2420 /www/nrich/html/content/id/2420/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>This is a $750$ ml bottle of concentrated orange squash.</p> <p align="center"><mdo:image height="176" align="top" width="69" alt="Bottle of orange drink" src="OrDrink1.gif" bgcolor=""></mdo:image></p> <p>It is enough to make fifteen $250$ ml glasses of diluted orange drink.</p> <p align="center"><mdo:image height="130" align="top" width="445" alt="15 cups of orange drink" src="OrDrink2.gif" bgcolor=""></mdo:image></p> <p align="center"> </p> <p>How much water is needed to make $10$ litres of this drink?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p><span class="editorial">You might have had to read this problem over several times before you understood it clearly - it wasn't easy! However, we have received many correct solutions and the majority of you tackled it in the same way. Esther explains how she went about solving the problem very well:</span></p> The answer is 8 litres.<br></br> <div style="clear: both;">First I found out how much juice there is in each cup of drink. The 750mls in the bottle makes 15 cups so each cup contains 750/15=50mls.<br></br> <div style="clear: both;">This means that each cup contains 250-50=200mls of water.<br></br> <div style="clear: both;">10 litres=10,000mls. We need to know how many cups this is. As each cup holds 250mls we need 10,000/250=40 cups.<br></br> <div style="clear: both;">Each cup holds 200mls of water so 40 cups will need 200 times 40=8,000mls or 8 litres of water.<br></br> <br></br> <p><span class="editorial">Esther also wrote:</span></p> <div style="clear: both;">There is another way using fractions.<br></br> <div style="clear: both;">The fraction of water in each cup is 200/250 or 4/5. This means that only 4/5 of the 10 litres is water. 1/5 of 10 is 2, so 4/5 is 8, and the answer is 8 litres.</div> <div style="clear: both;"></div> <p class="editorial" style="clear: both;">Excellent reasoning Esther, thank you. Pupils from Queens College Junior School used a similar method to the first way Esther described. Greg, Liam, George and Joe from Moorfield Junior School found a slightly different way:</p> <div style="clear: both;">First we found out how much orange squash was in each 250 ml glass. We did this by sharing the 750 ml into the fifteen glasses. This gave us 50 ml in each glass. We then knew that there must be 200 ml water in each glass (250-50).</div> <div style="clear: both;"><br></br> <div style="clear: both;">We then worked out how much water was in one litre of drink. This was 800 ml (200ml times 4).<br></br> <div style="clear: both;">Finally to find out how much water was in 10 litres we multiplied 800 ml by 10.<br></br> <div style="clear: both;">So the solution is that in 10 litres of drink there is 8000 ml (8 litres) of water. So we also worked out that there must be 2 litres of squash in the drink.</div> <div style="clear: both;"></div> <p class="editorial" style="clear: both;">Alex from Columbia Independent School, MO, USA worked at the problem in a similar way to Esther's second method:</p> <div style="clear: both;">Fifteen glasses contain 3750 ml because each glass has 250 ml and 250 * 15 = 3750 ml.</div> </div> </div> </div> </div> </div> </div> </div> </div> <br></br> <div style="clear: both;">Since we have only 750 ml of Orange drink, then we have 3000 ml, or 3 litres, of water.<br></br> <div style="clear: both;">So then each glass contains 200 ml of water which means that 80% of the diluted drink is water, because 200 is 80% of 250.<br></br> <div style="clear: both;">Then I found out that 4 glasses are equal to 1000 ml then I knew that 200 * 4 = 800. I knew that to prepare 1000 ml of orange drink I need 800 ml of water.<br></br> <div style="clear: both;">So 10 litres of orange drink need 8000 ml, or 8 litres, of water.</div> </div> </div> </div> <p><span class="editorial">Finally, pupils from Wilby School tackled the problem in a slightly different way again. Here is Georgina's solution:</span></p> <div>If you have a 750ml bottle of concentrated orange juice you can make 15 cups of juice. Each cup contains 250ml of juice.<br></br> <div style="clear: both;">I am trying to make 40 cups of juice, I need to know how much water I need.<br></br> If I make 15 cups of juice I need 750ml of juice and 3000ml of water.