I can use very simple set notation to describe parts of the Venn diagram e.g. A intersection B

3

Band

Objectives

Hegarty

Maths Clip

D S M

4

I can use very simple set notation to describe parts of the _{Venn diagram e.g. A intersection B} 351 I can find and justify probabilities for outcomes of an

event in more complex problems.

351

I can apply the knowledge that the sum of probabilities of all mutually exclusive outcomes is 1 in more complex situ-ations.

351

Given a theoretical probability I can calculate an estimate for the number of times a given event will occur.

352

I can determine probabilities from frequency tables and two-way tables.

422

I understand the difference between experimental and theoretical probability.

356

I can draw frequency trees based on given information to show expected outcomes.

352

5

Given a theoretical probability and an experimental out-_{come I can make judgements about fairness.} 368 I can use a frequency tree to find a probability. 369

I can fill in more complex Venn Diagrams where multiple pieces of information must be inferred.

373

I can use very simple set notation in the context of proba-bility.

373

I can fill in more complex Venn Diagrams where multiple pieces of information must be inferred and subsequently calculate probabilities.

351

I can show given information on a probability tree dia-gram

373

I can determine the probabilities for 2 successive inde-pendent events using a probability tree diagram.

373

I can determine the probabilities for 2 successive inde-pendent events using a probability tree diagram, includ-ing contexts where combinations must be considered.

373

I can use a probability tree diagram to represent out-comes of dependents events (e.g without replacement).

Band

Objectives

Hegarty

Maths Clip

D S M

6

I can show and calculate with more complex information _{on a probability tree diagram including with more than 2} events or choices.

363

I can use a probability tree diagram or otherwise to cal-culate simple conditional probabilities.

361

I can fill in more complex Venn Diagrams where multiple pieces of information must be inferred, including with more than 2 sets.

351

I can compare the results of experimental probability with theoretical probabilities to make judgements about fairness in more complex situations.

356

I can use a tree diagram to calculate probabilities of com-bined dependent events (e.g. without replacement).

361

I can determine simple amounts of permutations with analytic methods e.g. using factorials.

352

I can determine simple amounts of combinations with analytic methods.

352

7

I can fill in more complex Venn Diagrams where multiple _{pieces of information must be inferred, including with} more than 2 sets and use this to calculate probabilities.

361

I can work with simple algebraic expressions for probabil-ities

5

Tier 3 Vocabulary Probability

Likely

Definitions

A branch of maths concerning numerical descriptions of how likely an event is to occur.

Having a high probability of something will occur

Date:

LO:

I can apply the knowledge that the sum of probabilities of all mutually exclu-sive outcomes is 1 with simple fractions and decimals.

Did you know…

Modelling probabilities by experimenting can help scientists predict the outcomes of random events.

Clip:

357

Tier 3 Vocabulary Sample Space

Outcomes

Definitions

Sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Possible result of an outcome.

Date:

LO:

I can create a sample space for two successive events e.g. possi-ble numbers when two dice are rolled.

Did you know…

Calculating probabilities let you work out if a game is fair.

Clip:

670

A) Find P (of getting a 3) = 2/36 (There are two 3’s out of 36)

B) Find P (greater than 8) = 10/36 10 numbers bigger than 8 (coloured in)

MISCONCEPTION

If events are random then the results of a series of independent events are equally likely, e.g. Heads Heads (HH) is as likely as Heads Tails (HT)

19

Tier 3 Vocabulary Sample Space

Outcomes

Definitions

Sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Possible result of an outcome.

Date:

LO:

Using the product rule for counting and combinations

Did you know…

Factorial in maths is written as !. So five factorial is 5!.

You work out factorials like this… 5! = 5 x 4 x 3 x 2 x 1 = 120 3! = 3 x 2 x 1 = 6

Clip:

352

We have listed all the

possi-ble outcomes.

So 3 starters and 4 mains

gives 12 possibilities.

How many choices of boys

are there? 10

How many choices of girls

are there? 12

So 10 x 12

5 people can play 4 other

people.

So, 5 x 4 = 20

They only play each other

once rather than home and

away so halve it!!!

21 A) 10 possible digits

B) As there is 10 possible outcomes for each digit it is 10 x 10 x 10 x 10 = 10000 C) 10 x 10 x 10 x 5 = 5000 (4th digit even so can only have 0, 2, 4, 6, 8 as the digit)

Tier 3 Vocabulary Relative Frequency

Outcomes

Definitions

How often something happens divided by all the outcomes

Possible result of an outcome.

Date:

LO:

Given a theoretical probability I can calculate an estimate for the number of times a given event will occur.

Did you know…

It is a GCSE requirement that pupils know packs of cards.

Clip:

352/356

27

Using relative frequencies to test bias

Example

If I flipped a coin 100 times, how many heads would I expect to get?

You would expect 50 heads and 50 tails. This obviously might not be the case but the more trials you do the more likely you are to get nearer to 50/50.

