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The Guides for Effective Instruction in Mathematics Revised

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C1.2 Create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations.

Activity 1: Brick Wall (Representations of a Shrinking Pattern)

Present students with the following image of a brick wall:

Wall composed of 18 bricks.

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

Example of a possible solution

Representation using words

  • The first row of the wall is composed of 6 bricks.
  • The second row of the wall is composed of 5 bricks.
  • The third row of the wall is composed of 4 bricks.
  • I assume that the fourth row will be 3 bricks, the fifth will be 2 bricks, and the sixth will be 1 brick.

Table of values

Term Number 1 2 3 4
Number of Bricks 6 5 4 3

Activity 2: Representations of a Pattern Using a Table of Values

Present students with the following table of values:

Term Number (n) 1 2 3 4
Perimeter of the triangle (P) 3 6 9 12

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

Example of a possible solution

Graphical Representation

Graphical representation of the relationship between the rank of the figure and the perimeter of the triangle. Perimeter of the triangle from zero to 12. Rank of the figure from zero and 4.

Illustration

Illustration of a non-numerical sequence with increasing patterns of an isosceles triangle.One: the side of the triangle has value of one.2: the side of the triangle has value of 2.3: the side of the triangle has value of 3.4: the side of the triangle has value 4.

Algebraic Expression

P = n × 3 or P = 3n

Source : adapté de En avant, les maths!, 6e année, ML, Algèbre, p. 7.