C2.1 Add and subtract monomials with a degree of 1 that involve whole numbers, using tools.
Skill: Adding and Subtracting Monomials With a Degree of 1 Involving Whole Numbers
Monomials with a degree of 1 with the same variables can be added together; for example, 2m and 3m can be combined as 5m. Monomials with a degree of 1 with the same variables can be subtracted; for example, 10y – 8y = 2y.
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. It is important for students to explore addition and subtraction of monomials using different representations to develop their sense of operations.
Examples
- Represent the addition of monomials using algebra tiles.
Representation of an additional monomials using algebraic tiles.Equation:3 “x”, plus 2 “y”, plus 3 “x”, plus 1 “y”.Figure with 3 blue squares, 2 yellow rectangles, 3 blue squares and one yellow rectangle. Equation: 6 “x”, plus 3 “y”.Figure with 6 blue squares overlaying in a column and 3 yellow squares overlaying in a column.
- Represent subtraction using interlocking cubes.
- Represent subtraction using the number line.
\(9n - 2n = \mathord{?}\)
Since monomials have only been explored since grade 6, it is important to assign context and meaning to the variables.
Knowledge: Monomial With a Degree of 1
A monomial with a degree of 1 has a variable with an exponent of one. For example, the exponent of m for the monomial 2m is 1. When the exponent is not shown, it is understood to be one.
Examples of monomials with a degree of 2 are x2 and xy. The reason that xy has a degree of 2 is because both x and y have an exponent of 1. The degree of the monomial is determined by the sum of all the exponents of its variables.
Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.