Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Add and subtract integers accurately.
• Multiply and divide integers using the correct sign rules.
• Solve problems with multiple operations using BODMAS.
• Use a number line to visualize addition and subtraction.
• Apply integer concepts to real-world problems.

Lesson summary

In Grade 7 Mathematics, understanding whole numbers and integers is absolutely crucial. It's not just about numbers; it's about building a solid foundation for more advanced mathematics like algebra and geometry. Whole numbers and integers are used every day, from managing money to understanding temperatures and even interpreting sports statistics. For South African learners, this topic helps with things like budgeting household expenses, calculating change at the local spaza shop, and understanding scores in cricket or rugby matches. This week, we'll delve deeper into working with integers, specifically focusing on addition, subtraction, multiplication, and division of integers.

Lesson notes

What are Integers? Integers are whole numbers (no fractions or decimals) that can be positive, negative, or zero.

Examples of integers include: -3, -2, -1, 0, 1, 2, 3, and so on. They extend infinitely in both positive and negative directions. Whole numbers are a subset of integers - they include 0, 1, 2, 3, and so on, but not negative numbers. The Number Line A number line is a visual representation of numbers, including integers. Zero is in the middle, positive numbers are to the right, and negative numbers are to the left. The further to the right you go, the larger the number. The further to the left you go, the smaller the number. Adding Integers Adding two positive integers: This is straightforward addition, just like with whole numbers. For example, 3 + 5 =

8. Adding two negative integers: Add the numbers (ignoring the negative signs), and then put a negative sign in front of the answer. For example, (-3) + (-5) = -

8. Think of it as owing R3 and then owing another R5 - you now owe R

8. Adding a positive and a negative integer: Subtract the smaller number (ignoring the signs) from the larger number (ignoring the signs). The sign of the answer is the same as the sign of the larger number.

For example: (-7) + 3 = -4 (7 is larger than 3, and 7 is negative, so the answer is negative). Think of owing R7 but paying back R3 – you still owe R4. 7 + (-3) = 4 (7 is larger than 3, and 7 is positive, so the answer is positive). Think of having R7 but owing R3 – you have R4 left over. Subtracting Integers Subtracting integers can be tricky.

The key is to remember: Subtracting a number is the same as adding its opposite. a - b = a + (-b) a - (-b) = a + b For example: 5 - 3 = 5 + (-3) = 2 5 - (-3) = 5 + 3 = 8 Multiplying and Dividing Integers The rules for multiplying and dividing integers are the same: Positive x Positive = Positive Negative x Negative = Positive Positive x Negative = Negative Negative x Positive = Negative The same rules apply for division.

For example: 3 x 4 = 12 (-3) x (-4) = 12 3 x (-4) = -12 (-3) x 4 = -12 12 / 3 = 4 (-12) / (-3) = 4 12 / (-3) = -4 (-12) / 3 = -4 BODMAS/PEMDAS (Order of Operations) When an expression has multiple operations, we need to follow the order of operations, often remembered using the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Remember that division and multiplication are done from left to right, as are addition and subtraction.

Worked example

Calculate: -5 + 8 - 3

Solution: We perform addition and subtraction from left to right.

-5 + 8 = 3

3 - 3 = 0

Therefore, -5 + 8 - 3 = 0

Calculate: (-2) x 5 + 12 / (-3)

Solution: We follow BODMAS/PEMDA

S. First, multiplication and division:

(-2) x 5 = -10

12 / (-3) = -4

Now, addition:

-10 + (-4) = -14

Therefore, (-2) x 5 + 12 / (-3) = -14

Calculate: 2(3 - 5) + 4

Solution: We follow BODMAS/PEMDA

S. First, brackets:

3 - 5 = -2

Now, multiplication:

2 x (-2) = -4

Finally, addition:

-4 + 4 = 0

Therefore, 2(3 - 5) + 4 = 0

Guided Practice (With Solutions)

Question 1: Calculate: -7 + 4

Solution: We are adding a negative and a positive integer. 7 is larger than 4, and 7 is negative, so the answer will be negative. 7 - 4 =

3. Therefore, -7 + 4 = -

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

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

8. Question 3: Calculate: (-4) x (-6)

Solution: A negative multiplied by a negative is a positive. 4 x 6 =

2

4. Therefore, (-4) x (-6) = 24.