Column Jumping: An Investigation

In my new book, Charlotte Mason’s Living Math, I encourage families to explore the world of math by asking big, open-ended questions.

[Now available exclusively in my Playful Math Store! Ebook only at the moment, but print editions are coming soon.]

Here’s an example of such a question, an excerpt from my earlier book, 70+ Things To Do with a Hundred Chart: Number, Shape, and Logic Activities from Preschool to Middle School.

Have fun exploring math with your kids!

Column Jumping

Print your choice of hundred chart from any online resource or from my free Hundred Charts Galore booklet.

Choose any column of the hundred chart to study. For example, the threes column: 3, 13, 23, and so on.

• Pick any two numbers in that column and add them together. In which column will you find the sum?

• Try a different pair of numbers. Does their sum land in the same column?

• What if the numbers are so big they go off your chart, like 73 + 93? Will the pattern still work? How can you tell?

• What happens if you add four of the threes-column numbers together? Where do you find that sum?

• How many threes-column numbers do you have to add for the sum to land in the eights column? Does it matter which numbers you pick?

Make a chart of the column jumping pattern for the threes. If you add enough threes-column numbers, can you get to each of the other columns?

Swim in the Sea of Ideas

Examine other column jumping patterns.

• How many fours-column numbers do you have to add to land back in the fours column?

• Can you add fours-column numbers and end up in the sevens? Why not?

• What is the column jumping pattern for the tens?

Dive Deeper

Can you think of a way to predict the pattern for any numbers? If you choose a random column n, and you jump j times, could you tell how to know in advance where you’ll land?

Do you think column jumping works for subtraction?

• It’s easy to understand “add four of the numbers in the threes column.” But what might it mean to “subtract four of the numbers”?

• What happens when you subtract one threes-column number from another one? In which column will the difference land?

• What if you subtract a big number from a smaller one? Will the pattern extend into negative numbers?

What other questions can you ask?