Percentages - Lesson Plans

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					Calculating in Construction - Percentages




                                        Percentages
Lesson Focus
This lesson is to help learners understand and calculate using percentages.

Lesson Plan includes:
      Lesson instructions for trainers
      Worksheet 1 and 2 and answers

Knowledge of the following numeracy skills:
      Ability to use a calculator for basic operations
      Ability to read decimals and understand the place value of the digits

How this maths skill can be reinforced on the job:
In Construction, an understanding of the basic number concepts associated with
percentages are beneficial across many areas in the workplace, such as when
calculating and estimating quantities, calculating wastage, working with customer
invoices, trade discounts, GST and so on.

Lesson time:
      Approximately 30 minutes

Materials needed for this lesson:
      Worksheets for each learner
      Calculator for each learner
      Whiteboard
.

Lesson breakdown:
Suggested delivery strategy:


Step                      Trainer/Learner Activity


          1               Introduction to “percentage”

          2               Calculating a percentage of an amount
                          Worksheet 1 – Learners complete with trainer support / answers
          3               available

          4               Strategies for common percentages: Calculating 10%, 20%,
                          30%, 40%, 50%

          5               Strategies for common percentages: Calculating 25%, 50%, 75%

          6               Strategies for common percentages: Other simple percentages.

          7               Worksheets – Learners complete with trainer support / answers
                          available



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1.     Introduction to percentages


      Discuss the following ideas about percentages with the learners.

      A percentage refers to part of a whole amount where the whole amount is
       100%.

      So every time a percentage is stated it is like an amount out of 100.


Write the following examples on the board.


Example 1
         Suppose 20% of our group live on their own. What does this mean?

               The whole group is 100%. Of the whole group 20% live on their own.
                This tells us that 20 out of 100 people in our group live alone.

               Note that our group does not have 100 people in it, but if we think of the
                whole group as 100%, then if our group did have 100 people in it 20 of
                them would live alone.


Example 2
         Suppose 10% of our group were “mature age”? What does this mean?

               10% means 10 out of every 100, or 1 out of 10.

               1 in every 10 of the group is mature age.

               Note that our group does not have 100 people in it, but if we think of the
                whole group as 100%, then if our group did have 100 people in it 10 of
                them would be mature age.


Example 3
         Suppose only 25% of customers pay cash. What does this mean?

               25% means 25 out of every 100, or 1 out of 4.

               Only 1 out of every 4 customers pay cash.

               Note that we may not have 100 customers, but if we think of the whole
                group as 100%, then for every 100 customers we have, 25 of them
                would pay cash.




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2.     Calculating a percentage of an amount

      Explain the following method of calculating a percentage. Work through the
       examples with the learners.

For example, what is 25 kg as a percentage of 400 kg?

      Divide the 25 by the larger amount 400.
      Answer is 0.0625
      To write this as a percentage, multiply by 100
      0.0625 x 100 = 6.25

Your answer is 6.25%


For example, what percentage of $60 is $3?

      Divide the 3 by the larger amount 60.
      Answer is 0.05
      To write this as a percentage, multiply by 100
      0.05 x 100 = 5

Your answer is 5%


For example, what percentage of 10m out of 80m?

      Divide the 10 by 80.
      Answer is 0.125
      To write this as a percentage, multiply by 100
      0.125 x 100 = 12.5

Your answer is 12.5%


For example, what percentage is 120 mm out of 4 m?

      Because mm and m are different units, we need to change one of them so they
       are both the same. In this instance, it is easiest to change 4m to 4 000 mm.
      Divide the 120 by the larger amount 4 000.
      Answer is 0.03
      To write this as a percentage, multiply by 100
      0.03 x 100 = 3

Your answer is 3%




3.     Learners complete Worksheet 1 with trainer support and answers.



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4.     Calculating 10%, 20%, 30%, 40%, 50%.

Explain to learners that some percentages are easy to find if you know certain tips.
You are going to show them some of the simple ways of finding percentages.

                                      To find 10% of an amount

10% means 10 out of 100, or 1 out of 10.

