# Letter patterns

Purpose

In this unit we look at the number patterns we get from letters and numbers. We keep track of the numbers involved by drawing up a table of values. It’s important here to look for the pattern and see how the number of tiles changes from letter to letter.

Specific Learning Outcomes
• Draw the next shape in a pattern sequence.
• See how the pattern continues from one shape to the next.
• Draw up a table of values.
Description of Mathematics

Patterns are an important part of mathematics. They are one of the over-riding themes of the subject. It is always valuable to be able to tell the relation between two things in order to predict what will happen and understand how they inter-relate.

Patterns also provide an introduction to algebra proper as the rules for simple patterns can be first discovered in words and then be written using algebraic notation.

#### Links to Numeracy

This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular development of knowledge of skip counting patterns.

Help students focus on the number patterns by discussing the tables showing the numbers of tiles used in each successive letter pattern. Look at those patterns that are made by adding a constant number of tiles onto each successive letter. Highlighting numbers on a hundreds board or using a number line may also be helpful.

Questions to develop strategic thinking:
Which number comes next in this pattern?
How do you know?
Which number will be before 36 in this pattern? (or another number as appropriate)
How do you know?
What is the largest number you can think of in this pattern? How did you work it out?
Could you make a letter T with 34 tiles? How do you know?>

Required Resource Materials
Activity

#### Getting started

Starting with a simple pattern we build up the level of difficulty and see that it’s necessary to use a table to keep track of what is happening.

1. Build up the letter ‘I’ using coloured tiles or paper (see the diagram below).
How many tiles do we need for the first ‘I’? The second? The third? Who can tell me how many tiles we’ll need for the fourth ‘I’?
Can someone come and show us how to make the fifth ‘I’?
How many tiles will we need for the tenth ‘I’? Make it.
What is the number pattern that we are getting?
If we had 11 tiles, which numbered ‘I’ could we make?

2. Now let’s make it a bit harder. Let’s make an ‘I’ by adding a tile to the top and the bottom each time (see diagram). Repeat the questions from the last ‘I’ problem.
How many tiles do we need for the first ‘I’? The second? The third?
Who can tell me how many tiles we’ll need for the fourth ‘I’?
Can someone come and show us how to make the fifth ‘I’?
How many tiles will we need for the tenth ‘I’? Make it.
What is the number pattern that we are getting?
How many tiles do we add on at each step?
If we had 11 tiles, which numbered ‘I’ could we make?

3. It was easy to see what was happening in the original ‘I’ problem and to see how many tiles each ‘I’ needed. It wasn’t quite as easy with the second one we did. But what if we had a really difficult pattern? How could we keep track of what’s going on and see how many tiles we need for each letter?
Work them around to the idea of a table.
4. The original ‘I’ problem would give us an easy table. It would look like this:
 ‘I’ number 1 2 3 4 5 Number of tiles 1 2 3 4 5

What would the table look like where we added two tiles at a time?
Draw up the table with help from the students.

5. Now let the students complete the table for the letter pattern on Copymaster 1. Circulate the class while they are working and help them by asking leading questions such as:
How did you know how many tiles to use on the fourth ‘L’?
What is the pattern here?
Which ‘L’ in the sequence will use 27 tiles?
6. Bring the class back together and discuss their work.
Tell me what numbers you used to fill the table. (Check that they are correct by counting the tiles.)
What patterns can you see here?
How did you get the number of tiles for one ‘L’ from the one before?
How many tiles would you need for the 10th ‘L’?
If you had 23 tiles, what numbered ‘L’ could you make?

#### Exploring

For the next three days the students work at various stations continuing different number patterns and building up the corresponding tables. Notice that there are three series of stations here. In the first station, the students have to do a similar problem to the one that was done in ‘Getting Started’. In the second station the students have to find a missing shape in the pattern sequence. Finally in the third station they have to make their own pattern that fits the given table of values.  When the class seems to have finished most of the task, bring them back together to discuss their answers. Ask them the kind of questions that were used in ‘Getting Started’. Use the table to discuss the pattern involved and what the relation is between successive numbers in the sequence.

Day 1
The material for these stations is on Copymasters 1.1, 1.2, 1.3, 1.4. The students continue the pattern and complete the table.

Day 2
The material for these stations is on Copymasters 2.1, 2.2, 2.3, 2.4. The students find the missing element of the pattern and complete the table.

Day 3
The material for these stations is on Copymasters 3.1, 3.2, 3.3, 3.4. The students make up their own pattern to fit the values in the table.

#### Reflecting

On the final day let the students make up their own patterns using numbers instead of letters. Some students might want to leave gaps in the pictures of their shapes. Let the students share their patterns with the whole class. In the discussion, point out the importance of the table in seeing what the number pattern is.

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