Six Places to Visit

5655 /www/nrich/html/content/id/5655/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Well, we're going to look at visiting places. Here's the road map: <mdo:image width="550" height="372" src="roads.gif" alt="road map"></mdo:image> There are six places to visit: 1. Relations who live in the tall house; 2. Friends who live in the house with trees; 3. The wide school building; 4. The blue church; 5. The health centre with blue roof and pink walls; 6. The little pink shop which is leaning over. You live in the yellow house at the bottom of the map. Starting at your house, try to describe the journey to each of the six places. You'll need to describe the bends in the road [how much they turn] and which way to turn at junctions. Having done that what about trying this next one too: <mdo:image width="550" height="369" src="roads2.gif" alt="second road map"></mdo:image> We have the same places to visit, but they are in different places now. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Thank you to children from Knaphill School who sent lots of solutions to this problem. Kevin described very carefully how to get to each of the places: To the school: At the first junction, turn clockwise $90^\circ$ go forward past the tall house. When you see a turn, turn it by $45^\circ$ anti-clockwise. Go forward until you see a little pink shop that's leaning over, there, you will find the next junction, turn $45^\circ$ anti-clockwise then go forward. You will see a blue church. Go straight past it then there will be a third junction, turn clockwise $90^\circ$. Go forward till you see the fourth junction! At this junction, you turn clockwise and $90^\circ$. Go forward and soon you will see a white house with trees around it, ignore it. Carry on going forward until you see a turn, turn it by turning it clockwise $45^\circ$. Start going forward again, there will be another $45^\circ$ turn clockwise soon after, then you will come to the school. To the red house: Go forward until you see a turn, turn it by turning $90^\circ$ anti-clockwise. Go forward and you're there! To the tall house: Go forward until you see the first junction, turn $90^\circ$ clockwise go forward and then you'll be there. Easy-Peasy. To the pink shop that's leaning over: Go forward until you see the first junction, turn $90^\circ$ clockwise Go forward again, past the tall house. Then you'll see the second junction, turn $45^\circ$ anti-clockwise and go forward. That's where the pink shop that's leaning over is. To the blue church: Go forward until you see the first junction, turn $90^\circ$ clockwise Go forward again, past the tall house. You will see a $45^\circ$turn, turn anti-clockwise. Go forward again, then comes the 2nd junction, turn $45^\circ$ anti-clockwise, go forward and soon comes the blue church. To the house with trees: Go forward till you get to the first junction, turn clockwise by $90^\circ$ Go forward past the tall house, then the $45^\circ$ turn anti-clockwise Go forward till the second junction, turn $90^\circ$ clockwise Then you will come to a $45^\circ$ turn anti-clockwise, past the school Then you'll come to another $45^\circ$ anti-clockwise turn After that, go forward till another $45^\circ$ anti-clockwise turn! Go forward another little bit then you'll be at the house with trees! Jack from Eastwood Primary School described visiting all the places in one journey. This is what he wrote: <div>Starting at the yellow house, you move forward, passing the T junction on your right until you reach the end of the road. There, turn left $90^\circ$, move forward until you reach the red brick house with the blue roof. Enter the house.</div> When leaving the house, turn left and follow the road until it turns right $90^\circ$, continue forward and take the first turning on the left. Follow the road until you reach the tall house, and enter. <div>Come out of the house and turn left. Follow the road which turns left at a $45^\circ$ angle. At the Y junction, you will see a small white house on your left, enter.</div> When exiting the house turn left and follow the road forward until you see a blue church on your right-hand side. Visit the church. <div>Exit the church and continue in the same direction as before. When reaching the T junction, turn right. Continue forward and take the next turning on your right which is at a $90^\circ$ angle. Go forward until you reach a small cottage on your right, enter for some tea.