How to explain the concept of a variable to a 9-year old?

Question

My 9 year old daughter is heavily interested in science, robots, computers, … She asked me if I could teach her how to program a computer. So, we started with Scratch, a programming language specifically designed for kids.

She likes it a lot, and she enjoys getting visual results fast. Now we came to the point that you need a variable, and I have realized that she has not yet understood what a variable is. Of course, at school, they didn't have the concept of variables in mathematics yet (mind you, she is 9 years old).

I remember that when I learned to program, I was 12 years old, and I had a hard time grasping that, too. Although I'm a professional software developer, and I help other people a lot to learn to program, I find it very difficult to explain it to her in a sense, that she can understand, and that is suitable.

Of course I can say:

It's like a box, where you put the number 9 into it. If I ask you how old you are, then you don't say "9", but you give me the box, and I am going to look it up on my own.

That's an analogy, and she understands it, but it's difficult for her to transfer this idea to Scratch code. It doesn't feel correct.

If I say

It's just a name for a value, and everywhere where you normally would use the value itself, you can now use the name. This has the big benefit that you can change the value, but keep the name.

it feels correct, but it's not easy to grasp any more. To cut a long story short: In contrast to a loop (do this and that for a given number of times) or a decision (if X then Y), variables are way more abstract.

So, how would you explain the concept of a variable to a 9 year old, in a way, that it is easy to grasp AND correct at the same time, i.e. it has a direct relation to writing code?

Answer 1

Buffy's lovely answer shows well how two variables can refer to the same thing, but since we are in early cognitive development and working with Scratch, in which you can't pass parameters, and can't arrange for two different names to refer to the same instance/spawn, I wouldn't focus my efforts on that point yet. What matters is the idea of a holding place and mutability.

These concepts are hard to describe in a way that a 9-year-old would already know how to mentally model, but one very similar idea with which they are already familiar is the idea of a "role".

The President of the United States is currently Joe Biden. (You should substitute the head executive leader of whatever country your child lives in for this example.) But a few years ago, it was Donald Trump. Later, it could be Donald Trump again, or someone else entirely. When important things need to go to the president, they go to whoever is the president right now. They don't go to Donald Trump any more, and some day, they will no longer go to Joe Biden. But they always go to the President.

So, to put this into Scratch, we can make a String in scratch called President, and then we can use the set box to set President to "Joe Biden". We can then make an item in the main field that behaves as a button, that changes that variable to [insert your child's name here].

Now, we can create another value, called x, and set that to a zero. Now, when you press the button, change x by 4, and we can watch the variables change. Press the button 10 times, and the value becomes 40.

So, what can we say about x? Sometimes we say that x is 40, but is it really? Or does it just hold 40?

This is the most important early understanding to arrive at when describing a variable. When we say that x is 40, what we really mean is that x holds 40.

Answer 2

My usual explanation is related to names; specifically names of people. People have names. The names are not the people, but can be used to refer to the people.

Some people don't have any names at all. This is common just after birth at least, before the parents decide on a name.

Names can be changed. A person can have a name for a while and then later have a different name. So, different names can refer to the same person. Similarly we have come to rely on names known to only a few other people. A father might refer to his son as junior even if their names are not the same. Spouses often call each other honey without confusion.

Just as important, a name isn't necessarily permanently bound to a thing (person, value, object). A name like Sue could refer to one person in a given household, but a different person elsewhere. Also, a name like "kiddo" could refer to one child at a given moment, but to a different child, even in the same household, at a slightly later moment.

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Different names can refer to the same "object" at the same time. Different variables can reference the same thing at the same time.

A given name can refer to different objects, but not simultaneously. A variable can refer to one thing one moment but another at a different moment.

A given name can refer to a given object in one "place" but a different object in a different place.

Here "object" just means a value of some kind, not necessarily an object in an OO language. It could even refer to an operation, depending on the language.

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A variable, like a name, is an association between a word (more technically a symbol) and a value. Assignments in many languages establish the association. The association is valid in a place (scope) and for a time (duration).

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However, if your daughter has been studying algebra, you will need to make clear that what a mathematician calls a variable is quite different from what a computer scientist does.

