Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Compare and order integers using a number line.
• Add and subtract integers.
• Multiply and divide integers.
• Solve simple word problems with integers.

Lesson summary

This week, we delve deeper into the fascinating world of whole numbers and integers. Building on your previous knowledge, we'll be focusing on comparing, ordering, and performing operations (addition, subtraction, multiplication, and division) with integers. Understanding integers is crucial, not just in mathematics, but also in many real-life scenarios in South Africa. Think about temperature changes (especially in places like Sutherland), managing debt and savings (positive and negative bank balances), or even understanding altitude above and below sea level. It's a fundamental skill that empowers you to solve practical problems and make informed decisions.

Lesson notes

This week, we delve deeper into the fascinating world of whole numbers and integers. Building on your previous knowledge, we'll be focusing on comparing, ordering, and performing operations (addition, subtraction, multiplication, and division) with integers. Understanding integers is crucial, not just in mathematics, but also in many real-life scenarios in South Africa. Think about temperature changes (especially in places like Sutherland), managing debt and savings (positive and negative bank balances), or even understanding altitude above and below sea level. It's a fundamental skill that empowers you to solve practical problems and make informed decisions. By the end of this week, you will be able to: Objective 1: Compare and order integers using inequality symbols (>, )**: -1 > -4 (Negative one is greater than negative four). Less than (<): -3 < 1 (Negative three is less than one). Greater than or equal to (≥): x ≥ 2 (x is greater than or equal to two) Less than or equal to (≤): y ≤ -1 (y is less than or equal to negative one)

Example 1: Order the following integers from least to greatest: -5, 2, -1, 0, 4, -

3. Solution: Draw a number line (or imagine one).

The order from least to greatest is: -5, -3, -1, 0, 2, 4. 2.3 Addition of Integers: Adding integers with the same sign: Add their absolute values and keep the sign.

Example: (-3) + (-2) = -5 (Add 3 and 2 to get 5, keep the negative sign).

Example: 4 + 5 = 9 (Add 4 and 5 to get 9, keep the positive sign).

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 = -4 (The absolute value of -7 is 7, and the absolute value of 3 is

3. Subtract 3 from 7 to get

4. Since -7 has a larger absolute value, the answer is -4).

Example: 5 + (-2) = 3 (The absolute value of 5 is 5, and the absolute value of -2 is

2. Subtract 2 from 5 to get

3. Since 5 has a larger absolute value, the answer is 3).

Example 2: A temperature in Sutherland is -4°

C. It increases by 7°

C. What is the new temperature?

Solution: -4 + 7 =

3. The new temperature is 3°C. 2.4 Subtraction of Integers: Subtracting an integer is the same as adding its opposite. a - b = a + (-b)

Example 3: 5 - 8 = 5 + (-8) = -3 Example 4: -2 - (-6) = -2 + 6 = 4 2.5 Multiplication of Integers: Positive x Positive = Positive Negative x Negative = Positive Positive x Negative = Negative Negative x Positive = Negative A helpful rule: If the signs are the same, the result is positive. If the signs are different, the result is negative.

Example 5: 3 x 4 = 12 Example 6: (-2) x (-5) = 10 Example 7: 6 x (-1) = -6 Example 8: (-7) x 2 = -14 2.6 Division of Integers: The rules for division are the same as for multiplication: Positive ÷ Positive = Positive Negative ÷ Negative = Positive Positive ÷ Negative = Negative Negative ÷ Positive = Negative Example 9: 10 ÷ 2 = 5 Example 10: (-8) ÷ (-4) = 2 Example 11: 12 ÷ (-3) = -4 Example 12: (-15) ÷ 5 = -3 Guided Practice (With Solutions)

Question 1: Arrange the following integers in descending order: -2, 5, -7, 0, 3, -

1. Solution: Descending order means from greatest to least. So, we need to find the largest number first. 5, 3, 0, -1, -2, -

7. Commentary: Remember to read the question carefully. Descending order is the opposite of ascending order.

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

Solution: First, rewrite the subtraction as addition of the opposite: (-8) + 5 +

2. Then, add the numbers from left to right: (-8) + 5 = -

3. Then, -3 + 2 = -

1. Therefore, the answer is -

1. Commentary: Breaking down the problem into smaller steps makes it easier to avoid mistakes. Pay close attention to the signs.

Question 3: A company made a profit of R5000 in one month and a loss of R2000 in the next month. What is their overall profit/loss after two months?

Solution: We can represent the profit as +R5000 and the loss as -R

2

0

0

0. So, the overall profit/loss is +5000 + (-2000) = R

3

0

0

0. Therefore, the company made an overall profit of R

3

0

0

0. Commentary: Translate the word problem into a mathematical expression using integers. Profit is positive, and loss is negative.

Question 4: Calculate: (-3) x 4 ÷ (-2)

Solution: Following the order of operations (multiplication and division from left to right), we first calculate (-3) x 4 = -

1

2. Then, we divide -12 by -2: -12 ÷ (-2) =

6. The answer is

6. Commentary: Remember the order of operations. Multiplication and division have equal priority and are performed from left to right. Independent Practice (Questions Only) Order the following integers from least to greatest: 8, -6, 2, -10, 0, 4, -

3. Calculate: 7 - 9 + (-3).

Calculate: (-5) x (-2) +

8. Calculate: 18 ÷ (-3) -

4. A lift starts on the ground floor (0). It goes up 5 floors, then down 8 floors. Which floor is it on now? The temperature at 6 AM was -2°

C. By noon, it had risen by 9°

C. What was the temperature at noon?

Calculate: (-4) x (3 - 5). A farmer owes the bank R500.