Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Identify and represent integers on a number line.
• Compare and order integers using inequality symbols.
• Add and subtract integers.
• Solve real-world problems using integers.
• Understand and use additive inverses (opposites).

Lesson summary

This week, we will be diving deeper into the world of whole numbers and integers. Understanding these numbers is crucial because they form the foundation for almost all mathematical concepts you'll encounter throughout your schooling and in everyday life. From calculating budgets to understanding temperatures, knowing how whole numbers and integers work is essential. In South Africa, understanding budgeting and managing finances, understanding temperature variations, and even comprehending sports statistics rely heavily on this knowledge.

Lesson notes

What are Whole Numbers? Whole numbers are the set of numbers starting from 0 and continuing infinitely in the positive direction. They include 0, 1, 2, 3, 4, 5, and so on. They do not include fractions, decimals, or negative numbers. What are Integers? Integers are the set of whole numbers and their negative counterparts. This means they include all whole numbers (0, 1, 2, 3…) as well as their negative counterparts (-1, -2, -3…). Like whole numbers, they do not include fractions or decimals.

Think of it this way: Whole Numbers: 0, 1, 2, 3, ...

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

The Number Line: The number line is a visual representation of numbers. It extends infinitely in both positive and negative directions, with zero (0) at the center. Numbers to the right of zero are positive, and numbers to the left of zero are negative.

Example: Draw a number line and plot the following integers: -4, 2, -1, 0, 3 [Imagine a number line here with points marked at -4, -1, 0, 2, and 3] Comparing and Ordering Integers: When comparing integers, remember: Numbers further to the right on the number line are greater. Numbers further to the left on the number line are smaller. Negative numbers are always less than positive numbers. A number closer to zero is greater than a number farther from zero if both are negative. For example, -1 is greater than -

5. Example: Order the following integers from least to greatest: -5, 2, -1, 0, -3 Solution: -5, -3, -1, 0, 2 Symbols: > means "greater than" < means "less than" ≥ means "greater than or equal to" ≤ means "less than or equal to" Adding Integers: Adding integers with the same sign: Add their absolute values and keep the same sign.

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

Example: 4 + 5 = 9 (Add 4 and 5, which is 9, and 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 (7 is larger than 3. 7 - 3 =

4. Keep the negative sign because 7 is negative.)

Example: 5 + (-2) = 3 (5 is larger than 2. 5 - 2 =

3. Keep the positive sign because 5 is positive.)

Subtracting Integers: Subtracting an integer is the same as adding its opposite (additive inverse). The opposite of a number is the number with the opposite sign. The opposite of 5 is -

5. The opposite of -3 is

3. Therefore: a - b = a + (-b)

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

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

Example: Real-world Problem - Temperature Change The temperature in Johannesburg is 25°C during the day. Overnight, it drops to -2°

C. What is the difference in temperature?

Solution: We need to find the difference between 25 and -

2. This means we need to calculate 25 - (-2). 25 - (-2) = 25 + 2 = 27°C The difference in temperature is 27°

C. Example: Real-world Problem - Bank Account Sarah has R100 in her bank account. She spends R

1

5

0. What is her balance?

Solution: Sarah starts with R

1

0

0. Spending R150 means subtracting R150. 100 - 150 = 100 + (-150) = -50 Sarah's balance is -R

5

0. This means she is overdrawn by R

5

0. Guided Practice (With Solutions)

Question 1: Represent the following integers on a number line: -3, 1, -5, 0, 4 Solution: [Imagine a number line here with points marked at -5, -3, 0, 1, and 4]

Commentary: The number line should have markings at equal intervals. Ensure the students understand the placement of negative numbers to the left of zero and positive numbers to the right.

Question 2: Order the following integers from least to greatest: 7, -2, 0, -5, 3, -8 Solution: -8, -5, -2, 0, 3, 7

Commentary: Remind students to pay close attention to negative numbers; the larger the absolute value of a negative number, the smaller its value.

Question 3: Calculate: -6 + 4 - (-2)

Solution: -6 + 4 - (-2) = -6 + 4 + 2 (Subtracting a negative is the same as adding) = -2 + 2 (Calculate -6 + 4) = 0

Commentary: Break down the calculation into smaller steps. Emphasize the rule for subtracting a negative number.

Question 4: Thando owes his friend R

3

0. He earns R50 doing chores. How much money does Thando have after paying his friend?

Solution: Thando starts with -R30 (owing money). He earns R50, so we add R50. -30 + 50 = 20 Thando has R20 after paying his friend.

Commentary: This question integrates real-world application to reinforce the understanding of integers. Focus on framing debts as negative values.

Question 5: The temperature at the top of Table Mountain is 5°

C. The temperature at the bottom is 22°

C. What is the temperature difference?

Solution: 22 - 5 = 17 The temperature difference is 17°

C. Commentary: Although this problem doesn't directly use negative integers, it sets the stage for understanding relative temperature differences which can later involve negative temperatures (e.g., temperatures below zero). Independent Practice (Questions Only) Represent the following integers on a number line: -7, 2, -4, 5, -1.