**Unit: Mathematics of Timekeeping**

**Activity: Create your own math clock**

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**Our goal is to write the numbers to the proper places of the blank clock.**

**We can explore many mathematical concepts by using this activity.**

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**For thousands of years, devices have been used to measure and keep track of time. Sundials, pendulum clocks, hour glasses are used till the invention of mechanical clocks. Today atomic clocks are used to tell the time precisely.**

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**There is a very nice article and a video on “A History Of Timekeeping” Page by **__British Museum__**.**

**You may also check the **__History of Timekeeping__* Devices*** on Wiki**

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__Essential Questions:__

__Essential Questions:__

*Why 1 hour is 60 minutes?*

**This question can lead a discussion about factors and multiples.**

**What are the different number systems in human history (Babylonians to start with) that uses the ***sexagesimal counting system***?**

**Watch the video from**__Numberphile____.__**The current sexagesimal system of time measurement dates to approximately 2000 BCE from the Sumerians.**

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__STEAM Connections:__

__STEAM Connections:__

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*History of timekeeping*

**Please watch the "**__A Brief History of Timekeeping__**" by SciShow.**

**And read the article on **__Britannica for Kids__** or the article “**__A Chronicle Of Timekeeping__**” by Scientific American**

**Search about different types of clocks;**

**Sundials –**__Let’s make a sundial__**Water Clocks –**__B____uild your own water clock__**Hour clock****Pendulum clocks**

*Science;*

**Invention of the mechanical clocks**

**Mechanics of a clock – ready-to-use mechanism.**

**For the image and explanations, please check ****Britannica for Kids****.**

*A blank wall clock*

__Create Your Own Math Clock__

__Create Your Own Math Clock__

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**CONCEPT #1: FACTORS AND DIVISORS**

**If you can divide a number A by a number B, without remainder, we say that B is a factor (or divisor) of A, and that A is a multiple of B. **

**Factors always appear in pairs such as**

**12 = 1 x 12**

**12 = 2 x 6**

**12 = 3 x 4**

**1 and 12, 2 and 6, 3 and 4 are called the factor pairs. So, the whole list of factors of 12 is {1, 2, 3, 4, 6, 12}**

**The factors of 60 are _________****1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.**

**The total number of factors is of 60 is ___****12**

**CONCEPT #2: DIVISION AND FRACTIONS**

**We can define the non-whole number quantities by using fractions and decimals. For instance, a half is represented as ½ whereas a quarter is represented as ¼.**

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**In fact, most of the numbers can be represented as fractions.**

**0.2= 1/5**

**0.333.. =1/3**

**0.142856.. = 1/7**

**1 = 1/1 = 2/2 =3/3 …**

**1.5= 3/2 =6/4= 15/10 ..**

**2= 2/1 = 4/2 = 6/3 ..**

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**When we say half an hour it means you have ___****30 mins.**

**A quarter of an hour is only ____ ****15 mins.**

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**So half past ten: ____ ****10:30**

**A quarter past three: _____ ****3:15**

**A quarter to nine: _____****8:45**

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**CONCEPT #3: ANGLES**

**We need to divide the blank circular clock into 12 equal parts to be able to insert the numbers.**

**But how we can divide a circle into 12 equal pieces?**

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**It is time to explore angles. **

**What are the types of angles?**

**______________ **

** So we have a _____ ****360**** degrees angle to divide by ____ ****12**

**It means, the circle will have numbers to represent hours in every _____ ****30 degrees.**

**There are 60 minutes in every hour. So the minute-hand needs have _____****60**** stops. Since 360 degrees : 60 = 6, we need to put a little mark on every_____ ****6 degrees**** for the stops of the minute hand. **

**To be able to measure any given angle or draw an angle with a given measurement we need to use the _________ ****protractor. **

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**Angle Measurement is a very important skill for all of us to grasp in early ages. **
** If you need, lease watch the angle measurement video on YouTube “**__Drawing Angles With a Protractor__**”.**

**Let’s start putting a mark in every 6 degrees. **

**Do not worry we are going to do this only 60 times. **

**Do not forget to insert hours in every 30 degrees.**

**CONCEPT #4: CIRCLES**

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**Up to now, we have explored many concepts related with circles.**

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**To start with, we can figure out that all the points we have inserted on the circle are equidistant to its center. **

**The set of all equi-distant points from a given point is called a _____ ****circle.**** The place we put our protractor to measure and draw the angles- which is exactly in the middle of the circle is called the ______ ****center**** of the circle. The hour marks are on the ___ ****arc**** of the circle. If we connect the center of the clock where we are going to insert the minute and hour hand and any mark on the arc, that segment is called the _____****radius.**

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**Twice the radius is called _____ ****diameter****. Diameter can help you to figure out the dimensions of your clock. The clock I have has a diameter of 24 cm. So on the wall, if I find a square 24 by 24, my clock will definitely fit in it.**

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**Each angle we measure is called the ______ ****central angle.**

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**These terms will also help us to communicate better. **

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**If you want to color your clock, you may need to calculate the area of the clock to see how much paint you will need. The length of the radius helps us here. The area of any circle is π times the square of its radius. To make a rough estimate, you may multiply the square of your clock’s radius by 3. **

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**When we insert the battery in, the clock starts ticking. That moment is the one that we can start talking about time measurement and all related problems.**

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**We can definitely raise this to make a fancy mathematical clock. Pick a number or use the numbers of your birthday and try to express 1- 12 in terms of the number(s) you choose. You can use all the operations you know. **

**Mind the ***order of operation!*

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