Repeated Chance Experiments: a week of ready-to-teach maths

Five days of lessons for Year 3 Probability. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus a class results chart, spinners, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the class results chart large and cut out the spinners once; they are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. A chance experiment is something with outcomes we cannot predict, such as a coin flip. Repeating it and recording the results shows a pattern: about half heads over many flips. Results vary from run to run, and that variation is normal, not a mistake. Children will get different numbers from each other, so most answers this week come from their own data; the keys say what to expect.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 is a single flip, which cannot be predicted. Day 2 repeats it ten times, and Day 3 repeats the whole experiment to meet variation. Day 4 moves to a die with six outcomes, and Day 5 tries an uneven spinner and sees that many trials give a steadier pattern. It leans on Chance: Certain, Likely, Unlikely, Impossible (AC9M3P01) and Collecting and Recording Data (AC9M3ST01).

Materials for the week (one trip)

• From the classroom: pencils, scissors, paper clips, this pack printed.
• A coin for each child (play coins work), and a die for each pair.
• A soft mat or a tray for each pair, so coins and dice do not roll away.
• Print once, use all week: the class results chart (on A3 if you can) and the spinners.

Words for the word wall

chance, experiment, trial, outcome, heads, tails, predict, result, record, tally, repeat, vary, variation, equally likely, pattern

Dear families

This week in maths, Year 3 is doing chance experiments: flipping coins, rolling dice and spinning spinners many times, recording the results and talking about why they change.

Try this at home

• Flip a coin ten times together and tally heads and tails. Then do it again: is it the same?
• Roll a die twenty times and tally each number.
• Ask: can you tell what the next flip will be? Why not?
• Talk about why your results and your child’s class results might be different.

Our experiments this week

Fill one row a day: an experiment you tried and what you got.

Printed from the free seegongsik Repeated Chance Experiments teaching pack · seegongsik.com/au/y3/probability/AC9M3P02/pack

Flip once, flip again

A coin flip is a chance experiment with two possible outcomes, heads and tails. Before a flip, no one can say which will land, however hard they try: each flip is a fresh chance. Predicting and then flipping, ten times, shows how often a guess is right: about half the time.

We are learning to

• name the outcomes of a coin flip,
• predict, flip and record one result at a time,
• explain why one flip cannot be predicted.

Success criteria

• I can record each flip as H or T.
• I can explain why I cannot always predict a flip.

You need

A coin for each child (play coins work). A soft mat or a tray for each pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the flips; start Session B with what we found.

Watch for these ideas

• Thinking tails is due after some heads. The coin does not remember; each flip is fresh.
• Thinking a careful flip controls the result. Each fair flip can land either way.
• Counting a coin that rolled away or stood on its edge. Flip again onto the mat.

Answers

• Outcomes: heads and tails.
• Results: any ten H and T. Predictions are usually right about half the time, often 3 to 7 out of 10.
• Why: each flip is a fresh chance, and heads and tails are equally likely, so no one can always predict it.

Flip once, flip again

Predict, then flip

Write H or T for your prediction. Flip, write the result, then tick if you were right.

I was right ______ times out of 10.

Think about it

Can anyone always predict a coin flip? Why or why not?

Ten flips

Ten flips make one experiment: flip ten times, tally heads and tails, and write the totals. Heads and tails are equally likely, so about 5 and 5 is the likely result, but 4 and 6, or 7 and 3, happen often too. Comparing with classmates shows the same experiment can give different results.

We are learning to

• run ten flips as one experiment,
• tally the results and check they add up to 10,
• compare results with classmates and describe the difference.

Success criteria

• I can tally ten flips and check the total.
• I can say how my results and others’ are alike and different.

You need

A coin and a mat for each child. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the tally; start Session B with comparing.

Watch for these ideas

• A total that is not 10. Count the tally marks again.
• Thinking 6 and 4 means the coin is unfair. Results vary; that is normal.
• Changing a result to make it 5 and 5. Record what really happened.

Answers

• Tally: any heads and tails that add up to 10; 5 and 5 is the single most likely result, but others are common.
• Same: everyone’s heads and tails add to 10, and most are near 5 and 5. Different: the exact numbers.

Ten flips

My ten flips

Flip the coin ten times. Make a tally mark for each flip.

My group

Compare

What is the same about our results?

What is different, and why?

Run it again

Repeating the same experiment rarely gives the same result: one run of ten flips gives 4 heads, the next 6, the next 5. That run-to-run difference is called variation, and it is normal. Many runs on one class chart show the pattern: most runs land near 5 heads, and runs of 0 or 10 heads are rare.

We are learning to

• repeat the same experiment and record every run,
• describe the variation between runs,
• read the pattern in many runs on a class chart.

Success criteria

• I can record five runs of ten flips.
• I can explain why the runs are different.

You need

A coin and a mat for each child. The class results chart (cut-out sheet 1) on the wall. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the five runs; start Session B with Class 3B and the chart.

Watch for these ideas

• Thinking every run should give 5 heads. Results vary from run to run.
• Thinking a 2-head run is a mistake. It is unusual, not wrong.
• Leaving a run off the chart because it looks odd. Every run counts.

