Problem Solving with Our Special Visitors

Today we are holding a special event called

This is an afternoon for all the students to show a special person some of the things they have been using their netbook for in class.

We have prepared a problem solving activity for our students to solve with their special person.

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

Today’s Problem: Sealed Solution

This problem is from the NRICH website.

A set of ten cards, each showing one of the digits from 0 to 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?

Note: there is more than one solution.

Write your solution in a comment. You might like to say what problem solving strategy you used to work this out.

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24 thoughts on “Problem Solving with Our Special Visitors

  1. Hello 4KM and 4KJ,

    Charlotte and I think we could solve this problem by making a list of all the different sums that equal 8.
    these are some of the ones we came up with.
    6+2= 8

    Could one of these be the answer?

    Martine and Charlotte 🙂

  2. Dear 4KM and 4KJ,

    We have been working hard through all of the activities and now we got up to this one. I thought that this would be a little hard and it was.

    The answer to the maths problem is: 7,1 We found this activity fun and would like to do it all over again!

    Have you done it yet?
    Did you enjoy it?
    Was it hard?

    From ♥livia + Warick 🙂 😛 😀 ♥

  3. Hi 4KM and 4KJ,

    Liam and I calculated the answer to the question was 3 and 5 were in the ‘8’ envelope.

    We calculated this by starting with the ‘3’ envelope and assuming it had 1 + 2 in it.

    We then worked out the envelope ’14’ must have the number 8 or 9 in it, we assumed it had 8 in it.

    The ’13’ envelope must have a 7 or 9 in it, thus we assumed it had 9 and 4 in it.

    This meant the ‘7’ envelope must have the number 7 and 0 in it, leaving the ‘8’ envelope with the numbers 3 and 5 in it.

    So to concluded:
    3 = 3 + 2
    14 = 8 + 6
    13 = 9 + 4
    7 = 7 + 0
    8 = 3 + 5


    Liam and Liam’s Dad

    • Hi Liam and Liam’s dad,

      I really like the strategy you used to solve this tricky maths problem!

      It will be great to show your comment to the class tomorrow. It takes skill to explain your thinking so clearly.

      Well done and thanks for coming today,

      Mrs Morris

    • Hi Liam and Liam’s dad,
      great work one the problem
      and the working out it is
      very good so got to go bey have a
      great day
      from Alisha,

  4. Dear 4KM and 4KJ, these are the answers to todays puzzle.
    7 = 5+2
    8 = 1 + 7
    13 = 9 + 4
    14 = 8 + 6
    3 = 3 + 0

    Ryley and Peter

  5. Hello 4KM and 4KJ,
    Fabulous post.
    My dad (Joe) and I think that the numbers in the 8 envelope could be 8 and 0.

    From Joe and Anneliese

  6. Dear 4KM and 4KJ,

    Some of the possibilities are:
    5 and 3,4 and 4,6 and 2, 7 and 1

    Molly and her Aunty Nik.

  7. Dear 4KM and 4KJ,

    My dad and I think the envelope could contain the numbers 5 and 3, 7 and 1 and the last one is 6 and 2.

    best wishes
    Riley and his dad[Kent]

  8. Dear 4KM and 4KJ,

    We are going to tell to you the answer of the envelope problem.

    The strategy we were thinking was working backwards.

    We have to go.

    From Keira and Tammy. 😆

  9. Dear 4KM and 4KJ,
    My Mum and Little sister Evie (and I of course) loved doing most of the activities.

    Mum says:
    It was fun creating the Lego avatars of each other and the tagxedo’s. I also enjoyed doing the typing test, but apparently I am not as fast as Mrs Morris.
    Thank you for having us in your class room today, you all know so much about using your netbooks.

    Evie says:
    Evie enjoyed making the tagxedo’s and, sitting on my lap the whole time! (I typed this for her!)

    Paris (I) says:
    It was great having Mum and Evie come!

    Paris, Mum and Evie

  10. Dear 4KM and 4KJ,

    My mum and I think that in envelope 1. has 5 and 2
    envelope 2 has 7 and 1
    envelope 3 has 9 and 4
    envelope 4 has 8 and 6
    envelope 5 has 0 and 3

    From Shaun and Melissa

  11. hi guys,
    Me and My mum (Melody) think it is,
    6 is in the 8 envelope.
    Because 6+7=13 and then add 1 to make 14 then take away 11 and that equals 3.

    Princess and Melody

  12. Hi 4KM and 4KJ,

    My Dad and I thought we should have a go at the puzzle. We found it was a bit hard but we think we got it! Here is our answer:
    8+0=8 ➡ (We thought this one was in the 8 envelope)

    Dad and I used wrote the answers as a table.

    Looking forward to the next problem!

    Charlotte and Arran 😆

  13. Hello mrs morris and class,

    It’s Joshua [lee’s brother],
    your problem solving tactics are very original and work for most unreal and real problems.
    What I got from your question is addition problems that equal 8 here are some examples,
    1+7=8, 7+1=8, 6+2=8, 2+6=8, 3+5=8, 5+3=8
    as mrs morris said there are many different ways to solve your ploblams with more than just addition,

    bye for now make sure to visit my blog,

  14. Hi 4KM and 4KJ ]
    great working out one the problem
    I hope you and your mum,naan,pupa our your dad
    had fun

    from Alisha

  15. Dear 4KM and 4KJ,
    Thank you for posting your maths solving problems on the blog! I used one of your strategies to solve it. I used the “Act it out” strategy. I worked it out by using sticky notes and making envelopes. I enjoyed solving your problem a lot! I think the numbers that were in the 8 envelope were 5 and 3.
    Thank you for reading. Happy blogging
    From HT 3LB (

    • Hi HT 3LB,

      We’re happy to hear you tried this problem in your class! We certainly enjoyed solving it and we’re glad you did too.

      Best wishes,
      Mrs Morris

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