7466
/www/nrich/html/content/id/7466/
1
2011-06-16T08:41:20
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<ul id="stemLinks">
<li><a href="http://nrich.maths.org/7780">Warm-up</a></li>
<li><a href="http://nrich.maths.org/6331">Try this next</a></li>
<li><a href="http://nrich.maths.org/5861">Think higher</a></li>
<li><a href="http://nrich.maths.org/2564">Read: mathematics</a></li>
<li><a href="http://www.scienceofcooking.com/">Read: science</a></li>
<li><a href="http://en.wikipedia.org/wiki/Decision_making">Explore further</a></li>
</ul>
<div> </div>
<br></br>
<p><mdo:image alt="" src="turkey_chef.png" style="width: 254px; height: 230px; float: right;"></mdo:image>Tom is a keen cook, but doesn't find it easy to coordinate things when he's following a recipe. Recently he made a delicious supper of meatballs with tomato and bell pepper sauce, served on rice. Well, each element of the dish was delicious, but he really wanted them all ready at
the same time. Of course, it didn't help that the recipe didn't mention that the dish should be served with rice until the end ...<br></br>
<br></br>
Use a flowchart or similar to prepare a schedule for Tom. To cook the rice, allow 5 minutes for it to come to the boil, then 20 minutes simmering time. You will also need to allow sensible lengths of time for preparation of ingredients.<br></br>
</p>
<table style="border-spacing:5px;" border="1">
<tbody align="left">
<tr>
<td style="font-weight: bold;padding:5px;">Meatballs</td>
<td style="font-weight: bold;padding:5px;">Tomato and bell pepper sauce</td>
</tr>
<tr>
<td>Ingredients</td>
<td>Ingredients</td>
</tr>
<tr>
<td>
<ul>
<li>olive oil</li>
<li>1 red onion, chopped finely</li>
<li>2 1/4 cups minced lamb</li>
<li>1 large egg, beaten</li>
<li>2 tsp freshly squeezed lemon juice</li>
<li>1/2 tsp ground cumin</li>
<li>pinch of cayenne pepper, to taste</li>
<li>2 tbsp finely chopped fresh mint</li>
<li>salt and pepper</li>
</ul>
</td>
<td>
<ul>
<li>2 tbsp olive oil</li>
<li>5 large garlic cloves 2 oz shallots, chopped</li>
<li>2 large bell peppers, cored, seeded and chopped</li>
<li>1 lb fresh, ripe tomatoes</li>
<li>2 thin strips freshly pared orange rind</li>
<li>salt and pepper</li>
</ul>
</td>
</tr>
<tr>
<td>Method</td>
<td>Method</td>
</tr>
<tr>
<td>
<ol>
<li>Heat the olive oil in a skillet over medium heat. Add the onion and cook for about 5 minutes, stirring occasionally, until soft but not brown.</li>
<li>Remove the skillet from the heat, and allow the onion to cool.</li>
<li>Add the onion to the lamb with the egg, lemon juice, cumin, cayenne, mint, salt and pepper in a large bowl. Use your hands to squeeze all the ingredients together.</li>
<li>With wet hands, shape the mixture into small balls. Place on a baking sheet and chill for at least 20 minutes.</li>
<li>Heat a small amount of oil in a skillet, and arrange as many of the meatballs as possible in a single layer but without over-crowding them.</li>
<li>Cook over medium heat for about 5 minutes, until brown on the outside but still pink inside.</li>
</ol>
</td>
<td>
<ol>
<li>Heat the olive oil in a pan over medium heat. Add the garlic, shallots and bell peppers and cook for 10 minutes, stirring occasionally, until the peppers are soft but not brown. </li>
<li>Add the tomatoes, orange rind and salt and pepper and bring to a boil. </li>
<li>Reduce the heat as far as possible and let simmer uncovered for 45 minutes, or until the liquid evaporates and the sauce thickens.</li>
<li>Puree the sauce through a sieve or in a food processor. </li>
<li>Taste and adjust the seasoning if necessary.</li>
<li>Use at once, or cover and chill for up to 3 days.</li>
</ol>
<br></br>
<br></br>
<br></br>
<br></br>
</td>
</tr>
</tbody>
</table>
<p><br></br>
<br></br>
</p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><table style="width: 800px;border-spacing:1px;" border="1">
<tbody>
<tr>
<td style="text-align: center;padding:1px;">Timeline</td>
<td style="text-align: center;padding:1px;">Preparing Meatballs</td>
<td style="text-align: center;padding:1px;">Preparing Tomato and bell pepper sauce</td>
<td style="text-align: center;padding:1px;">Preparing rice</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">0 min</td>
<td style="text-align: justify;padding:1px;">Heat the olive oil in a skillet over medium heat. Add the onion and cook for about 5 minutes, stirring occasionally, until soft but not brown. Remove the skillet from the heat, and allow the onion to cool.</td>
<td style="text-align: justify;padding:1px;">Heat the olive oil in a pan over medium heat. Add the garlic, shallots and bell peppers and cook for 10 minutes, stirring occasionally, until the peppers are soft but not brown.</td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">10 min</td>
<td style="text-align: justify;padding:1px;">Add the onion to the lamb with the egg, lemon juice, cumin, cayenne, mint, salt and pepper in a large bowl. Use your hands to squeeze all the ingredients together. With wet hands, shape the mixture into small balls.</td>
<td style="text-align: justify;padding:1px;">Add the tomatoes, orange rind and salt and pepper and bring to a boil. Reduce the heat as far as possible and let simmer uncovered for 45 minutes, or until the liquid evaporates and the sauce thickens. This will take 50 minutes in all. </td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">20 min</td>
