D. Data · Data and Likelihood

Impossible, Possible, Certain: Making Predictions

D2.1 D2.2About 35 minutes

Learning goals

I can use the words impossible, possible, and certain.
I can use likelihood to make a prediction and a good decision.
I can predict whether another group of the same size will give similar data, and test my prediction.

Words to know

likelihood
How likely something is to happen.

impossible
It can NOT happen. It will never happen.

possible
It MIGHT happen. It could happen, or it could not.

certain
It WILL happen for sure.

more likely / less likely
Words to compare two possible events. More likely means it has a better chance.

prediction
A smart guess about what will happen, using what you know.

population
The whole group of people or things you collect data about, like "our class" or "the other Grade 1 class".

Let's get started!

Will it snow in Ontario in January? Will a dog drive the school bus tomorrow? Will the sun rise in the morning?

Some things will happen. Some things might happen. Some things can't happen at all! Today you will learn the math words for these.

The likelihood line: impossible, possible, certain.

Word	Meaning	Example
Impossible	It will NOT happen.	A moose will fly to the moon.
Possible	It might happen.	It will snow in Ottawa next January. (Very likely, but not for sure!)
Certain	It WILL happen.	Tomorrow will come after today.

Three likelihood words.

Possible can be likely or unlikely

Possible covers a lot! Some possible things are very likely (like snow in January in Canada). Some possible things are not very likely (like finding a loonie on the sidewalk today). They are still possible, because they could happen.

Complementary events: happens or does not happen

Every event has an opposite: it happens or it does not happen. These two are complementary events. They fit together like two puzzle pieces.

If something is certain to happen, then it is impossible that it does not happen.
If something is impossible, then it is certain that it does not happen.
If something is possible, then not happening is possible too.

Example: The sun will rise tomorrow is certain. The sun will NOT rise tomorrow is impossible.

Three bags of blocks. Bag A: 4 red. Bag B: 2 red and 2 blue. Bag C: 4 blue.

Worked example

Pulling a block from a bag

Without looking, you pull one block from each bag. Is getting a red block impossible, possible, or certain?

Bag A has only red blocks. Any block you pull will be red. Red is certain. Blue is impossible.
Bag B has red and blue blocks. You might get red or you might get blue. Red is possible. Blue is also possible.
Bag C has only blue blocks. There is no red block to pull. Red is impossible. Blue is certain.

Bag A: red is certain. Bag B: red is possible. Bag C: red is impossible.

Worked example

Making a prediction

A bag has 8 red counters and 2 blue counters. You will pull one without looking. Which colour do you predict? Why?

Both colours are possible, because there are some of each.
There are more red counters (8) than blue counters (2).
So red is more likely. Blue is less likely.

Predict red, because there are more red counters. But blue is still possible, so you could be surprised!

Using likelihood to make decisions

We use likelihood to make informed decisions every day:

Rain is possible today, so I will pack my rain jacket.
It is certain that it will get dark tonight, so I will bring my bike inside before bedtime.
It is impossible to be in two places at once, so I have to choose between the birthday party and the hockey game.

Will another group give the same data?

Ms. Roy's class (20 children) asked "What is your favourite fruit?" Next, they want to ask Mr. Singh's Grade 1 class, which also has 20 children. Will the data be the same?

Let's predict and then test.

Worked example

Predict and test

Ms. Roy's class: apples 8, bananas 6, grapes 4, oranges 2. Predict Mr. Singh's class.

Think: both groups are Grade 1 children, and both have 20 children. Children of the same age often like similar things.
Prediction: Apples will probably be the favourite again, and oranges will probably be the least. The numbers might not be exactly the same.
Test: Mr. Singh's class did the survey: apples 7, bananas 6, grapes 5, oranges 2.
Compare: Apples is still the most (7) and oranges is still the least (2). The numbers are close, but not exactly the same.

Our prediction was mostly right. The order was similar, but the frequencies were a little different. That is normal: different people give different answers!

Fruit	Ms. Roy's class (20)	Mr. Singh's class (20)
Apples	8	7
Bananas	6	6
Grapes	4	5
Oranges	2	2
Total	20	20

Comparing two populations of the same size. Source: surveys of two Grade 1 classes.

