Page 115 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Instructional Tips
Teachers can:
• provide students with scenarios, patterns, and visuals that can be generalized in a variety of ways in order to generate algebraic expressions for comparison;
• facilitate discussions about the similarities and differences between expressions when comparing them;
• encourage students to use various methods to compare expressions, and facilitate a discussion about the possible strengths and limitations of each method; for example, whether testing the expressions with a small number of values is enough to determine equivalence;
• use familiar measurement formulas to support students in making connections to equivalent algebraic expressions; for example, the perimeter of a rectangle can be represented as P =
l + w + l + w or P = 2l + 2w or P = 2(l + w);
• introduce scenarios that could expose common errors; for example, compare 2(x – 3) and 2x – 3;
• support students in developing an understanding of how different expressions can represent the
same relationships and how, at times, some representations are more useful than others;
• provide opportunities for students to:
o listen to and reflect on their peers’ reasoning, representations, and strategies;
o use coding, digital tools, and various concrete materials (e.g., algebra tiles, colour tiles,
interlocking cubes) to compare algebraic expressions.
Teacher Prompts
• Represent the expressions x2 + x2 + 4x and 2x(x + 2) with concrete materials. What do you notice about the representations? What is the same and what is different?
• What do you notice when you substitute the same value into the expressions 8x3 and (2x)3 and evaluate them?
• Is it possible to prove that expressions are equivalent by substituting the same value into both and checking whether they result in the same output? Why or why not?
• Examine two expressions and predict whether they are equivalent. What did you consider when making your prediction?
• What are some reasons that it might be helpful to write an expression in a different but equivalent way?
• What do you notice when you compare two expressions graphically? How can you use graphs to determine whether algebraic expressions are equivalent?
• Which strategy do you feel most confident using to compare expressions? Why?
• One pattern is represented by the expression 2x + 7, and another pattern is represented by the
expression x2 + 7. How are these two expressions similar, and how are they different? How are the two patterns similar and different?
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