</div> Come out of the cottage and turn right, move forward along the road where it will bend at a $45^\circ$ angle to the right, continue forward where the road will bend again to the right at a $45^\circ$ angle. Move forward, there will be a large school on your right-hand side, enter the school and go to Mr Leggett's maths lesson. Well done, Jack, that's a very efficient way of visiting each place in turn. Thank you to everyone else who sent us their detailed description. Unfortunately there isn't space to publish them all! </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Six Places to Visit</h2> Well, we're going to look at visiting places. Here's the road map: <mdo:image alt="road map" height="372" src="roads.gif" width="550"></mdo:image> There are six places to visit: 1. Relations who live in the tall house; 2. Friends who live in the house with trees; 3. The wide school building; 4. The blue church; 5. The health centre with blue roof and pink walls; 6. The little pink shop which is leaning over. You live in the yellow house at the bottom of the map. Starting at your house, try to describe the journey to each of the six places. You'll need to describe the bends in the road [how much they turn] and which way to turn at junctions. Having done that what about trying this next one too: <mdo:image alt="second road map" height="369" src="roads2.gif" width="550"></mdo:image> We have the same places to visit, but they are in different places now. </div> <h3>Why do this problem?</h3> <div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=5655&part=">activity</a> is a good one to try once children have some experience of turning and the measurement of the angles in degrees. It can also be an opener for looking at the angle turned rather than what might be called the internal angle.</div> <h3>Possible approach</h3> <div>This kind of activity can be best introduced by a pupil walking a path that requires some turning at junctions. You could set up a 'course' in the school hall or outside which involves going round obstacles, for example. You could then challenge pupils to imagine a bird's-eye view of the situation and sketch it. Then, a route could be drawn on the sketch and instructions given by one child to direct another child along the route. This could be an opportunity for the class to develop the necessary language so that the instructions are accurate.</div> <div>When working on the problem, it might be useful for children to have a copy of <a href="/content/id/5655/Worksheet.doc">this sheet</a> of the maps. The angles used are all multiples of $45^\circ$ so there will be no need for children to have protractors, rather they should be able to justify the amount of turn for example by referring to fractions, or multiples, of a right angle.</div> <h3>Key questions</h3> <div>How much of a turn is there at this junction or bend in the road?</div> <div>How are you finding the angles each time?</div> <h3>Possible extension</h3> <div>Older or more experienced pupils could try this third map with different places (where there are $1, 2, 3, 4$ or $5$ yellow houses) to start:</div> <div><mdo:image alt="" height="351" src="roads3.gif" width="500"></mdo:image></div> <div><a href="/content/id/5655/Worksheet2.doc">Here</a> is a sheet to print which contains this map.</div> <div>Childrencould find different lengths of routes to each of the five places to visit as well.</div> <h3>Possible support</h3> <div>Some of the play-mats that have road systems on them would be useful. A programable robot can be a useful aid as well.</div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> At a junction, imagine turning the direction you want to go. What part of a full turn would this be? How many degrees would it be? You could draw out the map on the ground outside (ask someone to help you) and walk along the route. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> There are obviously a number of solutions to each section but here are the more obvious and probably shortest routes. A/ 1/Straight on, then, Rt 90° 2/Straight on, then, Rt 90°, Lt 45°, Rt 90°, Lt 45°, Lt 45°, Lt 45° 3/ Straight on, then, Rt 90°, Lt 45°, Rt 90° 4/ Straight on, then, Rt. 90°, Lt 45°, Lt 45° 5/ Straight on, then, Lt 90° 6/ Straight on, the, Rt 90°, Lt 45° B/ 1/ Straight on, then, Rt 90°, Rt 45°, Lt 90°, Rt 45° 2/ Straight on, then, Rt 90°, Lt 45°, Lt 45°, Rt 90° 3/ Straight on, then, Rt 90°, Rt 45°, Rt 45° 4/Straight on, then, Rt 90°, Rt 45°, Lt 90°, Rt 45°, Lt 45°, Lt 45° 5/ Straight on, then, Rt 90°, Lt45°, Lt 45°, Lt 90° 6/Straight on, then, Lt 90° </mdoxml> 2 3 0 1 0 0 0 Six Places to Visit Can you describe the journey to each of the six places on these maps? How would you turn at each junction? 2D Geometry, Shape and Space Angles Admin Upper primary mapping document