Percentages - The Brilliant Club

[Pages:32]Percentages

Pupil Name

Handbook Designed by

Dr Buxton

Page 1

Timetable

Timetable ? Tutorials

Tutorial 1 (Baseline assessment)

2 3 4 5 6 (Final assessment) 7 (Feedback)

Date

/ / / / / / / / / / / / / /

Time

: : : : : : :

Timetable ? Homework Assignments

Homework Assignment Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Tutorial 5

Description

Location

Due Date

/ / / / / / / / / /

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Contents

Course Rationale

P4

Glossary of Keywords

P5

Tutorial 1 -- Baseline Assessment

P6

Tutorial 2 -- Multipliers and Percentages of Amounts

P7

Tutorial 3 -- Percentage Increase and Decrease

P13

Tutorial 4 -- Reverse Percentages

P18

Tutorial 5 -- Compound Growth and Decay

P22

Tutorial 6 -- Final Assessment

P27

Tutorial 7 -- Feedback

P28

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Course Rationale

Have you considered going to university when you finish school? The reason you have been selected for this course is because we believe you have the potential to thrive in higher education ? you just need to be given some more tools and opportunities to succeed! This is what Uni Pathways will provide for you ? an opportunity for you to improve your skills and think about how you can unlock your potential.

This year, the Uni Pathways course has a special focus on Percentages. This is a topic that features heavily in the Mathematics specification, therefore your mastery of it will go a long way to help you achieve the highest possible grade that you can by the end of Year 11.

Uni Pathways will not only help you with this topic, but it will also provide a glimpse into the world of metacognition. This effectively means "thinking about thinking", which is a strategy that will help you succeed in all of your GCSE subjects, not just Maths! Examples of the application of metacognition include revision strategies, self-evaluation of progress and deliberate practice.

But what does this mean? What is deliberate practice? Well here is an example of it in action: a group of eight-year olds practiced tossing bean bags into buckets in a PE lesson. Half of the kids tossed into a bucket from three feet away. The other half mixed it up by tossing into buckets two feet and four feet away. After 12 weeks, they were all tested on tossing beans bags into a threefoot bucket. Which group do you think performed best? It may surprise you to learn that the second group fared much better in this test, because they were exposed to variation and had chance to adjust their skills to different scenarios.

This strategy of deliberate practice is something you will see in the Uni Pathways course, and hopefully by the time you complete a final assessment, you will be able to decide for yourself which methods of revision/practice work best for you and why.

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Subject Vocabulary

Word

Definition

Percent

A specified amount in every hundred (out of one hundred).

Multiplier

A number used to multiply by an amount to find a new percentage.

Growth

Increase (the amount gets larger).

Decay

Decrease (the amount gets smaller).

Compound Decimal Iteration

More than one/once.

A whole number followed by a decimal point and further digits (e.g. tenths, hundredths, ...).

The repetition of a process for a certain number of times.

Add more words to this list as you come across them! If you are unsure about a word, look it up online (look at a few sources for definitions because some definitions can be hard to understPaangde!5)

Lesson 1 ? Multipliers and Percentages of Amounts

Objectives in this tutorial: 1. Convert between percentages and multipliers. 2. Calculate percentages of amounts using multipliers. 3. Set up and solve worded percentage problems (including with fractions).

Objective 1. Convert between percentages and multipliers.

The word `percent' translates to `out of one hundred'. Hence, typically we see percentages as numbers between 0 and 100, although it is possible for percentages to go beyond this upper limit. For example, 200% represents twice the original amount.

In order to convert from a percentage to a multiplier, you need to divide by 100.

Percentage

? 100

Multiplier

In order to convert from a multiplier to a percentage, you need to multiply by 100.

Multiplier

x 100

Percentage

Worked Example 1. Convert 32% to a multiplier.

Hundreds

Tens

Units

Tenths

Hundredths Thousandths

0

3

2

0

0

0

When dividing by 100, move the place value entries twice to the right.

Hundreds 0

Tens 0

Units 0

Tenths 3

Hundredths Thousandths

2

0

The above place value table describes the number 32. To obtain the correct multiplier, move all place value entries twice to the

right:

the multiplier.

The above place value table describes the number 0.32, which is

Hence, 32 ? 100 = 0.32.

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Hundreds 0

Tens 0

Units 0

Tenths 2

Hundredths Thousandths

0

0

The above place value table describes the number 0.2. To obtain the correct multiplier, move all place value entries twice to the right:

Hundreds

Tens

Units

Tenths

Hundredths Thousandths

0

0

0

0

0

2

The above place value table describes the number 0.002, which is the multiplier.

Hence, 0.2 ? 100 = 0.002.

Worked Example 3. Convert the multiplier 2.3 to a percentage.

When multiplying by 100, move the place value entries twice to the left.

Hundreds

Tens

Units

Tenths

Hundredths Thousandths

0

0

2

3

0

0

The above place value table describes the number 2.3. To obtain the correct percentage, move all place value entries twice to the left:

Hundreds

Tens

Units

Tenths

Hundredths Thousandths

2

3

0

0

0

0

The above place value table describes the number 230, which is the percentage.

Hence, 2.3 x 100 = 230, therefore our answer is 230%.

Practice 1. Convert between percentages and multipliers.

1. Convert the following percentages to multipliers:

2. Convert the following percentages to multipliers:

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3. Convert the following multipliers to percentages:

Assessment 1. Convert between percentages and multipliers.

1. What is 400% as a multiplier?

A 0.400

B 40,000

4 C

D 400

2. When all are converted to a percentage, which is the largest?

A 0.471

B 40.7%

C 4.007

D 4.7%

Objective 2. Calculate percentages of amounts using multipliers. You can use the following formula to find the percentage of a particular amount:

Amount

Multiplier

Percentage of amount

This formula works for any type of amount, such as ordinary numbers, currency and measurements.

Worked Example 1. Find 60% of 235.

The amount is 235. The percentage is 60%. Therefore, the multiplier is 60 ? 100 = 0.6.

Using the formula: 235 x 0.6 = 141.

60% of 235 is 141.

Worked Example 2. Find 35.5% of ?6,816.

The amount is ?6,816. The percentage is 35.5%. Therefore, the multiplier is 35.5 ? 100 = 0.355.

Using the formula: ?6,816 x 0.355 = ?2,149.68.

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