Algebraic Techniques Revision
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Variable: A letter that represents an unknown number
Substitution: Replacing a variable with a given value
Like terms: Terms with the same variables including powers
Like terms:
- 3x and 7x
- 2y² and 5y²
- 7xy and 4yx (why?)
Quick Revision: Variables and substitution
If x = 5, what is the value of:
Diagnostic Quiz 1: Substitution
Your turn (silent)
If a = 3 and b = 4, find:
Like Terms vs Unlike Terms
Like terms have the same variable AND the same power
Unlike terms have different variables OR different powers
Examples:
- 3x and 7x are like terms
- 2y² and 5y² are like terms
- 3x and 4y are unlike terms (different variables)
- 2x and 5x² are unlike terms (different powers)
Sorting Practice: Like or Unlike?
Pair 1: 4x and 9x
Pair 2: 3y and 2z
Pair 3: 7a² and 5a²
Pair 4: 2m and 8m³
Pair 5: 6p and 11p
Pair 6: 4t² and 7t
Pair 7: 3k and k
Pair 8: 5xy and 2xy
Adding Like Terms
When adding like terms, add the coefficients (numbers) and keep the variable part the same.
Examples:
- 3x + 5x = 8x
- 2y² + 7y² = 9y²
- 4a - a = 3a (remember a = 1a)
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Diagnostic Quiz 2: Adding Like Terms
Your turn (silent)
Simplify by adding like terms:
2x + 7x =
5y - 3y =
a + 4a =
6m² + 2m² =
8p - p =
3t² - t² =
4k + k + 2k =
9n - 5n + n =
Mixed Expression Practice
When expressions have unlike terms, we cannot add them together.
Examples:
- 3x + 2y cannot be simplified (different variables)
- 4a + 5a² = 4a + 5a² (different powers)
- 2p + 3p + 4q = 5p + 4q (collect the like terms only)
Simplify: 2x + 3y + 5x =
Simplify: 4a² + 2a + 3a² =
Simplify: 7m + 2n - 3m =
Simplify: 5k² + k + 2k² =
NATURAL BREAK POINT
End of Lesson 1 Optionn
Multiplying Algebraic Terms
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When multiplying: - Multiply the numbers - Multiply the variables (add the powers)
Examples:
- 3 × 2x = 6x
- 4a × 5 = 20a
- 2x × 3x = 6x² (because x × x = x²)
- 5y² × 2y = 10y³ (because y² × y = y³)
Multiplication Practice
3 × 4x =
5y × 2 =
2a × 3a =
4x × x =
6 × 2m =
3p × 4 =
5t × 2t =
y × 7y =
Dividing Algebraic Terms
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When dividing: - Divide the numbers - Divide the variables (subtract the powers)
Examples:
- 6x ÷ 2 = 3x
- 12a ÷ 4a = 3 (because 12 ÷ 4 = 3 and a ÷ a = 1)
- 8x² ÷ 2x = 4x (because 8 ÷ 2 = 4 and x² ÷ x = x)
Division Practice
8x ÷ 4 =
10y ÷ 5y =
12a² ÷ 3a =
15m ÷ 3 =
6p ÷ 2 =
14t ÷ 7t =
20x² ÷ 4x =
18n ÷ 6 =
Diagnostic Quiz 3: Multiplication & Division
Your turn (silent)
Calculate: - 3 × 5x = - 4y × 2y = - 12a ÷ 3 = - 8x ÷ 2x =
Calculate: - 6 × 2m = - 3p × 4p = - 15t ÷ 5 = - 10y ÷ 5y =
Calculate: - 2 × 7k = - 5n × 3n = - 18x ÷ 6 = - 12a ÷ 4a =
Mixed Practice: All Skills
If x = 4, find 3x + 5 =
Simplify: 2a + 5a - a =
Calculate: 3y × 4y =
Simplify: 7m + 2n + 3m =
Calculate: 15x ÷ 3 =
If y = 2, find y² + 3y =
Simplify: 4p² + 2p² - p² =
Calculate: 6a ÷ 2a =
Extension Challenge
For students who finish early:
If a = 3 and b = 2, find the value of 2a² + 3ab - b²
Simplify completely: 4x + 2y + 3x² + 5x - y + x²
Calculate: (3x × 2y) ÷ x
If p = 5, which expression has the largest value?
Lesson Summary
Today we revised:
Variables & Substitution: Replacing letters with numbers
Like Terms: Same variable, same power - can be added/subtracted
Unlike Terms: Different variables or powers - cannot be combined
Multiplication: Multiply numbers, add powers of variables
Division: Divide numbers, subtract powers of variables
Homework/Next Steps
Based on today’s diagnostics:
If students struggled with substitution: Practice basic substitution problems
If students struggled with like terms: More practice identifying and combining like terms
If students struggled with multiplication/division: Review the rules and practice simple examples
If students mastered everything: Move on to expanding brackets next lesson