Different groups, different data

If you ask a very different group, the data could be very different. If you asked 20 grandparents "What is your favourite TV show?", the answers would probably be very different from 20 Grade 1 children's answers!

Just for fun

Is it impossible, possible or certain that a moose will do your homework tonight?

Impossible. But it would be very helpful!

Hands-on activity

Predict and test at home

Part 1: Bag game. Put 8 spoons and 2 forks in a pillowcase or bag (or 8 socks of one colour and 2 of another). Predict which you will pull out more often. Pull one, record it with a tally mark, put it back, and shake. Do this 10 times. Was your prediction right?

Part 2: Likelihood talk. At dinner, take turns saying something that is impossible, possible, or certain for tomorrow. Others guess which word fits.

Part 3: Two groups. Ask 5 kids (friends, cousins) and 5 grown-ups the same question: "Which do you like best: winter, spring, summer, or fall?" Before you ask, predict: will the two groups answer the same way? Then compare.

Your turn

Is it impossible, possible, or certain? A cat will lay an egg.

Is it impossible, possible, or certain? It will rain next Saturday.

Is it impossible, possible, or certain? If you drop a ball, it will fall down.

A bag has only green marbles. Getting a green marble is certain. What about getting a NOT green marble?

A spinner has 3 blue parts and 1 yellow part, all the same size. Which colour is more likely?

Your class of 18 liked dogs best. Do you predict another Grade 1 class of 18 will also like dogs best? Is it certain?

Weather says snow is possible tomorrow. What is a good decision?

It's okay to be surprised

Predictions are smart guesses. Sometimes they are wrong, and that is okay! When a prediction is wrong, ask "What surprised me? Why?" That is how we learn.

More practice: warm-up

Impossible, possible, or certain? A fish will ride a bicycle to school.

Impossible, possible, or certain? You will see a dog on your walk today.

Impossible, possible, or certain? Saturday will come after Friday.

A bag has 🔴🔴🔴🔴. You pull one without looking. Is getting red impossible, possible, or certain?

Fill in the blank: A smart guess about what will happen is called a ___.

More practice: on your own

A bag has 🔵🔵🔵🔵🔵🔵🔵🟡🟡. Which colour is more likely to be pulled? Why?

A bag has 🟢🟢🟢. Getting a red counter is impossible. What about not getting a red counter?

A spinner is half red and half blue. Is landing on blue impossible, possible, or certain? What about landing on green?

Is it certain that it will be sunny on your next birthday? Explain.

Rain is very likely this afternoon. What is a good decision for recess? Explain.

Challenge

Find the mistake! Leah says, "Finding a loonie on the sidewalk is impossible." Is she right?

Make a bag of blocks where getting yellow is certain. Then change it so yellow is possible but not certain. Then change it so yellow is impossible.

Ms. Roy's class (20 children) chose: hot chocolate 11, milk 6, juice 3. Predict which drink Mr. Singh's class (also 20) will choose most. Then his class says: hot chocolate 10, milk 7, juice 3. Was your prediction right? Are the numbers exactly the same?

Check your understanding

Quiz

A bag has 5 red blocks and nothing else. You pull one. Getting red is...

The day after Monday is Tuesday. Which word fits best?

A bag has 1 blue and 9 yellow counters. Which is more likely to be pulled?

Getting a blue block from a bag of only red blocks is...

Two Grade 1 classes of 20 answer the same survey. What will most likely happen?

You will have pancakes for breakfast tomorrow. Which word fits best?

A bag has 6 green and 4 red counters. Pulling a purple counter is...

For parents and teachers

What your child is learning: to describe likelihood with impossible, possible and certain, understand complementary events (if something is certain to happen, it is impossible for it not to happen), make predictions and decisions (D2.1), and predict and test whether a second population of the same size will give similar data (D2.2).

Common mistakes:

Calling very likely events "certain" ("It's certain I'll get a treat!"). Ask: "Could it possibly not happen?" If yes, it is possible, not certain.
Calling unlikely events "impossible". Finding a loonie on the ground is unlikely but possible.
Expecting a prediction to come true every time. Talk about how predictions are best guesses.
Thinking two groups must give identical data. Emphasize similar versus the same.

How to help: Use likelihood words in everyday talk (weather, games, routines). Play simple bag or spinner games and keep tallies. Before any family survey, ask your child to predict first, then compare.