To find 10% of something, just move the decimal one place to the left.

For example,
    10% of $260.00 = $26.00
    10% of 95 kg = 9.5 kg
    10% of 1462 m = 146.2 m


                                   To find 20%, 30%, 40% or 50%

Find 10%, then multiply by 2, 3, 4, or 5 etc to get 20%, 30%, 40% or 50%.

Examples

To find 20% of $260.00

      10% of $260.00 = $26.00
      Multiply $26 by 2 to find 20%

Answer is $52



To find 30% of 95 kg

      10% of 95 kg = 9.5 kg
      Multiply 9.5 by 3 to find 30%

Answer is 28.5 kg.



To find 40% of 1492 kg

      10% of 1492 kg = 149.2 kg
      Multiply 149.2 by 4 to find 40%

Answer is 596.8 kg.




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5.     Calculating 25%, 50% or 75%


                          To find 25% of an amount
25% means one quarter, so divide by 4.

For example, find 25% of $300

300 divided by 4 = $75

                            To find 50% of an amount
50% means one half, so divide by 2.

For example, find 50% of $300

300 divided by 2 = $150

                           To find 75% of an amount
75% means three quarters, so divide by 4 and multiply by 3.

For example, find 75% of $300 =

300 divided by 4 = 75

Then multiply 75 by 3 = $225




6.     Other common percentages


                           To find 33% of an amount
33  % means one third, so divide by 3.

For example, find 33  % of $300

300 divided by 3 = $100

                             To find 5% of an amount
5% is half of 10% so find 10% and then divide by 2.

For example, find 5% of $300

10% = $30

Divide by two to find 5%.

Answer = $15



7.     Learners complete Worksheet 2 with trainer support and answers.



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Calculating in Construction - Percentages




      Worksheet 1 - Calculating Percentages
Write these as percentages.


                                                                                Percentage


1.     15 out of 25


2.     9 out of 45


3.     $14 out of $20


4.     5 km out of 20 km


5.     600 litres out of 900 litres


6.     45 m out of 60 m


7.     3 kg out of 40 kg


8.     250 mm out of 5 m.


9.     1200 m out of 4 km.


10. 30 cents out of $2.00.




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Calculating in Construction - Percentages




                          Worksheet 1 Answers
                         Calculating Percentages
Write these as percentages.


                                                                                Answer


1.     15 out of 25                                                              60 %


2.     9 out of 45                                                               20 %


3.     $14 out of $20                                                            70 %


4.     5 km out of 20 km                                                         25 %


5.     600 litres out of 900 litres                                             66.67%


6.     45 m out of 60 m                                                          75 %


7.     3 kg out of 40 kg                                                        7.5 %


8.     250 mm out of 5 m.                                                        5%


9.     1200 m out of 4 km.                                                       30 %


10. 30 cents out of $2.00.                                                       15 %




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Calculating in Construction - Percentages




        Worksheet 2 – Common Percentages
Using the strategies discussed for common percentages, calculate the
answers to these.


                                                                                Percentage


1.     25% of 2 000 m


2.     20% of 4 000 mm


3.     10% of 628 kg


4.     50% of 18 tonnes


5.     40% of 70 workers


6.     75% of $56


7.     10% of 2 765 mm


8.     30% of 40kg


9.     33  % of 600 tonnes


10. 5% of 9 000 m




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Calculating in Construction - Percentages




        Worksheet 2 – Common Percentages
                     Answers

                                                                                Percentage


1.     25% out of 2 000 m                                                         500 m


2.     20% of 4 000 mm                                                           800 mm


3.     10% of 628 kg                                                             62.8 kg


4.     50% of 18 tonnes                                                          9 tonnes


5.     40% of 70 workers                                                        28 workers


6.     75% of $56                                                                  $42


7.     10% of 2 765 mm                                                          276.5 mm


8.     30% of 40kg                                                                12 kg


9.     33  % of 600 tonnes                                                     200 tonnes


10. 5% of 9 000 m                                                                 450 m




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