This problem solving activity has an algebra focus.

In a class there are 20 students. They are wearing jerseys of **3 different colours **– blue, green, and red.

The class was lined up in a way that the **pattern of jerseys** was:

blue, blue, green, green, red, blue, blue, green, green, red...

What **colour** jersey is the last child in the class wearing?

How many students in the class are wearing a red jersey?

- Describe and continue a repeating and sequential patterns.
- Draw a picture or use equipment to solve a problem.

This problem involves recognising and continuing a 5 term repeating and sequential pattern. It also introduces the concept of multiples of 5 as every fifth child is wearing a red jumper. Students have to recognise the given pattern and arrange the 20 people in the given pattern to answer the questions.

- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
- Blue, green and red counters
- Colouring pens and pencils, paper

### The Problem

In a class there are 20 students. They are wearing jerseys of 3 different colours – blue, green, and red. The class was lined up in a way that the pattern of jerseys was:

blue, blue, green, green, red, blue, blue, green, green, red...

What colour jersey is the last child in the class wearing?

How many students in the class are wearing a red jersey?

### Teaching Sequence

- Using students in your class, form a repeating pattern using their shoe colour (eg., white, brown, white, brown).
- Without telling the students what pattern you are using, ask the students to join the line if they think that they could be the 5
^{th}member of the pattern. - Ask them to tell you why they have joined the line. They may have a valid reason even if it is different to yours.
- Repeat the process to see if anyone else could become the 5
^{th}member of the pattern. - Pose the problem to the class. Check that the students understand that they are finding out two things: the 20
^{th}person and how many are wearing red jumpers. - Provide counters, colouring pens and pencils, and paper to students. Ask the students to work out the problem. As the students work, ask them to explain the strategy that they are using.
- Share solutions.

#### Extension

Ask the students to make up repeating patterns using members of the class. The solution to this will dependent on the problem posed.

### Solution

The students can solve the problem systematically by writing down a table as below. Students with pre-writing level skills might draw shapes or write letters (i.e. B, G, R) to represent each member of the class (i.e. each term of the pattern).

To answer the questions in the problem, students need to write the numbers 1-20 and arrange the counters for jerseys in the given pattern.

1 | 2 | 3 | 4 | 5 |

BLUE | BLUE | GREEN | GREEN | RED |

6 | 7 | 8 | 9 | 10 |

BLUE | BLUE | GREEN | GREEN | RED |

11 | 12 | 13 | 14 | 15 |

BLUE | BLUE | GREEN | GREEN | RED |

16 | 17 | 18 | 19 | 20 |

BLUE | BLUE | GREEN | GREEN | RED |

On the other hand, the students might notice that the pattern repeats itself every five students. So the first, sixth, eleventh and so on students have blue jumpers. Using this idea all the questions can be answered.

The last child is wearing a red jersey because 20 = 5 + 5 + 5 + 5.

There are 4 red jerseys and they are worn by the students at 5, 10, 15 and 20.