WEEK 4 Finding Percenatages Percentage increase & decrease

STARTER On your notebook, write the following sets in the ROSTER NOTATION. {x : x is even and x ≤ 8} {x : x = 3n, n ∈ N, n ≤ 4} {x : x = n2, n ≤ 5, n ∈ N} {x : x is odd}

STARTER ANSWERS A = {2, 4, 6, 8} B = {3, 9, 27, 81} C = {1, 4, 9, 16, 25} D = {1, 3, 5, ......} 

OBJECTIVES Find percentages of quantities Interpret percentage as an operator. Use a multiplier to increase or decrease.

What is a percentage?

What is a percentage? A percentage is a ratio of a number to 100. The symbol % is used to indicate a percent. The word percent means “per cent” , “per hundred.” So 6% means “6 out of 100.”

Example Notice the 10 x 10 square grid. There are 100 total squares. Seven of the squares are colored. Seven red squares of 100 total squares can be shown like this: 7 100 = 7 %

Which of the following is an example of a percent? 67 23% A B Which of the following is an example of a percent?

Example 1: Modeling Percentage Write the percent modeled by each grid. A. B. shaded total _______ 32 100 ___ shaded total _______ 75 100 ___ = 32% = 75% Steps 9

Example 2: Modeling Percentage Write the percent modeled by each grid. A. B. shaded total _______ 44 100 ___ shaded total _______ 66 100 ___ = 44% = 66% Steps

Additional Example 3: Writing Percentage as Decimals Write 21% as a decimal. Method 1 Use pencil and paper. 21 100 Write the percent as a fraction with a denominator of 100. 21% = = 0.21 Divide 21 by 100. Method 2 Use mental math. 21% = 0.21 Move the decimal point two places to the left. I do: How did I calculate the percent to a decimal?

Example 1: 34% of 5 = (34/100) x 5 = 1.7 Example 2: 6% of 1.45 Finding Percentages of a number! Example 1: 34% of 5 = (34/100) x 5 = 1.7 Example 2: 6% of 1.45 = (6/100) x 1.45 = 0.087

Finding Percentages of quantities? Example 1: 21% of 650 AED = (21/100) x 650 = 136.5 AED Example 2: 85% of 38 KG = (85/100) x 38 = 32.3 KG Example 3: Find 3½% of $80 First > Express (7/2)/100 as a fraction = 7/200 = 0.035 Second > (0.035) x (80) = 80/15 = $2.80

Increasing and Decreasing Quantities by a Percentage When increasing or decreasing by a percentage, there are two ways to do this: Find the actual increase or decrease and add it to, subtract it from the original amount. Use a simple multiplication For example, to increase by 20%, multiply by 1.2. We increase an amount (b AED) by 20%. The increase is b AED x (20/100) = 0.2 b So the new price is b AED + 0.2b = (1 + 0.2)b = 1.2b A 20% increase is the same as to multiply by 1.2 to get the new price. 100% + 20% = 120% = 120/100 = 1.2 1.2 is the multiplier! A 20% decrease of 20% is the same as: 100% - 20% = 80% = 80/100 = 0.8 0.8 is the multiplier!

What is a multiplier? How does it help to increase and decrease the change in percentage? Example question 1 - Increase AED130 by 20%. An increase of 20% is an increase from 100% to 120%. To do this you would multiply by 120/100, which is the same as multiplying by 1.2. In other words, multiplying an amount by 1.2 is the same as increasing it by 20%. So the number 1.2 is the multiplier needed to do the calculation, which now looks like this: AED 130 x 1.2 = AED156, which is the answer.

Teacher to go over Example 4.4 & 4.5 (Maths iBook page 72 & 73)

CLASSWORK 1 Pair Activity On your notebook, show an organized solution on the following: G11 Mathematics Website WK 4 – L1 CLASSWORK 1 IGCSE Past Paper Questions on Percentage

CLASSWORK 2 Individul Activity On your notebook, show an organized solution on the following: iBook G11 Maths, page 75 – 76 #’s 1, 2, 3 a, c, f, h, 4, 5, 6

HOMEWORK On your notebook, show an organized solution on the following: iBook G11 Maths, page 76 #’s 7 & 8 Any classwork NOT finished

EXTENSION ACTIVITY For advanced students: On your notebook, show an organized solution on the following: G11 Mathematics Website WK 4 – L1 Extension Activity 1 Percentage

PLENARY Share one or two things you have learned in today’s lesson

THANK YOU! 