5929 /www/nrich/html/content/id/5929/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: center;"><mdo:image height="510" width="499" src="SeaBed4.jpg" alt="seabed4"></mdo:image></div> <div style="text-align: center;"></div> <br></br> <div style="text-align: center;"></div> <p style="text-align: left;">Well, here's a pretty scene, the underwater creatures and the tall lighthouse joined by a seagull and a cloud in the sky.</p> <div style="text-align: left;"></div> <p style="text-align: left;">There are black markings all the way up the lighthouse and on the support for the lighthouse going down to the sea bed. These markings are $1$ metre apart. I have left the numbering for you to do.</p> <div style="text-align: left;"></div> <p style="text-align: left;">The sea level is of course &quot;$0$&quot; and then positive numbers going up and negative numbers going down to the sea bed.</p> <div style="text-align: left;"></div> <p style="text-align: left;">If we think about the mouths of the creatures then we can see how much deeper they are from each other, or what distance they are apart.</p> <div style="text-align: left;"></div> <p style="text-align: left;">For example the (mouth of) the fierce looking blue and white fish near the middle is $1$ metre deeper than the (mouth of) the golden yellow fish.</p> <div style="text-align: center;"></div> <div>1. What number should be where the light shines from the lighthouse?</div> <div>2. What number should be where the (head of the) seagull is?</div> <div>3. What number should be where the (mouth of the) red crab, near the bottom, is?</div> <div>4. How far is it down from the (head of the) seagull to the (mouth of the) yellow fish?</div> <div>5. How far is it from the turtle, near the surface of the water, to the crab?</div> <div>6. There's a little brown sea-horse to the right of the lighthouse support. How far from the surface is it?</div> <div>7. How high above the sea level is the seagull flying?</div> <div>8. How far is the seagull from the sea-horse?</div> <div>9. How high is the pointed end of the cloud?</div> <br></br> <div>It would be interesting to know how you arrived at your answers.</div> <div>Did you write anything down to help you?</div> <br></br> <div>How about thinking up some questions of your own? Please do send them in - we would like to see your creative juices at work!</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We had some good solutions in for this challenge. Here is one from Heathfield house School sent in by Aran.</p> <br></br> 1. 6M<br></br> 2. 3M<br></br> 3. -7M<br></br> 4. 6M<br></br> 5. 7M<br></br> 6. 7M<br></br> 7. 4M<br></br> 8. 9M<br></br> 9. 4M<br></br> <br></br> <p class="editorial">Which was quite accurate and shows that the right idea was used. Thomas from St. Lukes had similar answers and was a little more accurate.</p> <div>1. 6</div> <div>2. 3</div> <div>3. -8</div> <div>4. 7 metres down</div> <div>5. 7 metres down</div> <div>6. 5 metres down</div> <div>7. 3m</div> <div>8. 8m up</div> <div>9. 4m up</div> <br></br> <p class="editorial">Well done to you both and thank you for sending them in.</p> <p class="editorial">Finally we had an email from Maisy Kate showing some further questions she had thought of. Here they are:</p> <p class="editorial"></p> <div>1. How far is the octopus to the water level?</div> <div>2. How far is the yellow fish to the sea-weed nearest the water level?</div> <div>3. How far is the sea-horse to where the light shines?</div> <div>4. How far is the lowest mark to the sea level?</div> <div>5. How far apart is the crab's claw and the point of the cloud?</div> <br></br> <p class="editorial">Ben, from JESS School in Dubai also sent in some questions of his own:</p> <div>How far is it from the sword fish to the cloud?</div> <div>How far down is the octopus?</div> <div>How far is it from the seaweed to the seagull? </div> <br></br> <p class="editorial">Thank you, Ben!</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Sea Level</h2> <br></br> <div style="text-align: center;"><mdo:image alt="seabed4" height="510" src="SeaBed4.jpg" width="499"></mdo:image></div> <div style="text-align: center;"> </div> <br></br> <div style="text-align: center;"> </div> <p style="text-align: left;">Well, here&#39;s a pretty scene, the underwater creatures and the tall lighthouse joined by a seagull and a cloud in the sky.