Often mathematical topics arise in books we are reading our children. After or during reading the story, we can explore those topics with them. For example, when reading If You Give a Moose a Muffin by Laura Numeroff, we could ask questions such as these:
I wonder how many muffins the moose ate?
Look at those empty muffin pans. There are 12 holes in each pan. That would be a dozen muffins in each pan. How many muffins in 2-dozen? 3-dozen? 12-dozen?
What if the moose ate 2-dozen and the boy ate 5-dozen? How many muffins did they eat all together? How do you know? Prove it to me. (Pause for their responses.) Here’s how I did it. I took 24+60=84. That’s how I know that 7*12=84.
When designing questions, we always adjust the numbers harder or easier depending on what our children can handle or would be challenged by. We could ask them to make up problems for us, and then share our strategies for solving them.
For another example with older children, suppose you are reading them ancient prophecies that have come true in Evidence that Demands a Verdict by Josh McDowell (1972, pp. 302-308). You could explore mathematical probabilities given in the book. Discuss the assumptions made to create the probabilities, and how to multiply the fractions to arrive at the probabilities given. Comparing the dates the prophecies were made would involve subtraction of large numbers as well.
For predictions about ancient Babylon, we could ask the following:
What were the individual probabilities given? (1/10 Babylon destroyed; 1/100 not reinhabited; 1/200 tents not pitched there by Arabians; 1/4 no sheepfolds there; 1/5 wild beasts will occupy the ruins; 1/100 stones will not be removed for other buildings; 1/10 men will not pass by the ruins.)
How can we multiply those fractions? Calculate the overall probability for the entire prophesy. (Multiply numerators in the top of the fractions--1x1x1x1x1x1x1=1. Then multiply the denominators in the bottom of the fractions--10x100x200x4x5x100x10=4,000,000,000. Divide numerator by denominator--1/4,000,000,000 which is one in four billion. Is this the number given in the book? (No, the book has a typo!)
What information could Peter Stoner have used to arrive at these probabilities? (e.g. The city had 311 ft. tall x 87 ft. wide double walls. Cyrus of Persia diverting the Euphrates River running through the city was clearly unexpected.)
When were the predictions made? (Between 783 and 586 BCE) What was that span of time? (197 years) When was Babylon destroyed? (October 13, 539 BCE). How many years fell between 586 BCE and 539 BCE? (47 years)
Overall, we want to engage our children in the math we encounter in everyday life. Often mathematical topics arise in books, and we can exploit the opportunity!