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Squeezy maths – Oddly enough

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By John Dabellteacher, writer and Ofsted-trained inspector

Squeeze every last bit of learning out of the concept of odd and even numbers with these mathematics investigations for KS2 children

Plastic numbers

Activities

  1. Odd and even phrases
  2. Odd number investigation
  3. Investigating zero
  4. More odds and evens puzzles
  5. Extra challenges

Odd and even phrases

Some children are at odds with numbers. They just don’t seem to get on. That’s hardly surprising, though, because all numbers can be fairly odd things at times!

For example, which is the odd one out from the following numbers?
6, 9, 13, 15, 17

One answer could be that 6 is the odd one out because it’s the only even number in the list. Talk about confusing! The language we use in maths needs to be precise to avoid confusion. So, before investigating odd and even numbers, it might be worth looking at some common expressions such as:
  • ‘odd one out’
  • ‘against all odds’
  • ‘odds and ends’
  • odds-on favourite’
  • ‘make no odds’
  • ‘break even’
  • ‘an even break’
  • ‘getting even’
  • ‘keep on an even keel’
  • ‘get even’
  • ‘even Steven’

We certainly need to think twice about maths language compared to everyday usage.

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Odd number investigation

Next, set up a challenge. Ask children to consider the following statement: If you add two odd numbers together the answer will always be odd.

Ask children to investigate some examples of adding two odd numbers and see what the answer is. How many times would you need to investigate before you agreed or disagreed with the statement? Then ask children to find out whether adding three, four or five odd numbers makes a difference.

Challenge maths groups or maths buddies to investigate odd and even rules for adding, subtracting and multiplying by completing a table similar to the one below.

Odds and evens table

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Investigating zero

Fast finishers and homework enthusiasts will often catch you out at odd moments with requests for something to do. Give them something mathematically meaningful to think about with this investigation: How would you prove whether zero is an odd or an even number?

Solution To answer this question you need to apply the rules for adding, subtracting and multiplying.
  • even ± even = even
  • odd ± odd = even
  • even × integer = even
Next, substitute some numbers into each of those rules, to end up with zero on the right-hand side each time. For example:
  • 2 − 2 = 0
  • −3 + 3 = 0
  • 4 × 0 = 0 So this shows that zero can be considered as an even number.

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More odds and evens puzzles

In maths groups or pairs, ask children to investigate whether some of these statements involving odd and even numbers are true or false. Encourage them to compare answers with another group or pair to see if they agree.
  • The sum of three even numbers and one odd number is always an even number.
  • The sum of three odd numbers and one even number is always an even number.
  • The sum of six odd numbers is always an even number.
  • The difference between two even numbers is always an even number.
  • The difference between an even number and an odd number is always an odd number.
  • The difference between two odd numbers is always an even number.
  • If you treble any odd number the answer is always an even number.
  • If you quadruple any even number the answer is always an even number.
  • If you quintuple any even number between 20 and 30 then the answer is sometimes odd.
  • If you add three odd numbers you will always make a prime number.
  • If you add three consecutive odd numbers you will sometimes make an even number.
  • The squares of all even numbers are even, and the squares of all odd numbers are odd.

You can encourage variation in these mini investigations. For example, you could ask children to start investigations with single digit numbers, then two-digit numbers, then three-digit numbers. Children could extend any of the puzzles by investigating larger numbers in the hundreds and thousands. You could also ask groups to come up with the definition of an odd number and an even number for a maths dictionary.

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Extra challenges

Some children will really enjoy getting their teeth into as many of these logic puzzles as possible! Here are some varied challenges for really keen children.

  • How many odd numbers are there between and including 7 and 15? (5)
  • How many odd numbers are there between 7 and 15? (3)
  • Can negative numbers be odd and even? (yes)
  • Are there more odd square numbers less than 100 or more even square numbers? (there are five of each – the odds are 1, 9, 25, 49, 81 and the evens are 4, 16, 36, 64, 100)

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Image © gokoroko/sxc.hu

Reviews

  1. Nick Flint
    on 13 January 2013

    Great resource (tiny mistake)

    This is excellent – thanks! Will be using it in class next week.

    However, my smartypants, 8yr old daughter noticed that there is a mistake on your investigation table: odd + odd = even (not odd)

    5out of 5

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