Applying the framework
The problem solving framework can be applied to help solve the following question.
Example
Each of the following sets of scales is balanced.
What size weight is needed to balance this set?
1. What do I have to do?
Read the question through twice. Highlight or underline the important pieces of information in the question.
2. What information do I need?
The fact that the scales are balanced means that the right-hand side of the scales is going to equal the left-hand side.
What is the question asking? The answer is going to be a weight, so the units will be in kilograms. It is not clear if the weight is a whole number or a decimal.
3. What information don鈥檛 I need?
Everything in this question is relevant to working out the answer.
4. What maths can I do?
The right-hand side of the scales is equal to the left-hand side so the scales are balanced.
This is the way into the question.
Step A
Look at the first set of scales.
Five square blocks weigh the same as 30 kg so divide 30 by 5 to find out what one block weighs.
\(30 \div 5 = 6 \:\text{kg}\)
Step B
Look at the second set of scales.
Two square blocks and 2 circular blocks weigh the same as 15 kg.
The square blocks are 6 kg each so take these away from the 15 kg.
\(15 - 6 - 6 = 3 \:\text{kg}\)
Divide this number by two to find out the weight of one circular block.
\(3 \div 2 = 1.5 \:\text{kg}\)
Step C
Use the answers from above to work out the weight of the third set of scales.
It has one square and three circular blocks.
\(6 + 1.5 + 1.5 + 1.5 = 10.5 \:\text{kg}\)
Therefore the weight needed to balance the third set of scales is 10.5 kg.
5. Is my solution correct?
It is important to check your calculations at the end. Check that all the scales balance if the square is 6 kg and the circle is 1.5 kg.
It may be useful to put numbers inside the squares and circles so that you have a clear image of the weights and numbers.
6. Have I completed everything?
It is important to check your calculations at the end. Check that all the scales balance if the square is 6 kg and the circle is 1.5 kg.
The answer should be a weight in kilograms. Ensure you have included the 鈥榢g鈥 units. Nothing else was asked for.