Listing Outcomes and Their Chances: a week of ready-to-teach maths

Five days of lessons for Year 5 Probability. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus experiment and outcome cards to match, twelve experiment cards to sort, 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 two card sheets once per pair. Have coins, dice, coloured pencils and scissors ready.
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. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: before asking how likely an outcome is, list every outcome once. Then look at how the experiment is made. If nothing favours one outcome over another, the outcomes are equally likely; if one outcome has more parts, more counters, more faces or a bigger section, it is more likely than the others. Year 5 compares chances in words and by counting; numbers for chances come in Year 6.

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

It builds on Year 4, where children ordered events from impossible to certain (AC9M4P01) and saw results vary when an experiment is repeated (AC9M4P02). Next in Year 5, children run experiments many times and use the results to compare outcomes (AC9M5P02); in Year 6, chances get numbers from 0 to 1 (AC9M6P01).

Materials for the week (one trip)

• From the classroom: a coin and a die per pair, two coins per pair for Day 4, an opaque bag and coloured counters to show the class, coloured pencils, scissors, this pack printed.
• For Day 3: one paper cup to toss, and one drawing pin to show (children do not handle it).
• Print once per pair: the experiment and outcome cards (Day 1) and the experiment cards to sort (Day 3).

Words for the word wall

chance experiment, outcome, possible outcomes, equally likely, not equally likely, favoured, more likely, less likely, fair, unfair

Dear families

This week in maths, Year 5 lists the possible outcomes of chance experiments and asks whether they are equally likely. A coin is equally likely to land heads or tails. A bag of 4 red jelly beans and 1 green one is not equally likely: red has four ways to be picked and green has only one.

Try this at home

• Find a board game with a die or a spinner. List its outcomes. Are they equally likely? How can you tell?
• Put 3 socks of one colour and 1 of another in a bag. Which colour is more likely to come out without looking? Why?
• Make up a dice game that is fair and one that is not. Which player would you rather be?

Our chance week, day by day

Fill one row a day. Write one experiment we looked at and its outcomes.

Printed from the free seegongsik Listing Outcomes and Their Chances teaching pack · seegongsik.com/au/y5/probability/AC9M5P01/pack

List the outcomes

A chance experiment is anything whose result cannot be known in advance, such as tossing a coin or spinning a spinner. Each possible result is an outcome. A list of outcomes names each one once: none missed, none repeated. The list depends on what is recorded. A spinner with four equal parts coloured blue, yellow, blue, green has 3 outcomes (blue, yellow, green); recording only ‘blue’ or ‘not blue’ gives it 2.

We are learning to

• list every possible outcome of a chance experiment, once each,
• tell outcomes apart from parts, counters and cards,
• see that the outcomes depend on what we record.

Success criteria

• I can list all the outcomes of an experiment, with none missed or repeated.
• I can explain why a spinner can have more parts than outcomes.

You need

The experiment and outcome cards (cut-out sheet 1), one set per pair, cut out. A coin and a die per pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the card match; start Session B with Part A.

Watch for these ideas

• Listing parts, counters or cards instead of outcomes, so one colour is written twice.
• Missing an outcome, often one with only one part or counter.
• Thinking an experiment has one fixed list, whatever is recorded.

Answers

• Cards: A 3, B 7, C 1, D 6, E 8, F 2, G 5, H 4.
• Part A: a. orange, blue, green (3); b. yellow, white, blue (3); c. 1, 2, 3 (3); d. B, A, N (3); e. green (1); f. small, big (2).
• Part B: Ava missed 6. Ben wrote orange twice; the outcomes are orange, blue, yellow. Cal is right: green, white. Part C: any colouring of the five parts that uses exactly three colours.

List the outcomes

A. List every possible outcome. How many outcomes are there?

B. Right, missed or repeated? Check each list.

C. Colour this spinner so that it has exactly three outcomes. List them.

Equally likely?

Outcomes are equally likely when each one has the same chance. Often we can tell by looking at how the experiment is made: a coin’s two sides are alike, a die’s six faces are alike, and a spinner’s parts are the same size, with each outcome on the same number of parts. A bag of 2 orange, 2 blue and 2 green counters gives 3 equally likely outcomes. The test: is any outcome favoured?

