1. Integer Rod Operations Adding and Subtracting

2. Representing Fractions Using Bars  How do we represent fractions using integer bars? Equal Parts 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 1.Represent the fraction with the smallest and least number of rods possible 2.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 3.Represent the fraction using the “race” as a guide using the common denominator rod and the least number of rods possible for the numerator 4.Do the operation

5. Six Steps Required - Continued 5.Simplify the representation – least number of rods possible 6.Interpret the representation in #5 as a fraction number answer

6. Do the Operation: Addition  Use one common denominator bar  Place both numerators (in order, from left to right) directly above the common denominator  Total of 2 rows

7. Simplify the Representation: Addition  Use one common denominator bar  Represent all with the least number of rods possible  Total of 2 rows

8. Addition –Concrete A. B. C. D. E. F. A. B. C. D. E. F.

9. Addition – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

10. Addition – Semi-Abstract

11. Do the Operation: Subtraction  Use one common denominator bar  Place the minuend (the sum) directly above the common denominator  Place the subtrahend (addend) directly above the minuend (the sum)  Use dashed lines to indicate the difference (missing addend) next to the subtrahend  Total of 3 rows

12. Simplify the Representation: Subtraction  Use one common denominator bar  Place the difference (missing addend) directly above the common denominator bar  Represent all with the least number of rods possible  Total of 2 rows

13. Subtraction – Concrete A. B. C. D. E. F. A. B. C. D. E. F.

14. Subtraction – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

15. Subtraction – Semi-Abstract