Estimating Crowd Sizes using Jacob's Method

This investigation focuses on estimating the size crowds or even large collections of objects using some very basic mathematics. Jacob's Method of counting large crowds involves creating a grid that divides a given area into equal size squares. An estimate is made by counting the number of people  in a few squares, then multiply the average obtained by the number of squares in the grid. 

What would happen if you use different size grids ? How do the estimates compare between pupils ? Could you get a more accurate estimate if you took all the estimates in the class and calculated th average? These and many more questions are presented on the worksheet provided along with a number of pictures of multiple objects and crowds with & without prepared grids for printing or viewing on a computer screen.

This activity encourages sharing and comparing of data, refining methods of collection of the data and discussion about the accuracy and limitations of the method used.

The package includes: 

Teachers Guidance Notes

An introduction into Jacob's Method and a guide to the Worksheets

Estimation Worksheet

A Worksheet for the students on how to use Jacob's Method and record the data.

A list of questions for discussion.

Estimation Crowds
To be used as a starter with the student's Estimation Worksheet containing 2 crowds of different densities. Pupils begin by guessing the size of each crowd, then estimate with a 6 square grid & 24 square grid using Jacob's Method.

Estimation Samples 1 and 2 

14 pictures to choose from all of which have a fairly even distribution: crowds of people, tomatoes,stars, trees, bricks, flowers, balloons, birds  and more.

Pupils estimate with no grid, a 6 square grid & 24 square grid, and are encouraged to experiment further with other grid sizes of their own.

Estimation Sample 3

7 more pictures to choose from, but this time the distribution of  the populations are not so even or regular, so its more challenging and opens up more questions.

They include a football crowd, bubbles, two other crowds, a shoal of fish and a herd of wildebeast.

There is lots to practice with & an excellent topic for critical thinking without the need for advanced math and can be extended into investigating bias in crowd counting.

Note: All the documents are printable.
To view the sample populations with the grids on a computer you will need the Adobe Acrobat Reader on a PC or Mac.

Common Core Links at 7th Grade

CCSS7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

CCSS7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.