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Maths History

Benjamin Banneker's clocks and stars

Use clock-making and astronomy to connect time, angles and careful measurement.

Quick answer

Benjamin Banneker used his knowledge of clocks and astronomy to make accurate timekeeping devices and predict the movements of stars and planets. His work showed how maths helps us understand time, angles, and the sky.

Learning outcome

By the end of this page, you will understand how clocks and stars use maths to help us measure time and find our way around the world. Success signs:
  • You can explain how a clock's hands show time using angles
  • You can name at least 3 things clocks and stars have in common
  • You can draw a simple clock and show where the hour and minute hands point
  • You can describe how Banneker used maths to make better clocks

Why this matters

Benjamin Banneker was a brilliant scientist who lived in the 1700s. He was one of the first African Americans to make important discoveries in science and maths. His clocks and star charts helped people know what time it was and where they were going. When you learn about clocks and stars, you're learning how maths helps us in our everyday lives. You might use this knowledge when you're planning your day, going on a journey, or even when you're looking up at the night sky!

How it works

Clocks and stars both use angles to tell time and show direction. A clock face is a circle, and circles have 360 degrees. The hour hand moves slowly, and the minute hand moves faster. When the minute hand points to 12, it's 0 minutes past the hour. When it points to 6, it's 30 minutes past the hour. Stars in the sky also move in circles, and their positions help people find their way. Banneker used this idea to build clocks that were more accurate than any before.

Examples you can see

Let's imagine you're looking at a clock face. If it's 3 o'clock, the hour hand points to 3 and the minute hand points to 12. If it's 4:30, the hour hand is halfway between 4 and 5, and the minute hand points to 6. Here's how the angles work:
  • At 12 o'clock, both hands point up, making a 0-degree angle
  • At 3 o'clock, the hour hand points to 3 and the minute hand points to 12, making a 90-degree angle
  • At 6 o'clock, both hands point in opposite directions, making a 180-degree angle
Try this with a real clock or draw one yourself. If you have a clock with hands, turn the minute hand from 12 to 3. You've turned it 90 degrees. Turn it from 3 to 6. You've turned it another 90 degrees. That's 180 degrees total.

Try it as a mini adventure

Adventure: Banneker's Star Map Challenge You are Benjamin Banneker, and you've been asked to help a group of explorers find their way through a forest. You have a special star chart that shows how the stars move. Your task is to help them understand how the stars can help them find north. Step 1: Draw a simple circle to represent the sky. Step 2: Mark the north point with a star. Step 3: Draw a line from the star to the middle of the circle. Step 4: Measure the angle between the line and the direction you're facing. Step 5: Use this angle to help the explorers know which way to go. Try this with your own compass or by drawing a simple star chart. If you're facing north and the star is 90 degrees to your right, you're looking east. If it's 90 degrees to your left, you're looking west.

Common mistakes

  • Mistake: Thinking that the hour hand moves 30 degrees each hour. Why it happens: Confusing the movement of the hour hand with the minute hand. Correct: The hour hand moves 30 degrees each hour, but it also moves a little bit with each minute.
  • Mistake: Believing that the minute hand moves 6 degrees each minute. Why it happens: Not understanding that the minute hand moves faster than the hour hand. Correct: The minute hand moves 6 degrees each minute, but it also moves 0.5 degrees with each minute the hour hand moves.
  • Mistake: Thinking that 12 o'clock is 360 degrees. Why it happens: Confusing the full circle with the position of the hands. Correct: 12 o'clock is 0 degrees, and the hands are pointing in the same direction.

Parent and carer guide

Parents, you can help your child understand clocks and stars by:
  • Using a real clock to show how the hands move and measuring angles
  • Going outside at night to look at the stars and discuss their positions
  • Playing games that involve telling time and understanding angles
  • Encouraging your child to draw their own star charts or clock faces
  • Discussing how Banneker's work helped people in the past and how it relates to today's technology
What to say: "Can you show me how the hands move on the clock?" "Look at the sky tonight. Can you see how the stars are in different positions?" "Let's make a simple star chart together." What not to worry about: Don't worry if your child makes mistakes. These are normal learning experiences. Focus on the process, not just the answer. Remember that Banneker's work was complex and took years of practice to perfect.

Practice questions

  1. What angle does the minute hand make with the hour hand at 3 o'clock?
  2. How many degrees does the hour hand move in one hour?
  3. What angle does the minute hand make with the hour hand at 6 o'clock?
  4. If the minute hand points to 9, what time is it?
  5. How many degrees does the minute hand move in one minute?
Answers:
  1. 90 degrees
  2. 30 degrees
  3. 180 degrees
  4. 45 minutes past the hour
  5. 6 degrees

FAQ

What did Benjamin Banneker invent?

Benjamin Banneker invented accurate clocks and created star charts that helped people navigate. He also wrote almanacs that included astronomical information.

How did Banneker use maths in his clocks?

Banneker used his knowledge of angles and measurements to make clocks that were more accurate than those made by others. He understood how the hands of a clock move and how to make them move precisely.

Why were Banneker's star charts important?

Banneker's star charts helped sailors and explorers find their way at night. They showed the positions of stars and planets, which were used for navigation before modern technology.

What can I learn from Banneker's work?

You can learn how maths helps us understand time, space, and navigation. His work shows that maths is useful in many different fields and can help people solve real-world problems.

How can I practice what I learned?

You can practice by drawing clocks, measuring angles with a protractor, or going outside to look at the stars. Try to understand how the positions of stars change over time and how this relates to timekeeping.