What do you look at to tell the time? Most of us look at a phone, a microwave, the car dashboard, or a digital alarm clock. All of those items display times digitally. Digital displays are easier to read because there’s no need to figure out which is the long hand or short hand and then count the minutes. However, due to so many digital clocks, children don’t get much practice reading analog clocks anymore. Some studies estimate that 80% of children don’t know how to read an analog clock.

While that may seem shocking to some, others wonder, “Why keep teaching an outdated system?” Why do schools (and maybe Grandma) cling to keeping the old style analog clocks on the wall? We don’t know about Grandma, but we know why math teachers use analog clocks……analog clocks help teach math.

**Analog Clocks Help Develop Number Sense**

Quickly do these math problems in your head.

4 x 15 =

2/3 of 60 =

7 x 5 =

40 is what proportion of 60

(hint: keep reading for tips to get the answers quickly)

With only 12 numbers making up the 60 minutes in the hour, each number on the clock indicates 5 minutes of time passing. Therefore twelve 5’s = 60 or 12 x 5 =60.

To figure how many minutes are past the hour, quickly skip count by 5. Thus when the minute hand points to 7, you will have skip counted 5 seven times to obtain 35 minutes. So 7, 5 times = 35 or 7 x 5 = 35.

**Analog Clocks Help with Proportional Thinking**

Why do people say, “It’s a quarter after 1” when looking at an analog clock, but say “it’s 1:15” when looking at a digital clock? A digital clock visually emphasizes the numbers while an analog clock visually emphasizes the proportions.

The clock is a great representation for observing what ½, 1/3 or 1/4 of a circle looks like.

The proportions can also be looked at mathematically as well as visual. If the minute hand is pointing to 3, 6, 9, or 12 the proportion of the amount of time passed after the hour will be a multiple of a quarter (1/4, 2/4, 3/4, 4/4) of an hour. Since ¼ (minute hand pointing to the 3) of the hour is 15 minutes, when the minute hand points to 9, 3/4 quarters of the hour or 45 minutes has passed.

So very quickly by looking at a clock you can see ¾ of 60 = 45

Using this same logic for 1/4s, since there are 4 1/4s or 15’s in an hour, we can determine that 15, 4 times or 15 x 4 = 60.

Now you know why people say “a quarter after” “half past” or “a quarter ‘til” the hour when using an analog clock.

If the minute hand is pointing to 4, 8, or 12 the proportion of the amount of time passed after the hour will be a multiple of a third of an hour. (1/3, 2/3, 3/3). Since 1/3 (minute hand pointing to the 4) of the hour is 20, when the minute hand points to 8, 2/3 of the hour or 40 minutes has passed.

Once again the answer for 2/3 of 60 can be quickly determined as 40

**The Magic of Number 12 **

An analog clock is based on the number 12. Proportional thinking is one of the fundamentals of math and the number 12 is a great number to illustrate this concept. Twelve is the smallest number that is divisible by 2, 3, and 4 with the answer always being a whole number (no decimals). In fact, the number 12 being divisible by so many numbers is the reason why it was chosen to represent a dozen. Bakers could easily break up the total equally in so many different ways.

**Why is Math Fluency Important?**

Math fluency reduces the mental effort it takes to do math. Just like fluent readers don’t need to sound out words, fluent mathematicians no longer need to do the basic arithmetic. Understanding the relationships of the numbers helps achieve this math fluency, which enables students to achieve critical thinking necessary for successful problems solving. Obtaining Math fluency in the early grades can be helpful to achieve success with higher math. Next time you visit Grandma, you may want to ask if she has a spare analog clock that you can use to help develop your proportional thinking and number sense.

At Mathnasium of Novi, we use a variety of tools to demonstrate proportions and encourage proportional thinking. An analog clock is one of many tools we use to develop number sense. Come visit us to see how else we *make math make sense*. Give our Center Director Jennifer a call at (248) 649-4448

Mathnasium offers Programs for K through 8^{th} grade, High School, and ACT/SAT Test Prep for both those looking to catch up or get ahead.

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