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Butterfly Flowers

Age 5 to 7 Challenge Level:

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.

From the Burke Ward Public School in Australia we had the following:

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.