# ROLL 3 DICE

Roll3Dice is our initiative aimed at getting parents and children to learn together in a very informal and enjoyable way.

It is vitally important that parents and children can spend time together educationally and this is a simple and fun way of doing this and improving a child’s number skills too.

Introduction

Whereas most parents have read to their young ones at some point, it’s unlikely that they have played a maths game or carried out a fun arithmetical equivalent.

As the name suggests, our Roll3Dice idea simply involves rolling three dice and encourages parents and children to work together to try and solve the maths problem in hand involving the three numbers and the four arithmetic operations.

How it works

Step 1: Roll three normal dice, each containing the numbers 1-6.

Step 2: Now, work together with pencil & paper to try and find all possible answers that can be made from 1-10 when using these three numbers once each and with + – × ÷ available.

Play Roll3Dice a few evenings each week and see a dramatic improvement in your child’s maths confidence, arithmetic skills and creative thinking.

Extra Roll3Dice Ideas

After rolling the dice, the usual activity is for both adult and child to try and figure out the possible answers together as a team, but as the child gets more familiar and experienced the two players could take turns to find one answer each until one of the players stumbles and loses the game.

Alternatively, after rolling a particular combination of numbers, the two players could browse at the possible answers below and challenge each other in a competition format to work out how to arrive at these answers in a specified time, but this period could decrease the more times Roll3Dice is played!

The possibilities are endless; parents, grandparents, carers and teachers will make up their own fun mathematical games involving the three numbers and their solutions.

All 56 combinations when playing Roll3Dice are shown below, together with the number of possible answers (up to 10 and shown in brackets) and the answers themselves.

The 1-2-4 combination, shown in bold, is the ONLY one where all ten answers are possible:

•  1-1-1      (3)     1, 2, 3
•  1-1-2     (4)     1, 2, 3, 4
•  1-1-3     (6)     1, 2, 3, 4, 5, 6
•  1-1-4     (6)     2, 3, 4, 5, 6, 8
•  1-1-5     (6)     3, 4, 5, 6, 7, 10
•  1-1-6     (6)     3, 4, 5, 6, 7, 8
•  1-2-2     (6)     1, 2, 3, 4, 5, 6
•  1-2-3     (9)     1, 2, 3, 4, 5, 6, 7, 8, 9
•  1-2-4   (10)   1, 2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-5     (9)     2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-6     (9)     2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-3-3     (8)     1, 2, 5, 6, 7, 8, 9, 10
•  1-3-4     (6)     1, 2, 6, 7, 8, 9
•  1-3-5     (7)     1, 2, 3, 7, 8, 9, 10
•  1-3-6     (7)     1, 2, 3, 4, 8, 9, 10
•  1-4-4     (5)     1, 2, 7, 8, 9
•  1-4-5     (5)     1, 2, 8, 9, 10
•  1-4-6     (5)     1, 2, 3, 9, 10
•  1-5-5     (4)     1, 2, 9, 10
•  1-5-6     (3)     1, 2, 10
•  1-6-6     (2)     1, 2
•  2-2-2    (5)      1, 2, 3, 6, 8
•  2-2-3    (7)      1, 2, 3, 4, 7, 8, 10
•  2-2-4    (7)      1, 3, 4, 5, 6, 8, 10
•  2-2-5    (6)      1, 4, 5, 6, 8, 9
•  2-2-6    (8)      1, 2, 4, 5, 6, 7, 8, 10
•  2-3-3    (7)      1, 2, 3, 4, 7, 8, 9
•  2-3-4    (8)      1, 2, 3, 4, 5, 6, 9, 10
•  2-3-5    (7)      1, 4, 5, 6, 7, 9, 10
•  2-3-6    (6)      1, 4, 5, 6, 7, 9
•  2-4-4    (7)      1, 2, 3, 4, 6, 8, 10
•  2-4-5    (6)      1, 2, 3, 6, 7, 10
•  2-4-6    (7)      1, 2, 3, 4, 5, 7, 8
•  2-5-5    (5)      1, 2, 3, 5, 8
•  2-5-6    (7)      1, 2, 3, 4, 7, 8, 9
•  2-6-6    (6)     1, 2, 3, 6, 9, 10
•  3-3-3    (5)     2, 3, 4, 6, 9
•  3-3-4    (6)     2, 3, 4, 5, 9, 10
•  3-3-5    (4)      1, 4, 5, 6
•  3-3-6    (6)      1, 3, 5, 6, 7, 9
•  3-4-4    (5)      2, 3, 4, 5, 8
•  3-4-5    (7)      2, 3, 4, 5, 6, 7, 8
•  3-4-6    (6)      1, 2, 5, 6, 7, 8
•  3-5-5    (5)      2, 3, 4, 7, 10
•  3-5-6    (7)      2, 3, 4, 7, 8, 9, 10
•  3-6-6    (5)      2, 3, 4, 8, 9
•  4-4-4    (4)      2, 3, 4, 5
•  4-4-5    (4)      3, 4, 5, 6
•  4-4-6    (6)      2, 5, 6, 7, 8, 10
•  4-5-5    (4)      3, 4, 5, 6
•  4-5-6    (7)      2, 3, 4, 5, 6, 7, 10
•  4-6-6    (5)      3, 4, 5, 8, 9
•  5-5-5    (4)      2, 4, 5, 6
•  5-5-6    (4)      4, 5, 6, 7
•  5-6-6    (4)      4, 5, 6, 7
•  6-6-6    (4)      2, 5, 6, 7

We’d love to hear from you whether you have any queries or issues regarding the answers or even if you just want to share your own innovative ways of playing Roll3Dice.

Please feel free to email us or send a tweet to @7puzzle. Learning together at home can be very rewarding.