We are learning to

• decide whether the outcomes of an experiment are equally likely,
• give a reason from the parts, counters, faces or sides,
• change an experiment so that its outcomes are equally likely.

Success criteria

• I can say whether outcomes are equally likely, and why.
• I can make a spinner or a bag whose outcomes are equally likely.

You need

An opaque bag with 2 orange, 2 blue and 2 green counters (or any three colours, two of each). Coloured pencils. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by showing the bag again.

Watch for these ideas

• Thinking equal parts are enough, when one colour is on more parts than another.
• Saying ‘equally likely’ for any experiment where every outcome is possible.
• Thinking a spinner with many parts cannot have equally likely outcomes.

Answers

• Part A: a. orange, blue, green; yes: 1 part each. b. blue, white; no: blue 4 counters, white 2 counters. c. blue, green, yellow; no: blue 2 parts, green 1 part, yellow 1 part. d. orange, blue; yes: 4 parts each. e. 1, 2, 3, 4, 5, 6; yes: 1 face each. f. green, yellow, white; no: green 1 counter, yellow 2 counters, white 2 counters.
• Part B: a. two parts of each colour. b. add 2 blue counters, or take out 2 yellow ones. Part C: no; a die has one face for each number, so 6 and 2 are equally likely. A 6 can feel harder when a game needs one.

Equally likely?

A. List the outcomes. Are they equally likely? Why?

B. Make it equally likely

C. Mia says rolling a 6 on a die is harder than rolling a 2. Is she right? Explain.

Not equally likely

Outcomes are not equally likely when the experiment favours some of them: one outcome has more parts, a bigger section, more counters or more faces. From a bag of 5 blue counters and 1 orange, blue has 5 ways to be picked and orange has 1. Sometimes an object’s shape decides it, as with a bottle top, and only trying it many times shows which outcome is favoured.

We are learning to

• sort experiments into equally likely and not equally likely,
• say what favours an outcome,
• tell when looking at an experiment is not enough.

Success criteria

• I can explain why the outcomes of an experiment are not equally likely.
• I can name the favoured outcome and say why it is favoured.

You need

The experiment cards (cut-out sheet 2), one set per pair, cut out. A bag of 5 blue counters and 1 orange, a paper cup, and a drawing pin to show (children do not handle it).

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the sort; start Session B with Part B.

Watch for these ideas

• Thinking that ‘not equally likely’ means the less likely outcome cannot happen.
• Judging by the number of outcomes, not by how many ways each outcome has.
• Thinking a bag with more colours must be unfair, even when each colour has the same number of counters.

Answers

• Part A: equally likely A, D, E, G, J, L; not equally likely B (5 is on 2 faces), C (its shape), F (orange is half of the spinner), H (2 O cards), I (not 6 is on 5 faces), K (4 yellow).
• Part B: a. 3 (3 is on 3 faces); b. yellow (yellow is three quarters of the spinner); c. white (5 white).
• Part C: point up, point down. Probably not equally likely, but looking cannot show which is favoured: drop it many times and count each outcome (the next unit, AC9M5P02).

Not equally likely

A. Sort the experiment cards. Write the card letters.

B. These outcomes are not equally likely. Which outcome is favoured? Why?

C. A drawing pin can land point up or point down.

1. List the outcomes.   ______________________________
2. Do you think the outcomes are equally likely? Can you tell for sure just by looking?
3. How could we find out?

Which is more likely?

When outcomes are not equally likely, we compare them. Count the ways each outcome can happen: a die with faces 1, 1, 1, 2, 2, 3 has 1 on 3 faces, 2 on 2 faces, 3 on 1 face, so 1 is the most likely and 3 the least likely. On a spinner with sections of different sizes, compare the size of the sections instead. More ways, or more room, means more likely; the same number of ways means equally likely. The least likely outcome can still happen.

We are learning to

• compare outcomes by counting their ways,
• compare the sections of a spinner by their size,
• order outcomes from most likely to least likely.

Success criteria

• I can say which outcome is more likely, and give a reason.
• I can order outcomes from most likely to least likely.

You need

Two coins per pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the two coins.

Watch for these ideas

• Choosing a favourite colour, or the outcome that came up last time.
• Counting the sections of a spinner rather than comparing their size.
• Saying the least likely outcome will never happen.

