Page 110 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Instructional Tips
Teachers can:
• provide concrete representations and contexts to support students when they are generalizing relationships, especially non-linear relationships;
• share examples of how expressions are used in coding and how, depending on the coding language, they can be represented using words, abbreviated text, or symbols;
• provide examples of relationships that students might represent in different ways, such as generalizing an expression for perimeter or a given visual representation, to support the concept of equivalent algebraic expressions (see C1.3);
• support students in making connections to Strand B: Number by providing patterns and number relationships for them to generalize;
• provide opportunities for students to:
o use concrete materials such as algebra tiles, pattern blocks, colour tiles, or beads to
represent and generalize relationships;
o generalize algebraic expressions in various ways, such as by using words, abbreviations,
and/or symbols.
Teacher Prompts
• How can generalizing a mathematical relationship be helpful?
• How can describing a mathematical relationship in words help you generalize it with symbols?
• What are some of your observations about this relationship? How can those observations help
you generalize the relationship?
• Write a different algebraic expression to represent the same relationship.
• What algebraic expression can you create to represent elements of this set of numbers (e.g., even
numbers, perfect squares, triangular numbers)?
Sample Tasks
1. Provide students with a set of cards with various relationships expressed in words, with numbers, and with visual representations, as well as cards with corresponding algebraic expressions. Have them match the relationship cards to the corresponding expression cards. Consider leaving out some information on the cards so that students can complete them to show understanding of the relationship.
2. Provide students with a visual representation and several possible algebraic expressions. Have them match the appropriate expression(s) to the visual representation and justify their selections. For example:
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