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, −10y − 8y = −18y).
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: 2x + (-4x) + 3x + 2x.
STRATEGY 1
Visual Representation
Step 1: I use algebraic tiles to represent the algebraic expression 2x + (-4x) + 3x + 2x.
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.
Source: En avant, les maths!, 8e 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: (3x + -2y) + (4x + 4y).
STRATEGY 1
Visual Representation
Step 1: I use algebraic tiles to represent the algebraic expression (3x + ( -2y)) + (4x + 4y).
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 7x + 2y.
STRATEGY 2
Algebraic Representation
I group like terms to simplify the expression.
Source: En avant, les maths!, 8e année, CM, Algèbre, p. 4-5.
Knowledge: Binomials
Irreducible algebraic expression composed of two monomials linked together by addition or subtraction.
Example
5x + 3; a - 4b
Source: En avant, les maths!, 8e année, CM, Algèbre, p. 2.