Chance Simulator — Year 6 Statistics and Probability

Step 1

Choose your chance device

Pick the one that matches the game you are testing.

Step 2

Set up your spinner

Your sample space

Every outcome, with its probability written three ways
Outcome	Sections	Fraction	Decimal	Percentage

Teacher note. The three representations regenerate live, so changing one section of the spinner changes all three at once. That is the Lesson 2 point made visible. Ask what stays the same when the fraction is left unsimplified.

Step 3

Choose how many trials

A trial is one spin, one draw, one roll or one toss.

Step 4

Predict what will happen, then run it

Work out each probability yourself, then write how many times you think each outcome will come up.

Show me how to work this out

There are two ways to do it. They always give the same answer, so use whichever one you find easier.

Method 1 — divide, then multiply.
A spinner has 5 equal sections and 2 of them are red, so red is 2 out of 5.
Divide the number of trials by 5, then multiply by 2.
For 200 spins: 200 ÷ 5 = 40, then 40 × 2 = 80.

Method 2 — turn it into a decimal first.
2 out of 5 means 2 ÷ 5 = 0.4.
Then multiply by the number of trials: 0.4 × 200 = 80. The same answer.

Use a calculator for the dividing if you need one. The thinking is in choosing the steps, not in the arithmetic.

Now try it on your own set-up:

Teacher note. "Show me how to work this out" gives both methods — divide-then-multiply, and convert-to-decimal-then-multiply — then rebuilds the calculation live from the student's own set-up with the answers left blank. A student can copy the structure without being handed the number. Calculators are explicitly permitted for the division, so arithmetic does not become the barrier to the probability thinking.

With "Predict first" on, the fraction, decimal and percentage columns in the sample space are replaced by question marks until a prediction is locked in. Students have to derive the probability from the picture rather than read it off the screen — this is the estimation clause of AC9M6P01 doing real work. Turn it off only for demonstrations. "Run 20, 200 and 2000" produces exactly what assessment item A5 asks for and adds all three runs to My results.

What happened

Run the simulation to see your results.

What do "expected" and "observed" mean?

Expected is what the maths says should happen. If an outcome has a probability of 1/4 and you run 200 trials, you expect 1/4 of 200, which is 50.

Observed is what actually happened when you ran it. It is almost never exactly the same as the expected number, and that is completely normal.

Relative frequency is the observed count divided by the number of trials. It turns your result into a number you can compare with the probability directly.

Teacher note. The bar graph is the default because it shows the comparison the achievement standard actually asks for: observed frequency against expected frequency. Read it left to right, one outcome at a time — hollow bar is what the maths predicted, solid bar is what happened.

"How results settle" is the second view and it is optional. It needs teacher framing before students see it: the horizontal axis is stretched so each step is ten times the last, which no Year 6 student will infer unaided. It only becomes available at 200 trials or more, and it starts at trial 10 rather than trial 1, because the first few trials swing between 0% and 100% and that wobble misleads more than it teaches. Use it in Lesson 5 as a whole-class demonstration on the board, not as something students interpret alone.

Mystery dice

One of these two dice is fair. The other is weighted. Nothing on this screen tells you which one — you have to work it out from the evidence.

What does "weighted" mean?

Weighted means the die has been secretly changed so one face comes up more often than the others. It still has six faces and every face is still possible — they are just no longer equally likely.

On a fair die, every face has a probability of 1/6, which is about 17%. On this weighted die, one face is three times as likely as the others, so that face has a probability of 3/8, which is about 38%.

The catch: with only a few rolls, a fair die can easily look weighted, and a weighted die can easily look fair. That is what you are up against.

Rolls each time

Die A

—

rolls so far

Face	Count	Relative freq.

Die B

—

rolls so far

Face	Count	Relative freq.

Before you look. Write down three things: which die you think is weighted, how many rolls you needed before you were sure, and what result would have changed your mind.

The answer.

Teacher note. The weighted face is chosen at random, and which die carries it is decided fresh each time, so an answer cannot travel between groups or between your two classes. At 20 rolls, about three quarters of groups get it right, one in eight gets it wrong, and one in eight cannot separate the two dice at all — so expect roughly a quarter of the room to be wrong or stuck. At 60 rolls that rises to 97% correct. That is the lesson. Do not let anyone reveal until every group has committed a written answer including the trial count they would need to be sure.

My results

Every simulation you run is saved here automatically, newest at the bottom, so you can compare a 20-trial run with a 2000-trial run side by side. Print this page or copy it into Excel for your assessment.

Nothing is saved when you close this page. Copy or print your results before you finish, or they are gone.

Every run, in the order you ran them
Run	Device	Trials	Outcome	Probability	You predicted	Expected	Observed	Difference	Relative freq.
You have not run a simulation yet. Go to "Set up & run".

Reading the last two columns. Difference is observed minus expected — positive means more than you expected, negative means fewer. Relative frequency is observed divided by trials. Watch how these two behave differently as the trial count goes up. They do not do the same thing.

Teacher note. Those two columns are the crux, and students routinely conflate them. The raw difference usually grows as trials increase; the relative frequency settles. A student who writes "the difference gets smaller" without naming which difference has not yet understood item A6. Press them to name the column.