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If we draw numbers arranged in twos you can see if they are odd or even. These numbers are even. You can see they are even across the top.<br></br>
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<mdo:image width="401" height="176" alt="even numbers" src="Odd%26Even1.png"></mdo:image><br></br>
These numbers are odd. You can see they have an odd square sticking out at the top.<br></br>
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<mdo:image width="360" height="173" alt="odd numbers" src="Odd%26Even2.png"></mdo:image><br></br>
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I am going to add two even numbers, 8 and 4. This means I am going to put them together. I have also turned them round so they fit in better.<br></br>
Is the answer odd or even?<br></br>
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<mdo:image width="172" height="60" alt="add" src="Odd%26Even3.png"></mdo:image><br></br>
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What about these two? Is the answer odd or even?<br></br>
Can you write down the numbers which have been added?<br></br>
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<mdo:image width="116" height="59" alt="add" src="Odd%26Even4.png"></mdo:image><br></br>
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Now I am going to add an odd number to an even number.<br></br>
Is the answer odd or even?<br></br>
Can you write down the numbers which have been added?<br></br>
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<mdo:image width="174" height="61" alt="add" src="Odd%26Even5.png"></mdo:image><br></br>
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What about these two?<br></br>
Is the answer odd or even?<br></br>
Can you write down the numbers which have been added? <br></br>
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<mdo:image width="175" height="60" alt="add" src="Odd%26Even6.png"></mdo:image><br></br>
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Finally, I am going to look and see what happens when I add two odd numbers.<br></br>
Is the answer odd or even?<br></br>
Can you write down the numbers which have been added?<br></br>
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<mdo:image width="173" height="61" alt="add odd" src="Odd%26Even7.png"></mdo:image><br></br>
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What about these two?<br></br>
Is the answer odd or even?<br></br>
Can you write down the numbers which have been added?<br></br>
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<mdo:image width="172" height="59" alt="add" src="Odd%26Even8.png"></mdo:image><br></br>
I had to turn the pictures round so they fitted. Have go yourself.<br></br>
You can cut the shapes out of squared paper or use <a href="/content/id/7785/Odd%26Even.pdf">this sheet</a>. <br></br>
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<mdoxml version="1.0"><h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<p><a href="http://nrich.maths.org/7785&part=">This problem</a> is designed to help young children to create a proof that two odd numbers added together always give an even answer. This is very different from deriving general proof through exploring different cases. </p>
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<h3>Possible approach</h3>
<div>It is worth spending time exloring a numbers of cases and you might like to do this by following through the ideas below.</div>
<div>You could start by getting the whole group to count in twos. Repeat but starting with one, so the odd numbers are counted.</div>
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<div>Next you could show the group how to draw the numbers in twos on squared paper to show the "odd one" sticking out or an "even" top. It is better if they can cut out the various numbers because these can then be turned over. Alternatively the children could make models using Multilink or Numicon.</div>
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<div>At the end of the lesson the group could come together again to discuss their findings and show their work.</div>
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<h3>Key questions</h3>
<div>Is this number odd or even? How do you know?</div>
<div>Try counting in twos. Does the number come up?</div>
<div>Why not draw it on the squared paper and see if there is an odd square sticking out?</div>
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<h3>Possible extension</h3>
<p>Learners could make larger numbers. Alternatively they could do this problem picturing numbers in a different way <a href="http://nrich.maths.org/2158&part=">Numbers as Shapes</a> or even try this stage 2 problem, <a href="http://nrich.maths.org/2790&part=">Number differences.</a></p>
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<h3>Possible support</h3>
<p>Suggest cutting out the numbers from 1 to 10 from squared paper and numbering each square. (2 cm squared paper would be best for this.) Some children may need help with the actual cutting.<br></br>
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Draw the numbers on squared paper and, if possible cut them out.<br></br>
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Odd and even
Draw numbers arranged in twos to see if they are odd or even. Even numbers are even are across the top. Odd numbers have an odd square sticking out. What happens when we add them?
Numbers and the Number System
Odd and even numbers
Numbers and the Number System
Counting
Using, Applying and Reasoning about Mathematics
Representing
Using, Applying and Reasoning about Mathematics
Generalising