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Integer Rod Operations

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gzifa
26 diapositives · 391 Views · Aug 07, 2014

Learn the essential steps for performing integer rod operations—addition, subtraction, multiplication, and division—with minimal rods. This guide provides a systematic 6-step approach to represent fractions using integer rods, ensuring clarity and efficiency. Discover how to find common denominators, simplify representations, and interpret results effectively. Whether you're a student or educator, enhance your understanding of fraction representation using visual tools. Join the race to mastering these operations today!

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Integer Rod Operations
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  1. Integer Rod Operations Adding, Subtracting, Multiplying, and Dividing

  2. 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

  3. 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

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

  5. 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

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

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

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

  9. Adding – Semi-Abstract

  10. 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

  11. 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

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

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

  14. Subtraction – Semi-Abstract

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

  16. 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

  17. 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

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

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

  20. Multiplication – Semi-Abstract

  21. 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

  22. 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

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

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

  25. Division – Semi-Abstract

  26. 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