# Opportunities: Beginner Teacher's Book by M Harris, David Mower

By M Harris, David Mower

Possibilities is a brand new five-level direction for teens. Modules of topic-based devices supply wealthy, modern content material according to a wide selection of knowledge topics. With a discovery method of grammar and an in advance concentrate on vocabulary, possibilities guarantees the simplest language studying for college kids.

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Extra resources for Opportunities: Beginner Teacher's Book

Sample text

1. Always moving downward, we see that the only way to get to G from A is via D. But there is only one path to D and only one path from D to G. Thus, there is only one path from A to G, and we enter a 1 under G on the diagram, as shown. 2. The only way to get to H from A is via D or E. Since there is only one path from A to D and one from D to H, there is only one path from A to H via D. However, since there are two paths from A to E and one path from E to H, there are two paths from A to H via E.

It also provides elementary school students with ways to experiment with numbers. 4 1 Pascal’s triangle 1 1 1 1 7 1 1 1 8 9 1 10 15 28 120 15 70 1 6 21 56 126 252 1 5 35 126 210 4 20 56 1 10 35 84 36 45 10 21 1 3 6 4 6 1 3 5 1 1 2 1 8 28 36 84 210 1 7 120 1 1 9 45 10 1 The array is named after the French mathematician Blaise Pascal (1623–1662), who showed that these numbers play an important role in the theory of probability. However, the triangle was certainly known in China as early as 1303 by Chu Shih-Chieh.

8 Look for a pattern.