7044 /www/nrich/html/content/id/7044/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Here is a machine with four coloured lights. Each light responds to a rule. <br></br><br></br> When you type in a number, lights go on if their rule is satisfied. <br></br> If the number satisfies more than one rule, then more than one colour will light up<br></br><br></br> Type in some numbers and see which lights you can switch on.<br></br> <br></br><br></br> <div style="background-color:#000;padding:20px;padding-bottom:20px;width:260px;height:280px"> <div style="position:relative;"> <label style="position:absolute;top:10;color:#fff;font-size:12px;font-family:helvetica,arial,sans-serif">Type in a number</label> <input id="numberText" type="text" value="0" name="number" tabindex="1" maxlength="8" size="8" style="position:absolute;top:-10px;left:130px;font-size:1.2em" /> <img id="red" src="red.png" style="position:absolute;left:20px;top:30px;opacity:0;z-index:1" /> <img id="redOff" src="redOff.png" style="position:absolute;left:20px;top:30px;opacity:1;z-index:0" /> <img id="yellow" src="yellow.png" style="position:absolute;left:120px;top:30px;opacity:0;z-index:1" /> <img id="yellowOff" src="yellowOff.png" style="position:absolute;left:120px;top:30px;opacity:1;z-index:0" /> <img id="green" src="green.png" style="position:absolute;left:20px;top:130px;opacity:0;z-index:1" /> <img id="greenOff" src="greenOff.png" style="position:absolute;left:20px;top:130px;opacity:1;z-index:0" /> <img id="blue" src="blue.png" style="position:absolute;left:120px;top:130px;opacity:0;z-index:1" /> <img id="blueOff" src="blueOff.png" style="position:absolute;left:120px;top:130px;opacity:1;z-index:0" /> <input id="restartButton" name="restartButton" type="button" value="Restart" style="position:absolute;top:260px" /> <br style="clear:both" /> </div> </div> <br></br><br></br><br></br> What is the smallest number which lights them all up?<br></br><br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Thomas of QEGS Wakefield identified the rules:</span><br></br>  <br></br> <div style="margin-left: 40px;">To light the YELLOW light the rule is: &lt; $30$</div> <div style="margin-left: 40px;">To light the RED light the rule is: Have an odd tens digit</div> <div style="margin-left: 40px;">To light the BLUE light the rule is: Multiple of $5$</div> <div style="margin-left: 40px;">To light the GREEN light the rule is: Is odd </div> <div style="margin-left: 40px;"> </div> <div><span class="editorial">Ahmad reasoned well to explain the minimum number which lit up all the lights:</span></div> <div> </div> <div>The answer is $15$.</div> <div>Its tens digit is the smallest, from the allowed, which is $10$. Its unit digit is $5$ ; it is not zero because then it would be even and wouldn't light the green. It is also less than $30$.  </div> <br></br> <p><span class="editorial">Are you both sure that the yellow light only lights up for numbers under $30$?</span></p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Light the Lights</h2> Here is a machine with four coloured lights. Each light responds to a rule.<br></br> <br></br> When you type in a number, lights go on if their rule is satisfied.<br></br> If the number satisfies more than one rule, then more than one colour will light up<br></br> <br></br> Type in some numbers and see which lights you can switch on.<br></br> <br></br> <br></br> <div style="background-color:#000;padding:20px;padding-bottom:20px;width:260px;height:280px"> <div style="position:relative;"><label style="position:absolute;top:10;color:#fff;font-size:12px;font-family:helvetica,arial,sans-serif">Type in a number</label> <input id="numberText" maxlength="8" name="number" size="8" style="position:absolute;top:-10px;left:130px;font-size:1.2em" tabindex="1" type="text" value="0"></input> <mdo:image id="red" src="red.png" style="position:absolute;left:20px;top:30px;opacity:0;z-index:1"></mdo:image> <mdo:image id="redOff" src="redOff.png" style="position:absolute;left:20px;top:30px;opacity:1;z-index:0"></mdo:image> <mdo:image id="yellow" src="yellow.png" style="position:absolute;left:120px;top:30px;opacity:0;z-index:1"></mdo:image> <mdo:image id="yellowOff" src="yellowOff.png" style="position:absolute;left:120px;top:30px;opacity:1;z-index:0"></mdo:image> <mdo:image