This task, the game of 20,

involves two students: player A and player B working together as

a collaborative team to compete against

a computer agent in solving a problem called the game of 20.

The game of 20 involves the students working together against the computer to reach

a value of 20 by placing the counters sequentially on a grid.

The students need to identify critical scores in order to win the game.

Recognizing critical scores means that they must observe patterns.

In particular, they need to observe the pattern of

behavior of the computer agent every time they play the game.

It is the computer's pattern of behavior that provides the key to the solution.

Having recognized the patterns,

the collaborating partners need to formulate rules and hypotheses,

test and reflect upon those,

and then check out whether or not they are correct.

This task involves a number of patterns relevant to the mathematics curriculum.

There are six pages in the task.

Five pages present a subtask where the students begin the game

at various stages allowing for varying degrees of difficulty.

The first page allows the students to play the game in

full to help their understanding of the task concept.

In the second page,

the students begin with the game total of 18.

The third page at a game total of 13,

and the fourth page a game total of six.

Page five presents students with a number line from which they collaboratively

select which numbers they believe to be crucial to succeed in the game.

The students are assessed on whether they implement the numbers correctly within

the game play on the subsequent task page,

page 6, when they replay the game in full.

Both students select numbers which are combined to represent their team number or score.

Each student needs to consider the input of their partner when selecting a number.

As well as considering which number the computer will select.

There are several rounds of number selection until the game total reaches 20.

If either team, students or computer enter

an amount that exceeds the total of 20, that team loses.

The aim of the game is for the student team to reach

the exact game total of 20 before the computer.

We want this time to look for evidence of particular skills in

the students behavior as they collaboratively solve this task.

Look for evidence of the social skill responsiveness.

Within the game of 20 task,

students ability to ignore accept or

adapt contributions from their partner can be assessed.

Students who are strong in this skill may be observed selecting

a particular number after their partner

has sent them a chat message containing that number.

It can be inferred from this indicator that their partner has contribute to

that their activity and the student has

accepted and incorporated this contribution into their game play.

Another example of this skill might be observed the students work through to page 5,

when each has to agree on which numbers are

critical for a win by selecting them on the number line.

The students who are less adept at this skill might not

accept or consider contributions from their partner even if they're correct.

This can be seen when a student deselects a number from

the number line that their partner has previously selected.

Students who are more collaborative tend to take more responsibility for their team,

and ensuring their activities as well as

their partner activities required for the task success are completed.

One example in this task is when one student

attempts an activity and then report their actions to the partner.

This can be observed if the student resets the team number,

chats with their partner,

and then they change the numbers selected before progressing with the game.

It can be inferred from this activity that

the student wasn't satisfied with the initial number selection,

has opted to reset and then reported this to their partner,

concluding with alternative number options.

A cognitive skill that is evident in this task is called

cause and effect or identifying rules.

The extent to which students use their understanding of cause and

effect to plan and execute can be assessed in this task.

Students who are less proficient in this skill may undertake

the activity with no clear regard for the consequences of their actions.

However, more proficient students use their understanding of cause and

effect to plan and execute a strategy or activity.

One example of a proficient student in this task is one who selects specific numbers on

the number line and then proceeds to use

these numbers in the game play on subsequent task pages.

It can be inferred from this action that the student has determined

these numbers to be critical to success from the previous game play,

and intends to use them in order to succeed in the game.

An important cognitive skill that this task enables us to

identify is what we call reflecting and monitoring or testing hypotheses.

Students can be assessed on their abilities to hypothesize effectively.

Students who are not effective in formulating hypotheses tend

to maintain one single approach throughout.

They're not flexible and therefore fail to monitor their progress efficiently.

Students who have strong skills in developing

hypotheses tend to reflect more on their previous actions,

monitor their progress, reorganize a problem,

and try multiple approaches as they gain further information.

An example in this task is if the student opts to

retry the game after they've already attempted it and won the competition.

On each task, on each task page,

the student can opt to retry each subtask page.

By doing so, the student is attempting to reflect on

the course of action that caused them to previously fail,

and is attempting another approach in order to gain

a different outcome and a successful solution.

Now, watch as the students complete the game of 20 task.

Listen to the discussion and notice the skills being demonstrated

from both the narrative and the direct observation of the actions.

In these task, you and your partner are going to play as a team against the computer.

The object of the game is to make a total of exactly 20,

so my team and the computer take it in turns to select a number to go on the board.

Your total move will be a combination of your number and your partner's number.

To get the idea, play as many times as you like against the computer.

So I'm going to try to move these coins onto the board,

but that's not doing anything.

Oh, okay, so I can select a number here.

Let me see what my partner can do.

My partner says that they don't have any numbers.

I have numbers, so I'll let them know that.

My partner has selected number one,

and so now I've got some numbers.

So, what are we need?

We need to get to 20 and we're playing against the computer.

So if I pick four then,

so we're going to make him move a five.

And the computer moved a three.

So now we're up to eight. So the computer's moved,

so we can make another move now.

So the computer's moved to eight.

So now we have to think through what number we should play.

I can't choose the number until my partner does.

Why isn't my partner picking a number?

Pick a number already.

I'm going to choose three.

My partner can either play one or two.

I'm not quite sure what number we should play so my partner's played.

Now we're up to 16.

So if I play a four, we'll get to 20,

which would mean we would win.

We got to 21,

so we didn't do very well there.

Well, we can retry.

The thing is we can retry. We can start again.

Let's try playing five again as our first move.

Well, I feel like one or one.

I'll mark a one.

I think we should play five again.