Page 68 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Teacher Facilitation: The teacher is monitoring the class as students are creating their representations and notices that two students are approaching the task by starting with different representations. The teacher checks with the students to see if they are okay with sharing with the rest of the class their work so far. The students agree, and the teacher pauses the class and invites the students to share. The teacher reinforces the idea that mathematicians use different representations as starting points in their problem solving and consolidates the critical understanding that different starting points and approaches can lead to the same result. These two students share their reasoning for why they chose to start with the representations that they did, and elaborate on how they made connections and decisions as part of their thinking process.
Students’ Responses: The student who started with a graph shared that they like to see whether they are creating a line that has a positive slope or a negative slope. For them, a visual representation is a helpful starting point. The student who started with the table of values shared that they wanted to create their linear relation by seeing the pattern between each pair of points. For this student, being able to see the numbers side by side helps to show the relationship between the numbers.
Teacher Facilitation: The teacher encourages the rest of the students to think about why they chose the representation that they did, and then asks them to also think about the benefits of being aware of the reasons behind their decisions. The teacher also prompts a discussion about the connections among the different representations and how each of them provides information, such as comparing the amount the graph goes up or down at each iteration with the change in the value in the chart of the dependent variable. Next, this might also be compared to the slope, and the meanings all explicitly connected.
Teacher Reflection [consider the effectiveness of messaging]: The teacher reflects on the effectiveness of their comments about various representations – whether students connected their own experiences with the summary that the teacher shared when facilitating the discussion. The teacher may continue to reflect on the direction of future lessons, and on whether more activities are necessary or helpful for students to better appreciate the importance of connecting various representations.
Instructional Tips
Approaches to Instruction of Social-Emotional Learning Skills
See the section Elements of the Grade 9 Mathematics Course – Social-Emotional Learning (SEL) Skills in Grade 9 Mathematics for essential information on approaches to instruction.
Opportunities for Planning Instruction
Teachers are encouraged to look for opportunities to highlight and embed explorations of and connections to social-emotional learning skills, where appropriate, within the learning throughout the course, in order to support students in developing and applying these skills.
When reviewing the Instructional Tips provided in each strand and planning for instruction throughout the course, teachers consider how to use strategies such as the sample strategies outlined in the section
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