Certain, Likely, Unlikely, Impossible: a week of ready-to-teach maths about chance

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 chance word cards, event cards, 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. Cut out the word cards, the event cards and 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. Chance words sit in order on a line: impossible (it can never happen), unlikely (it probably will not), likely (it probably will) and certain (it will every time). An outcome is one thing that could happen: a coin has two, heads and tails. The more ways something can happen, the more likely it is, and a reason for a chance word always points to the outcomes, never to luck.

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 orders the four chance words, and Day 2 places everyday events on the line. Day 3 lists outcomes, which Day 4 counts to compare chances and judge fairness. Day 5 gathers it all into reasons. It leans on Collecting and Recording Data (AC9M3ST01) and Unit Fractions and the Whole (AC9M3N02).

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils, paper clips, this pack printed.
• A coin and a die for each pair, and a cloth bag with a few coloured counters or marbles.
• A long rope or a strip of masking tape across the floor, for a human chance line.
• Cut out once, use all week: the word cards, the event cards and the spinners.

Words for the word wall

chance, impossible, unlikely, likely, certain, outcome, possible, event, equally likely, fair, more likely, less likely, reason, because

Dear families

This week in maths, Year 3 is learning the words of chance (impossible, unlikely, likely and certain) and giving reasons for them.

Try this at home

• At breakfast, ask: will it rain today? Is that likely or unlikely? Why do you think so?
• Play a game with a die and talk about which numbers can and cannot come up.
• Put some coloured pegs or socks in a bag: which colour are you most likely to pull out?
• Ask your child to name something certain and something impossible.

Our chances this week

Fill one row a day: an everyday event, its chance word, and the reason.

Printed from the free seegongsik Chance teaching pack · seegongsik.com/au/y3/probability/AC9M3P01/pack

The chance line

Chance words sit in order on a line: impossible at one end, certain at the other, and unlikely and likely in between. Impossible means it can never happen; certain means it will happen every time. Unlikely and likely are the uncertain middle, leaning one way or the other, and most everyday events live there.

We are learning to

• name the four chance words,
• put them in order from impossible to certain,
• say what each word means, with an example.

Success criteria

• I can put the four words in order.
• I can give an example for each word.

You need

The chance word cards and the event cards (cut-out sheet 1). A rope or a strip of masking tape across the floor. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the human chance line; start Session B with the worksheet.

Watch for these ideas

• Using likely and certain as if they meant the same. Certain means every time, without fail.
• Thinking unlikely means impossible. Unlikely things can still happen.
• Calling something certain because it usually happens. Usually is likely.

Answers

• Order: impossible, unlikely, likely, certain.
• Meanings: 1 certain, 2 unlikely, 3 impossible, 4 likely.
• Examples: any sensible event for each word, such as night coming (certain) or a pig flying (impossible).

The chance line

Order the words

Write impossible, unlikely, likely and certain on the chance line, in order.

Match the meaning

My examples

Draw and write an event for each word.

Place the event

Placing an event on the chance line means asking: must it happen, might it, or can it never? “It will get dark tonight” must happen, so it is certain; “You roll a 0 on a die” can never happen, so it is impossible. Most events sit in between, and choosing likely or unlikely needs a reason: how many ways it could happen, or what usually happens.

We are learning to

• place everyday events on the chance line,
• choose between likely and unlikely, with a reason,
• write events for each chance word.

Success criteria

• I can place an event on the chance line.
• I can give a reason for my choice.

You need

The chance word cards and the event cards (cut-out sheet 1). The worksheet.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Choosing by what we want to happen. Ask what will probably happen, not what we hope.
• Saying impossible for something rare. Rare things are unlikely; impossible means never.
• A word with no reason. Say because: how many ways, or what usually happens.

Answers

• Events: 1 certain (night comes every day); 2 impossible (a die only has 1 to 6); 3 likely (most of the marbles are yellow); 4 unlikely (99 other tickets could win); 5 certain (a birthday comes once every year); 6 impossible (cats cannot bark); 7 unlikely (only 1 and 2 are less than 3); 8 likely (most people at school wear shoes).
• Own events: any likely and unlikely events, each with a reason.

Place the event

Write impossible, unlikely, likely or certain. Then write your reason.

Events of my own

Something likely:

Something unlikely:

List the outcomes

An outcome is one thing that could happen. A coin has two outcomes, heads and tails; a die has six, 1 to 6; a spinner has one for each colour. Listing every outcome comes before judging chance, and it shows what impossible means: an outcome that is not on the list, like a 7 on a die, can never happen.

We are learning to

• list every possible outcome of a coin, a die, a spinner and a bag,
• count the outcomes,
• spot an outcome that is impossible because it is not on the list.

Success criteria

• I can list all the outcomes.
• I can explain why an outcome is impossible.

You need

For each group: a coin, a die, a spinner (cut-out sheet 2) with a paper clip, and a bag with orange, blue and green counters. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after listing; start Session B with the impossible outcomes.

Watch for these ideas

• Leaving outcomes out. Check the whole thing: every face, every colour.
• Listing a colour once for each marble. Each colour is one outcome, however many marbles share it.
• Listing an outcome that cannot happen. A 7 is not on a die, so it is impossible.

