GEEM - Skills and Knowledge

C2.1 Add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools.

Skill: Adding and Subtracting Monomials With a Degree of 1 Involving Integers

Only like terms can be combined when monomials are added. Monomials with a degree of 1 with the same variables can be subtracted (for example, $- 10 y - 8 y = - 18 y$ ).

Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.

Concrete and visual representations are essential to promote understanding of this concept.

Example

Add the following monomials: $2 x + (- 4 x) + 3 x + 2 x$ .

STRATEGY 1

Visual Representation

Step 1: I use algebra tiles to represent the algebraic expression $2 x + (- 4 x) + 3 x + 2 x$ .

Step Two: I group like terms together.

Step Three: I eliminate the pairs of tiles that have opposite values since they result in a zero value.

I get 3 groups of x, that is 3x.

STRATEGY 2

Algebraic Representation

I handle the algebraic terms in parentheses and simplify the algebraic expression.

$\begin{aligned} 2 x + (- 4 x) + 3 x + 2 x & = 2 x - 4 x + 3 x + 2 x \\ = - 2 x + 3 x + 2 x \\ = x + 2 x \\ = 3 x \end{aligned}$

Source: translated from En avant, les maths!, 8^e année, CM, Algèbre, p. 3.

Skill: Adding Binomials With a Degree of 1 Involving Integers

Only like terms can be combined when binomials are added.

Example

Add the following binomials: $(3 x + - 2 y) + (4 x + 4 y)$ .

STRATEGY 1

Visual Representation

Step 1: I use algebra tiles to represent the algebraic expression $(3 x + - 2 y) + (4 x + 4 y)$ .

Step Two: I group like terms together.

Step Three: I eliminate the pairs of tiles that have opposite values since they result in a zero value.

I get 7 groups of x's and 2 groups of y's, that is $7 x + 2 y$ .

STRATEGY 2

Algebraic Representation

I group like terms to simplify the expression.

$\begin{aligned} 2 x + (- 4 x) + 3 x + 2 x & = 2 x - 4 x + 3 x + 2 x \\ = - 2 x + 3 x + 2 x \\ = x + 2 x \\ = 3 x \end{aligned}$

Source: translated from En avant, les maths!, 8^e année, CM, Algèbre, p. 4-5.

Knowledge: Binomials

Irreducible algebraic expression composed of two monomials linked together by addition or subtraction.

Example

$5 x + 3, a - 4 b$

Source: translated from En avant, les maths!, 8^e année, CM, Algèbre, p. 2.