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1.) Attempt 1:  No teacher instruction or interference for first 15 minutes. Students were assessed on whether they: a) Had the confidence to attempt the problem and b) Had the persistence to continue to attempt to problem solve for the entire 15 minutes

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1.) Attempt 1:  No teacher instruction or interference for first 15 minutes. Students were assessed on whether they: a) Had the confidence to attempt the problem and b) Had the persistence to continue to attempt to problem solve for the entire 15 minutes

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2.) Attempt 2: Whilst the student had been on the correct path, the student had not yet made her results clear for another student to interpret. She was encouraged to utilise a strategy that we had used on a recent task. That is when she went back and added the tree diagram. Finally I shared with her how we could create a table and asked her to comment on which display would be clearer for her peers to interpret.

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2.) Attempt 2: Whilst the student had been on the correct path, the student had not yet made her results clear for another student to interpret. She was encouraged to utilise a strategy that we had used on a recent task. That is when she went back and added the tree diagram. Finally I shared with her how we could create a table and asked her to comment on which display would be clearer for her peers to interpret.

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3.) Interesting observation: The student ended up getting off task attempting to explore why if: 1/2 = 50%, 1/3 = 33%, 1/4 = 25% Why is one third not the same difference from 1/2 and 1/4. She didn't think logically it was right that the difference between a third and a quarter could be 8% but from 1/3 to half  17%. As in both cases the denominator only had a difference of 1 from 1/3.

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3.) Interesting observation: The student ended up getting off task attempting to explore why if: 1/2 = 50%, 1/3 = 33%, 1/4 = 25% Why is one third not the same difference from 1/2 and 1/4. She didn't think logically it was right that the difference between a third and a quarter could be 8% but from 1/3 to half  17%. As in both cases the denominator only had a difference of 1 from 1/3.

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4.) Part 2: Involved the students carry out a game of 21 rounds to see if the results truly were random. The loser of the game was then shown the suggested strategy from the ReSolve resource. A second game consisting of another 21 rounds ensued. Students were asked to display their win results at bottom of table. As shown in the sample, this student also converted them to a decimal and percentage.

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4.) Part 2: Involved the students carry out a game of 21 rounds to see if the results truly were random. The loser of the game was then shown the suggested strategy from the ReSolve resource. A second game consisting of another 21 rounds ensued. Students were asked to display their win results at bottom of table. As shown in the sample, this student also converted them to a decimal and percentage.

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Sample 3

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5.) Video of student explaining their mathematical reasoning of task

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5.) Video of student explaining their mathematical reasoning of task

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7.) Here student is beginning to look at the results from different angles to determine if the strategy did in fact alter the randomness of the game. The investigation hasn't been completed.

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7.) Here student is beginning to look at the results from different angles to determine if the strategy did in fact alter the randomness of the game. The investigation hasn't been completed.

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6.) Student collating all of her class' game one and two results- aiming to use data to analyse whether the strategy had an impact on 'randomness'.

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6.) Student collating all of her class' game one and two results- aiming to use data to analyse whether the strategy had an impact on 'randomness'.