Patterns in Linear Equations
Strand: Patterns and Relations (Patterns)
Outcomes: 1 and 2
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider
ways to assess and build on students' knowledge
and skills related to patterns. You may choose
to use indicators from prior grades to help
to determine what students should know or understand.
Consider using open-ended questions to more
accurately assess what students are able to
communicate and do.
Research has shown that students often have
misconceptions about the concept of variables.
Usiskan (1988) identified three different ways
that variables are used:
- As a specific unknown with a single value;
e.g., 2n + 15 = 5n + 3.
Students often are asked to solve for the
unknown value.
- As a pattern generalizer; e.g., 2n +
5 where n can have an infinite number
of values.
- Variables that change in relation to one
another; e.g., C = 2πr,
where the measure of the radius (r)
affects the value of the circumference (C).
It is important that students have an opportunity
to think about the different ways that variables
are used, as in these outcomes, possibilities
2 and 3 are both used.
Ways to Assess and Build on Prior Knowledge and Skills 
B. Choosing Instructional Strategies
Consider the following general strategies for
teaching patterns in Grade 9.
- Students should be engaged in conversations
and discussions of open-ended questions to
build confidence and competence with mathematics.
- When students are given opportunities to
communicate their thinking (either orally
or in writing), explain their reasoning and
listen to the strategies used by other students,
there are more opportunities to deepen their
understanding.
- Have students model patterns using hands-on
material or drawings that help them understand
the connections between different representations.
- Students should examine how geometric and
numeric patterns can be represented in multiple
formats, including oral descriptions, symbols,
tables and graphics. They should also be
able to verify their answers by substitution.
C. Choosing Learning Activities
Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.
Grade 9