id="green" src="green.png" style="position:absolute;left:20px;top:130px;opacity:0;z-index:1"></mdo:image> <mdo:image id="greenOff" src="greenOff.png" style="position:absolute;left:20px;top:130px;opacity:1;z-index:0"></mdo:image> <mdo:image id="blue" src="blue.png" style="position:absolute;left:120px;top:130px;opacity:0;z-index:1"></mdo:image> <mdo:image id="blueOff" src="blueOff.png" style="position:absolute;left:120px;top:130px;opacity:1;z-index:0"></mdo:image> <input id="restartButton" name="restartButton" style="position:absolute;top:260px" type="button" value="Restart"></input><br style="clear:both"></br>  </div> </div> <br></br> <br></br> <br></br> What is the smallest number which lights them all up?<br></br>  </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/7044&amp;part=">This problem</a> requires children to make sense of information and work in a systematic way. It is a motivating context in which they use their knowledge of number properties.</div> <br></br> <h3>Possible approach</h3> <div>This activity will require children to have access to computers, ideally in pairs.</div> <br></br> <div>You could start by dividing the board into two columns, one headed with a tick and the other headed with a cross. Ask learners to suggest numbers, and write each suggestion in the appropriate column according to a rule of your own choice. Make it clear to the class that the activity is designed to model working like a scientist - there is no-one to say whether they have the right answer or not. So they can come up with a hypothesis for your rule, but you will not confirm their hypothesis, you will only place numbers in the appropriate column.</div> <br></br> <div>Here are some suggestions for rules:</div> <ul> <li>Odd numbers</li> <li>Numbers bigger than $20$</li> <li>Multiples of $10$</li> </ul> <div>Once the class has tried the activity with a couple of rules and everyone is reasonably convinced their hypothesis holds, move on to the main task.</div> <br></br> <div>To introduce the main task, show the interactivity and demonstrate entering a couple of numbers to see what lights up. Make sure learners understand that more than one light may be lit up at once, and that each light is governed by its own simple rule. Learners should work in pairs at a computer, and their challenge is to try to light up all the lights.</div> <br></br> <div>While the class is working, note any particularly good ways of recording or working systematically, and highlight them to the rest of the class.</div> <br></br> <div>Towards the end of the time working on the problem, leave some time for the class to come together to share what they have done. As well as discussing the number that lit up all the lights, encourage children to explain how they approached the problem.</div> <br></br> <h3>Key questions</h3> <div>Which numbers have you tried? What happened?</div> <div>Which number would be good to try next? Why?</div> <div>How will you remember which lights each number lights up?</div> <br></br> <h3>Possible extension</h3> <div>Learners could be challenged to find some rules so that it would be impossible to light all four lights. If appropriate, they might also have a go at <a href="http://nrich.maths.org/7035&amp;part=">this similar problem</a> which uses slightly higher-level mathematics.</div> <br></br> <h3>Possible support</h3> <div>Some children might find it helpful to use a <a href="/content/id/7044/1-100_NumberGrid.pdf">hundred square</a> to record their findings.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">How will you keep track of what happens with each number you try?<br></br> You might find a <a href="/content/id/7044/1-100_NumberGrid.pdf">hundred square</a> useful.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">odd, multiple of 5, odd tens digit, less than 31<br></br></mdoxml> 2 4 0 1 0 0 0 Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights? Numbers and the Number System Odd and even numbers Numbers and the Number System Factors and multiples Numbers and the Number System Comparing and Ordering numbers Numbers and the Number System Place value Information and Communications Technology Interactivities Using, Applying and Reasoning about Mathematics Making and testing hypotheses Admin Lower primary mapping document