5994 /www/nrich/html/content/id/5994/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> My measurements have got all jumbled up!<br></br> <br></br> Drag the <a href="/content/id/5994/Measurement.zip">entries</a> in the table up and down until all the measurements match up sensibly. For some items there are a few numbers which would be valid. You have to juggle them to find a combination where every measurement is valid.<br></br> <br></br> This page will be different every time you load it or refresh it - so if you have unscrambled one set of measurements, you can try a new set. See if you can do it with fewer uses of the 'score' button!<br></br> <br></br> <span style="font-weight: bold;">Small version for getting used to the idea:</span><br></br> <br></br> <mdo:flash height="201" width="801"><param value="/content/id/5994/Measurement3.swf" name="movie" ></param><param value="9" name="flashplayerversion" ></param><param value="true" name="allowfullscreen" ></param></mdo:flash><br></br> <br></br> Score - each item gets a maximum of three marks:<br></br> <ul> <li style="margin-left: 40px;">correct type of unit</li> <li style="margin-left: 40px;">within 20% of our estimate</li> <li style="margin-left: 40px;">within 1% of our estimate</li> </ul> On the large version, a good strategy is to drag finished items to the top of the list, so they won't get mixed around by your later work. If there are a few similar numerical values in your list, you might need to swap pairs over to get the last few marks.<br></br> <br></br> <span style="font-weight: bold;">Large version for a real workout!</span><br></br> <br></br> <mdo:flash height="681" width="801"><param value="/content/id/5994/Measurement.swf" name="movie" ></param><param value="9" name="flashplayerversion" ></param><param value="true" name="allowfullscreen" ></param></mdo:flash><br></br> <br></br> The following sets of cards are available if you want students to work away from the computer. They will of course lose the facility to check their results online.<br></br> <a href="/content/id/5994/Card_sort_1.doc">Card sort 1</a><br></br> <a href="/content/id/5994/Card_sort_2.doc">Card sort 2</a><br></br> <a href="/content/id/5994/Card_sort_3.doc">Card sort 3</a><br></br> Alternatively, you could right click over a table and select the option to print.<br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Chelsea from the Thomas Deacon Academy suggested a strategy for tackling this problem:</p> To solve <span style="font-weight: bold;">All in a Jumble</span> you must first solve the common sense solutions which you already know of.<br></br> This may take some of the jumbled questions off your list. <br></br> <br></br> Secondly you cross off the answers you definitely know are incorrect. <br></br> <br></br> You may have about 5-6 questions left. If you do not know these then you could take a guess. <br></br> At least you know you have got most of the questions right by common sense!<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3>Why do this problem?</h3> <p><a href="http://nrich.maths.org/public/viewer.php?obj_id=5994">The problem</a> presents many different quantities and units. It involves thinking about large and small numbers and &#39;back of an envelope&#39; estimations and unit conversions. It offers an ideal opportunity for class discussion and convincing arguments.</p> <br></br> <br></br> <h3>Possible approach</h3> <div>In preparation for a lesson in a computer room, show the small interactivity to the class, and ask for volunteers to move items and explain their reasons. Set homework to research different units and bring their notes to the computer lesson. Showing students a few different sets of 15 items, could suggest some unfamiliar units to look up.</div> <br></br> <div>Ask students to work in pairs, so they must discuss and convince each other (e.g. like when couples play "Who Wants to be a Millionaire"). They could settle which items are a "final answer" and drag these to the top of the list. They could choose one item to "ask the audience" - and have a short plenary where these questions are asked and answered by other students in the class.</div> <br></br> <div>For most of the lesson, allow students to work at the task, using exercise book/whiteboard to control/motivate - eg students could write the scores they get each time they check. The whiteboard could be a leader board, with "100% and number of tries" recorded to motivate others. With some classes, it may be appropriate to encourage students to write out their estimating processes and unit conversions, in their exercise books. Students could also record useful numerical facts.</div> <br></br> <h3>Key questions</h3> <div>Which of the units could be used here?</div> <div>Which of the items are easiest/hardest?</div> <div>What do you know that is relevant here?</div> <br></br> <h3>Possible extension</h3> <p>Challenge students to get "100% in 3 tries" twice in a row!<br></br>  </p> <h3>Possible support</h3> <p>Print a few copies of some of the 15 question tables (see note at end of the problem). Ask students to identify all the items on one sheet which measure length, say. They could delete all other items and all inappropriate units. In small groups, ask students to estimate the different lengths in any units of their choice, and convert these estimates to other sensible units. Based on this working, ask them to match up item, number and unit for all the lengths.<br></br> <br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Start with the items that you are most confident about.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> s<a href="/content/id/5994/Measurement.swf">w</a>f<br></br> </mdoxml> 2 4 0 0 1 0 0 My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid. Measures and Mensuration Imperial units Measures and Mensuration Metric units Measures and Mensuration Temperature Measures and Mensuration Time Measures and Mensuration Compound measures Measures and Mensuration Speed Measures and Mensuration Volume and capacity Measures and Mensuration Area Measures and Mensuration Length/distance Measures and Mensuration Mass and weight Measures and Mensuration Measures - generally