### How the Guess and Check Method works

Learning about Guess and Check is a bit like playing the Guess-the-number game.

Your friend thinks of a number from 0 to 100 and you need to guess what the number is. What do you do?

You’ll probably start by making a random guess. If your guess is too large, your second guess will be smaller. If your next guess is too small, you’ll guess a larger number. This goes on for some time as you adjust your guess to fit the conditions and that’s when you’ll get the right answer!

Wait, whaaat? Does that mean I’ll have to keep guessing forever?

Of course not! Instead of making random wild guesses, we’ll need to learn how to make smart guesses. Although there is no hard and fast rule that stops you from making 10 or 20 guesses, we would want to limit ourselves to 2 rounds of guessing and checking before we get the correct answer on the third. We’ll see how to do that in a while.

### Examples of Guess and Check Math Problems

Let’s look at some examples of Guess and Check Math Problems!

What do they have in common?

There are 15 puppies and birds at a pet shop. There are 42 legs altogether.

How many puppies are there?

There are 27 coins in Mrs Lee’s wallet. The coins are made up of 20-cents and 50-cents coins. Given that the total amount in the bag is $9.90, how many 20-cents coins are there?

Did you realize that Guess and Check Math problems usually involve a total that’s made up of a few kind of things? Most of the time, we’ll be asked to find the number of each thing that make up that total.

In the first question, the given total is the number of puppies and birds. The question is asking us to find the number of puppies.

In the second question, we are given the total number of 20-cent coins and 50-cents coins and we are asked to find the number 20-cent coins.

### How do we Master the Guess and Check Method?

In order to do that, we’ll need to know how to:

- build a Guess and Check Table
- determine if our guess is too high or too low
- decide if we should increase or decrease our guess

When we are busy making guesses, it is easy to lose track of the numbers that we have tried along with their calculations. Therefore, it is important to have a table to help us organize our guesses in a neat visual way. One look at the table at any time keeps us updated of the guesses we have made and this lets us make future guesses more logically.

Let’s use this Guess and Check Math problem as an example to see how a table can be built.

There are 15 puppies and birds at a pet shop. There are 42 legs altogether.

How many puppies are there?

To start drawing the table, we’ll need to think about what we know from the question and organize them into columns.

From the first sentence, we know that we have some number of puppies and some number of birds. Let’s put them into 2 columns.

Next, we are given the total number of legs, so we’ll definitely have a column labeled as the total number of legs.

Is that all?

Well, not really.

We’ll need the table to make sense. This refers to understanding the relationship between the different columns and filling in the gaps. Here, we’ll need to show how we are able to derive the total number of legs that is stated in the last column.

We know that we can obtain the total number of legs by adding the number of puppies’ legs and the number of birds’ legs, correct? Let’s add those columns in as well.

Finally, we’ll include a “Check” column at the end of the table to help us keep track of our progress!

As a good rule of thumb, we would usually put the answer that we are guessing in the first column of the table. In this case, we are guessing the number of puppies which is already in the first column, so all is good. Otherwise, we will simply move the columns around and make sure they form a logical flow of thought from left to right.

Ideally, we will want to minimize the number of guesses to make. This can be done by making use of our observation skills and accuracy in estimation!

So a smart choice will be to start by GUESSing a number that lies somewhere in between. In this case, we have a total number of 15 pets, so “somewhere in between” would be half of 15. Bearing in mind that we can’t possibly have 7.5 pets, we will start with either 7 or 8. So let’s start by guessing that we had 7 puppies and fill up the columns from left to right accordingly.

If we had 7 puppies and each puppy has 4 legs, we’ll have 7 multiplied by 4 legs which gives us 28 puppy legs. Let’s put that into our table.

How many birds do we have?

To calculate that, we’ll subtract the number of puppies from the total number of pets. Subtracting 7 puppies from a total of 15 pets, we’ll get 8 birds.

Now, how many bird legs do we have? Let’s multiply the number of birds (8) by 2 since each bird has 2 legs. This gives us an answer of 16.

How do we know if our guess was correct? We find the total number of legs by adding the number of puppies’ legs to the number of birds’ legs.

Can you see that there’s a logical flow of thought as we move from the first column to the last? The calculations are done to help us CHECK if our guess is correct.

Now, here’s the exciting part! Let’s compare this to the total number of legs that is given in the question and the total number of legs that we get when we guessed that there were 7 puppies. Since 44 is more than 42, we know that our guess is slightly too high and it’s incorrect. So let’s record that in the last column. We can put a cross along with a short reason why our guess is incorrect.

#### C. Determining if our guess is too high or too low

How good our first guess is depends on how close it is to our target.

Now, to make a good second guess, we’ll COMPARE the total no. of legs that we obtain and see HOW FAR it is from the number that is given in the question.

In this case, our calculations showed us that our guess resulted in 44 legs, but we only need 42 legs. That’s a little bit more than what we need! This means that our first guess is a little too high.

#### D. Decide if we should increase or decrease our guess

Since we know that we need to reduce the number of legs, the question we’ll need to think now is whether we should we increase or decrease the number of dogs?

If you said “decrease’, good job! Hence, we’ll pick a smaller number for our next guess.

It’s time to make a second guess and repeat the steps. Instead of 7, let’s guess 6.

#### E. Guessing and Checking (Round 2)

Starting with 6 as the number of puppies, we’ll work systematically from left to right to find the answers for the various columns.

We should be able to get the values in the table (see right).

It only takes 2 tries to get our answer in this question, but it didn’t happen by chance. That’s because when we made the first guess, we were able to get some information about how far away from the answer our guess is and we were able to make a good second guess. See how making informed logical changes to our guesses gets us closer to the right answer?

### An alternative method – The Assumption Method

Although the Guess and Check method is introduced in Primary 3, students are taught the Assumption Method in Primary 4. This is because the problem sums in the Guess and Check questions in Primary 3 use smaller numbers and they are easier to work with. However, depending on your accuracy of estimation of making the guesses, some students may end up spending too much time figuring the right answer as their list of guesses grows longer. These give way to room for making careless mistakes.

Using the Assumption Method, on the other hand, involves lesser steps and is much faster once you get the hang of it. Lesser steps mean lesser room for careless mistakes and faster means more time to check for careless mistakes. It’s easy to understand really, you can always check out our explanation on the Assumption Method if you think you’re up for it.