This problem solving activity has an algebra focus.

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?

- Use simple problem solving strategies.
- Solve a simple problem involving number.

Students explore problem solving strategies such as using equipment and drawing pictures. Students will also need to use their counting skills to solve the problem.

Patterning is introduced in the context of two pegs holding each towel on a washing line. Students are challenged to explore a new 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.

- Copymaster of the problem (Māori)
- Copymaster of the problem (English)
- Pegs, clothes and a washing line (or pictures)

### 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. Methods might include drawing, using materials, or acting out the problem.
- 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). How many towels does she wash?

Mrs Parore thinks of another method she can use when hanging out her washing. She thinks that each peg can be used to hang one out towel. How many towels can she hang with 9 pegs?

Mrs Parore washes 12 towels and uses her 9 pegs to hang them out on the washing line. How many towels can she not hang out, if she uses her second method?

### 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, if 2 pegs are used to hang out each towel. Mrs Parore washes 6 towels.

9 towels can be hung with 9 pegs.

If Mrs Parore washes 12 towels and then uses 9 pegs to hang out her towels (with 1 peg per towel), then she will not be able to hang out 3 of her towels.