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.

Starter of The Day Transum Mathematics Topics


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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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Answers

Christmas Present Ideas

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Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

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The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

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This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

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All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

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If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more...

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Click the images above to see all the details of these gift ideas and to buy them online.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

 

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Laptops In Lessons

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

Laptops In Lessons

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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

In 1901, the British philosopher and mathematician Bertrand Russell uncovered a possible paradox that necessitated a modification to set theory. One version of Russell's Paradox involves a town with one male barber who, every day, shaves every man who doesn't shave himself, and no one else. Does the barber shave himself?

From The Math Book published by Sterling

Interesting number paradox

Did you know that all numbers are interesting?

Proof: Assume there exists a set of uninteresting numbers. This set would have a smallest number, which is interesting because it is the smallest uninteresting number. But a number cannot be both interesting and uninteresting, so the assumption that there exists a set of uninteresting numbers must be wrong and hence, all numbers must be interesting.

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