2353
/www/nrich/html/content/id/2353/
1
2011-02-01T00:00:01
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Move from the START to the FINISH by moving across, down or up to the
next square. You can only move into each square once.
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Add the numbers as you go.
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<mdo:image src="grid.gif" bgcolor="" alt=" Four by four grid containing numbers 1, 2 nd 3" height="198" width="211" align="top" />
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Find the path that gives the smallest total.
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Find the path that gives the highest total.
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Find a path that equals exactly 12.
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How many paths make 12?
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<p>Olivia and Poppy from St Mary's School, and Yanqing from Lipson Community College all suggested that the smallest total they could find is 8 using the route: 1-2-1-1-1-1-1.</p>
<p>Eva who goes to Benenden School sent in the largest total and describes the route:</p>
<p>1 (right to) 2 (right to) 1 (right to) 2 (down to) 1 (left to) 3 (left to) 3 (left to) 2 (down to) 1 (down to) 2 (right to) 1 (up to) 1 (right to) 1 (down to) 3 (right to) 1 Total = 25</p>
<p>Eva also sent in a path that made 12:</p>
<p>1 (right to) 2 (down to) 3 (down to) 1 (right to) 1 (down to) 3 (right to) 1</p>
<p>Emma from Maryhill High School found a different route that also has a total of 12:</p>
<p>1-2-3-3-1-1-1</p>
<p>Children at New Earswick Primary School found some other solutions to make 12:</p>
<p>Alex found:</p>
<div style="clear: both;">1(right to) 2 (down to) 3 (down to) 1 (down to) 1 (right to) 3 (right to) 1.</div>
<div style="clear: both;"> </div>
<div style="clear: both;">Ben found:<br></br>
1 (down to) 2 (right to) 3 (right to) 3 (down to) 1 (right to) 1 (down to) 1.
<div style="clear: both;"> </div>
<div style="clear: both;">Josh found:<br></br>
1 (down to) 2 (right to) 3 (right to ) 3 (right to) 1 (down to) 1(down to) 1.
<div style="clear: both;"> </div>
<p style="clear: both;">Perhaps one of the last two is the same as Emma's - but well descibed, Alex, Ben and Josh.</p>
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<h3><span style="font-weight: bold;">Why do this
problem?</span></h3>
<a href="http://nrich.maths.org/public/viewer.php?obj_id=2353&part=index">
This activity</a> can be fun to do and involves the pupils doing a
number of calculations - probably without them realising it. It has
the facility to be extended very easily. This problem provides
children with the opportunity to make sense of numbers and reason
about them. Systematic working is also involved. <br></br>
<br></br>
<h3>Key questions</h3>
<div>How did you decide on your route?</div>
<br></br>
<h3>Possible extension</h3>
<div>Ask the pupils to invent new ones and ask them how they make
them harder/easier.</div>
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<h3>Possible support</h3>
<div>Some templates of the 4 by 4 square could be useful.</div>
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Try looking for the lowest numbers on the grid.
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Will visiting the largest number of squares give us the greatest total?
Can we visit all the squares?
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Smallest total: 8 Route: 1-2-1-1-1-1-1
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Largest total: 24 Route: 1-2-3-2-1-3-1-1-1-1-1-2-1-3-1
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Totals of 12: 1-2-3-3-1-1-1
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<p>
1-2-1-3-1-3-1
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<p>
1-2-3-1-1-3-1 (two ways)
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5
1
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0
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Here to There 1 2 3
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Decision Mathematics and Combinatorics
Combinations
Using, Applying and Reasoning about Mathematics
Working systematically
Numbers and the Number System
Comparing and Ordering numbers
Calculations and Numerical Methods
Addition & subtraction