**Age**: 7.75

**Date**: June 2, 2015

**Presentation**: Numerical Decanomial with Paper Rectangles and Squares

After the Decanomial layout we did last week (or was it the week before? The days blur…), **Thumper** is doing the numerical layout this week.

You can watch a video of how it’s done on youtube:

You’re basically doing the decanomial layout using paper. Now, when I was making my Cultivating Dharma album, I got confused by the writeup because it was not very clear. I had to cross reference with the video and other write-ups to come up with my current version. In the video, you will see that the papers are all the same size. But after doing some research I thought using graph paper and having sizes that are equivalent to their actual multiplication size (1×1, …10×10) is better.

You have 10 envelopes, on the outside labeled Decanomial 1, 2, 3, etc and one labeled Squares 1-10. On the inside, you have two sets of numbers for each decanomial:

- Decanomial 1: 2, 3, 4, 5, 6, 7, 8, 9, 10
- Decanomial 2: 6, 8, 10, 12, 14, 16, 18, 20
- Decanomial 3: 12, 15, 18, 21, 24, 27, 30
- etc.

Basically it has the numbers for that decanomial, assuming you haven’t used it already in the previous one. For example, decanomial 1 is 1×1, 1×2, 1×3, etc. “Decanomial 2” is 2×1, 2×2, 2×3, 2×4, etc. But since 2×1=2 was already in decanomial 1, and 2×2=4 is in the “Squares 1-10” envelope, you don’t need to include these.

In the write up, you have the child lay out diagonally the squares 1-10 first, then you build Decanomial 1, 2, 3, etc. You can talk about the multiplication table, to pick up the tickets in random and place them etc.

**What We Did**

Given how old **Thumper** is, and my own laziness, I really did not follow the presentation. I basically showed her my write up and said, we’re making this table, which is a paper representation of the bead layout you did last week. I showed her how you would mark off squares and rectangles on the graph paper and cut them out; reminded he she needed to write the value of the rectangle on the paper; that she does NOT have to mark and cut in order. She could very well do 1×1, 1×2, 2×1, 1×3, 3×1, etc. I know she knows half of her multiplication table so there is no need for order for us as part of learning process. I also told her she would glue these rectangles on our Ikea roll.