### Teaching and Group Activities for Understanding

**Day 1 Teaching**

Explain that the cubit was an early unit of measurement used in Egypt around 5000 years ago. This is the distance from the elbow to the fingertip. Can you see any problems they might have had with this unit of measurement? Agree that it was not a ‘standard’ unit. Describe digit, span, palm, hand, foot, yard and arm span.**Group Activities**

-- Find body measurements and find relationships between them.

-- Draw a scatter graph of arm spans and heights. Find the mean measurements of digits, palms, spans and cubits in the group.

**Day 2 Teaching**

Explain that Fermi estimates involves making fast, rough estimates using quantities which are difficult or impossible to measure directly. How many hairs do you think are on your head? What might be a sensible way to find out? Agree that it would take a long time to count them all, but an estimate can be made by finding how many are in a smaller area, and then multiplying by the number of areas.

**Group Activities**

-- Make a range of ‘Fermi’ estimates – approximate calculations of large numbers - such as the numbers of hairs on your head.

**Day 3 Teaching**

How many blades of grass do you think might be in the school field? Could we split up and count them all between us? Explain how ecologists make a quadrat (sampling frame), count what is inside, move it to different places and find an average. How many insects do you think might be on our field?

**Group Activities**

-- Make a Fermi estimate of the number of blades of grass on the school field and numbers of insects/daisies visible on it. Decide what size quadrats to use and calculate the area of the field.

**Day 4 Teaching**

Show children how to take their pulse. Children run for 30 seconds then retake their pulse. Repeat after running for 1 minute, 2 minutes, and then finally for 3 minutes. Show children how to draw a line graph of the results.**Group Activities**

-- Construct and interpret line graphs to investigate the effect of different forms of exercise on heart rate.

**Day 5 Teaching**

The astrolabe was possibly invented in Greece either by Hipparchus, a 2nd century BCE astronomer, or Apollonius of Perga, a 3rd century BCE mathematician. We are going to make an astrolabe to measure the heights of trees and buildings. Show children one you prepared earlier. Show children how it works.

**Group Activities**

-- Make an astrolabe and use it to work out the height of the school building, trees or other tall structures.