Model Method - Questions and Answers


Question posted by Cameron from country unknown:

Grade/Level : 5th Grade

There are three times as many ducks as sheep on a farm. All the ducks and sheep have 2400 feet altogether. How many more ducks than sheep are there?



Step 1: Since there are 3 times as many ducks as sheep, draw 3 boxes to represent 3 ducks and 1 box to represent 1 sheep. This means that for every 3 ducks, there would be 1 sheep. For the ducks, label each box "2 legs" and for the sheep, label each box "4 legs". Thus, each set of 3 ducks and 1 sheep has (3X2) + (1X4) = 10 legs.

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Step 2: Draw a dotted arrow to show that when we repeat the drawing of the set, we will eventually arrive at a total of 2400 legs.



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From the model,

2400 legs / 10 legs = 240 sets

Since there are 2 more ducks than sheep in each set,

240 sets X 2 more ducks in each set = 480 more ducks

Therefore, there are 480 more ducks than sheep altogether.