[Pri20150519WNRT] Girls in the Stadium

Question

     Teachers!  Do you ever realise how you set questions?  This must be a pretty small stadium.  Or else a very sparse one.  Which stadium would allow you to book it for its use when there are relatively so few people?  Anyway, let us ignore that and get on with the “problem”.

     I am going to illustrate my Distinguished Ratio Units method, as usual.  You can use bar models if you want.  There are many ways to skin the cat, as they say.

Solution

     We organise the given information by setting up a table.  We work out that there are  560  males in total.  I used “triangle” ratio units for the adults and “circle” units for the children.  You can use anything you like, as long as you make it clear they are different.

My favorite tactic is to equalise one of the ratio units.  It is particularly easy to use units that with the number  1.  Let us multiply the left column by  2,  as shown below.  Imagine what would happen if each male was cloned to have two copies of each person.

The circle units are now equalised.  This serves as a stepping stone or a bridge to connect 2  “triangle”  units with  6  “triangle” units.  By comparison and subtraction, we figure out that  4  “triangle” units correspond to  400.  And we can work out the rest easily.

Ans:  There are  520  girls.

Final Remarks

     Distinguished Ratio Units are easy to use.  The strategy is:

          (1)  use different types of units marked by differently-shaped outlines

          (2)  look for a unit with “1”, multiply to equalise the unit of that type

          (3)  compare the other type of unit and solve that

          (4)  solve the rest of the problem

With this method, you do not need to worry about drawing and redrawing bars, or cutting bars into many smaller bars.  You can just concentrate on the problem modelling and thinking.

HeuristicsUsed

H02. Use a diagram / model    (use an effective one J)

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in another way

H11. Solve part of the problem

Suitable Levels

* Primary School Mathematics

* other syllabuses that involve whole numbers and ratios