I was able to figure out most of the game but the one thing I don't understand is what we are supposed to do with the children lying around the map.

In the game they are called "Folk".  In the Save.txt files, each one is listed as a "Native".  Things that you can do with them are as follows:

Build for each one a "Crude Hut" or a "Crude Brick Hut".

Use the "Basic Millinery Bench" to make various hats for them.

Use the "Rocking Chair" to make various clothing, hats, and wigs for them.

Create foods such as "Crude Bread", "Mushroom Soup", "Cooked Salmon", and "Apple Pie".

Feed the foods to them.

Use the "Crude Wash Tub" to wash the dirty Mushroom Soup pots after the Folk have eaten the Soup.

After the Folk eat some foods, their clothing and hats get dirty and the Folk themselves get dirty.

Use the "Crude Basket" to take the dirty clothes and dirty hats off of them.

Use the "Crude Wash Tub" to wash the dirty clothes, dirty hats, and dirty Folk.

Use the "Crude Basket" to hang the wet washed clothes and hats on the "Clothes Line" to dry them off.

Use the "Crude Basket" to take the dried clothes and hats to the Folk.

In the top left corner of the game will be shown the number of Folk that you have dealt with and their happiness level.  One goal of some players of the game is to get all 100 of the Folk to be shown as "Extremely Happy".  If you can do that, please take a screenshot showing the 100 Extremely Happy Folk and post it on this site.  Good luck.