Both 9 and 10 can be made up in 2 different ways by adding pairs of the numbers 1, 2, … 6, that is

9 = 3 + 6 = 4 + 5

10 = 4 + 6 = 5 + 5

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10.

What about the case of 3 dice?

Is a score of 9 more likely then a score of 10 with 3 dice?

Click here for the Notes for Teachers.

24 Responses to Grades 7 to 10 Nines and Tens

  1. King Flanis says:

    Yes in case of three dice 10 can be too possible to get

  2. Tombi Mona says:

    Quite interesting and thought – provoking activity!With two dice, expected outcomes to get a 9 are (6/3; 4/5; 3/6 & 5/4),The expected outcomes to get a 10 are (5/5; 6/4 & 4/6)There are 4 combinations of ways to get a 9 as compared to 3 combinations of ways to get a 10 which makes makes it more probable to get a 9 than a 10 when throwing two dice.

  3. Stombles Magadlela says:

    In the case of 3 dices you can have
    5+4+1=10
    2+3+5=10

    5+3+1=9
    6+2+1=9
    It is highly possible with 3 dices to have the sum of 9 and 10

  4. Cynthia Fries says:

    You are right in thinking there are many more ways of making both 9 and 10 when you have 3 dice. Your learners will have to be very systematic when they start listing these combinations. Don’t forget that 5+4+1 is different from 5+1+4 which is different from 4+5+1 which is different from ….

  5. Joyce Rooimes says:

    I gave my grade 6 learners this problem, I ask them to find the possible numbers that will give us 9. here are their solutions with 3 dice.
    1+2+6=9, 2+3+4=9, 3+5+1=9, 5+2+2=9, 4+3+2=9,3+3+3=9, 4+4+1=9. i gave homework for finding possible numbers for 10 and more for 9.

  6. Ntholeng Lekhetha says:

    My Grade 6 learners gave me these possible chances of sums of 10.
    1+3+6=10,
    2+3+5=10,
    3+4+3=10,
    4+5+1=10,
    4+4+2=10,
    6+2+2=10,

  7. Msuthu Mdleleni says:

    The activity was very interesting to learners.They enjoyed it and we noticed that throwing three dices you get many combinations of 9 and 10 than when using two dices.I also let them draw tally table inorder to record each throw so as to find out which number has got most scores and which one had few scores

  8. Fezzy Gxothiwe says:

    Grade4&5.I did the nines & tens activity with my children today.One is in grade4&the other in grade5.They got these answers:
    5+2+2=9
    1+6+2=9
    4+3+2=9
    5+3+1=9

    5+2+3=10
    2+4+4=10
    1+4+5=10
    6+3=1=10
    6+2+2=10
    3+3+4=10

    More than giving me the possible answers they enjoyed playing with the dice.Learning through play is the best way for children.

  9. Zim Wopa says:

    I gave my grade 9 learners this problem, they took a lot of time as a result I treated it as a homework. I wanted each learner to work on his/her own and have enough time to think about it. It went well because when we do it the following day others manage to identify their mistakes and misunderstandings.

  10. Ntosh Pinda-Nkonjane says:

    Hi Toni, this was achallenging exercise to my grade 8 learners. They struggled a lot to work it out and I’ve dicovered that maths exercises need a lot of time for effectiveness. That has made me to have morning classes so as to provide more time. That has assisted me in that I was able to identify heir problem areas.

  11. Ntholeng Lekhetha says:

    My Grade 6 learners also did this and they came up with the following:
    1+2+6
    2+1+6
    6+1+2
    2+2+5
    2+2+5
    3+2+4
    2+3+4

    • Sari Smit says:

      That looks good Ntoleng. As one can see there are many possible combinations of making 9 and 10 with three dice. As Cynthia said, you REALLY have to be very SYSTEMATIC in how you find all the possibilities for making 9 and 10. For example take the last combinations of 3+2+4 and 2+3+4: It looks as if your learners realise that those are two different combinations, which they are. They need to remember that they are working with 3 dice. Try to get them to further investigate that combination of 2, 3 and 4 and then …..

  12. Simthe Nolusu says:

    I gave this to my grade 8 learnerssome of them responded positively others took a long time to get answers.

  13. Rose Moleko says:

    My grade 6 learners enjoyed this activity. Some of them took a long time to understand that 2+3+4,2+4+3 and 3+2+4 for example are not the same.after demonstrations and explanations by their peers, the different groups came up with possible answers and other numbers were also tried using dice.

