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\[ 4x + 7 \]
Welcome to Grade 8 Algebraic Language. Algebra uses letters to represent numbers. In this lesson you'll learn to identify the parts of an expression, substitute values, and translate word statements into algebra.
\[ \text{Patterns, Functions and Algebra} \]
Suggested duration: 60 minutes
Focus: Variables, constants, coefficients, terms, exponents, algebraic expressions, and substitution.
By the end of the lesson, you should be able to:
\[ 1,\,3,\,5,\,7,\,\ldots \]
Before you start, you should already know: number patterns, multiplication facts, integers, basic order of operations, and simple input-output relationships. These are the building blocks algebra is built on.
\[ 4x - 3y + 8 \]
Let's learn the language of algebra.
| Word | Meaning | Example |
|---|---|---|
| Variable | A letter that represents an unknown or changing number | \(x,\,n,\,a\) |
| Coefficient | The number multiplying the variable | In \(5x\), the coefficient is 5 |
| Constant | A number without a variable | In \(3x+7\), the constant is 7 |
| Term | Parts separated by \(+\) or \(-\) signs | \(4x-3y+8\) has three terms |
| Exponent | Shows repeated multiplication | In \(x^2\), the exponent is 2 |
| Expression | A mathematical phrase without an equals sign | \(3x+5\) |
| Equation | A mathematical sentence with an equals sign | \(3x+5=20\) |
\[ n \;\rightarrow\; 2n+1 \]
Look at this pattern of sticks:
| Figure number (\(n\)) | Number of sticks |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
\[ ? \]
Test your understanding:
\[ 2n+1 \]
Explanation: \(2n\) means \(2\times n\). \(+1\) means one extra stick is added. \(2n+1\) is an algebraic expression — it lets us find the number of sticks for any figure number \(n\).
\[ 4x+7 \]
Algebra uses letters to represent numbers. \(4x+7\) means \(4\times x + 7\). If \(x=5\): \(4(5)+7 = 20+7 = 27\).
\[ 7x^2-3x+5 \]
Identify the parts of \(7x^2-3x+5\):
| Part | Answer |
|---|---|
| Terms | \(7x^2\), \(-3x\), \(5\) |
| Variable | \(x\) |
| Coefficients | \(7\), \(-3\) |
| Constant | \(5\) |
| Exponent | \(2\) (in \(x^2\)) |
\[ 3x+4 \qquad \text{vs} \qquad 3x+4=19 \]
An expression has no equals sign: \(3x+4\). An equation has an equals sign: \(3x+4=19\).
\[ 9a+6 \]
Identify the coefficient, variable, and constant in \(9a+6\).
Coefficient: \(9\)
Variable: \(a\)
Constant: \(6\)
\[ 5(4)-2=18 \]
Find the value of \(5n-2\) if \(n=4\).
\(5(4)-2 = 20-2 = 18\)
\[ 3x+7 \]
Write an expression for "Seven more than three times a number."
Let the number be \(x\). Three times the number is \(3x\); seven more than that is \(3x+7\).
\[ 12x \quad 4a+9 \quad 6x-2y+5 \]
Complete these with your teacher's support. Type your answer and click Check.
\[ 8x+3y-4 \quad -6m+11 \quad 4a^3 \]
Test your knowledge! Try to solve these on your own.
\[ 4x-7 \quad 2x+9 \quad 6x \quad x-12 \]
Keep going — try these on your own.
\[ \text{Check your work} \]
Once you've finished the Independent Activity, reveal the answers below to check your work.
\[ 4x \;\neq\; 4+x \]
| Misconception | Correction |
|---|---|
| Learners think \(4x\) means \(4+x\). | Remind them that \(4x = 4\times x\). |
| Learners ignore negative signs in terms. | The sign belongs to the term. |
| Learners confuse expression and equation. | An equation has \(=\); an expression does not. |
| Learners substitute negative values without brackets. | Use brackets when substituting negative values. |
\[ -8x \quad 5x+13 \quad 2n+1 \]
Complete these final questions to check your understanding before leaving!