Positive, negative numbers and zero; representing on number line; operations on integers.
📖 4 min read · 4 worked examples · 8 practice questions
First, we'll understand what positive, negative numbers and zero mean, then see how to place them on a number line, and finally practice adding and subtracting them. This table shows our learning objectives and how they line up with the Kenya Grade 8 curriculum – by the end of the lesson you'll be able to solve integer problems confidently. Let's get started by visualizing integers on a number line; picture it like a road where zero is the city center, positive numbers are houses to the east, and negative numbers are houses to the west.
Today we'll explore what integers are and why they matter in everyday life. First, notice the line of numbers: …, -3, -2, -1, 0, 1, 2, 3, … These are the integers—all whole numbers that extend infinitely in both the positive and negative directions. Positive integers, like 1, 2, 3, often represent a gain or increase—think of earning more money or moving eastward on a map. Negative integers, such as -1, -2, -3, show a loss or decrease—like losing livestock or moving westward. Zero sits right in the middle and means no change; a farmer who neither gains nor loses animals is at zero. To recap: integers include all whole numbers, positives signify increase, negatives signify decrease, and zero means steady.
Everyone, let's explore how we place integers on a number line. Notice the centre point is zero. Anything to the right is positive, and anything to the left is negative. Here we have -5 on the far left. That represents five units west of the origin. Moving a little right, -3 marks three units west. At the centre, 0 is our reference point – the school itself in our Kenyan example. To the right, 3 shows three kilometres east of the school, written as +3. At the far right, 5 represents five kilometres east, or +5. When we say "3 km east of the school" we plot a point at +3, and "4 km west" would be at -4, just one step further left from -3. Any questions before we move on to adding and subtracting these integers?
Let's work through our first example: locating the integer –7 on a number line that runs from –10 to 10. First, read the problem statement carefully: we need to mark –7 on this number line. Notice the leftmost tick labeled –10. That gives us our starting point for negative numbers. From –10, count forward five units to reach –5, then continue two more units to arrive at –7. Here is the point we place on the line, and we label it –7. Great job following the counting steps!
Class, let's work through a concrete example of adding two positive numbers. The problem we need to solve is 4 plus 3 – what number do we get? First, we start at zero on the number line. Then we move right four steps to reach 4, and from there move three more steps to the right. We land on 7, which is the sum of 4 and 3. Think of it like buying four mangoes at the market and then adding three more – you end up with seven mangoes. We can write the whole process as 4 + 3 = 7. Any questions before we move on?
Class, let's work through Example 3: adding a positive and a negative integer. The problem is 5 + (–2). We start at zero, move five steps to the right, then two steps to the left. Notice the line here showing the movement: rightward arrow for the +5, leftward arrow for the –2. After both moves we land at +3, meaning a net gain of three units. 5 + (–2) equals 3. Any questions before we move on?
Let's wrap up today's lesson with a quick summary and see how integers show up in our everyday lives. First, remember that integers let us model gains and losses—whether it's money earned or spent, temperature rising or falling, or altitude changes when we climb a hill. Notice the bullet point here lists money, temperature, and altitude—common examples you'll encounter around Nairobi and beyond. Second, the number line is a powerful visual tool; it helps us see how adding a positive or negative moves us right or left, making abstract operations concrete. Finally, next time we'll explore how to multiply and divide integers, building on this foundation. Great work today, everyone—keep thinking about where you see gains and losses in your own lives, and we'll continue the adventure next class.
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