Dice may arguably be the most powerful mathematical manipulative in the world.  Their versatility is unmatched and I bet you’ve even got a few laying around your house.  Rolling dice can be used to teach and practice math skills in a variety of ways from preschool all the way through high school.  So what are you waiting for?  Grab a die or some dice and let’s get learning!

A die is one of the very first mathematical tools your little one can use!  They’re readily available and zero prep.  Keep reading to get your little one learning in minutes.

## Counting

In their most basic sense, dice can be used for counting.  Roll the dice and count the dots.  This simple activity engages the youngest mathematicians for quite some time. 6 sides and 21 dots to count in all on each die!  Rolling dice and counting the dots helps to reinforce one to one correspondence skills time and time again.  Grab a die, teach them to roll, and get your little mathematician building their skills.

Let’s try it out:  How many dots are in the circle?  Touch each dot with your child as they count.  1, 2, 3, 4, 5 – 5 dots in all!

Once rolling dice and counting the dots becomes old hat, it’s time to move onto addition.  Dice rolling is perfect for early addition practice as the dots are built in security – if you’re not sure how to add just count the dots!  Roll a 3 and a 6, count them all up to get 9.  Roll a 2 and a 4, count them all up to get 6.  What’s more, rolling dice makes practicing addition fun because the simple action of dice rolling makes the math seem almost like a game.

Let’s practice:

2 dots + 2 dots = 4 dots

6 dots + 3 dots = 9 dots

## Probability

Dice and probability go hand in hand in the math classroom.  There are so many applications and dice allow endless opportunities for practice.  Now here’s where things can get complicated! We can learn a lot of probability when working with dices.

### Simple Probability

One roll, six possibilities – again and again and again.  This makes die rolling the perfect way to practice probability.

The outcomes are not as overwhelming as a deck of cards yet not as simple as the flip of a coin.

For every roll, there is a

.

chance that you will roll a specific number.  What are the chances you’ll roll a 3 when you roll the die?

.

What are the chances you’ll roll a 6 when you roll the die?

.

Die rolling probability practice is simple but powerful!

Let’s break it down:  when you roll a die there are 6 possible outcomes.

What is the probability of rolling a 5?  There is one 5 in the chart above and there are six possible outcomes so the probability of rolling a five is one in six.  The same holds true for every one of the six possible options!

Let’s take it up a notch: How about the question –  What is the probability of rolling a 3 OR a 6?  Simply add the two simple probabilities together to get the answer.

The probability of rolling a 3 OR a 6 when you roll a die is

.

The same applies to all other combinations when you roll a die.

Look at it like this:  You have the same six outcomes from above.

Only this time you want to know the probability of rolling a 2 OR a 5.  How many of the pictures above show a 2 OR a 5?  Two.

So the probability of rolling a 2 OR a 5 is two possibilities out of six possibilities total or a two in 6 probability.  We can write it like this:

.

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### Complex Probability

If you want to step things up complexity wise, add a second dice to the equation.  When you are rolling two dice, the probability possibilities increase exponentially.

There is only one way to roll a 2 when rolling two dice (a one and a one), but there are many ways can you roll a 6 when rolling two dice and even multiple ways to roll a 3 when rolling two dice.  Check out all of the possible dice rolling combinations below.

We can look at these dice rolling combinations either numerically or visually.

Outcome List of Combination total
2 1+1 1
3 1+2, 2+1 2
4 1+3, 2+2, 3+1 3
5 1+4, 2+3, 3+2, 4+1 4
6 1+5, 2+4, 3+3, 4+2, 5+1 5
7 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 6
8 2+6, 3+5, 4+4, 5+3, 6+2 5
9 3+6, 4+5, 5+4, 6+3 4
10 4+6, 5+5, 6+4 3
11 5+6, 6+5 2
12 6+6 1

Now, if we want to find the probability of rolling a specific number on our two dice we must divide the number of combinations that will achieve the desired result by the total number of possible combinations.

When rolling two dice the total number of possible combinations is 36 since

We can continue and calculate the probability of rolling each specific number when rolling two dice.

 2 3 4 5 6 7 8 9 10 11 12

Let’s test it out:  Using two dice, what is the probability of rolling an 8?

If you reference the top chart you’ll see that there are eight possible combinations that add to 8.

Remember, there are thirty-six options in all.  All of that information leads us to the answer that there are eight possible ways to roll an 8 out of thirty-six total possibilities.  Simply put, an

probability.

### Even MORE Complex Probability

Throw in another die and things will get harder right away!  Rolling three dice is a perfect way to practice diagrams.  At this point, it’s gotten too complicated to figure the probability of a dice roll by simply counting the options.  We need a way to organize our options.  Enter the diagram.

Let’s try it out:  What is the probability of rolling a 4 on ALL three dice?

First, draw your diagram.  Then, multiply along the branches.

Like this:

Probability of rolling a 6 on dice one

.

Probability of rolling a 6 on dice two

.

Probability of rolling a 6 on dice three

.

There is a 1 in 216 chance of rolling a 6 on ALL three dice.

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