# Math teacher substitutes for drill

Many schools have a drill period or what they call a phys ed, physical training or PT period.  So did Tanya’s school. The PT teacher took the students out on the school grounds or to the gym and made them do a few exercises. In this school, PT teacher was old and sometimes he be absent. Then some other teacher had to substitute for him.  This time, the substitute was a math teacher.  He took the students to the field for the drill period.

When the teacher took the students to the school ground for a drill, they wondered what he was going to do. He did not know any drill exercises. When they went outside, they saw that he had drawn many parallel lines in the field. The lines were 1 meter apart.  There was another set of parallel lines crossing them.  These lines were also 1 meter apart.  As a result, they formed little squares 1 meter long and 1 meter 1 wide.

# Area occupied per student

He asked one student to stand in a square in the front right corner.

Then he announced that each square was 1 square meter in area because it was 1 meter long and 1 meter wide.  The student was standing on the 1 square meter area of the field.

Hr called three more students so that now there were 4 students standing: two in the front 2 row and the other 2 standing behind them.  The teacher said that they were now standing on a 4 square meter  area.

Then he asked 5 more students.  All 9 students were now in a 3 x 3 formation and occupied 9 squares.

Next he added 7 more students to make a 4 x 4 formation which occupied 16 squares.  He called them 42 squares.

The class had a total of 25 students.  He told them that if they stood with the others, they would make a 5 x 5 formation.  He said that was because 52  = 25.

The students thought that this is an interesting drill class.  He also told them, “The length of a line can be measured in meters. The area of a square or any other shape is measured in square meters.  If all the students  were to be placed in a cube, the volume of the cube will be measured in cubic meters”

The bell rang and the students went back inside the school for other classes.

# Challenge

The school playground is 50 meters long and 40 meters wide.  If the math teacher makes the  1 meter long and 1 meter wide squares in the whole playground, how many squares could he make?  If there are only 500 students in the school and he makes squares to give maximum area for each student, how much area would that be?  What size squares could you make from that area so that each student has to occupy one square?

Solution: A 50 meter x 40 meter field will have an area of 2000 square meters. As shown in this picture, thin lines are 1 meter apart.  The field makes 2000 squares.

If only 500 students have to occupy the field, each student could get a 2000/500 = 4 square meter space.  This is also shown as a square drawn in the picture.