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The problem
In a class there are 20 children. 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 wearing? |
| How many children are wearing a red jersey? |
What is this problem about?
This problem involves recognising and continuing a 5 member 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.
Achievement Objectives
Algebra (level 1)
- continue a repeating and sequential pattern.
Mathematical Processes
- devise and use problem solving strategies (draw pictures, use equipment)
Resources
- Blue, green and red counters
- Copymaster of the problem (English)
Specific learning outcomes
The students will be able to:
- describe and continue a repeating and sequential patterns
- draw a picture or use equipment to solve a problem
Teaching Sequence
- Using children in your class form a repeating pattern using shoe colour (eg., white, brown, white, brown).
- Without telling the children what pattern you are using ask the children to join the line if they think that they could be the 5th member of the pattern.
- Ask them to tell you why they have joined the line. (Remember that they may have a valid reason even if it is different to yours.)
- Repeat the process to see if anyone else could become the 5th member of the pattern.
- Pose the problem to the class. Check that the children understand that they are finding out two things: the 20th person and how many are wearing red jumpers
- As the students work on the problem ask them to explain the strategy that they are using.
- Share solutions.
Extension to the problem
Ask the children to make up repeating patterns using members of the class.
Solution
The children can do the problem mechanically by writing down a table as below.
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 children might notice that the pattern repeats itself every five
children. So the first, sixth, eleventh and so on children 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 children at 5, 10, 15 and 20.