Answers

• My runs: any five runs whose heads and tails each add up to 10.
• Class 3B: most often 5 heads (4 runs); fewest 3; most 7; no run had 10 heads.
• Why different: each flip is a fresh chance, so each run comes out differently. That is variation.

Run it again

My five runs

Each run is ten flips. Record the heads and the tails, then add a mark to the class chart.

Class 3B’s runs

Class 3B did ten runs of ten flips. These are the heads in each run:

1. Which number of heads came up most often? ______
2. What was the fewest heads in a run? ______ The most? ______
3. Did any run get 10 heads? ______

Why are the runs different?

Roll the die

A die has six possible outcomes, 1 to 6, all equally likely. Roll it thirty times and the six tallies come out close, but almost never equal: one face gets a little ahead, by chance. That does not make it easier to roll; with many more rolls the counts tend to even out.

We are learning to

• list the six outcomes of a die,
• roll and tally thirty times, and check the total,
• explain why equally likely faces still get different counts.

Success criteria

• I can tally thirty rolls.
• I can explain why one face can come up most without being more likely.

You need

A die and a mat for each pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the rolls; start Session B with Class 3C and putting it together.

Watch for these ideas

• Thinking 6 is the hardest number to roll. Every face has the same chance.
• Calling a face lucky after it wins once. Counts vary by chance.
• Tallies that do not add up to 30. Count the marks again.

Answers

• My rolls: any tallies that add up to 30; each face usually comes up between 2 and 9 times.
• Class 3C: 2 came up most (12 times), 3 least (8 times), 60 rolls in all. No, 2 is not easier to roll: every face is equally likely, and the counts vary by chance.

Roll the die

Thirty rolls

Roll the die thirty times. Make a tally mark for each roll, then write the totals.

Class 3C

Class 3C rolled a die 60 times. This is what they got:

1. Which face came up most? ______ Which came up least? ______
2. Does that mean the face that came up most is easier to roll? Why?

Uneven, and more is steadier

When outcomes are not equally likely, the bigger part comes up more often over many trials. A spinner that is half orange and a quarter each blue and green should land on orange about half the time, but only over many spins: in a few spins anything can happen. The more an experiment is repeated, the steadier the pattern.

We are learning to

• predict the results of an uneven spinner from the size of its parts,
• spin, record, and compare the results with the prediction,
• explain why more trials give a steadier pattern.

Success criteria

• I can say which colour will come up most, and why.
• I can explain why more spins or flips help.

You need

The uneven spinners (cut-out sheet 2) with paper clips and pencils. The worksheet. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the spins; start Session B with Mia’s flips and the quiz.

Watch for these ideas

• Expecting each colour equally often. Orange is half the spinner, so about half the spins.
• Judging from a few spins. A few spins can surprise us; many spins show the pattern.
• Thinking more flips make heads more likely. More flips make the share steadier, not heads more likely.

Answers

• Prediction: orange, because it covers half the spinner.
• Spins: tallies that add up to 20; orange usually comes up about 10 times (often 6 to 14), blue and green about 5 each.
• Mia: 52 of 100 is closer to half than 7 of 10; with more flips the share of heads is steadier.

Uneven, and more is steadier

Spin twenty times

Was your prediction right? ______________

More is steadier

Mia flipped a coin. After 10 flips she had 7 heads. After 100 flips she had 52 heads. Which result is closer to half of the flips? Why does flipping more help?

Class results chart: heads in ten flips

Print this chart, on A3 if you can, and put it on the wall. On Day 3, after each run of ten flips, a child colours one box in the column for the number of heads they got, starting from the bottom. The chart grows into the shape of the class’s results.

Teacher note: most boxes usually fill near 4, 5 and 6; the 0, 1, 9 and 10 columns stay almost empty.

Uneven spinners

Cut out the four spinners, one for each group. Each is half orange and a quarter each blue and green. To spin, hold a paper clip at the centre with the point of a pencil and flick the clip.

Give each group a few practice flicks before counting; a flick that stops on a line is spun again.

What we know: Repeated Chance Experiments

Work on your own.

1. List all the possible outcomes when you roll a die. ______________________
2. How many heads did Jay get? ______ How many tails? ______
3. Jay flips ten more times. Will he get the same number of heads again? Why? ______________________________
4. Two classes each rolled a die 30 times. Will their tallies be the same? Why? ______________________________
5. A spinner is half orange and half blue. In 20 spins, about how many orange would you expect? ______
6. On the spinner in question 6, which is more likely: orange or green? ______________
7. After 10 flips, Ali had 8 heads. After 100 flips, he had 49 heads. Which is closer to half? ______________
8. Why do we repeat an experiment many times? ______________________________

Answers and marking guide

Answers

1. 1, 2, 3, 4, 5, 6.
2. 4 heads and 6 tails.
3. Maybe, maybe not: results vary each time, so the number of heads will probably be different.
4. Probably not: each set of rolls varies by chance.
5. About 10 (a few more or fewer is normal).
6. Orange: it covers half the spinner; green is a quarter.
7. 49 of 100 is closer to half.
8. To see the pattern: one try, or a few, can surprise us; many trials give a steadier result.

A quick three-level guide

Eight questions, three ideas. A child at standard expects results to vary and still sees the pattern that many trials show.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: one flip, ten flips, runs that vary, die rolls, and the uneven spinner with more trials.