5546
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2011-02-01T00:00:01
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<div style="text-align: center;">LET'S LOOK AT A STREET!</div>
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<div style="text-align: center;"><mdo:image alt="Real Street" height="129" src="Real%20Street.jpg" width="211"></mdo:image></div>
<br></br>
Most of the streets around here have their numbers going in order from one side of the street to the other - so that odds end up on one side and evens on the other.<br></br>
So here's what is could be like:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="5Houses" height="167" src="The%20Street5.jpg" width="433"></mdo:image></div>
<div style="text-align: left;">Looking from above the numbers could appear as:</div>
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<div style="text-align: center;"><mdo:image alt="AA" height="65" src="AAStreet.jpg" width="426"></mdo:image></div>
<br></br>
Well you can imagine walking down this street and adding the house numbers in various ways.<br></br>
You could start with adding in pairs across the street:<br></br>
<div style="text-align: center;"><mdo:image alt="AB" height="64" src="ABStHouseSimple%20Add.jpg" width="425"></mdo:image></div>
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and carry on as far as you can.<br></br>
Explore the answers you get for these additions. What do you notice?<br></br>
Can you explain why?<br></br>
<br></br>
If you want to go a bit further with this you could change the grouping of houses in different ways. How about:<br></br>
<br></br>
A.<br></br>
<div style="text-align: center;"><mdo:image alt="AC" height="141" src="ACStHouseXAdd.jpg" width="429"></mdo:image></div>
<br></br>
<div>Or:</div>
<br></br>
<br></br>
B.<br></br>
<div style="text-align: center;"><mdo:image alt="AD" height="146" src="ADStHouseAdjAdd.jpg" width="427"></mdo:image></div>
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But maybe the houses are already grouped in some way - like all semi-detached:<br></br>
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<div style="text-align: center;"><mdo:image alt="AE" height="65" src="AEStHouseSemi.jpg" width="384"></mdo:image></div>
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Then one side of the street the totals are: 4, 12, 20, etc<br></br>
and the other side are: 6, 14, 22 etc.<br></br>
<br></br>
You could continue this and explore it further.<br></br>
<br></br>
Some streets have terraces of three houses together:<br></br>
<div style="text-align: center;"><mdo:image alt="AF" height="64" src="AFStHouse3%27s.jpg" width="401"></mdo:image></div>
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and some have fours:<br></br>
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<div style="text-align: center;"><mdo:image alt="AG" height="64" src="AGStHouse4%27s.jpg" width="417"></mdo:image></div>
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You can explore the addition of these groups too!<br></br>
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<p><span class="editorial">Nick, Harish and Jonathan from Mason
Middle School investigated these street numbers in groups of three.
They wrote:</span></p>
When you add the first number on the top and the third number on
the bottom they equal seven.<br></br>
Also the third number on the top and the first number on the bottom
equal seven. Finally, the second number on the top and the second
number on the bottom also equal 7.<br></br>
If you add the diagonals two away <span class="editorial">(I think
this means the six houses which have numbers 5, 7, 9 and 6, 8
10)</span> they become 15. The sum is 8 more than before.<br></br>
<br></br>
<p><span class="editorial">Ella from the British School in
Amsterdam did a similar thing and said that the diagonal totals are
the same number.</span></p>
<p class="editorial">I wonder whether anyone can explain why?</p>
<p class="editorial">We'd love to hear about other things you
investigate. Please don't worry that your solution is not
"complete" - we'd like to hear about anything you have tried.
Teachers - you might like to send a summary of your
children's work.</p>
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Each of these challenges can lead to pattern investigations and the
activity also lends itself to pupils inventing their own new
challenges that involve the house numbers.<br></br>
<br></br>
Whenever patterns arise some of the older pupils can be asked "Why
are these sequences like they are?", whilst younger pupils can be
asked simply "What do you notice about the answers we've
got?".<br></br>
An extension may be suitable for some pupils that comes from
comparing the results from the sequences that we get when the
houses are grouped. <br></br>
<br></br>
In general, the following mathematical process is a good one to go
through with pupils in many different activities:<br></br>
<br></br>
1. Get one set of answers that form a sequence (in this case the
totals for semis);<br></br>
2. Change the rules slightly and get a new set of answers (for
example for houses grouped in 3's);<br></br>
3. Change that rule again and continue (houses grouped in 4's, 5's,
6's etc.);<br></br>
4. Compare the sequences that have been generated by looking at
similarities and differences;<br></br>
5. See what you notice and whether you can find out WHY some of
these similarities and differences occur.<br></br></mdoxml>
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You could just add diagonal pairs. What do you notice?<br></br>
What happens if you keep adding? For example, starting at 1, add 4,
then 5, then 8 etc. Could you predict the pattern of totals? <br></br></mdoxml>
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Street Sequences
Investigate what happens when you add house numbers along a street
in different ways.
Numbers and the Number System
Comparing and Ordering numbers
Calculations and Numerical Methods
Addition & subtraction
Using, Applying and Reasoning about Mathematics
Investigations
Sequences, Functions and Graphs
Sequences