Polynomials

Strand: Patterns and Relations (Variables and Equations)
Outcomes: 5, 6, and 7

Step 2: Determine Evidence of Student Learning

Guiding Questions

What evidence will I look for to know that learning has occurred?
What should students demonstrate to show their understanding of the mathematical concepts, skills and Big Ideas?

Using Achievement Indicators

As you begin planning lessons and learning activities, keep in mind ongoing ways to monitor and assess student learning. One starting point for this planning is to consider the achievement indicators listed in the Mathematics Kindergarten to Grade 9 Program of Studies with Achievement Indicators. You may also generate your own indicators and use them to guide your observation of the students.

The following indicators may be used to determine whether or not students have met the specific outcomes for understanding polynomials. Can students:

create a concrete model or a pictorial representation for a given polynomial expression?
write the expression for a given model of a polynomial?
identify the variables, degree, number of terms and coefficients, including the constant term, of a given simplified polynomial expression?
describe a situation for a given first degree polynomial expression?
match equivalent polynomial expressions given in simplified form; e.g., 4x − 3x² + 2 is equivalent to
–3x² + 4x + 2?

The following indicators may be used to determine whether or not students have met the specific outcome for adding and subtracting polynomials concretely, pictorially and symbolically. Can students:

model addition of two given polynomial expressions concretely or pictorially, and record the process symbolically?
model subtraction of two given polynomial expressions concretely or pictorially, and record the process symbolically?
identify like terms in a given polynomial expression?
apply a personal strategy for addition or subtraction of two given polynomial expressions, and record the process symbolically?
refine personal strategies to increase their efficiency?
identify equivalent polynomial expressions from a given set of polynomial expressions, including pictorial and symbolic representations?
identify the error(s) in a given simplification of a given polynomial expression?

The following indicators may be used to determine whether or not students have met the specific outcome for multiplication and division of polynomials expressions by monomials, concretely, pictorially and symbolically. Can students:

model multiplication of a given polynomial expression by a given monomial concretely or pictorially, and record the process symbolically?
model division of a given polynomial expression by a given monomial concretely or pictorially, and record the process symbolically?
apply a personal strategy for multiplication and division of a given polynomial expression by a given monomial?
refine personal strategies to increase their efficiency?
provide examples of equivalent polynomial expressions?
identify the error(s) in a given simplification of a given polynomial expression?

Sample behaviours to look for related to these indicators are suggested for some of the activities listed in Step 3, Section C: Choosing Learning Activities.