In CS, a variable can actually vary, so the term is much closer to the truth. In math, especially algebra, the word variable is often used for an "as yet to be determined" but definite value (or set of values). It doesn't actually vary. Mathematicians also call them "unknowns", but that just means "not yet known until we solve this thing" but still, a definite value. In CS, variables have definite but changeable values. They are never "unknown" to the computer, but may be to the programmer who isn't actually tracing the program.

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A note on "sameness".

When we say $x = 3; y = 3;$ we don't imply that there are two threes.

When we say $x = 3; ... x = 4;$ we don't imply that three has somehow become four.

In the first we simply mean that we have two distinct references (names) for 3 and in the second we mean that the (old) reference to 3 is now a reference to something else.

While every experienced programmer understands this, it can become a bottleneck for a novice. Three is three.

Answer 3

What about this?

You have a lot of values that you need to remember, so you put a label on each one (a little piece of paper to remind you what this value means) so you can find the value easily when you need it.

Answer 4

The variable that children are most familiar with is score: whether in computer games, sports or board games, a child will almost certainly understand that a score is a value that is clearly not constant.

Variables are abstract, but using familiar examples turns this into something easy to grasp.

Once numeric variables are understood, you can extend the metaphor to cover string variables in a related example, e.g. the word to guess or the player's name.

Answer 5

Memory is a linear sequence of storage locations.

Like a lined sheet of paper.

Take a lined sheet of paper and choose a line.

In the left margin, write a label.

The variable is that label - it gives a name to a spot.

Now look for the label and write something to the right of the margin.

That is assignment.

Answer 6

I just saw Buffy's answer so all credits to @Buffy and though I could simplify it with one word in a way that 9 year old me would have understood.

(Although bear in mind I was also mucking around with Visual Basic 6 at 9 years old so this could also be very inaccurate & harder to grasp)

A nickname.

x = "the name of the program in scratch";

x is the nickname of what you're making in scratch

A way to implement this (not sure if possible in Scratch as I've never used it): Make X the title of the application/game/program and tell her to change the program's nickname (x) and then the programs full name/first name.

It might also help to explain the possibility of errors (if any are possible), example being, rename the x variable where it's defined, but not referenced, then watch the errors pop up for unknown variable 'x' because you "changed the 'nickname' without telling anyone"

Answer 7

It might be a bit indirect but around that age I bootstrapped myself from fill in the blank math problems through basic algebra to more generalized variable use.

eg I started with having been given problems like:

5 + __ = 9, what number goes in the blank?

From there naming the blank to get to basic algebra problem:

5 + X = 9, solve for X.

From there a programming variable just lets you use the same place holder repeatedly. (While the same is true of variables in math systems of equations, etc are probably a bit too advanced for the average 9 year old.)

Answer 8

If I remember correctly, Scratch has two kinds of variables - object-bound and global. When teaching my son about Scratch, at the time of introducing variables I told him he had been working with object variables/properties the whole time: the position x and y (and to a lesser extent the object sprite/appearance (not sure what it is called in the English version of Scratch)).

From there it was easy to introduce more (custom) variables as more properties of the corresponding character - whether the monster is alive or not, how much energy it has, etc.

The general concept of variable (not bound to a specific object) can follow later: instead of "something we know about an object", talk of "something we know".

Answer 9

If this child plays Minecraft, you can try the following analogies:

• A variable is like a chest with a sign next to it. You can put stuff into a chest (assignment). This "stuff" in the chest is the value of the variable.
• A function is like a workbench, which transforms inputs (like wood) into the result (like wood planks in Minecraft).

It is also helpful to explain to the child that the assignment operator (=) is better represented by an arrow (<-).

Then it becomes more logical:

var chest;

chest = "some value"; // chest <- "some value";

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A completely different strategy would be to learn the assignment construct by heart. Of course, she should only learn the building blocks (e. g. the syntax and meaning of assignment to a variable) of programming by heart, NOT the solutions. You can add an Anki card with the following contents:

Question: If you execute the statement

var chest = "bla";

what will chest contain thereafter?

