C1.3 Determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns that have repeating elements, movements, or operations.
Activity 1: Steamboat (Extend, Predict and Justify)
Build a steamboat using a red trapezoid and an orange square. Add a blue diamond to represent steam.
Present the following problem:
How many geometric mosaics does it take to build 10 steamships?
Solving this problem allows students to discover the relationship between the number of boats and the number of mosaics needed to build them. Grade 3 students solve this problem by filling in a table of values or even constructing their own table of values. Students are then asked to describe the rule in the following.
Example of a Table of Values
| Number of boats | 1 | 2 | 3 | … |
|---|---|---|---|---|
| Pattern blocks | 3 | 6 | 9 | … |
Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 48.
Activity 2: The Pattern in My Name
Give students a 5-by-5 grid. Ask them to write their first name as in the grid below and to colour the first letter of their first name each time it appears. Have them discover that some names form a pattern in a 5-by-5 grid and others do not.
Ask questions in order to bring out the relationship between the dimensions of the grid and the number of letters composing a given name in order to find a pattern. For example:
- What would happen if you coloured the first letter of your name?
- What would happen if you wrote your first and last name? only your last name?
- Is there a pattern rule?
- Would it be the same as the pattern rule in the repetition of your name?
For example, if you write the six letters of the name Sandra in the grid, you can see that the arrangement of each letter in the grid forms a pattern. Each of the letters is arranged in a slanted line (for example, the letter S). If we were to write a 5-letter name like Mary in a grid of the same dimensions, we would also observe a pattern, i.e., the arrangement of each letter vertically. On the other hand, if we wrote a seven letter name like Martine in a 5 by 5 grid, the pattern of the arrangement of each letter would form a line less clear than the vertical line. It is important to note that the dimensions of the grid as well as the number of letters in the first name influence the pattern formed by the repetition of the first name.
Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 47.