Tessa, at age 5: 1 tangent  x + 1 tangent  x =  2 tangent x, + +

(Don's granddaughter!)

July 21, 2001

Don asked "What's 1 plus 1?". Tessa said "2". Don asked "What's 1 ten plus 1 ten?". Tessa answered "twenty". Don said "Yes, 2 tens". And then they continued like that. After this 5-minute math session, most of her aunts and uncles gave her problems like these and she could do them correctly. In fact, she did verbally, 1/7 + 1/7 = 2/7, 1 tangent x + 1 tangent x = 2 tangent x, and 1 negative + 1 negative = 2 negative. She also kept giving other people problems like these!

The next day July 22, 2001, Don asked Tessa "What is 1x2 + 1x2 = ?", Tessa said "2x2 ". Then she said "Oh Grandpa, give me harder ones!" Don gave her 2 tangent x - 1 tangent x. She wasn't sure about the subtraction, so Don just showed her 2 fingers and took away 1 finger, saying 2 take away 1 = 1. So Tessa could do 2 tangent x - 1 tangent x = 1 tangent x.

Notice Tessa writes her 2's and 5's backwards and Don never said anything to her! Her Mom said she had done 10 + 10 = 20 recently.

Why does Don think this is an important lesson? For one thing, the kids really get excited about handling large numbers quickly. Two, there is a pattern to these that they understand. And 3, this is algebra they are doing, not just arithmetic- because 1 of anything + 1 of the same thing is always 2 of the same thing or as they say in algebra: 1x + 1x = 2x.

Don had Terri, Tessa's Mom, put the 3D Multiplication Tables together (see the stack). Then Terri worked with Tessa on it. Here are some pictures of this.


To other discoveries
To download Don's materials
Mathman home