Ladybirds in the Garden

For ideas about how to open up this activity, you may like to read Bernard Bagnall's article Opening Out .

We had lots of responses to this problem - thank you to you all. Lachlan from St Faith's School sent a solution to the first part of the question:

    two sevens =14
    four fours=16

Ann and Daniel who are both 10, wrote this a slightly different way:

    7+7=14
    4+4+4+4=16

Ann and Daniel then continued with the rest of the question, writing the sums in order of size. Julia from St Anne's C of E Primary School and Michael from St Alfred's College also tackled the problem in this way. Here is Michael's solution:

    4=4
    7=7
    4+4=8
    4+7=11
    4+4+4=12
    7+7=14
    4+7+4=15
    4+4+4+4=16
    4+7+7=18
    4+4+4+7=19
    4+4+4+4+4=20
    7+7+7=21
    4+7+4+7=22
    4+4+4+4+7=23
    4+4+4+4+4+4=24
    4+7+7+7=25
    4+7+4+7+4=26
    4+4+4+4+4+7=27
    7+7+7+7=28
    4+7+4+7+7=29

Dylan, Robert, Shani and Amy who are all 7 years old, approached it a slightly different way (and have come up with some different solutions) which is just as good, although they have missed out a few:

    4=4
    4+4=8
    4+4+4=12
    4+4+4+4=16
    4+4+4+4+4=20
    4+4+4+4+4+4=24
    4+4+4+4+4+4+4=28

    7=7
    7+7=14
    7+7+7=21
    7+7+7+7=28

    7+4=11
    7+4+4= 15
    7+4+4+4=19

    7+7+4=18
    7+7+4+4+4=26
    7+7+4+4+4+4= 30

Can you see where the missing sums would fit into the pattern they've created?

In conclusion, Michael says that the impossible numbers are: 1, 2, 3, 5, 6, 9, 10, 13, 17.