Answer: Text (string) "bla".

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Finally, repetition is your friend. My child started to understand these concepts after we've done several algorithm lessons on FreeCodeCamp. I cannot remember how often I repeated the concept of assignment to my child (always in a different programming problem) until he started to understand it.

Answer 10

The box analogy seems good to me. If you want to continue the programming "language" analogy, variables are pronouns. In English, we rely on people using context to figure out what a pronoun refers to, but in programming we explicitly tell the computer what the pronoun refers to. You could have variable names like "it", "that", "the_thing", "the_other_thing" to reinforce that.

Something else to consider is to ask her how to do something. "Play dumb", so she has to be really explicit. If you choose the task well, she will repeatedly say things like "Take the thing that you got in step 4 and ..." This will then lead to the concept of "What if we could just use some short name, instead of having to say 'the thing you got in step 4' each time?"

Answer 11

Honestly all these analogies are extremely confusing. The box analogy was the best. I would just add to it.

You have a box that has its entrance restricted like those block match toys for babies (to match shapes - for example they only take circles, or stars, etc). Some boxes only take stars (int), squares (string) etc. The box is small and only has enough space to fit one shape.

But your box has certain properties. The bottom of the box has a one of these restricted opening to allow blocks to be pushed out the other side. So because the box is small, if you try to push another star into the box when there is already a star in there, it pushes the old one out and then only the new one is inside. This handles the idea of replacing values. And then of course types are explicit. If you try to put another shape into the box it wont fit.

When you want to use the item you stored away in the box, you tell your program (assistant) to go fetch the box from the closet and bring it back to you so you can see what's inside. If you don't use the box as storage your program (assistant) is kind of forgetful (really old assistant) and may misplace the information.

So this is why you store important things you want to remember inside the boxes.

I think that covers all the bases. That is how I would explain variables.

This seems like a very straightforward analogy. There is no abstraction which means even a kid can understand it in terms of real physical things. Children tend to have issues understanding abstraction, which is why algebra is generally left for when their brains are more developed. So this real world simple comparison should be understandable.

Answer 12

On Steam is the game Human Resource Machine. While it is a game it is played using simple programming commands as blocks like Scratch, has an input and output conveyor and several places to hold intermediate calculations or values, think variables. Latter in the game you can even name the locations.

While some of the problems are too hard for someone 9 years old, the upside of the game is that it gives you a visual representation to the abstract concept of a variable. It also has a character that moves the boxes around and performs simple operations such as add based on the commands.

As such when I read your question what I see as the true question is how do I get a 9 year old to understand a variable as an abstract concept. The game gives helps in that it gives the player a concrete and visual representation of a variable as something concrete being interacted with the game character. Once the player understands what a variable is, they can abstract that away in the way professional programmers do with many concepts.

Also I would not consider a variable as the first abstract concept a child learns but the concept of words and numbers. The words are typically one word to one concrete item. A number is one value to a count of concrete items. A number can also be a way to give a unique name to group of similar items. A variable in one of its simplest is one word to one item that has similar properties or relationships but that can be replaced as time progresses.

When I introduce variables I state that a variable has a name but in some languages also has a type. So in teaching variables it can help to also introduce the concept of type.

Answer 13

There are a number of fine answers already here. This is how I thought of doing it, and it might provide another alternative that should be suitable for a 9 year old, and possibly younger. It should be something that gives a good visual image for the child to picture mentally.

If I were speaking to the 9 year old:

Say one day you decide you're really curious about the number of blue cars that pass your house on a typical day. That makes you think about the red cars, too, and the total number of cars.

So, you get three cups - a blue one, a red one, and a clear one. Also you get a big stack of pennies. You sit on the porch all day. Every time a car goes by, you put a penny in the clear cup. If the car is blue, you also put a penny in the blue cup. If the car is red, you also put a penny in the red cup.

At the end of the day, you count the number of pennies in the blue cup. That's the number of blue cars that went by. You do the same thing with the red cup, and that's the number of red cars that went by. Finally, you count the pennies in the clear cup, and that's the total number of cars that went by.