<br></br> <div style="clear: both;">If Imake 30 cups of water Ineed 1500ml of juice and 6000ml of water.<br></br> <div style="clear: both;">I cannot make 40 by adding 15 and 30 together so Ihave to make 10 cups. I only need to find out how much water Ineed to make 10 cups because if Iadd how much water Ihave in 30 cups and how much water Ihave in 10 cups together I will get 40 cups worth of water.<br></br> <div style="clear: both;">In 10 cups there is 2000ml of water. 6000ml + 2000ml = 8000ml.<br></br> <div style="clear: both;">There are 8000ml of water in 40 cups of juice.</div> </div> </div> </div> </div> </div> <p class="editorial">Thank you very much to all those who sent solutions - even if there isn't room here to mention you personally.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Orange Drink</h2> <br></br> <p>This is a $750$ ml bottle of concentrated orange squash.</p> <p align="center"><mdo:image align="top" alt="Bottle of orange drink" bgcolor="" height="176" src="OrDrink1.gif" width="69"></mdo:image></p> <p>It is enough to make fifteen $250$ ml glasses of diluted orange drink.</p> <p align="center"><mdo:image align="top" alt="15 cups of orange drink" bgcolor="" height="130" src="OrDrink2.gif" width="445"></mdo:image></p> <p align="center"> </p> <p>How much water is needed to make $10$ litres of this drink?</p> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <a href="http://nrich.maths.org/public/viewer.php?obj_id=2420&amp;part=index">This question</a> tackles proportion in a real context. It also needs systematic thinking to sort out the information and take a step-by-step route to the solution.<br></br> <h3>Possible approach</h3> <div>You could introduce this problem to learners simply as it stands and then, without saying anything more, give them a few moments to think completely on their own about what they might do. (They might like to jot some ideas down on paper or a mini-whiteboard.) Next, invite children to talk to a partner about a possible approach and suggest that they come to an agreement about how the problem might be tackled. At this stage, you could ask for some suggestions, or you might want to leave them to begin. However, after some time of working together, it would be good to draw attention to a range of different approaches by asking a few pairs to explain what they are doing. Emphasise that there is not just one way to go about this problem - you are looking for clear descriptions of a possible start. You could also invite pupils to share different ways of recording or jotting.</div> <br></br> <div>In a plenary session you could use this as an opportunity for some children to model a logical approach. In order to reach a solution to this problem, it is a matter of thinking about what we can work out from the information and then using this to answer the question.</div> <br></br> <h3>Key questions</h3> <div>How much juice is there in each glass of drink?<br></br> <div style="clear: both;">How much water is there in each glass of drink?<br></br> <div style="clear: both;">How many glasses of drink are there in a litre? In $10$ litres?<br></br> <div style="clear: both;">What fraction of the made-up drink is water?</div> </div> </div> </div> <br></br> <h3>Possible extension</h3> <div>You could extend this problem into a school-based context, for example, if every child in your school had a $250$ ml drink of this drink on sports day, how many $750$ ml bottles of concentrated orange squash would be needed? You might like to encourage some children to look at <a href="http://nrich.maths.org/6870&amp;part=">Mixing Lemonade</a>.</div> <br></br> <h3>Possible support</h3> <div>Before trying this problem, some children might find it helpful to look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=4784&amp;part=index">Blackcurrantiest</a> which looks at the concept of proportion.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>How much water is needed to make one <em>glass</em> of the drink?<br></br> How many glasses of drink are there in a litre? In $10$ litres?<br></br> What fraction of the made-up drink is water?</p> <br></br></mdoxml> 2 4 0 1 0 0 0 A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink? Fractions, Decimals, Percentages, Ratio and Proportion Calculating with fractions Fractions, Decimals, Percentages, Ratio and Proportion Calculating with ratio & proportion Admin Upper primary mapping document