Description: In Lesson 12, students use the distributive property to establish the 9 = 10 - 1 pattern for multiplication. Students analyze multiplication and division problems using units of 9, drawing models, and writing equations using a letter to represent the unknown. These lessons are intended to provide students with continuous experience relating three numbers to find the unknown, as well as to deepen their understanding of the relationship between multiplication and division. Lessons 13 and 14 focus on the study of patterns as they relate to the fact 9 = 10 - 1. Students discover that the tens digit in the product of a nines fact is 1 less than the multiplier and that the ones digit in the product is 10 minus the multiplier. They also see that the digits of the nines facts' products produce a sum of 9, as in the example above (2 + 7 = 9). Lesson 15 parallels the final lessons of Topics B and C.

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