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The Guides for Effective Instruction in Mathematics Revised

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C2.2 Evaluate algebraic expressions that involve whole numbers and decimal tenths.

Skill: Evaluating Algebraic Expressions Involving Whole Numbers and Decimal Tenths

To evaluate an algebraic expression, the variables are replaced with numerical values, and calculations are performed based on the order of operations.

When students are working with formulas, they are evaluating expressions.

Replacing the variables with numerical values often requires the use of brackets. For example, the expression 4.5m becomes 4.5(m) and then 4.5(7) when m = 7. The operation between 4.5 and (7) is understood to be multiplication. 

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

Example

Evaluate the algebraic expression 3x + a - 1 if x = 2 and a = 1.5.

Evaluate the Algebraic Expression With an Illustration

To evaluate this expression, I place a group of 3x plus the variable a, minus 1. Then, I replace the variable x with the value of 2 and the variable a with the value of 1.5. Having all my values in the expression, I can now evaluate the expression.

2 equations:3 squares are marked with an ‘x’, plus, one square marked ‘a’, minus, one square marked 1.3 squares marked 2, plus, one square marked 1 coma 5, minus, one.

Here are my calculations

\(\displaylines{\begin{align} \color{blue} 2 \color{black} + \color{blue} 2 \ \color{black} + \color{blue} \ 2 \color{black} + \color{red} 1.5 \color{black} - 1 &= \color{blue} 6 \color{black}+ \color{red} 1.5 \color{black} \ - \ 1 \\ &= \color{black}7.5 \ - \ 1 \\ &= 6.5 \end{align}}\)

Evaluate the Algebraic Expression Symbolically

\(\displaylines{\begin{align} 3x+a \ - \ 1 &= 3 \ (2) + 1.5 \ - \ 1 \\ &= 6 + 1.5 \ - \ 1 \\ &= 7.5 \ - \ 1 \\ &= 6.5 \end{align}}\)

Source : inspired by En avant, les maths!, 6e année, CM, Algèbre, p. 3-4.

Knowledge: Algebraic Expression

An expression is a numeric or algebraic representation of a quantity. An expression may include numbers, variables, and operations. Specifically, an expression such as 3 + n + 4 is an algebraic expression, since it contains numbers and symbols.

Note: An expression containing only numbers is a numeric expression, for example 5 - 2.

Source : Curriculum de l’Ontario, Programme-cadre de mathématiques de la 1re à la 8e année, 2020, Ministère de l’Éducation de l’Ontario.