Solving Problems: Sealed Solution

In 3/4D, we are creative thinkers. Today, we are holding a Family Blogging Afternoon. Miss Fraser thought it could be a good idea to work with our family members after we have completed our blogging quiz on this number problem.

We have a number of different problem solving strategies that we can use in our maths. Perhaps one of these strategies will help solve today’s problem?



Today’s problem is called Sealed Solution

*This problem comes from the Nrich website

A set of ten cards, each showing one of the digits fromΒ 0Β toΒ 9, is divided up between five envelopes so that there are two cards in each envelope. The sum of the two numbers inside it is written on each envelope:


What numbers could be inside the “8” envelope?

*There is more than one solution!

Write your solution in a comment. What problem solving strategies did you use?

37 thoughts on “Solving Problems: Sealed Solution

  1. Dear 3/4d,
    we found out that the solution to the problem is 8 and 0 and 7 and 1. We worked it out by using a piece of paper using the numbers 0 to 9 and crossing them out as we go.
    From Felicity, Auntie Leaf and Sophie

    • Hi Felicity, Aunty Leaf & Sophie!
      What a great problem solving strategy. I think you have found the correct answer. Could there be more possibilities?
      From Miss Fraser πŸ™‚

      • Yes there certainly was another answer … 5 and 3 πŸ™‚ felicity had had enough of doing maths but I came home to work out the last

        • Hi Aunty Leath,
          I can certainly believe that Felicity had enough of doing Maths! I know she loves her reading much more. Well done with your persistence!
          From Miss Fraser πŸ™‚

  2. Hi 3/4D,
    Thank you for inviting me to your classroom for the Family Blogging Session.
    I had fun and was very interested to see all the technology that you are using. I also did some Maths with Sarah to work out what was in the envelope. I will keep an eye on your blog. From Sarah’s Nan

    • Hi Diane,
      Thank you for leaving such a great quality comment and thank you for visiting our classroom. I’m glad that you and Sarah were able to work on the Maths challenge together! What solutions did you both find?
      From Miss Fraser πŸ™‚

  3. 7 8 13 14 3
    7+0 5+3 9+4 8+6 2+1

    I worked it out by trying heaps of different combinations and when I got one wrong I rubbed it out and kept trying and I found one of the right answers.
    Can you make another one of these questions?

    From Zach and Michelle (MUM)

    • Hi Andrea,
      I bet you were surprised to discover that YAPPY was not actually describing Brodie! Thank you for coming to our Blogging Afternoon.
      From Miss Fraser πŸ™‚

  4. we made a list of the numbers and eliminated the unique solutions until only 0 and 8 were left the solution is 8 and 0 in the 8 envelope
    from Katie and her pa

  5. I have been enlightened to the powers of the internet and more importantly blogging, this can be a great educational tool that can be very informative for both students and parents. It can also be great to share experiences with other bloggers and blogging groups. I really appreciated the opportunity to participate in the afternoon.
    Tylers Dad.

  6. Dear Miss Fraser,
    Jessica is worried I won’t leave a good quality comment….I hope I don’t let her down. I had fun today in your class and was pleased to learn about blogging and how to do it safely. I think this is an important skill your class is learning and I hope Jessica pays attention πŸ™‚

    Kind regards, Belinda
    P.S. Do you think this was a good quality comment?

    • Hi Belinda,
      I don’t know what Jess is worried about – I think you have left a GREAT quality comment! Thank you for visiting our class today, we really enjoyed ourselves. Stay tuned for announcing the winners of our quiz!
      From Miss Fraser πŸ™‚

    • Hi Mitch,
      Great problem solving. My question for you is, “Isn’t 3+5 the same as 5+3?” Even though the cards are flipped around, they are still the same cards aren’t they?
      From Miss Fraser πŸ™‚

      • I agree Miss Fraser, we did discuss this at the time, but Mitch has put them all in, which is doubling up…. Maths is fun though and we can learn so much…

  7. I hope all the students in 3/4D and their family members had an awesome afternoon at the family blogging event!

    • Hi Kathryn,
      The students AND the special visitors had a great time! We loved doing the quiz because it really tested our knowledge – and our skills in finding the correct information, which is a very important part of reading comprehension. Hope you had a nice day too.
      From Miss Fraser πŸ™‚

  8. Hello learning lizards I’m Ethan a from 3/ blogging day looked fun I would have invited mum and dad but our class didn’t have it but it really looked fun.hope I see you around.

  9. Dear 3/4 d
    what does your class like best about addition, problem solving and subtraction.
    I love math.
    From Liam Felicity’s cousin

    • Hi Liam,
      Thanks for stopping by and leaving a comment on our blog. How funny that you love Math because I know it is not Felicity’s favourite subject! I love doing problem solving. What is your favourite part of Maths?
      From Miss Fraser πŸ™‚

    • Hi Baylen,
      Thanks for having a go at the challenge. We found a problem with your solution though. The cards could not be 4 and 4 as there is only 1 number 4 card. Also, check your work as you have put 3+3 making 8.
      From 3/4D

  10. Hello, we wrote a list of the cards numbered 0 to 9 on a piece of paper and worked out all the possibilities of cards which could be in each envelope.

    We then worked out which two cards could be in each envelope, without using the same card twice!

    We decided envelope “8” would contain cards 7+1 if the envelopes contained the following cards:

    7 – 5+2
    8 – 7+1
    13 – 9+4
    14 – 8+6
    3 – 0+3

    Charlotte and Rose πŸ™‚

    • Great problem solving Charlotte and Rose!
      You have done such a great job at explaining your problem solving strategy, which is not an easy thing to do.
      I know that there is also possible answer that the “8” envelope could contain. Could you find it?
      From Miss Fraser πŸ™‚

  11. I think I have worked it out – I think that
    the “7” envelope has cards 3 & 4
    and that
    the “14” envelope has cards 5 & 9

    This blog is a great way for us to share in 3/4D activities


  12. Hi 3/4 D,
    I think that your problem solving strategies are great! I am in year 10 and still use strategies like this to work out difficult maths equations

  13. I love a good Mathematical problem to solve.

    There are a total of 3 solutions to this problem, with the possible combinations of cards in the envelope totaling 8 being:
    0 and 8
    1 and 7
    3 and 5

    I reached the solution by using a list of possible combinations and eliminating any numbers that could not fit in a certain envelope (IE the only possible numbers in the last envelope would be 0 and 3, or 1 and 2. Also the numbers 0, 1, 2, 3, and 4 could not be in the envelope totaling 14, and so on).

    From Michael -Mitch’s cousin, and Mathematics enthusiast πŸ˜‰

  14. Hi my name is Cameron,
    I am Phoenix’s uncle. I chose the envelope with the number 13 on it. I came up with the following possible solutions:
    I used the strategy find a pattern.
    Keep up the great work!

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