter example for question 5 - so even if you don't want to include 0 and negatives as 'whole numbers' the statement is still false. I hope no one will debate whether or not 1 is a 'whole number'!
  • Paula, Gillingham School
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  • Unfortunately, the answer sections gives a different statement for number 5 in that the word 'negative' is missing in the question. Will try it on the kids anyway and see if they spot the mistake. Thanks.
  • Hannah, South Yorkshire
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  • Enjoyable but Made my brain hurt! I loved this and would love to see more of these starters.
  • Dartmouth Academy 5/6P, Dartmouth
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  • We're confused. If 5 is wrong then 1 is wrong and if 5 is correct then one is correct which makes it wrong.......Or does it????
  • Matthew Zhao, Year 7, Brisbane Boys' College, Toowong, Brisbane
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  • It was an enjoyable paradox. Good trick!
    Keep it up, Transum!
  • MrMiss, Essex
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  • Not quite a paradox as multiplying by 1 doesn't make things bigger and the first square number is 0 so the first 10 add up to 285.
  • Par Radox,
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  • I always tell lies.
  • St Mark's, Year 5
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  • We would like a check button at the end please!

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