We had these solutions sent in to this task, which are worth looking at carefully.

Mishika from Bal Bharati Public School, India sent in the following:

First I have joined flowers with the butterflies.

I have added 10 with 5 to make 15

Then added 10 with 6 to make 16

Then added 10 with 2 to make 12

Then added 10 with 9 to make 19

Then added 10 with 4 to make 14

Then added 10 with 1 to make 11

Last I added 10 with 7 to make 17

But I found that there is no pair for the flower 18.

Anvi from James Allen's Prep School wrote:

There are 8 flowers, all numbered between 10 and 20.

There are 16 butterflies, 8 of which are numbered 10.

First I ordered all pairs, each having a number 10 butterfly.

Next, I added the pair.

I then placed the sum of each pair on the corresponding flower.

There was no flower with number 13, hence butterflies 10 and 3 cannot go in any flower.

No pair added to 18, so there can be no butterflies on flower 18.

Macy-May from All Saints C of E Primary School
wrote:

So I made all the numbers up but not 18 because there was no 8 and there was only 3 left over:

10+5=15;

10+6=16;

10+2=12;

10+____=18;

10+9=19;

10+4=14;

10+1=11;

10+7=17

The only flower that did not have a butterfly was 18.

Students worked in small groups for this investigation. Initially, each group noticed something different which they shared with the whole class:

- the flowers were different colours (two flowers have the same colour and they followed each other in a counting sequence)

- each flower had a two-digit number (11-19)

- nine flowers

- each of the numbers on the flowers had a 1 in the tens column (eg. 13 is 1 ten and 3 more)

After listening to what each group had noticed students started investigating which butterflies could go together to equal a total on a flower. Groups discovered they needed a butterfly with 10 on it beside each flower (for the value of the 1 in the tens position) and a one-digit butterfly that

added to it to make the total of the flower (e.g.10+3=13).

They changed the tasks slightly and produced this result:

(Clicking on the image will open a larger version in a new page.)

Thank you for these.