Guess and Check

Most students I’ve encountered shun away from using the Guess and Check strategy. Its name itself is a misnomer and contributes to them misunderstanding how to use the strategy. It’s a powerful strategy that requires no guessing, but rather, a few systematic steps. Guess and Check questions appear frequently and will reward 4-5 marks to the student who would take the effort to learn it.

Scenario A

204 eggs were packed into big and small cartons. Each big carton contained 12 eggs and each small carton contained 6 eggs. There were 8 more big cartons than small cartons. How many big cartons were used?

In this scenario, the question does not give us the total number of cartons.

Target: To find the combination of small and big cartons such that the total number of eggs would be 204.

Step 1: Draw the table.

Step 2: We work out the next row by adding 1 to each carton type and find the total number of eggs.

This means from a total of 114 eggs, it would take 5 more rows to reach a total of 204, our target.

Step 6: Fill in the table to test and confirm that we got our target.

As you can see, we hit the target. To answer the question, 14 big cartons were used.

Scenario B

Mrs Tan bought 60 goldfish and angelfish altogether. Each goldfish cost $28 and each angelfish cost $7. She spent $70 more on the goldfish than the angelfish. How many goldfish did Mrs Tan buy?

In this scenario, the question gives us the total number of fish.

Target: To find the combination of goldfish and angelfish such that the difference in costs would be $70.

Step 1: Draw the table.

Step 2: We work out the next row. As the difference in costs in the first row is more than the target, we need to decrease it. We do so by decreasing the number of the more expensive goldfish by 1 and increasing the number of the less expensive angelfish by one. The total number of fish should always be 60.

This means from a difference of $630, it would take 16 more rows to reach a difference of $70, our target.

Step 6: Fill in the table to test and confirm that we got our target.

Again, we hit the target. To answer the question, Mr Tan bought 14 goldfish.

As you can see, there is no guesswork involved. One simply needs to figure out which scenario applies and carry out the respective steps. However, knowledge is half the battle. At the end of the day, practice makes permanent!

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