Integers!!!

1. Integers!!!

2. INTEGERS!!!! • Numbers can be both positive and negative. • When working with negative numbers there are rules that must be followed. • Think of some ways that you use negative numbers????

3. Visualisation • Think of a greenhouse. • To regulate the temperature the owner must use ice blocks, and hot coals to decrease/increase the temperature. • Each ice cube (-1) lowers the temperature by 1 degree • Each hot coals (+1) increases the temperature by 1 degree.

4. The Math • The greenhouse is 34º C. • Tomatoes grow best @ 27º • How many Ice Cubes are needed to cool down the greenhouse? 32º + ? Ice cubes = 27º 32+(-5) = 27 5 ice blocks are needed.

5. Example #2 Each red chip equals (+1) each blue chip equals (-1) a) ●●●● ●●●●● There are 9 blue chips -4 + (-5)= -9 **When the chips are all the same color, you can just count the number of chips. B) ●●●●●●●● ●● -8 + 2 = -6

6. Rules • Opposite integers cancel each other out. • -5 + 5 = 0 • 5 + (-5) = 0 • This is called the “Zero Principle” • Positive integers can be written w/o the + • Strategy: “Subtract the two numerals and take the sign of the bigger one”

7. Subtracting Integers • 3 – (-2) ●●● = ●●● ●● ●● = ●●● ●● ●● = ●●● ●● Start with 3 Red. Add 2 blue and 2 red using the zero principle. Take away 2 blue to subtract -2. The integer chips represent the sum 3 + 2. The answer is 5. You can subtract an integer by adding its opposite.

8. Method #2 • Instead of subtracting an integer, we may add the opposite! A) -4 – (-2) = -4 + 2 = -2 B) -3 – 5 = - 3 + (-5) = -8

9. Greenhouse Example #2 • The greenhouse is -7º C. • Ice wine tastes best @ 2º • How can we raise the temperature in the greenhouse? -7 + ? Hot coals = -2º Or -7 - ?Ice Cubes = -2 -7 + 9 = 2 or -7 – (-9) = 2