  14. Sdumo Msindo says:

    I gave this problem to grade 9 learners. They discovered that for two dice there is a possibility of getting more scores of 9 than of 10 because 10 is affected by 5+5.
    For three dice they discovered that a score of 10 is more probably to get than a score of 9- 9 is affected by 3+3+3.

  15. Patricia Kotyi says:

    I shared this problem with my grade 10 learners,they struggled to get the solution.But they said there is a possibility of getting more scores of 10 than nine because 10 is made by 5 sets of numbers whereas 9 is made by 4 sets of numbers.

  16. Simthe Nolusu says:

    Score of 10 is more likely to get since there are more chances of 10 than 9

  17. Zuzaz Mazuza says:

    9 appears more often 3,6;4,5 appears most in the dice 3,4$5 it is likely to find them. Same applies to the 3dices 9 will appear more often.

  18. Nelly Malamlela says:

    for two dice 9 is likely to get more scores than 10 but when it comes to three dice 10 is likely to score more. this is what my Saturday class learners told me. As for the rest of the class I will introduce the topic in the third term.

  19. Vuyo Mthembu says:

    For two die the combinations to make 9 is mostly to happen ,than that of 10, looking at the combination of 9 we have ,3+6 =9,4+5=9 ,for 10 we have 5+5 =10 ,6+ 4 =10
    But the actual combinations for 9 are 4+5,5+4,3+6 and 6+3 (4 combinations). For 10 ,combinations are as follows 5+5,6+4 and 6+4 (3 combinations ) that is why 9 is more likely than 10) This activity is based to learners ,but I did it with grade 9 teachers as a warm up activity,it was not very easy as we think it is supposed to be.
    For 3 die ,assumptions were that as 9 was more likely to be formed in 2 die also this is supposed to be the same up until we highlighted the possibilities as follows: Sum to be 10,
    Combinations are 1+3+6 (6arrangements) ,2+3+5(6arrangements)
    1+4+5 (6arrangements) ,2+2+6 (3arrangements)
    3+3+4 (3arrangements) 4+4+2 (3arrangements)
    total possible outcomes for 10 is 27

    Combinations for getting 9 are 1+2+6 (6arrangements)
    2+3+4 (6arrangements)
    3+1+5 (6arrangements)
    2+2+5 (3arrangements)
    4+4+1 (3arrangements)
    3+3+3 (1arrangements)
    Then the total possible outcomes for 9 is 25
    Looking foward to check from your comments whether our assumption is correct. We furher discussed that this activity can be used when introducing probability.

  20. toni toni says:

    This is a good exercise in mathematical thinking.

    Give learners time to find ALL the combinations of numbers on the dice that add up to 9 or 10. If they don’t find them all in one lesson encourage the learners to keep looking. Put a chart on the wall and mark up the combinations that the class has already found. Give a lot of praise to any learner who finds a new combination and write it on the chart. Keep encouraging them to look for more possibilities until they find them all.

    As a good teacher you will be trying to encourage learners to think for themselves. Don’t help too much but you may need to help everyone in the class to understand that there are 6 different ways that you arrange 3 things so there are 6 ways of scoring 10 with the same 3 numbers, for example, 1+2+6, 1+6+2, 2+1+6, 2+6+1, 6+1+2, 6+2+1.

    You could get 3 learners to stand at the front and ask them to change places so they arrange themselves in as many different ways as possible. Get another learner to record the 6 arrangements on the chalkboard.

    With 2 dice there are 4 ways of getting a total of 9 and only 3 ways of getting a total of 10. With 3 dice there are 25 ways of getting a total of 9 but 27 ways of getting a total of 10. So you are more likely to throw a 9 with 2 dice and you are more likely to throw a 10 with 3 dice.

    The arithmetic is easy. To make sure you have found ALL the possibilities requires clear thinking and a systematic method of checking all possibilities.

  21. Corinne Angier says:

    When learners are muddled about 1+ 2 + 6 being different from 2 + 1 + 6 it can be helpful to imagine the dice are different colours. then it is easier to see that
    1 Green 2 blue 6 red
    is different from
    1 blue 2 green 6 red

    P.S sorry I don’t have a photo yet.

  22. Spush Mgilane says:

    A score of 10 is possible when throwing with 3 dice because there is a lot of possible outcomes like 4,5;1
    6,2,2
    5;3;2

  23. Tau Tamako says:

    My grade 09 learners could realize that more combinations could give the results of 9 than 10 when two dice were used, but when three dice were used there were more chances of getting a 10.

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