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Make a Systematic List Strategy

Singapore Math Heuristics Made Easy

What does it mean to Make a Systematic List in Math?

Making a systematic list means writing all the possible solutions to a word problem in a logical and organized way and this is very useful when you are solving a word problem that has more than one answer to it.

How to Solve Math Problems by Making a Systematic List?

Let’s look at an example of a word problem that we can use the making a systematic list strategy.

You are given the 4 number cards as shown. How many different 2-digit numbers can be formed from them?

How would you go about solving this question?

Well, one way is to list down any possible numbers that comes to mind.

But the thing is, how do you know if you have exhausted all the possibilities? To make matters worse, there may also be times where you might repeat a number or skip a number without knowing it.

The worse thing that could happen when you are problem solving is to redo everything when you are halfway through the process. I’m sure you wouldn’t want to go through the frustration and waste time, correct?

That’s why in order to keep track of our solutions and make sure that we have covered all possibilities, it is important for us to do it step by step in a certain order.

Let’s see how to use the make a systematic list strategy to solve the problem that we had earlier on.

How to Make a Systematic List?

Looking at the 4 digits that we have, we are going to start listing the possible numbers by using the first digit, 9.

We are going to pair 9 up every possible digit moving from left to right. So looks like we have 92, 91 and 93, great! These are the possible numbers that can be formed starting with the digit 9. Following so far?

Once we are done with that, we are going to move on to the second digit which is 2 and repeat the same process in order again. So this time round, we’ll have 29, 21 and 23. See how nothing gets skipped or repeated?

And once we are done with that, we’ll do the same thing with the third digit. What numbers will you list? I hope you got 19, 12 and 13.

And because we have 1 more digit left, we are going to do the same for that digit as well. Going from left to right again, we have 39, 32 and 31.

Well done, everyone! We have gone through the digits systematically and listed all the possibilities 2-digit numbers can be formed from the 4 digits. By counting the numbers that we have, we can tell that we have 12 2-digit numbers can be formed.

Making a Systematic List by Branching

Besides using the systematic list in this form, we can also use branching to help us keep track of all the different ways we can form the numbers. Let’s see how branching works!

When we do branching, we are going to start by listing the digit 9. When we do that, we can tell that we have another 3 digits that we can pair it up with and they are 2, 1 and 3.

Following so far?

Then, we’ll list the next digit 1. What are the digits that can be paired with it? We have 9, 2 and 3.

And lastly, the digit 3 can be paired with 9, 2 and 1. Can you see that?

Because we did this in such an organized manner, we didn’t leave any room for careless mistakes.

Now, did you notice anything interesting about what we have? There are 3 possible ways to form a number for each card, correct? We can form 3 numbers that starts with the digit 9, we can also form 3 numbers that start with the digit 2 and the same thing applies for the digits 1 and 3 as well.

Take a minute to think about this. Can you think of a shortcut to find the number of 2-digit numbers that can be formed from the 4 cards? If you said multiply the number of cards by the possible number of numbers that we can form, you’re right! 4 cards x 3 ways each give us a total of 12 numbers and that’s our answer to this question!

Now that you have a better understanding of how to use lists to organize information and solve word problems, don’t forget to practice using this strategy with the questions in Practicle.

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