7557 /www/nrich/html/content/id/7557/ 1 2011-09-08T19:48:20 <mdoxml version="1.0"><p>We have three rods that are each $2$ units long.</p> <p>The different colours are used to make the diagrams clearer and they always remain in the same place i.e the blue as the bottom layer, the green as the top layer and the red as the middle layer. </p> <p>The challenge is to find how many different ways you can stack these rods.</p> <p>The rule is that a small cube must sit squarely on top of another small cube.</p> <p>It does not matter if they are likely to topple over.</p> <p>Both these two arrangements fit the rule.</p> <p style="text-align: center;"><mdo:image src="2%20sets%20of%203%202%27s.jpg"></mdo:image></p> <p>However, these two arrangements do not fit the rule as the rods have to be lined up squarely and each little cube must sit on top of one other cube and not overlap two cubes. </p> <p style="text-align: center;"><mdo:image src="2%20sets%20of%203%20%202%27s%20NOT.jpg"></mdo:image></p> <p>How can you convince someone that you have found all the possibilities?</p> <p> </p></mdoxml> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://www.nrich.maths.org/7557">activity</a> acts as a further extension to <a href="http://www.nrich.maths.org/1997">Two on Five</a>. It&#39;s an activity that is intended to give opportunities for those pupils to explore deeply using their intuition and flair in the area of spatial awareness, also with an opportunity to create a system for solving such problems.</div> <br></br> <h3>Possible approach</h3> <div>As this activity is three star and is intended to challenge the best ones  in the class., it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.</div> <div> </div> <h3>Key questions</h3> <div>Tell me about what you have found.<br></br> Can you describe the ways that you arrived at these shape arrangements?<br></br> How did you construct these on the computer?</div> <br></br> <h3>Possible extension</h3> <div>For those who are successful they should be encouraged to try <a href="http://www.nrich.maths.org/7949">Building with longer rods</a>.</div> <br></br> <h3>Possible support</h3> <div>It will probably be helpful to have interlocking cubes available and different kinds of squared paper.</div> <br></br> <br></br></mdoxml> 2 5 0 1 0 0 0 Using, Applying and Reasoning about Mathematics Investigations Transformations and their Properties Reflections Using, Applying and Reasoning about Mathematics Working systematically