**Introduction**

Proportion in grades 4 though 6 involve reasoning and calculating with direct proportions. It is important that students recognize situations where proportions are being used. Calculation with proportions often has the aim of making situations comparable. In this respect they are closely related to fractions, percentages, and decimals. In a certain sense, a proportion is a more general concept, which is reflected in fractions, percentages, and decimals in a more specific way. The ratio table plays a large role in calculating with proportions. Students must not only be able to work with the ratio table when it is provided, but they must also be able to recognize situations where it can be useful.

**Goal**

The students are able to understand thoroughly the matter of ratio and proportion, and to solve the problem related to proportion using variety of method such as ratio table.

**A Learning-Teaching Trajectory**

Explanation of the picture above

Symbol | Description |

. | The activity where teacher gives introduction about proportion using a story based on proportion context. |

square | The parameters that use to know what students ready to go to next activity. |

Activity 1 | The activity where students could give several examples of proportion in everyday life based on their experience, make ratio of two units given by them as many as possible, and explain why and how they find it. |

Activity 2 | The activity where students try to construct and understand the table ratio concept, for example doubling, adding, multiplication, dividing, and unitizing, based on the cases given like how to find the ratio between distance and time, how to find the relationship between how many liters that the car is needed and its distance namely ‘fuel consumption’, and the ratio of the cost of jam to its weight. |

Activity 3 | The activity where students try to make the numbers comparable and give reasoning proportions based on the information provided like how to know the best player of some basketball players throwing the ball in several times by using ratio table, fraction, or percentage. |

Activity 4 | The activity where students try to find and solve a problem related to indirect proportion using ratio table in formal context like how to find the relationship among the height, the length and the area when enlarging a photograph. |

**Conclusion**

Learning trajectories hold promise for improving professional development and teaching in the area of early mathematics. For example, the few teachers that actually led in-depth discussions in reform mathematics classrooms saw themselves not as moving through a curriculum, but as helping students move through levels of understanding. Further, writer suggests that professional development focused on learning trajectories increases not only teachers’ professional knowledge but also their students’ motivation and achievement. Thus, learning trajectories can facilitate developmentally appropriate teaching and learning for all students.

## Leave a Reply