C1.2 Create and translate repeating and growing patterns using various representations, including tables of values and graphs.

Activity 1: Decorative Strip (Representing a Pattern)


A decorative strip for a wall is created using wooden strips of equal lengths forming a shape that is repeated several times. All shapes are glued together.

The table of values below shows the quantity of wooden strips required for one shape, 2 shapes, 3 shapes, 4 shapes, and 5 shapes.

Terms, t 1 2 3 4 5
Strips, s 7 14 21 28 35

Allow students to represent the situation using the strategy of their choice.

Examples

Representing the situation with words

The growing pattern can be described as follows:

If there is 1 shape to create the decorative strip, this one is composed of 1 group of 7 strips.

If there are 2 shapes to create the decorative strip, this one is composed of 2 groups of 7 tabs, that is 14 strips.

If there are 3 shapes to create the decorative strip, this one is composed of 3 groups of 7 strips, that is 21 strips.

If there are 4 shapes to create the decorative strip, this one is composed of 4 groups of 7 strips, that is 28 strips.

If there are 5 shapes to create the decorative strip, this one is composed of 5 groups of 7 strips, that is 35 strips.

Students may also notice that the regularity rule of the pattern is that the number of tabs increases by 7 from one shape to the next.

Representing the situation with a graphical representation

Image Graphic representation of the amount of each shape « s » and the number of tabs « n ». shape one: 7 tabs. shape 2: 14 tabs. shape 3: 21 tabs. shape 4: 28 tabs. shape 5: 35 tabs.

Representing a situation using a diagram

Image A representation image of semi-concrete material of “X”, and number of shapes “s”, and number of tabs “n” Term one: 7 “X”. Term 2: 14 “X” Term 3: 21 “X” Term 4: 28 “X” Term 5: 35 “X”

Source: translated from L’@telier – Ressources pédagogiques en ligne (atelier.on.ca).

Activity 2: The Growing Square (Representing Patterns)


Ask students to examine the pattern below and represent it using a table of values and a graph.

A blue square. Then the blue square is placed in a larger square. Then another larger square.

Source: translated from L’@telier – Ressources pédagogiques en ligne (atelier.on.ca).