Paradox

A Maths Starter of The Day

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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Keywords: Starter | Multiple Intelligences

  • Wikipedia,
  • Wednesday, April 25, 2007
  • "A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition."
  • *Natalie, London
  • Thursday, May 24, 2007
  • "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
  • Tuesday, April 28, 2009
  • "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
  • Friday, May 01, 2009
  • "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
  • Wednesday, May 06, 2009
  • "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
  • Wednesday, May 06, 2009
  • "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
  • Thursday, May 07, 2009
  • "Sorry, Rhonda, it is possible to have a negative integer."
  • Nick Ball, Enoree, South Carolina
  • Thursday, May 06, 2010
  • "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
  • Thursday, May 06, 2010
  • "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
  • Monday, June 21, 2010
  • "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."

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Answer

Mathematically speaking the only incorrect statement is number 5. Multiplying by a negative whole number makes a positive value smaller.
But if there's only one statement wrong then statement 1 must be wrong too; but then two statements are wrong so statement 1 is correct.
Let's solve this paradox by agreeing that statement 1 is wrong because it refers to a box rather than a rectangle. What do you think?