Mrs Parore is hanging out her towels to dry.

She puts **two pegs on each towel**.

How many pegs does she need to hold 4 towels?

Mrs Parore sees that her peg box is running low.

She puts one peg on the corner of two towels.

This way she only needs 3 pegs for 2 towels.

How many pegs does she need for 4 towels now?

Students explore problem solving strategies such as using equipment and drawing pictures.

Patterning is introduced as two pegs hold each towel on a washing line. Students are challenged to explore another pattern when one peg is used between a pair of towels.

Patterns underpin mathematics. Almost all mathematical activity is aimed at finding a pattern of some sort.

Pegs, clothes and a washing line.

### The Problem

Mrs Parore is hanging out her towels to dry. She puts two pegs on each towel. How many pegs does she need to hold 4 towels?

Mrs Parore sees that her peg box is running low. She puts one peg on the corner of two towels. This way she only needs 3 pegs for 2 towels. How many pegs does she need for 4 towels now?

### Teaching sequence

- Talk about washing.
*Does your family hang clothes out on a line?*

How do you use the pegs? - Have some of the students hang ‘washing’ on a line in the classroom.
*How many pegs did they use?* - Read Mrs Parore’s problems and discuss ways students might record their solutions.
- Ask supporting questions as students work.
- Have several students show and explain their solutions to the class.

#### Extension

Mrs Parore needs 12 pegs to hang out her towels. (Two pegs per towel and each peg is only used to hang one towel.) How many towels does she wash?

If Mrs Parore uses the peg-saving method of hanging out her washing, how many towels can she hang with 9 pegs?

### Solution

Students may use a range of representations to show:

8 pegs are needed to hang four towels.

Five pegs are needed to hang four towels.

#### Solution to the Extension:

Students may use a range of representations to show:

6 towels are hung with 12 pegs.

8 towels are hung with 9 pegs.