Polynomials

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

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

If students have difficulty in solving the basic facts using strategies, consider the following.

Review the operations with integers, which apply to operations with polynomials.
Provide time for students to reflect on their learning by using graphic organizers such as the Frayer Model or Concept Definition Map.
Make sure that students understand the language and operations with polynomials by using algebra tiles, sketching their results and providing explanations to justify their thinking.
Remind students that although an area model is one interpretation of multiplication, multiplication can also mean repeated addition or equal groups. When multiplying by a constant, students may not be able to form a rectangle but may be able to form equal groups.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies, such as:

Activity 1: Students could use algebra tile models containing three different variables and create two or three polynomials with five or six different terms. Students should make a drawing of the polynomials and record the polynomials symbolically. Students could then combine the like terms using the tiles symbolically.

Activity 2: Have students explore multi-step questions involving both sums and differences.
For example: (5a² – 4a – 3) – (2a² – 6a) + (9a² – 3a – 7).

Activity 3: Extend the multiplication of polynomials by monomials to include a series of the sum or difference of several products. For example: 2y(2y + 1) + 3x(2y – 1) – 2x(y + x + 5).

Activity 4: Have students apply the algorithm for long division to the division of a polynomial by a monomial.