The next step (Roll3Dice Answers, 1-30)

If, as a parent/carer/teacher, you have seen the benefits of Roll3Dice and want to push on, we fully recommend the following activity.

It’s exactly the same concept as above, but a little more challenging, with the target numbers now in the range 1-30:

•  1-1-1      (3)    1, 2, 3
•  1-1-2     (4)    1, 2, 3, 4
•  1-1-3     (6)    1, 2, 3, 4, 5, 6
•  1-1-4     (6)    2, 3, 4, 5, 6, 8
•  1-1-5     (6)    3, 4, 5, 6, 7, 10
•  1-1-6     (7)    3, 4, 5, 6, 7, 8, 12
•  1-2-2     (6)    1, 2, 3, 4, 5, 6
•  1-2-3     (9)    1, 2, 3, 4, 5, 6, 7, 8, 9
•  1-2-4    (10)   1, 2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-5    (12)   2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15
•  1-2-6    (14)   2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18
•  1-3-3     (9)    1, 2, 5, 6, 7, 8, 9, 10, 12
•  1-3-4    (11)    1, 2, 6, 7, 8, 9, 11, 12, 13, 15, 16
•  1-3-5    (13)    1, 2, 3, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20
•  1-3-6    (14)   1, 2, 3, 4, 8, 9, 10, 12, 15, 17, 18, 19, 21, 24
•  1-4-4    (10)   1, 2, 7, 8, 9, 12, 15, 16, 17, 20
•  1-4-5    (12)   1, 2, 8, 9, 10, 15, 16, 19, 20, 21, 24, 25
•  1-4-6    (13)   1, 2, 3, 9, 10, 11, 18, 20, 23, 24, 25, 28, 30
•  1-5-5    (10)   1, 2, 9, 10, 11, 20, 24, 25, 26, 30
•  1-5-6     (9)    1, 2, 10, 11, 12, 24, 25, 29, 30
•  1-6-6     (6)    1, 2, 11, 12, 13, 30
•  2-2-2    (5)     1, 2, 3, 6, 8
•  2-2-3    (8)     1, 2, 3, 4, 7, 8, 10, 12
•  2-2-4    (9)     1, 3, 4, 5, 6, 8, 10, 12, 16
•  2-2-5    (9)     1, 4, 5, 6, 8, 9, 12, 14, 20
•  2-2-6   (11)     1, 2, 4, 5, 6, 7, 8, 10, 14, 16, 24
•  2-3-3   (11)     1, 2, 3, 4, 7, 8, 9, 11, 12, 15, 18
•  2-3-4   (13)    1, 2, 3, 4, 5, 6, 9, 10, 11, 14, 18, 20, 24
•  2-3-5   (14)    1, 4, 5, 6, 7, 9, 10, 11, 13, 16, 17, 21, 25, 30
•  2-3-6   (14)    1, 4, 5, 6, 7, 9, 11, 12, 15, 16, 18, 20, 24, 30
•  2-4-4   (12)    1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 24
•  2-4-5   (14)    1, 2, 3, 6, 7, 10, 11, 12, 13, 14, 18, 22, 28, 30
•  2-4-6   (13)    1, 2, 3, 4, 5, 7, 8, 12, 14, 16, 20, 22, 26
•  2-5-5   (10)    1, 2, 3, 5, 8, 12, 15, 20, 23, 27
•  2-5-6   (15)    1, 2, 3, 4, 7, 8, 9, 13, 15, 16, 17, 18, 20, 22, 28
•  2-6-6    (9)    1, 2, 3, 6, 9, 10, 14, 18, 24
•  3-3-3    (8)    2, 3, 4, 6, 9, 12, 18, 27
•  3-3-4   (10)   2, 3, 4, 5, 9, 10, 13, 15, 21, 24
•  3-3-5   (10)    1, 4, 5, 6, 11, 12, 14, 18, 24, 30
•  3-3-6   (10)    1, 3, 5, 6, 7, 9, 12, 15, 21, 27
•  3-4-4   (11)    2, 3, 4, 5, 8, 11, 13, 16, 19, 24, 28
•  3-4-5   (13)    2, 3, 4, 5, 6, 7, 8, 11, 12, 17, 19, 23, 27
•  3-4-6   (14)    1, 2, 5, 6, 7, 8, 12, 13, 14, 18, 21, 22, 27, 30
•  3-5-5   (10)    2, 3, 4, 7, 10, 13, 20, 22, 28, 30
•  3-5-6   (14)    2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 21, 23, 27
•  3-6-6    (9)     2, 3, 4, 8, 9, 12, 15, 18, 24
•  4-4-4    (6)     2, 3, 4, 5, 12, 20
•  4-4-5    (9)     3, 4, 5, 6, 11, 13, 16, 21, 24
•  4-4-6   (10)    2, 5, 6, 7, 8, 10, 14, 20, 22, 28
•  4-5-5    (9)     3, 4, 5, 6, 14, 15, 21, 25, 29
•  4-5-6   (12)    2, 3, 4, 5, 6, 7, 10, 14, 15, 19, 26, 29
•  4-6-6    (9)     3, 4, 5, 8, 9, 12, 16, 18, 30
•  5-5-5    (7)      2, 4, 5, 6, 15, 20, 30
•  5-5-6    (7)     4, 5, 6, 7, 16, 19, 25
•  5-6-6    (6)     4, 5, 6, 7, 17, 24
•  6-6-6    (6)     2, 5, 6, 7, 18, 30

Mathematically Possible board game

To take yet another step forward, and put all the above into practice, click Mathematically Possible for details of our popular board game that uses three numbers.

Played exactly like Roll3Dice, but involves lots of strategy and decision-making as well as the arithmetic calculations described above.