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.


Share

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

  • Wikipedia,
  •  
  • A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition.
  • Natalie, London
  •  
  • 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
  •  
  • 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
  •  
  • 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
  •  
  • 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
  •  
  • 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
  •  
  • Sorry, Rhonda, it is possible to have a negative integer.
  • Nick Ball, Enoree, South Carolina
  •  
  • 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
  •  
  • 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
  •  
  • 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
  •  
  • I loved this starter it really made me think and involved some good classroom discussions.
    Thanks.
  • Kiwi, New Zealand
  •  
  • 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
  •  
  • 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
  •  
  • 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
  •  
  • Enjoyable but Made my brain hurt! I loved this and would love to see more of these starters.
  • Dartmouth Academy 5/6P, Dartmouth
  •  
  • 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
  •  
  • It was an enjoyable paradox. Good trick!
    Keep it up, Transum!
  • MrMiss, Essex
  •  
  • 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,
  • Friday, September 29, 2017
  • I always tell lies.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.5 out of 5 based on 167 votes.


Previous Day | This starter is for 6 May | Next Day

 

Answers



Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=May6

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=paradox

Student Activity


Their are three mitsakes
in this message.


Visual Paradoxes

Visual Paradoxes

If you randomly select one of the possible answers to this multiple choice question what is the probability you are correct?

a) 20%

b) 40%

c) 60%

d) 20%

e)  0%


Boy and Dog Speech Bubble

I ALWAYS
TELL LIES

Apple

©1997-2017 WWW.TRANSUM.ORG