C1.1 Identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values.
Activity 1: Compare Equations of Growing and Shrinking Patterns
Divide students into teams. Prepare a series of statements in the form y = mx + b. Students should compare the equations, determine the constant rate and the initial value, and identify which are growing and which are shrinking. Encourage discussion among team members.
Example
Identify and compare the constant rates and initial values of the following equations:
| C = 4x + 5 | C = -2x + 5 |
| C = 2x + 10 | C = -4x + 10 |
Which ones are growing? shrinking? How do you know?
Activity 2: The Shrinking Pattern
Divide the students into teams. Present the pattern to them and ask the teams to identify all the properties related to this pattern and to justify their statements.
Nonnumeric sequence with decreasing patterns.Total 13 squares. Rank one: 5 squares overlaying horizontally and 5 squares overlaying vertically, and 4 squares diagonally from the center. Rank 2: 4 squares overlaying horizontally and 4 squares overlaying vertically, and 3 squares diagonally from the center.Rank 3: 3 squares overlaying horizontally and 3 squares overlaying vertically, and 2 square diagonally from the center.
Source: En avant, les maths!, 7e année, CM, Algèbre, p. 8.
Ensure that they consider the term number, the initial value and the constant rate. In addition, they should be able to tell if it is growing or shrinking.
Ask the following question:
- Can this pattern continue to infinity? Explain.
Complete the analysis by asking them to graph the pattern.
Ask the question:
- Should the points be connected in the graph? Why do they have to be connected?
Activity 3: Constant Rate and Initial Value of a Linear Pattern
Project the graphical representations of linear patterns on the board. Using the colours of the lines, the student must respond to the instructions given. Students analyze and work individually. Discuss the students' solutions as a class.
Examples of lines and instructions
- Organize the following lines in increasing order of constant rate.
- Organize the following lines in increasing order of initial value.