The cups are variables, and each has a name - the blue cup is a variable named blue-cars, the red cup is named red-cars, and the clear cup is named total-cars. Each variable holds a number, the number of pennies in the cup.

Oh, and by the way, you're the program. We can empty the cups and run you again tomorrow to count the cars.

There are other things you can do, too. You can add the number of pennies from the blue cup and red cup, and see how many red and blue cars there were combined. If you want to get really fancy, you could count the number in the clear cup, then subtract the red cars and subtract the blue cars to see how many cars there were of other colors that you didn't count.

Answer 14

I like to explain it as a placeholder. So that I don't have to read and write so much.

I have a friend named John Jacob Jingleheimer Schmidt. His name, John Jacob Jingleheimer Schmidt, is my name too. Whenever I go out with John Jacob Jingleheimer Schmidt, the people always shout. There goes John Jacob Jingleheimer Schmidt. John Jacob Jingleheimer Schmidt is my best friend. John Jacob Jingleheimer Schmidt likes to go down the slide at the park. John Jacob Jingleheimer Schmidt has brown hair.

Or I could just write at the top of the paper

JohnsName = John Jacob Jingleheimer Schmidt

I have a friend named JohnsName. His name, JohnsName, is my name too. Whenever I go out with JohnsName, the people always shout. There goes JohnsName. JohnsName is my best friend. JohnsName likes to go down the slide at the park. JohnsName has brown hair.

This often prompts "Can't I just say John instead?" and I tell them "Yep, we could even just say "J = John Jacob Jingleheimer Schmidt" and make it even shorter."

"Plus if John changes his name in the future we only have to change it at the top of the paper. "

Answer 15

In Python, Java, or JavaScript, I talk about the type system as an ecosystem of different species of smart data. Objects are self-aware chunks of memory to which you can send messages and which can do work for you. I will frame this discussion in JavaScript.

Example in Node

> console.log("foo".length);
3

As you know, it rapidly becomes tedious to do this with literals. That's when we do this.

> var x = "foo";
> x.length
3

The variable is like a phone number. It gives you a means by which you can communicate with its object. Assignment binds an object to a "phone number." On a deeper level, a variable knows WHERE its object is in memory and knows how to find it. Hey, that's like your phone. If you get on an airplane and fly to Des Moines, your mother can still dial the number and ring you even though you have moved. The key idea: A variable knows how to find its object. This is my initial explanation before I get into complexities such as scope.

Answer 16

A variable is just a box you put something in. And, if later you decide you want to put something different in the box, you can.

The reason I use this analogy is quite simple. As I explained to my daughter; the box doesn't change, only the contents. Further, the contents only change if and when you decide they should. I was going to expand the idea to take in constants (i.e, a box which can never be opened) but drove myself round the twist trying to figure out how the stuff got into the box in the first place!

Answer 17

I find the "box" aspect is far more important than the named aspect. Maybe it's personal bias. However, we can combine the two: it's a named box. So you can say "Go look in the 'object color' box."

If you're working with pure data (no objects), it may be effective to set up a white board, and mask off a few "boxes." Each box gets a name like "number of chores done today." Concepts like "Add 1 to the number of chores done today" start to become really meaningful that way! And it just so happens that the word for these spaces on the whiteboard is "box," which is similar to the 3d boxes you might put objects in.

Even better, it puts her in an excellent position to deal with the nuanced behavior of reference mechanics when she gets there. If you're used to thinking of variables as spaces on a whiteboard, writing references to objects, like referencing the members of your family by name, is easier. For many people, the jump to reference mechanics is a real struggle because they got used to the idea of "x is my bear, that's in a box on the shelf" rather than "x is a variable referencing my bear. Y also references the same bear." (I personally have struggled to help people with reference mechanics because it forces them to unlearn whatever models they used up to that point, and unlearning is hard)

You can even use different color markers for references and data. That starts to get them used to the idea that there is some fundamental difference between the word "dad" and a reference to Golo Roden.

Answer 18

Do you use a dry-erase board anywhere to keep track of chores, or a shopping list?

An erasable space is a great way to teach the use of a variable.

