C2.1 Add monomials with a degree of 1 that involve whole numbers, using tools.
Skill: Adding Monomials With a Degree of 1 Involving Whole Numbers
Only monomials with like variables, such as 3m and 2m, can be added. Concrete and visual representations are essential to promote understanding of this concept.
You cannot add monomials that do not have the exact same variables; for example, 5a + 10b ≠ 15ab.
Source: Ontario Ministry of Education, Mathematics Curriculum, Grades 1-8, 2020.
It is important for students to explore addition of monomials using different representations to develop their sense of operations.
Here are some examples:
- Represent the addition of monomials using algebra tiles.
- Add up using cubes.
The value of a cube is represented by c.
Then the value of the structure below is equivalent to c + c + c + c = 4c.
If we have 5 structures like the one shown above, the total value is 4c + 4c + 4c + 4c + 4c = 20c.
- Add using the number line.
Numerical line from zero to ten. A brace highlights 3 "x" plus brace for 5 "x", EQUALS 8 "x". A line is divided into 6 equal segments. Each segment is named "m". "m" plus, "m" plus, "m" plus, "m" plus, "m" plus equals 6 "m.
Since monomials are explored for the first time in Grade 6, it is important to assign context and give 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.