Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Accurately add and subtract integers.
• Correctly multiply and divide integers.
• Simplify numerical expressions using BODMAS.
• Solve real-world problems using integers.

Lesson summary

This week, we delve deeper into the world of whole numbers and integers. Building upon what we learned in the previous weeks, we will focus on performing various operations (addition, subtraction, multiplication, and division) with integers, understanding the rules governing these operations, and applying these skills to solve real-world problems. Understanding integers is vital because they are used to represent quantities that can be both positive and negative, such as temperatures, bank balances (overdrafts!), altitudes relative to sea level, and even changes in stock prices.

Lesson notes

Integers: Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.

Examples: -3, -2, -1, 0, 1, 2, 3, ...

Addition of Integers: Adding integers with the same sign: Add their absolute values and keep the same sign.

Example: -3 + (-5) = -(3 + 5) = -8

Example: +4 + (+2) = +(4 + 2) = +6 Adding integers with different signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the integer with the larger absolute value.

Example: -7 + 3 = -(7 - 3) = -4 (because the absolute value of -7 is larger than the absolute value of 3)

Example: 5 + (-2) = +(5 - 2) = 3 (because the absolute value of 5 is larger than the absolute value of -2)

Subtraction of Integers: Subtracting an integer is the same as adding its opposite.

Example: 5 - 3 = 5 + (-3) = 2

Example: 2 - 5 = 2 + (-5) = -3

Example: 4 - (-2) = 4 + 2 = 6

Example: -3 - (-1) = -3 + 1 = -2 Multiplication of Integers: Positive x Positive = Positive

Example: 3 x 4 = 12 Negative x Negative = Positive

Example: -2 x -5 = 10 Positive x Negative = Negative

Example: 4 x -3 = -12 Negative x Positive = Negative

Example: -6 x 2 = -12 Division of Integers: Division follows the same sign rules as multiplication. Positive ÷ Positive = Positive

Example: 10 ÷ 2 = 5 Negative ÷ Negative = Positive

Example: -15 ÷ -3 = 5 Positive ÷ Negative = Negative

Example: 8 ÷ -4 = -2 Negative ÷ Positive = Negative

Example: -20 ÷ 5 = -4 Order of Operations (BODMAS/PEMDAS): This is crucial when simplifying expressions with multiple operations. Brackets / Parentheses Orders / Exponents Division and Multiplication (from left to right) Addition and Subtraction (from left to right)

Example: 2 + (3 x -4) - 5 ÷ (-1) = 2 + (-12) - (-5) = 2 - 12 + 5 = -10 + 5 = -5 Real-world Example 1: Temperature changes in Johannesburg. If the temperature at 6 AM is -2°C and it rises by 7°C by midday, what is the temperature at midday?

Solution: -2 + 7 = 5°C Real-world Example 2: Calculating bank balance with an overdraft. Thando has R50 in his bank account. He spends R80 on airtime. What is his new bank balance?

Solution: 50 - 80 = -

3

0. His new balance is -R30 (an overdraft of R30). Guided Practice (With Solutions)

Question 1: Calculate: -8 + 5 - (-2)

Solution: -8 + 5 - (-2) = -8 + 5 + 2 (Subtracting -2 is the same as adding 2) = -3 + 2 (Combining -8 and +5) = -1

Commentary: We first handled the subtraction of the negative number, converting it to addition. Then, we added the integers from left to right.

Question 2: Evaluate: (-3) x 4 ÷ (-2)

Solution: (-3) x 4 ÷ (-2) = -12 ÷ (-2) (Multiplying -3 and 4) = 6 (Dividing -12 by -

2. A negative divided by a negative is a positive)

Commentary: We followed the order of operations, performing multiplication before division since they have equal priority and we work from left to right.

Question 3: Simplify: 10 - 2 x (3 - 5)

Solution: 10 - 2 x (3 - 5) = 10 - 2 x (-2) (Solving the expression inside the brackets first) = 10 - (-4) (Multiplying -2 and -2) = 10 + 4 (Subtracting a negative is the same as adding) = 14

Commentary: Remember to always address the brackets first! This example clearly demonstrates the importance of BODMA

S. Question 4: The temperature in Cape Town was 12°

C. It dropped by 5°C during the night. What was the temperature the next morning?

Solution: 12 - 5 = 7°C

Commentary: This is a simple subtraction problem. We are subtracting the drop in temperature from the initial temperature. Independent Practice (Questions Only)

Calculate: -15 + 7 - 3 Evaluate: 6 x (-4) ÷ 2 Simplify: 8 + 3 x (5 - 7) A lift starts on floor

5. It goes up 3 floors, then down 7 floors. On which floor is it now?

Calculate: -2 + (-5) - (-8) + 1 Evaluate: (-10) ÷ (-2) x (-3)

Simplify: 12 - 4 ÷ (1 - 3) John has R200 in his account. He withdraws R

2

5

0. Then he deposits R

1

0

0. What is his final balance? The temperature at 7 AM was -5°

C. It increased by 3°C every hour for the next 4 hours. What was the temperature at 11 AM?

Simplify: -3 x [4 + (-2) x (6 - 8)]