This is a word problem:
Mary has 6 bananas. She uses some of them to bake some banana bread. She now has 2 bananas left. How many bananas did she use? |
When children are presented with this type of problem, they are working on specific skills, in this case addition and subtraction. We would want them to recognise that this is a "take away" scenario: 6 bananas - some bananas = 2 bananas. This problem can be solved by applying an simple procedure.
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This is a more complex problem:
Seth invited lots of friends to his birthday party. After the party, 7 of his friends spent the night. There was one-fifth of the cake left over and the kids decided to have this as their late night snack. They decided it would only be fair if they all got an equal portion of the cake. They all wanted to know how much of the cake they would get for snack. What fractional part of the cake did each child get? Draw and label how much of the cake will be eaten by one child for snack. Explain your reasoning and decisions for how you drew this diagram. Seth claims that to find the answer you can use the expression 8 ÷ 1/5. His friend, Frankie, says that the expression would 1/5 ÷ 8. Who is correct? Why? |
Obviously, this question is much longer and has many different parts. We must hold some information in order to make sense of what the problem is asking us to figure out. Because there are many different aspects to this problem, the solution is not immediately evident, nor is the most efficient way to solve it.
This 'problem' could have been written as a simple word problem, but then we would not have to justify why our idea makes sense and the decisions we made in order to solve the problem. Being able to PROVE IT, is an important aspect of mathematics. It is not enough to just get an answer, we have to be able to explain why the answer makes sense in a given context. |