You can even get into data types!

Booleans - eg: a tick in a box or the words yes/no against a task trash taken out. I know one mum who had a checklist at the door, so ticking off everything on the list would be essential before going to school, then the list gets erased back to all false on getting home, ready for the next day.

Integers - have a box for number of times someone has to dry dishes this week, with the tally written next to it. That gives the concept of accumulating and rewriting a value.

A calendar on which you can only write or add stickers is a WORM (Write Once Read Many) device. Without getting into the acronym, it's a good way to discuss the idea of being able to change something vs being able to get a value from it.

Answer 19

I'm not sure there's a "magic" explanation you can give her such that she will achieve "crystal clarity." I think with most people, and especially with kids, you need to demonstrate this and then "let it sink in." One of the first programs I wrote (guided by my then much older IBM 370 systems programmer brother-in-law) specifically to learn what variables are and how they are used computed Fibonacci numbers. I think we used Fortran back then. You get the idea though.... you have a 3 variables, sum, num1 and num2. You know the rest... Get your daughter to write a program that does that. Even help her write it. A lot. Just involve her in the writing and show her how it dumps out:0, 1, 1, 2, 3, 5, 8, ...

It will sink in.

Answer 20

I remembered an exercise for children in the Etoys-System I read about some time ago. It does that not by explaining what a variable is but by introducing the need for variables.

In the exercise children create a car in the Etoys-System (it's based on Squeak) that can drive around on the screen. They also create a steering wheel which can be used to steer the car.

This demostrates the need for variables because the facing of the wheel is connected to the facing of the car. It connects two properties of the micro-world without specifying what the value of the properties is.

You can find the paper with the exercise at http://vpri.org/pdf/rn2005001_learning.pdf says it is a good way to teach about variables. The exercise is on page 2.

Answer 21

I would use integer math. On a sheet of paper, set up a small arithmetic table with three columns marked X, Y and 10. Include a '+' between X & Y and an '=' between Y & 10. Fill in 10 down the rows, and start by plugging figures into the X & Y. So, row 1 will have 1 for X and 9 for Y, row 2 will have 2 for X and 8 for Y etc.

Have your daughter fill in the information for the rest of the rows and then point out that X and Y are the variables - because their values can vary - and can have a range of answers that are all correct.

This will not only point out the variable concept, but also help out when they throw algebra at her at school in a few years.

Answer 22

This answer is probably a little more advanced than you're looking for, but it might help somebody else in the future, especially if they're working in a Java-like language.

I really like this description: Cup Size -- a story about variables.

This describes variables as cups. You have different sized cups, which means they can hold different types of things. Each cup has a name written on it, so you can say "give me the thing in the large cup with a name of X".

It then talks about the more advanced idea of references, which it describes as remote controls. A remote control goes in a cup, and points to a TV.

It also has a follow-up article: Pass-by-Value Please, which describes the fact that one TV can have multiple remote controls, each in a cup, and swapping out one of the remote controls for one that points to a different TV doesn't change the original TV. Like I said this is more advanced than you care about, but it really helped me understand the idea of pass-by-reference vs pass-by-value back when I was still figuring that stuff out.

Answer 23

Well the question is of great importance because that of variable is arguably the most subtle but fundamental thing to learn, especially so at the reported young age. The subtlety remaining also for more mature people, so much that a great number of people using variables when programming are not so good in explaining what they are.

There is really no computation without variables, as if you want any input to be taken care of, you will need a variable (except particularly crazy languages designed specifically for the task). And it's acceptable that a computation without input is not really a computation. Granted, technically you might want to compute many digits of $\tau = 2\pi$, and you don't need any input for it (or do you?), but the example is quite clearly pathological, not representative of the normal situation that we want to teach for, and we can avoid entering this realm. A computer that always does the same thing becomes boring soon.

So your points are really well thought out: a first explanation looking simple and wrong, and a second one looking correct but difficult. This is quite natural, being the concept actually difficult, it's not really possible to give a simple and correct explanation.