Answers

• Part A: a. orange: 5 − 2 = 3 more counters. b. white (4), yellow (2), green (1).
• Part B: a. blue (half), yellow (three eighths), green (an eighth). b. green and orange are equally likely (3 parts each); blue is the least likely (2 parts).
• Part C: HH, HT, TH, TT; heads 2, 1, 1, 0. 1 head is the most likely: it has 2 ways (HT and TH); no heads and two heads have one way each.

Which is more likely?

A. Pick a counter without looking.

B. Spin the spinner.

C. Toss two coins: a first coin and a second coin.

Compare and make it fair

Comparing experiments brings the week together: list the outcomes, decide whether they are equally likely, and if not, say which is more likely. A game is fair when each player is equally likely to win. Roll a die: if Jai wins on 1 or 2 and Lena wins on 3, 4, 5 or 6, Lena has 4 ways to win and Jai has 2, so the game is not fair. Changing the set-up fixes it: Jai wins on 1, 2 or 3 and Lena on 4, 5 or 6.

We are learning to

• compare experiments by their outcomes and their chances,
• change a set-up so that its outcomes are equally likely,
• decide whether a game is fair.

Success criteria

• I can say which experiments have equally likely outcomes, and why.
• I can change an unfair set-up into a fair one and explain why it is now fair.

You need

A die. Mini whiteboards for the quiz. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by playing the dice game.

Watch for these ideas

• Calling a game fair because both players can win.
• Thinking an unfair set-up can be fixed in only one way.
• Mixing up the number of outcomes with the number of ways each outcome has.

Answers

• Part A: 1. orange, white; yes. 2. green, yellow; yes. 3. less than 3, 3 or more; no; 3 or more. 4. blue, yellow, green; no; blue. 5. odd, even; yes.
• Part B: a. the same number of each colour, such as 4 more white counters, or 4 fewer blue ones. b. change one orange part to blue: 2 parts each.
• Part C: no; yellow is on 3 parts and green on 2, so Ella is less likely to score. One fix: Ella also scores on blue, making 3 parts each.

Compare and make it fair

A. Compare the experiments.

B. Make it fair

C. Is the game fair?

Experiment and outcome cards

One set per pair (Day 1). Cut out all sixteen cards. Match each experiment card to the outcome card that lists all of its possible outcomes, each once.

Outcome cards

Teacher note: each experiment has exactly one outcome card. The matches are on the Day 1 plan.

Experiment cards to sort

One set per pair (Day 3). Cut out the cards and sort them into two piles: outcomes equally likely, and outcomes not equally likely.

Teacher note: six of each. The sort is on the Day 3 plan.

What we know: Listing Outcomes and Their Chances

Work on your own.

1. List every possible outcome of this spinner. How many outcomes are there?

   _______________________________   How many? ______
2. Pick a counter without looking. Are the outcomes equally likely?Yes □    No □

   Why? _______________________________________
3. Circle the experiment whose outcomes are equally likely.
   a. a spinner that is half blue, a quarter orange and a quarter green

   b. a card from ten cards numbered 1 to 10, recording odd or even

   c. a counter from a bag of 3 green and 1 yellow
4. Pick a counter without looking. Which colour is more likely? How many more counters does it have?

   ______________________
5. Order the colours of this spinner from most likely to least likely.

   ________   ________   ________
6. Roll a die. Ruby wins on a 6 and Tom wins on 1, 2, 3, 4 or 5. Is the game fair? Explain.
7. What could you add to this bag, or take out, so that white and green are equally likely?

   ______________________
8. Ty says: ‘This spinner has three colours, so each colour is equally likely.’ Is Ty right? Explain.

   ____________________________________

Answers and marking guide

Answers

1. green, orange, blue: 3 outcomes
2. yes: 2 counters of each colour
3. b: 5 odd cards and 5 even cards
4. blue: 7 − 2 = 5 more counters
5. yellow (five eighths), orange (a quarter), blue (an eighth)
6. no: Tom has 5 ways to win and Ruby has 1
7. add 3 green counters, or take out 3 white ones
8. no: orange is half, blue is a third, green is a sixth of the spinner, so orange is the most likely

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by counting the ways each outcome can happen rather than counting colours or guessing.

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: listing, equally likely, not equally likely, more likely, and comparing and making it fair.