<td style="text-align: justify;padding:1px;">Place on a baking sheet and chill for at least 20 minutes.</td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">30 min</td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: justify;padding:1px;">To cook the rice, allow 5 minutes for it to come to the boil</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">40 min</td>
<td> </td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: justify;padding:1px;">20 minutes rice simmering time</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">50 min</td>
<td style="text-align: justify;padding:1px;">Heat a small amount of oil in a skillet, and arrange as many of the meatballs as possible in a single layer but without over-crowding them. Cook over medium heat for about 5 minutes, until brown on the outside but still pink inside. Probably you need to cook two times for such amount of meat. So, it will take 10 minutes at all.</td>
<td style="text-align: justify;padding:1px;">Puree the sauce through a sieve or in a food processor. Taste and adjust the seasoning if necessary.</td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
</tbody>
</table>
<p> </p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><h3>Why do this problem?</h3>
This is one of a series of problems which students might encounter in Food Technology. <br></br>
The problem originated in a real situation when someone cooked a beautiful meal, only noticing in the last five minutes that the recipe said 'Serve with rice' - by which time it was too late, if the rest wasn't to be ruined.<br></br>
Mathematically, it gives practice in organising information. One way to tackle it would be to draw a flow chart, then put times onto each stage. Alternatively, students could use a Gantt chart.<br></br>
<h3>Key questions</h3>
Do you have all the information you need to get started? If not, how can you find it?<br></br>
<br></br>
Are you going to start from the beginning of the recipe or the end, working backwards?<br></br>
<br></br>
Do you need to start with just one flow chart, or two?
<h3>Possible extension</h3>
<a href="http://nrich.maths.org/8073">Olympic Logic</a> gives students a good work-out in logical thinking.
<h3>Possible support</h3>
<a href="http://nrich.maths.org/7780">Tom Learns to Cook</a> is a simpler problem requiring scheduling stages in cooking a meal.</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><table style="width: 800px;border-spacing:1px;" border="1">
<tbody>
<tr>
<td style="text-align: center;padding:1px;">Timeline</td>
<td style="text-align: center;padding:1px;">Preparing Meatballs</td>
<td style="text-align: center;padding:1px;">Preparing Tomato and bell pepper sauce</td>
<td style="text-align: center;padding:1px;">Preparing rice</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">0 min</td>
<td style="text-align: justify;padding:1px;">Heat the olive oil in a skillet over medium heat. Add the onion and cook for about 5 minutes, stirring occasionally, until soft but not brown. Remove the skillet from the heat, and allow the onion to cool.</td>
<td style="text-align: justify;padding:1px;">Heat the olive oil in a pan over medium heat. Add the garlic, shallots and bell peppers and cook for 10 minutes, stirring occasionally, until the peppers are soft but not brown.</td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">10 min</td>
<td style="text-align: justify;padding:1px;">Add the onion to the lamb with the egg, lemon juice, cumin, cayenne, mint, salt and pepper in a large bowl. Use your hands to squeeze all the ingredients together. With wet hands, shape the mixture into small balls.</td>
<td style="text-align: justify;padding:1px;">Add the tomatoes, orange rind and salt and pepper and bring to a boil. Reduce the heat as far as possible and let simmer uncovered for 45 minutes, or until the liquid evaporates and the sauce thickens. This will take 50 minutes in all. </td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">20 min</td>
<td style="text-align: justify;padding:1px;">Place on a baking sheet and chill for at least 20 minutes.</td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">30 min</td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: justify;padding:1px;">To cook the rice, allow 5 minutes for it to come to the boil</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">40 min</td>
<td> </td>
<td style="text-align: center;padding:1px;"> </td>
<td style="text-align: justify;padding:1px;">20 minutes rice simmering time</td>
</tr>
<tr>
<td style="text-align: center;padding:1px;">50 min</td>
<td style="text-align: justify;padding:1px;">Heat a small amount of oil in a skillet, and arrange as many of the meatballs as possible in a single layer but without over-crowding them. Cook over medium heat for about 5 minutes, until brown on the outside but still pink inside. Probably you need to cook two times for such amount of meat. So, it will take 10 minutes at all.</td>
<td style="text-align: justify;padding:1px;">Puree the sauce through a sieve or in a food processor. Taste and adjust the seasoning if necessary.</td>
<td style="text-align: center;padding:1px;"> </td>
</tr>
</tbody>
</table>
<p> </p></mdoxml>
2
3
0
0
1
1
0
Hmm ... when should Tom have put the rice on ...
Creating a schedule to cook a meal consisting of two different recipes, plus rice.
Decision Mathematics and Combinatorics
Logic
Decision Mathematics and Combinatorics
Critical path analysis
Applications
Food technology
Applications
STEM - design technology
STEM mapping
STEM - Scheduling
STEM mapping
STEM - Real World
STEM mapping
STEM - Food Tech