algebra/equality

Expectations: C 2.1, C 2.2, C2.3

Key Concepts

-A monomial with a degree of 1 has a variable with an exponent of one. For example, the exponent of m for a monomial 2m is 1. When the exponent is not shown, it is understood to be one.

-Monomials with a degree of 1 with the same variables can be added together;for example, 2 m and 3 m can be combined as 5m.

Note:

-Examples of monomials with a degree of 2 are x² and xy. The reason that xy has a degree of 2 is because 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.

-Adding monomials using tools supports students in understanding which monomials can be combined. Only monomials with the same variables (like terms) can be combined.

Teacher Note: The form of an equation is a mathematical sentence with an equals sign. For some students, the equality sign poses a difficulty. Although they are comfortable with, for example the sentence 4 +5- ___., they interpret the equality sign to mean” find the answer”. Therefore when students see the sentence ___ - 4= 5, they may not be sure what to do as they think the answer is already there. Similarly, students might solve 4 +___= 5 by adding 4 and 5 to “get the answer.”

The notion of an equation as an expression of balance is not apparent to them. This long-standing problem is exacerbated by the fact that many calculators require the equals key to be pressed to an answer, so students are reinforced in interpreting the = sign as synonymous with “get the answer”.

It is important for students to recognize that the equality sign should be viewed as a way to say that the same number has two different names, one on either side of the equals sign.

Source: Small, M. (2013) Making Math Meaningful to Canadian Students, K-8. Nelson Education (pp.624-625)