Integer Rod Operations

1. Integer Rod Operations Multiplying and Dividing

2. Representing Fractions Using Bars • How do we represent fractions using integer bars? • Part to whole • Whole changes as necessary to make equivalents • A train is two rods put together – ALL trains must have at least one E in them • We will ALWAYS use the least number of bars possible to make a representation • Do NOT draw more lines on representations than necessary

3. Six Steps Required • Represent the fraction with the smallest and least number of rods possible • Race the denominators to a tie. This will ALWAYS take 3 rows – the new common denominator is at the bottom

4. Six Steps Required - Continued • Represent the fraction using the “race” as a guide using the common denominator rod and the least number of rods possible for the numerator • Do the operation

5. Six Steps Required - Continued • Simplify the representation –least number of rods possible • Interpret the representation in #5 as a fraction number answer

6. Race Representation: Multiplication • Use one common denominator bar • The numerator will represent the SECONDfactoronly • Do NOT represent the first factor

7. Do the Operation: Multiplication • Use one common denominator bar • Place the numerator of the second factor directly above the common denominator • Look at the first factor in the problem • Treat the numerator of the second factor as the denominator of the first factor • Place a bar above it that represents the numerator for the first factor • Total of 3 rows

8. Simplify the Representation: Multiplication • Use one original common denominator bar • Place the top bar from the step above directly above the common denominator bar • Represent all with the least number of rods possible • Total of 2 rows

9. Multiplication – Concrete A. B. C. D. E. F. A. B. C. D. E. F.

10. Multiplication – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

11. Multiplication – Semi-Abstract

12. Do the Operation: Division • Use one common denominator bar • Place the divisor (the factor) directly above the common denominator • Place the dividend (the product) directly above the divisor (the factor) • Total of 3 rows

13. Simplify the Representation: Division • Use the divisor (the factor) as the new common denominator • Place the dividend (the product) directly above the divisor (the factor) • Represent all with the least number of rods possible • Total of 2 rows

14. Division – Concrete A. B. C. D. E. F. A. B. C. D. E. F.

15. Division – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

16. Division – Semi-Abstract