The box analogy is not really so bad anyway, and it may be useful for understanding. The main obstacle in this case I would say is the "why" should one care about such boxes? I am afraid that this problem is in big part a fault of the tool: this is the main reason I don't like scratch as a beginner's tool. Yes it's nice and funny and interactive and everything, but it just lacks the most important of the concepts: that of variable/input. Or it makes it unnecessarily difficult to learn about the concept.

I agree with what someone noted in the comments: when I was very young and learned about it, a variable was "a name that can/will be substituted with some arbitrary value". It's also incredibly correct. It was so immediate for the young me that I remember wanting to put variables everywhere, without having a clue what I was doing, it was just there where the magic happens, and the magic was what interested me. For what attains to the mechanism of variables, this is it. There are some people who do not understand this, but I have a very hard time imagining what might be missing, being it so natural for me. I guess in the specific context of your daughter, she might be capable of understanding, given what she is already doing. For others, maybe boxes work.

But the main point is still missing: why would we want to use variables?

The effective way to learn here is usually not by some explanation, but by examples. Conceive problems and situations where variables are needed, show the idea once or twice and then experiment with novel situations. As already noted, this might not appear extremely natural in scratch. If you instead find one or more interesting ways of doing it in that environment, please let me know because I'm very curious.

Of course, the name "variable" is also sometimes misleading if one is not careful: there is nothing varying, and any example situation that relies solely on changing values will fail to give a profound meaning.

What must be conveyed instead is the necessity for the code to manage different situations in a homogeneous way, which is nothing more than the idea of wanting some input.

For a much better structured pedagogical path in learning from absolute zero, playfully for young ages, forget scratch and see instead the great HTDP https://htdp.org/ .

Answer 24

Has she done basic algebra? "A white box has three marbles in it, and a blue box has four marbles in it. If I have six white boxes and five blue boxes, how many marbles have I got?" Is her maths up to this level yet? At age 9, I'd hope so.

You can also make life easier by calling the variables something meaningful, which is good programming practise anyway. So your variables would be "number_of_marbles_in_a_white_box", "number_of_marbles_in_a_blue_box", "number_of_white_boxes", "number_of_blue_boxes", and "number_of_marbles". Restrain your natural tendency to use shorter names.

Answer 25

The issue is that a variable is not just one thing -- it can do a variety of things -- and also, that variables do not exist in nature. Nothing else in a person's experience behaves in all of the ways that a variable can. So, you need a ramp that begins simply and describes the various variations of variables.

Early computers did not have any programming, they were circuits connected by cables. If you wanted a push-button to affect the computer, you used a wire to connect the push-button to a circuit. When Binary Coding came along, you could get the input from the button by reading a value from a numbered memory address. Assembly language allowed you to give that address a name. You could call it ButtonValue or something, and just test it with an IF statement. But you could also define another variable, like Input1, and put the value in there, along with some other input values and then feed that to some code you wrote. Now we have the idea of named locations, and assignment. Good, but not nearly far enough.

A collection of similar variables can be put together in an Array, and then a variable used to index through the array. Any child should understand that, because they have all stood in line and called out numbers one by one. Finally, there is the idea of indirection, that a variable can decide which variable to refer to. I could have a variable called Greeting, and based on the current time, put one of three other variables in it, holding values like: "Good morning", "Good afternoon" and "Good Evening". Add a variable for the student's name and this program will be able to greet anyone at any time. We used variables so that the strings (Good Morning, etc) can be easily changed, possibly at the direction of a variable called Language...

Nothing else in the world works that way, but with these simple examples, it should be clear to any nine year old. The problem then will be keeping them off the computer. I spent a lot of hours writing programs to output geometric figures in text on a PDP-11 terminal.

Answer 26

For a nine year old, you can say that a variable is a "change item", such as weather in the environment. On the other hand, if it proves too challenging to explain it, you can kindly postpone this subject until she is old enough to appreciate it. Bear in mind that kids at this age are not very good in abstract thinking. Try again when she is about 12-13.

Answer 27

First explain the kid meaning of variable as something that keeps changing (like weather). Then he will get idea about the word and then tell him, in CS how we assign a value to the variable and how we are able to change it afterwords