Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Simplify algebraic expressions by combining like terms.
• Evaluate algebraic expressions by substituting values.
• Solve simple one-step equations.
• Translate word problems into simple algebraic equations.
• Check the solution to an equation.

Lesson summary

Algebra is a powerful tool that helps us solve problems by using symbols and letters to represent unknown quantities. In Grade 7, we're building a foundation for future math and science courses.

Think about it: when you’re planning a stokvel contribution or calculating the cost of airtime for the month, you're already thinking algebraically, even if you don't realize it! Understanding algebraic expressions and simple equations makes these calculations much easier and allows you to make informed decisions. It also helps in understanding financial literacy concepts later on.

Lesson notes

a) What is an Algebraic Expression? An algebraic expression is a combination of numbers (constants), letters (variables), and mathematical operations (+, -, ×, ÷). A variable is a symbol (usually a letter) that represents a number we don't know yet. A constant is a number that has a fixed value.

Example: `3x + 5` is an algebraic expression. Here, 'x' is the variable, 3 is the coefficient of x, and 5 is the constant. b)

Simplifying Algebraic Expressions: Combining Like Terms Like terms are terms that have the same variable raised to the same power. We can combine like terms by adding or subtracting their coefficients. Remember, you can only combine like terms!

Example 1: Simplify `4a + 2a - a` Solution: All terms are 'a' terms (like terms). 4a + 2a - a = (4 + 2 - 1)a = 5a Example 2: Simplify `5x + 3y - 2x + y` Solution: Identify like terms (x terms and y terms). 5x - 2x + 3y + y = (5 - 2)x + (3 + 1)y = 3x + 4y Example 3: Simplify `7p + 2q - 3p + 5 - q + 2` Solution: Identify like terms (p terms, q terms, and constants). 7p - 3p + 2q - q + 5 + 2 = (7 - 3)p + (2 - 1)q + (5 + 2) = 4p + q + 7 c) Evaluating Algebraic Expressions To evaluate an algebraic expression, we substitute given numerical values for the variables and then perform the operations.

Example 1: Evaluate `2x + 3` when `x = 4` Solution: Substitute x = 4: 2(4) + 3 = 8 + 3 = 11 Example 2: Evaluate `p² - q` when `p = 3` and `q = 5` Solution: Substitute p = 3 and q = 5: (3)² - 5 = 9 - 5 = 4 Example 3: Evaluate `(a + b) / c` when `a = 6`, `b = 4`, and `c = 2` Solution: Substitute a = 6, b = 4, and c = 2: (6 + 4) / 2 = 10 / 2 = 5 d) Solving Simple One-Step Equations An equation is a statement that two expressions are equal. The goal of solving an equation is to find the value of the variable that makes the equation true. To do this, we use inverse operations. Whatever we do to one side of the equation, we MUST do to the other side to keep the equation balanced.

Key Inverse Operations: Addition and Subtraction are inverse operations. Multiplication and Division are inverse operations.

Example 1: Solve `x + 5 = 12` Solution: To isolate 'x', we subtract 5 from both sides: x + 5 - 5 = 12 - 5 x = 7 Example 2: Solve `y - 3 = 8` Solution: To isolate 'y', we add 3 to both sides: y - 3 + 3 = 8 + 3 y = 11 Example 3: Solve `3z = 15` Solution: To isolate 'z', we divide both sides by 3: 3z / 3 = 15 / 3 z = 5 Example 4: Solve `a / 4 = 2` Solution: To isolate 'a', we multiply both sides by 4: (a / 4) 4 = 2 4 a = 8 e) Translating Word Problems into Equations This is a crucial skill. Look for keywords that indicate mathematical operations: "Sum," "plus," "added to," "more than" → Addition (+) "Difference," "minus," "subtracted from," "less than" → Subtraction (-) "Product," "times," "multiplied by" → Multiplication (×) "Quotient," "divided by," "ratio" → Division (÷)

Example: "Thando has x airtime minutes. After using 10 minutes, she has 25 minutes left. Write an equation to represent this situation." Solution: x - 10 = 25 f) Checking Solutions After solving an equation, always substitute your solution back into the original equation to verify that it is correct.

Example: If we solved x + 5 = 12 and got x = 7, then: 7 + 5 =

1

2. This is true, so our solution is correct. Guided Practice (With Solutions)

Question 1: Simplify the expression: `6b + 4 - 2b + 1` Solution: Identify like terms: 6b and -2b are like terms, and 4 and 1 are like terms.

Combine like terms: (6b - 2b) + (4 + 1)

Simplify: 4b + 5

Commentary: We grouped the 'b' terms and the constant terms together before combining them. Make sure to pay attention to the signs (+ or -) in front of each term.

Question 2: Evaluate the expression `5m - n` when `m = 2` and `n = 7` Solution: Substitute the values: 5(2) - 7 Multiply: 10 - 7 Subtract: 3

Commentary: Remember the order of operations (BODMAS/PEMDAS). Multiplication before subtraction.

Question 3: Solve the equation: `p - 8 = 3` Solution: To isolate 'p', add 8 to both sides of the equation: p - 8 + 8 = 3 + 8 Simplify: p = 11 Check: 11 - 8 =

3. This is correct.

Commentary: We use the inverse operation (addition) to undo the subtraction.

Question 4: Translate the following into an equation: "The cost of a taxi fare is R15 plus R5 per kilometer (k). If the total fare is R40, what is the distance?" Solution: Define the variable: Let k represent the number of kilometers.

Write the equation: 15 + 5k = 40

Commentary: We've translated the word problem into a mathematical equation, but we haven't solved it yet! That comes later. Independent Practice (Questions Only)

Simplify: 8x - 3y + x + 5y Simplify: 12p - 5 + 3 - 7p + 2q Evaluate: 4a + 6b, when a = 3 and b = 1 Evaluate: x² - 2y, when x = 5 and y = 8 Solve: m + 9 = 15 Solve: w - 4 = 7 Solve: 6n = 24 Solve: r / 5 = 3 Write an equation: If you double a number (n) and add 3, the result is

1

1. Solve: 2x + 5 = 11 (Hint: This is a two-step equation! Subtract 5 from both sides first, then divide by 2.)