A PROBLEM SOLVING PLAN IN MATHEMATICS

Example :

You plan to ship 5 books to your brother who is studying in a boarding school.The table below shows the masses of the books. Is it possible to ship the books in 2 boxes, each with a mass of 6 kilograms or less? Explain. 

Reading and Planning

Read and Understand :

What do you know ?

The mass of each box must be 6 kilograms or less.

The table gives the mass of each book.

What do you want to find out?

Is it possible to put the boxes in 2 boxes so that each box has a mass of 6 kilograms or less?

Make a Plan :

How can you relate what you know to what you want to find out?

Check that the total mass of the books doesn't exceed 12 kilograms. If it does, you can't divide the books as you want.

Use the strategy guess, check and revise to choose books for each box.

Solving and Looking Back

To solve the above problem about shipping books, carry out the plan. Then check the answer.

Solve the Problem :

The total mass of the books :

1.4 + 2.1 + 3.8 + 1.9 + 2.5 = 11.7 kg.

So it may be possible to ship the books as you want. 

Now use the strategy guess, check and revise. Put the 3 lightest books in one box and the 2 heaviest in the other. 

The mass of the second box is more than 6 kg.

Try switching books B and E. 

The mass of each box is less than 6 kg.

Answer :

It is possible to ship the books in 2 boxes, each with a mass of 6 kg. or less. Put books A, D and E in one box and books C and B in the other box.

Look Back :

It makes sense that the box with 3 books contains the 2 lightest books and the box with 2 books contains the heaviest book. So, the answer is reasonable.

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