The more trials is always the most accurate result to use.

MISCONCEPTION

If I flipped a coin 10 times.

I get a head 4 times and tails 6 times therefore the coin must be biased.

Yes we would expect 5H and 5T but that is just expected probability.

If someone did this experiment 1000000 times and got 600000 and 400000 then you may say that this is a biased coin.

Tier 3 Vocabulary Intersection Union Set

Definitions

The middle of a Venn - both things. Everything of a Venn - all things.

The group of numbers/people you are using to place in Venn

Date:

LO

:

I can use very simple set notation in the context of probability.

Did you know…

Venn diagrams are used on the real world all the time. Here this is a Venn diagram describing how the Ameri-can governance works.

Clip:

373

Do Now

1) Expand A) 3(x + 7) B) 6(x - 2) C) 10(x - 1) D) x(x + 2) 2) Work out 1.4 x 2.3

3) Find the area of

4) Find the nth term of

35

MISCONCEPTION

Tier 3 Vocabulary Intersection Union Set

Definitions

The middle of a Venn - both things. Everything of a Venn - all things.

The group of numbers/people you are using to place in Venn

Date:

LO

:

Harder Venn diagrams

Did you know…

Clip:

373

Do Now

1) Expand A) 5(x + 1) B) 4(y - 6) C) y(x - 1) D) x(2x + 5) 2) Work out 2.1 x 4.35

3) Find the area of

4) Find the nth term of

Example(s)

With 3 it works the same. We can put 0 on the outside and 4 in the middle. Always go from the middle out.

So we look at the Spanish and French overlap. There is 9 but we have 4 who study Spanish and French as well as German. Meaning we have 9 - 4 = 5 who just study S and F. Now repeat for the others.

Tier 3 Vocabulary Frequency

Definitions

Number of times an event or a value occurs (total)

Date:

LO:

I can determine probabilities from frequency tables

Did you know…

A frequency tree can be used to record and organise information given as frequencies. This can then be used to calculate probabilities.

Clip:

422

Do Now

1) Expand

A) 6(c + 7) B) 5(a - 9) C) 2y(x - 5) D) a(a + b)

2) Work out

16 x 2.41

3) Find the area of

4) Find the nth term of

45

A person is picked at random, what is the probability the were female?

68/100 (female/total)

What is the probability a male liked ATC?

51

Tier 3 Vocabulary Frequency

Class

Definitions

Number of times an event or a value occurs (total) Another word for group

Date:

LO

:

I can determine probabilities from frequency tables and two-way

Did you know…

Two way tables are used everywhere as an easy way to display data. During the Covid Pandemic the Government used 2 way tables.

Clip:

422

Do Now

1) Expand and simplify

A) 5(x + 1) + 2(x + 4) B) 6(x + 3) - 2(x + 1)

2) Simplify

y7 x y2

3) Find the shaded area of

4) Find the first 4 terms of

53

A) 66/360 (Y8 BOY/TOTAL)

B) 66/208 (Y8 BOY/ TOTAL BOYS)

C) 66/110 (Y8 BOY/TOTAL Y8)

Tier 3 Vocabulary Independent Events

Definitions

An event that does not affect the other event. (eg flipping a coin and rolling a dice)

Date:

LO:

I can determine the probabilities for 2 successive independent events using a probability tree diagram.

Did you know…

The word probability comes from the Latin word ‘probabiltas’ which can have different meanings. In Europe it is a measure of ‘authority’ of a witness in legal cases.

Clip:

373

Do Now

1) Expand and simplify

A) 6(2x + 3) + 5(x - 4) B) 10(x + 1) - 3(x - 2)

2) Simplify

y9 x y21

3) Find the shaded area of

4) Find the first 4 terms of

59

MISCONCEPTIONS

Remember AND = X and then OR = +

So multiply your probabilities and NEVER get an answer bigger than 1.

Remember when multiplying decimals:

0.3 x 0.4 = 1.2

0.3 x 0.4 = 0.12

65

Tier 3 Vocabulary Dependent Events

Definitions

An event that is affected by the other event.

(eg eating a chocolate from a box of chocolates and then another)

Date:

LO:

I can use a tree diagram to calculate probabilities of combined de-pendent events (e.g. without replacement).

Did you know…

The oldest known dice ever excavated is 5000 years old. Dice used to be called ‘bones’ because they were made from a bone in the ankle of hoofed animals.

Clip:

361

Do Now

1) Expand and simplify

A) 9(5x + 1) + x(x - 2) B) 2(x - 9) - 6(x - 5)

2) Simplify

y3 x y-6

3) Find the shaded area of

4) Find the first 4 terms of

MISCONCEPTIONS

Remember probability is the likelihood BEFORE the pick.

So when it says 2 are chosen you give the probability before 1st pick and before 2nd pick. We only remove one from the total.