Copyright © University of Cambridge. All rights reserved.

## 'Butterfly Flowers' printed from http://nrich.maths.org/

## Butterfly Flowers

Look at the butterflies and the numbers they have. The flowers also have numbers.

Can you find $2$ butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

Which pair of butterflies has no flower to go to?

Which flower cannot have a pair of butterflies on it?

### Why do this problem?

This problem addresses a difficulty that many children experience with the numbers from ten to twenty. The "teens" often cause more trouble than other decades up to $100$. English speakers have a particular problem because of the irregularity of the language used. "Fourteen" can so easily be muddled with "forty" so
that many children will write "$41$" instead of "$14$". By focusing on creating the numbers between $11$ and $19$ using $10$ and adding a single digit number, the problem gives an opportunity to practice building these numbers from one ten and different numbers of units.

### Possible approach

Ask the children about the numbers on the butterflies: are any of them the same? Can they separate them into two groups? Using a butterfly from each group, can they make the numbers on the flowers? You could start by discussing how a number, for example, fifteen is made up from $10$ and $5$.

This problem would fit in well with other work on on tens and units or on place value.

These cards could be used to introduce the problem. They can also be useful as a set of cards for matching activities or for continuing the problem in pairs. For long-term use the cards should be laminated.

### Key questions

What goes with ten to make this number?

What goes with this number (for example, $3$) to make this number (for example, $13$)?

### Possible extension

The cards could be used to make other pairs or sets of numbers that total to different target numbers or children could make up a game using them for other children to play. Multople sets of the cards will increase the number of possible solutions.

### Possible support

When children are counting together make sure that the "teens" are well differentiated from the "tens", for example, that "sixteen" is well differentiated from "sixty".

Some children respond well to using the counting from Catherine Stern's book "Children Discover Arithmetic". It can be called something like "Funny Counting". The numbers between $9$ and $22$ go, "onety, onety-one, onety-two ..... onety-nine, twoty, twoty-one..." The numbers get quite regular with this counting at 60!