Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Represent whole numbers and integers on a number line.
• Compare and order integers, including understanding absolute value.
• Add and subtract integers using number lines and rules.
• Apply the commutative and associative properties of addition.

Lesson summary

This week, we're diving into the world of whole numbers and integers. Whole numbers are the counting numbers we use every day, like 1, 2, 3, and so on, including zero. Integers include all the whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...). Understanding these numbers is fundamental to almost everything we do in mathematics. From calculating the cost of groceries to understanding temperature changes, integers and whole numbers are essential tools. In South Africa, knowing how to work with these numbers is vital for managing budgets, understanding statistics about our country, and even playing games!

Lesson notes

Whole Numbers: These are the numbers 0, 1, 2, 3, and so on. They are used for counting things that can be counted in whole units.

Example: The number of learners in your class is a whole number. You can’t have half a learner!

Integers: These are whole numbers and their negative counterparts. They include ..., -3, -2, -1, 0, 1, 2, 3, ... . Integers are useful for representing quantities that can be both positive and negative, like temperature above and below zero, or money earned and money owed.

Example: If you have R50 and spend R70, you have a debt of R

2

0. We can represent this as -R

2

0. Number Line: A visual representation of numbers, where numbers are placed at equal intervals along a line. It extends infinitely in both positive and negative directions. It is a very useful tool for understanding the relationship between numbers and for performing addition and subtraction of integers.

Absolute Value: The distance of a number from zero on the number line. Absolute value is always non-negative. The absolute value of a number a is written as |a|.

Example: |-5| = 5 (because -5 is 5 units away from 0) and |5| = 5 (because 5 is 5 units away from 0).

Comparing and Ordering Integers: On the number line, numbers increase as you move from left to right.

Therefore, a number on the right is always greater than a number on the left.

Example: -3 -4 (because 2 is to the right of -4 on the number line).

Addition of Integers: Same Signs: If you are adding two integers with the same sign (both positive or both negative), add their absolute values and keep the same sign.

Example: (+3) + (+5) = +8 and (-4) + (-2) = -6 Different Signs: If you are adding two integers with different signs, subtract their absolute values (larger minus smaller) and keep the sign of the integer with the larger absolute value.

Example: (+7) + (-3) = +4 (because 7 - 3 = 4, and 7 has a larger absolute value than -3). Also, (-9) + (+2) = -7 (because 9 - 2 = 7, and -9 has a larger absolute value than 2).

Subtraction of Integers: Subtracting an integer is the same as adding its opposite. a - b = a + (-b).

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

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

Example: -3 - 2 = -3 + (-2) = -5 Properties of Addition: Commutative Property: The order in which you add integers doesn’t change the result. a + b = b + a.

Example: 3 + (-2) = 1 and (-2) + 3 = 1 Associative Property: When adding three or more integers, the way you group them doesn't change the result. (a + b) + c = a + (b + c).

Example: (2 + (-3)) + 4 = -1 + 4 = 3 and 2 + ((-3) + 4) = 2 + 1 = 3 Guided Practice (With Solutions)

Question 1: Represent the integers -4, 0, 3, and -1 on a number line.

Solution: Draw a number line. Mark zero in the middle. Mark equal intervals to the left and right of zero. Place each integer at its corresponding position on the number line. [Imagine a number line here, with -4, -1, 0, and 3 clearly marked] Question 2: Compare the integers -5 and -

2. Which one is greater?

Solution: On the number line, -2 is to the right of -

5. Therefore, -2 > -

5. Think of it as owing R2 is better than owing R5!

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

Solution: We are adding two integers with different signs.

Subtract the absolute values: 6 - 4 =

2. The integer with the larger absolute value is -6, which is negative.

Therefore, the answer is -

2. Question 4: Calculate: 3 - (-5)

Solution: Subtracting a negative is the same as adding a positive: 3 - (-5) = 3 + 5 =

8. Question 5: Verify the commutative property of addition for the integers 2 and -

7. Solution: We need to show that 2 + (-7) = (-7) + 2. 2 + (-7) = -5 (-7) + 2 = -5 Since both expressions equal -5, the commutative property holds true. Independent Practice (Questions Only) Order the following integers from least to greatest: -8, 5, -2, 0, -10,

3. Find the absolute value of: a) -12 b) 7 c) 0 Calculate: (-5) + (-3)

Calculate: (+8) + (-2)

Calculate: (-7) - (+4)

Calculate: 2 - (-9) A thermometer reads -3°C. The temperature rises by 7°C. What is the new temperature? A bank account has a balance of R

2

0

0. A withdrawal of R350 is made. What is the new balance?

Simplify: -5 + 3 - 2 + 8 - 1 Verify the associative property of addition for the integers -2, 3, and -4.