</p> <div style="text-align: left;"> </div> <p style="text-align: left;">There are black markings all the way up the lighthouse and on the support for the lighthouse going down to the sea bed. These markings are $1$ metre apart. I have left the numbering for you to do.</p> <div style="text-align: left;"> </div> <p style="text-align: left;">The sea level is of course "$0$" and then positive numbers going up and negative numbers going down to the sea bed.</p> <div style="text-align: left;"> </div> <p style="text-align: left;">If we think about the mouths of the creatures then we can see how much deeper they are from each other, or what distance they are apart.</p> <div style="text-align: left;"> </div> <p style="text-align: left;">For example the (mouth of) the fierce looking blue and white fish near the middle is $1$ metre deeper than the (mouth of) the golden yellow fish.</p> <div style="text-align: center;"> </div> <div>1. What number should be where the light shines from the lighthouse?</div> <div>2. What number should be where the (head of the) seagull is?</div> <div>3. What number should be where the (mouth of the) red crab, near the bottom, is?</div> <div>4. How far is it down from the (head of the) seagull to the (mouth of the) yellow fish?</div> <div>5. How far is it from the turtle, near the surface of the water, to the crab?</div> <div>6. There&#39;s a little brown sea-horse to the right of the lighthouse support. How far from the surface is it?</div> <div>7. How high above the sea level is the seagull flying?</div> <div>8. How far is the seagull from the sea-horse?</div> <div>9. How high is the pointed end of the cloud?</div> <br></br> <div>It would be interesting to know how you arrived at your answers.</div> <div>Did you write anything down to help you?</div> <br></br> <div>How about thinking up some questions of your own? Please do send them in - we would like to see your creative juices at work!</div> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=5929&amp;part=">problem</a> is a good way to increase familiarity with negative numbers on a number line. In answering the questions, children are beginning to calculate with negative numbers but in a context that will give them confidence rather one which they perceive as difficult.</div> <br></br> <h3>Possible approach</h3> <div>It would be a good idea to print out the picture so that children can put on the numbers and more easily use a ruler to see which objects are at a certain level. To make the link with calculation more explicit, you could have a go at writing number sentences for some of the questions as a class, then challenge the children to complete number sentences for the other questions. Pupils can then go on to invent questions of their own and, in particular, they could find alternative ways of asking the same question. For example:</div> <div>What depth is the octopus?</div> <div>What number will the octopus be at?</div> <div>How far from the surface is the octopus?</div> <br></br> <h3>Key questions</h3> <div>Tell me about the depth of these fish.</div> <div>How do you know? How are you working this out?</div> <br></br> <h3>Possible extension</h3> <div>You could invite children to make up as many questions as they can which have, for example, the answer $3$m. This allows them to be as creative as they like, and is a good way to assess their understanding.</div> <br></br> <h3>Possible support</h3> Some children will benefit from having a go at the <a href="http://nrich.maths.org/public/viewer.php?obj_id=5836&amp;part=index">Swimming Pool</a> problem before this one.<br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> How about using the lighthouse like a number line?<br></br> Try counting the markings, one by one.<br></br> Perhaps you can do a calculation in your head rather than counting? How?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br> 1/ +6 near the top of the lighthouse.<br></br> 2/ +3 at the mouth of the sea-gull.<br></br> 3/ -8 at the crab.<br></br> 4/ 6metres from seagull to Yellow fish.<br></br> 5/ 7 metres from the Turtle to the Crab.<br></br> 6/ The Sea-horse is at a depth of 5 metres.<br></br> 7/ The Seagull is at a height of 3 metres.<br></br> 8/ There's 8 metres from the seagull to the sea-horse.<br></br> 9/ The cloud is 4 metres high.<br></br></mdoxml> 2 3 0 1 0 0 0 The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures? Calculations and Numerical Methods Addition & subtraction Numbers and the Number System Positive-negative numbers Admin Upper primary mapping document