Answers

• Outcomes: a coin: heads, tails (2); a die: 1, 2, 3, 4, 5, 6 (6); this spinner: orange, blue, green, yellow (4); a marble from this bag: orange, blue, green (3).
• Impossible: a die, 7 and 0; this spinner, purple; a marble from this bag, white.

List the outcomes

List every outcome

Which are impossible?

Circle each outcome that can never happen.

More ways, more likely

The more ways something can happen, the more likely it is. A bag of 5 orange marbles and 1 blue makes orange likely; with no orange it is impossible, and with only orange it is certain. Two outcomes are equally likely, a fair chance, when they have the same number of ways to happen: a die has three even faces and three odd ones.

We are learning to

• compare the counts in a bag to judge how likely a colour is,
• decide whether two outcomes are equally likely,
• explain whether a game is fair by counting the ways.

Success criteria

• I can say how likely a colour is from the counts in a bag.
• I can say if a game is fair, and why.

You need

Cloth bags and coloured counters. The spinners (cut-out sheet 2) with paper clips. Dice and coins. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the bags; start Session B with the games.

Watch for these ideas

• Judging by the colour on top. Count the marbles of each colour.
• Thinking a game is fair because both players can win. Fair means the same number of ways.
• Thinking a 6 is harder to roll than a 1. Every face of a die has the same chance.

Answers

• Bags, picking orange: A impossible, B certain, C likely, D unlikely, E equally likely as blue.
• Games: 1 fair (one head and one tail); 2 not fair (3 orange parts and only 1 blue); 3 fair (three numbers each); 4 not fair (one number against five).
• Make it fair: such as 1, 2 or 3 you win, 4, 5 or 6 I win.

More ways, more likely

Pick one marble

Is picking orange impossible, unlikely, likely or certain? If orange and blue are the same, say so.

Is the game fair?

Why that word?

A chance word is only half an answer; the reason is the mathematics. A good reason points to the outcomes: impossible, because there are no green marbles; likely, because 5 of the 6 marbles are orange. Reasons about luck, wishes or looks do not count.

We are learning to

• give a reason for a chance word, using the outcomes,
• tell a good reason from one about luck or looks,
• make a bag of marbles to match a chance word.

Success criteria

• I can explain a chance word with a reason about the outcomes.
• I can make a bag for each chance word.

You need

Coloured pencils. Bags and coloured counters. The worksheet. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the reasons; start Session B with the bags and the quiz.

Watch for these ideas

• Reasons about luck or wishes, such as “I feel lucky”. Point to the outcomes.
• A likely bag that is all blue. That is certain; likely means probably, not every time.
• Calling a half-and-half bag likely. Equal counts are equally likely.

Answers

• Reasons: 1 every face of a die is a number from 1 to 6; 2 there are no white marbles in the bag; 3 only 1 of the 6 parts is blue; 4 5 of the 6 marbles are orange; 5 a coin has one head and one tail.
• Bags, picking blue: certain, all 6 blue; impossible, no blue at all; likely, 4 or 5 blue; unlikely, 1 or 2 blue.

Why that word?

Give the reason

Make the bag

Colour the marbles blue or orange so that picking blue matches the word.

Chance word cards and event cards

Cut out the four word cards and the twelve event cards. On Day 1, lay the word cards along a rope for a human chance line; on Day 2, groups place each event card by its word and agree a reason.

Teacher note: impossible: A rock will start to sing; You will grow wings and fly to school; Your pencil will turn into a frog. unlikely: You roll a 6 on a die; You pick a blue marble from a bag of 1 blue and 9 orange; You pick the one gold sticker from a box of 50. likely: You roll a number bigger than 1 on a die; Someone in our class will lose a tooth this year; You will see the moon in the sky one night this month. certain: Thursday will come after Wednesday; You spin orange on a spinner that is all orange; It will be cold at the South Pole next winter.

Spinners to make

Cut out each spinner. To spin, hold a paper clip at the centre with the point of a pencil and flick the clip. The fair spinner has equal orange and blue parts; the unfair one has 3 orange parts and 1 blue. Children colour the third to make a spinner of their own.

A paper clip spinner works best on a flat desk; give each a few practice flicks before counting.

What we know: Chance

Work on your own.

1. Write the four chance words in order, from impossible to certain. ____________________________________
2. You roll a 9 on a die. Which word fits? ______________
3. The sun will set this evening. Which word fits? ______________
4. Picking a green marble from the bag in question 4 is ______________ .
5. List all the outcomes when you toss a coin. ______________________
6. On the spinner in question 6, is orange or blue more likely, or are they the same? ______________
7. Why is picking a white marble from the bag in question 4 impossible? ______________________________
8. Colour the bag in question 8 so that picking blue is likely.

Answers and marking guide

Answers

1. Impossible, unlikely, likely, certain.
2. Impossible: a die only has 1 to 6.
3. Certain.
4. Unlikely: 1 green and 7 yellow.
5. Heads, tails.
6. They are equally likely: 2 orange parts and 2 blue parts.
7. There are no white marbles in the bag.
8. 3 or 4 of the 5 marbles blue (5 blue would be certain).

A quick three-level guide

Eight questions, three ideas. A child at standard uses all four words correctly and backs each one with a reason about the outcomes.

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: the chance line, placing events, listing outcomes, more ways and fairness, and giving reasons.