June Vacation Chap 9.2 RATE (L1) Rate in Everyday Situation

What's defined in Wikipedia: Rate (mathematics)
In mathematics, a rate is a ratio between two measurements, often with different units.[1]. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity. The most common type of rate is "per unit time", such as speed, heart rate and flux. Rates that have a non-time denominator include exchange rates, literacy rates and electric flux.

When we describe the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

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Rate is commonly used in our daily life. Here are some examples:

40 km/h - 40 kilometres per hour
30 steps/min - 30 steps in per minute
2 l/hour - 2 litres per hour
67 words/min - 60 words per 1 min
80 m/week - 80 metres per week
25km/l - 25 kilometres per 1 litre
$90/m³ - $90 per cubic metre

Think of 2 real life situations in which we use the concept of rate to describe useful information.

Here is an example:
The Singapore Flyer rotates at the rate of 0.24 m/s or 0.76 km/h
(http://www.singaporeflyer.com/en/about-us/fun-facts-about-singapore-flyer.html)

June Vacation Chap 9.2 RATE (L2) A Twist to the Red Riding Hood Adventure

Read the following short story... you will be able to find descriptions related to RATE...

Once upon a time, there was a little girl who lived in a village near the forest. Whenever she went out, the little girl wore a red riding cloak, so everyone in the village called her Little Red Riding Hood.

One morning, Little Red Riding Hood asked her mother if she could go to visit her grandmother as it had been a while since they'd seen each other.

"That's a good idea," her mother said. "We usually visit grandma twice a month. However, because of common tests, you have not visited Grandma this month! She would be upset if she doesn't see you soon!"

["Rate" in the story: 2 visits in ONE month]

Based on what you understand about the term "rate", you will now continue to build the story from where the last person has commented... Everyone will contribute to one part of this Marathon Story. Your part of the story should have at least one description related to to RATE.

Complete this in the Facebook Group "Mathematics In Real Life"
Title of Post: S1-02 Story Marathon (L2) A Twist to the Red Riding Hood Adventure

June Vacation Chap 9.2 RATE (L3) CONSTANT Rate vs AVERAGE Rate

Here are 2 scenarios:

• The tap in the bathroom leaks - 2 drops of water droplets for every minute. 2 drops of water/minute is considered as "CONSTANT RATE".
• Benoît Lecomte, the French long distance swimmer was the first man to swim across the Atlantic Ocean at the rate of 43.6 miles in a day. 43.6 miles/day is considered as "AVERAGE RATE".

Are you able to tell the difference between CONSTANT Rate and AVERAGE Rate?
When do we use CONSTANT rate and when to use AVERAGE rate?

Attempt the following Quiz... It may help you to sharpen your thoughts...

June Vacation Chap 9.2 RATE (L4) Self-Paced Learning

1. Mathematics Textbook 1B

(a) Go through Chapter 9 (p9 to p11)
(b) Attempt Exercise 9.2 Q1 to Q10.
Enter your answers to Exercise 9.2 under Comments. Label your Answers with Question numbers.

2. ACELearning Portal: eLearning Portal

> Subject: Secondary 1 Express
> Additional Arithmetic
> Ratio, Rate and Speed: Choose Rate

(a) Go through video lessons: Rate, Average Rate, Example 1, Example 2
(b) Try Practice Drills on your own to check your understanding
Note: An email has been sent to all students via the AceLearning

June Vacation Chap 9.2 RATE (L5) Can he catch up with her?

Grace left home at 6.30 am to walk to school. 10 minutes later, her brother Shamus saw her wallet on the dining table. He grabbed the wallet and hopped onto his bicycle and rode after Grace.

Shamus rode his bicycle 3 times as fast as Grace walked.
Q1: What time was it when Shamus caught up with Grace?
Q2: If the school is 800m from home, did Shamus reach Grace before she arrived at school?

Use the following to guide you...

• What information do you know from the problem?
• What else do you need to know to solve the problem?
• Pick a reasonable number for the information you need.