Bob's Bird-seed

Here is a great problem adapted from Contexts for Learning Mathematics by Cathy Fosnot

The key to this problem is using the landmark fraction of 5/8 to find the rest of them.  Thinking about the numbers in terms of money is very helpful, as it contextualizes the problem into something that is more easily understood.  The next great aspect of it is that it forces the children into making a table, or a ratio comparison chart.

Where to start?  Some students will look right away at 5/8 and see that we can easily find the 90kg bag by just making an equivalent fraction (5 x 18 =90 and 8 x 18=144, therefore the 90kg bag costs \$144.

The easiest way to do this problem is to find the landmark fraction for 10kg a bag.  Though 10kg is not on the list, the fact that customers scoop their own bags leads you to believe that 10kg would be possible.  So, if we take our initial 5/8, and make an equivalent fraction (5x2=10 and 8x2=16, therefore a 10kg bag costs \$16).  With this information we can solve for 1kg, again by using equivalent fractions.  We find that 1kg costs \$1.60.  From here, the rest falls into place using equivalent fractions and multiplication (or division).

Great problem solving skills, though it will need a lot of previous scaffolding in using equivalent fractions.