This is an investigation using numbers
You need a book and a pen and paper
You can use this type of problem with any book or thick magazine.
Secretly riffle through the pages of the book and note the pages where you stopped. Without letting your child see the pages, add up the numbers and challenge them to find the same pages.
The numbers on the two pages add up to 59. What are the pages?
If the numbers on the two pages added up to 135. What are the pages?
How about 267?
What do you notice?
Are the totals always odd? Why? How do you know?
Is there a quick way to work the numbers out?
Let your child talk to you about the problems. If they find a quick way to work out the numbers ask if they can prove that it would always work.
If they find it difficult to come up with an explanation, let them look through he book at the page numbers. Encourage them to start off looking at the first few pairs of pages. Do they notice the odd/even number pattern? How does this help?
You can also help their thinking by choosing a pair of pages and saying something like:
"The left-hand page is page number 12,
what will the sum be for both pages?"